UNIVERSITY OF CALGARY. A Standalone Approach for High-Sensitivity GNSS Receivers. Tiantong Ren

Transcription

1 UNIVERSITY OF CALGARY A Standalone Approach for High-Sensitivity GNSS Receivers by Tiantong Ren A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA SEPTEMBER, 2014 Tiantong Ren 2014

2 Abstract Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS) can provide users with accurate navigation and timing services worldwide. Recently, processing weak GNSS signals has been receiving growing attention because of the increased demand for navigation in signal challenged environments, e.g., indoors, under dense foliage canopies, in urban canyons, etc. High-sensitivity GNSS receivers are preferred for the improved acquisition and tracking capabilities under degraded signal environments. The current mainstream highsensitivity GNSS receiver design utilizes assisted-gnss to maximize performance. However, the assistance source is not always available and the cost of additional communication channels is often a requisite concern. In light of this, the standalone performance of high-sensitivity GNSS receivers is addressed in this thesis. In order to achieve bit wipe-off and extend coherent integration time, a newly proposed standalone high-sensitivity GNSS receiver uses Maximum-Likelihood (ML) bit synchronization and ML bit decoding algorithms to estimate the location of bit boundaries and the bit values from GNSS signals. A systematic performance analysis of ML bit synchronization and ML bit decoding is achieved. The theoretical performance models of ML bit synchronization and ML bit decoding are developed based on statistical theory. In order to further improve the performance of ML bit decoding, the benefits of using the advanced tracking algorithms in standalone mode to improve ML bit decoding are analyzed using a software GNSS receiver. Those advanced tracking algorithms include: vector tracking, ultra-tightly coupled architecture and open-loop tracking. Finally the estimated data bit values are used to extend coherent integration via the ML-based bit wipe-off, and the accuracy and ii

3 reliability of the whole system are assessed in the navigation domain. The results of the vehicular field tests in dense foliage and urban canyon environments show the advanced tracking algorithms can improve the successful decoding rate (SDR) of bit values about 2% to 30% depending on signal power. Meanwhile, by extending coherent integration time from 20 ms to 100 ms using ML-based bit wipe-off in the standalone approach, the position and velocity accuracy has been shown to be improved about 50% in the vehicular field tests. In this thesis, two innovative strategies are proposed to mitigate the high bit error rate (BER) problem in MLbased bit wipe-off, and an innovative signal power based multipath mitigating algorithm is proposed. Finally, in order to improve the performance of ML bit synchronization, an innovative collective bit synchronization approach for weak GNSS signals using multiple satellites is proposed. The benefits of using collective bit synchronization to improve the detection rate of bit boundary positions are analyzed using a software GNSS receiver. iii

4 Acknowledgements First of all, I would like to thank my supervisor, Dr. Mark Petovello for his professional guidance and continuous encouragement during my Ph.D. study. Further, I would like to express my gratitude to the professors from PLAN group, Dr. Gérard Lachapelle, Dr. Kyle O Keefe and Dr. John Nielsen, for their advice and support. The financial support of General Motors of Canada, the Natural Science and Engineering Research Council of Canada is also acknowledged. I am also grateful to those colleagues and friends Tao Li, Zhe He, Sergey Krasovski, Peng Xie, Srinivas Bhaskar, Bo Li, Da Wang, Paul Verlaine Gakne, Bernhard Aumayer, Tao Lin, Yuqi Li, Rakesh Kumar, Jingjing Dou, Niranjan Vagle, Erin Kahr, Maryam Najamfshar, Anup Dhital and Mohammad Mozaffari in the PLAN Group who helped with my field tests and shared discussions. Finally, and most importantly, I would like to thank my parents and wife, for their unconditional love, encouragement and understanding through all of my years of study. This work would not have been possible without their support. iv

5 Table of Contents Abstract... ii Acknowledgements... iv Table of Contents...v List of Tables... viii List of Figures... ix List of Abbreviations and Symbols... xiii Chapter One: Introduction Background Navigation Challenges in Signal Challenged Environments Requirements of high-sensitivity GNSS Receiver Assisted-GNSS Bit Synchronization and Bit Decoding Advanced Tracking Algorithms Collective Signal Processing Using Multiple Satellites Limitations of Previous Works Objective and Contributions Innovations Thesis Outline...27 Chapter Two: Systematic Analysis of ML Bit Synchronization and Decoding Methodology Signal Model Acquisition and Tracking ML Bit Synchronization ML Bit Decoding Building Observations and Navigation Solution Theoretical Performance Model Theoretical Performance Model of ML Bit Synchronization Theoretical Performance Model of ML Bit Decoding Other Factors Impacting the Performance of ML Bit Synchronization and ML Bit Decoding Factors Impacting ML Bit Synchronization Factors Impacting ML Bit Decoding Summary...80 Chapter Three: Improving ML Bit Decoding and Navigation Performance in Vector-Based High- Sensitivity GNSS Receiver Different GNSS Receiver Architectures Scalar-Based Software GNSS Receiver GSNRx Vector-Based Assisted-GNSS High-Sensitivity Receiver GSNRx-hs Vector-Based Standalone High-Sensitivity Receiver GSNRx-hs-sa Correlator Outputs Selecting Strategies for Extending Coherent Integration Time...86 v

6 3.2.1 Strategy I: Selecting Correlators Based on Satellite s Elevation Angle Strategy II: Selecting Correlators Based on Estimated C/N Test Description Dense Foliage Test for ML Bit Decoding and Navigation Urban Canyon Test I & II for ML Bit Decoding and Navigation Field Test Equipment and Configuration Dense Foliage Test Result Performance of ML Bit Decoding in Dense Foliage Test Benefits of Extended Coherent Integration Time in Assisted-GNSS Extending Coherent Integration Time Using Estimated Data Bits in Dense Foliage Test Urban Canyon Test I Result Performance of ML Bit Decoding in Urban Canyon Test I Benefits of Extended Coherent Integration Time in Assisted-GNSS Extending Coherent Integration Time Using Estimated Data Bits in Urban Canyon Test I Limitations of GNSS Only Solution Summary Chapter Four: Improving ML Bit Decoding and Navigation Performance in Ultra-Tightly Coupled High-Sensitivity GNSS Receiver Standalone Ultra-Tightly Coupled High-Sensitivity GNSS Receiver GSNRx-hs-dr-sa Vehicle Sensor Configuration Test Description of Urban Canyon Test II for ML Bit Decoding and Navigation Urban Canyon Test II Result Bit Decoding Performance in Ultra-Tight Receiver Performance of Assisted-GNSS and DR only solution Ultra-Tight Integration of Assisted-GNSS and DR System Navigation Results in Standalone Ultra-Tightly Coupled High-Sensitivity GNSS Receiver with ML Bit Decoding Summary Chapter Five: Collective Bit Synchronization Methodology of Collective Bit Synchronization Tests Description Monte Carlo Simulation GNSS Simulator Test Field Test Monte Carlo Test Result GNSS Simulator Test Result Field Test Result Summary Chapter Six: Conclusion and Future Works Conclusions Performance of ML Bit Synchronization and ML Bit Decoding vi

7 6.1.2 Improvement by Using Vector Tracking Improvement by Using Ultra-Tightly Coupled Architecture Performance of Collective Bit Synchronization Future Work References vii

8 List of Tables Table 2.1: Front-end parameters used for collecting GNSS data for the performance test of ML bit synchronization and ML bit decoding Table 3.1: Front-end parameters used for collecting GNSS data in three tests Table 3.2: Average C/N 0 of different satellites in the dense foliage test Table 3.3: Average C/N 0 of different satellites in Urban Canyon Test I Table 4.1: RMS position and velocity errors in GNSS only solution, DR only solution, and ultratight integration Table 4.2: RMS position and velocity errors in GNSS only solution, DR only solution, ultra-tight integration, and ultra-tight integration with the multipath mitigation algorithm Table 5.1: Signal power assigned to each satellite in the GNSS simulator test (signal power remained constant throughout the test) Table 5.2: Front-end parameters used for collecting GNSS data in two tests viii

9 List of Figures Figure 1.1: Trajectories obtained from the commercial receivers in urban navigation (from O Driscoll et al 2011)... 3 Figure 1.2: Position performance of the standard GNSS receiver in urban navigation by employing least squares (from Xie 2013)... 4 Figure 1.3: A general picture of Calgary downtown (Downtown Calgary, by Kirk Cumming, Panoramio, Web. April 5, 2007 < 4 Figure 1.4: Normalized correlator output as a function of Doppler errors for different bit synchronization errors... 7 Figure 1.5: Architecture of a high-sensitivity GNSS receiver with external bit aiding Figure 2.1: CAF output in the acquisition stage for a 42 db-hz signal with 1 ms coherent integration time Figure 2.2: Basic navigation data demodulation scheme Figure 2.3: Correlator output (I/Q) from PLL/DLL as a function of time in the tracking stage.. 37 Figure 2.4: Demonstration of modulated bits in correlator output Figure 2.5: Cross-correlation output of one navigation data bit in ML bit synchronization Figure 2.6: Probability density functions of Gaussian distribution for different chosen parameters. Upper-left: mean is 10 and standard deviation is 1. Upper-right: mean is 0 and standard deviation is 1. Lower-left: mean is 10 and standard deviation is 5. Lower-right: mean is 0 and standard deviation is Figure 2.7: Theoretical and simulated performance of ML bit synchronization as a function of signal strength. Different numbers of navigation data bits are considered. Ten thousand trials were simulated for each C/N0 value Figure 2.8: Theoretical and simulated performance of ML bit decoding in the phase-locked mode. Different numbers of navigation data bits are considered Figure 2.9: Theoretical and simulated performance of ML bit decoding in the frequency-locked mode. Different numbers of navigation data bits are considered Figure 2.10: Simulated performance of ML bit synchronization as a function of signal strength. Different numbers of navigation data bits with different kinds of bit sequences are considered Figure 2.11: Simulated and real performance of ML bit synchronization as a function of signal strength. Different numbers of navigation data bits are considered in phase-locked mode and frequency-locked mode Figure 2.12: RMS errors of Doppler estimation as a function of signal strength. Two different coherent integration times are considered Figure 2.13: In phase correlator output in phase-locked mode Figure 2.14: Simulated performance of ML bit synchronization with 20 bits. Different Doppler errors are considered Figure 2.15: Simulated performance of ML bit synchronization with 100 bits. Different Doppler errors are considered Figure 2.16: Simulated and real performance of ML bit decoding as a function of signal strength. 2 bits to be decoded at a time are considered in phase-locked mode and frequency-locked mode Figure 2.17: Vector diagram when the phase error is less than π/ Figure 2.18: Vector diagram when the phase error is larger than π/ ix

10 Figure 2.19: Simulated performance of ML bit decoding with a 2-bit sequence. Different Doppler errors are considered Figure 2.20: Simulated performance of ML bit decoding with a 5-bit sequence. Different Doppler errors are considered Figure 3.1: Architecture of a scalar-based GNSS receiver, GSNRx Figure 3.2: Architecture of an assisted-gnss high-sensitivity GNSS receiver, GSNRx-hs Figure 3.3: Architecture of a standalone high-sensitivity GNSS receiver with ML bit decoding, GSNRx-hs-sa Figure 3.4: Field test trajectory near the University of Calgary Figure 3.5: Dense foliage environment in the field test Figure 3.6: Dense foliage environment facing vertically upwards Figure 3.7: Sky plot in the dense foliage test Figure 3.8: C/N0 of all satellites in view in the dense foliage test estimated by GSNRx-hs Figure 3.9: Field test trajectory in Urban Canyon Test I Figure 3.10: Urban canyon environment in Urban Canyon Test I Figure 3.11: Sky plot in Urban Canyon Test I Figure 3.12: C/N0 of all satellites in view in the Urban Canyon Test I estimated by GSNRx-hs Figure 3.13: Field test trajectory in Urban Canyon Test II Figure 3.14: Urban canyon environment in Urban Canyon Test II Figure 3.15: Sky plot in Urban Canyon Test II Figure 3.16: C/N0 of all satellites in view in in Urban Canyon Test II estimated by GSNRx-hs Figure 3.17: The land vehicle with navigation systems for field data collection. The upper-left picture shows a NovAtel GPS-702-GG antenna and a LCI IMU on top of the vehicle. The upper-right picture shows a National Instruments PXI-5600 front-end inside the vehicle. The lower picture shows the land vehicle Figure 3.18: C/N0 of PRN 14 in scalar tracking and vector tracking in the dense foliage test Figure 3.19: Performance of ML bit decoding as a function of signal strength in scalar tracking and vector tracking in the dense foliage test Figure 3.20: Estimated Doppler values of PRN 14 in scalar tracking and vector tracking in the dense foliage test Figure 3.21: Performance of ML bit decoding in scalar tracking and vector tracking in the dense foliage test Figure 3.22: RMS position and velocity errors with different coherent integration times in the bit aiding mode in the dense foliage test Figure 3.23: Position errors in north, east and up as a function of time for different coherent integration times in the bit aiding mode in the dense foliage test Figure 3.24: Velocity errors in north, east and up as a function of time for different coherent integration times in the bit aiding mode in the dense foliage test Figure 3.25: RMS position and velocity errors in different directions by using Strategy I in the dense foliage test Figure 3.26: Cumulative C/N0 plots of all satellites in the dense foliage test Figure 3.27: RMS position and velocity errors in different directions by using Strategy II in the dense foliage test Figure 3.28: Trajectory results by using Strategy II in the dense foliage test x

11 Figure 3.29: Performance of ML bit decoding as a function of signal strength in scalar tracking and vector tracking in the Urban Canyon Test I Figure 3.30: Performance of ML bit decoding in scalar tracking and vector tracking in Urban Canyon Test I Figure 3.31: RMS position and velocity errors with different coherent integration times in the bit aiding mode in the Urban Canyon Test I Figure 3.32: Position errors in north, east and up as a function of time for different coherent integration times in the bit aiding mode in the Urban Canyon Test I Figure 3.33: Velocity errors in north, east and up as a function of time for different coherent integration times in the bit aiding mode in the Urban Canyon Test I Figure 3.34: RMS position and velocity errors in different directions by using Strategy II in the Urban Canyon Test I Figure 3.35: Trajectory results by using Strategy II in the Urban Canyon Test I Figure 3.36: Trajectory results in GNSS only mode by using Strategy II in the Urban Canyon Test II Figure 4.1: Architecture of a conventional ultra-tight receiver with external bit aiding, GSNRxhs-dr Figure 4.2: Architecture of ultra-tight integration of GNSS and traditional INS mechanizations Figure 4.3: Architecture of a new ultra-tight receiver with ML bit decoding, GSNRx-hs-dr-sa Figure 4.4: C/N0 of PRN 25 in scalar-based receiver and ultra-tight receiver in the urban canyon test Figure 4.5: Performance of ML bit decoding as a function of signal strength in scalar-based receiver and ultra-tight receiver in the urban canyon test Figure 4.6: Performance of ML bit decoding in scalar-based receiver, vector-based receiver and ultra-tight receiver in the urban canyon test Figure 4.7: Cumulative C/N0 plots of all satellites in the urban canyon test Figure 4.8: Performance of ML bit decoding with different search space in ultra-tight receiver in the urban canyon test Figure 4.9: Trajectory results of GNSS only solution and DR only solution in the urban canyon test. The blue line is the reference trajectory; the red line is the result of GNSS only solution with the coherent integration time of 100 ms by bit aiding; and the green line is the result of DR only solution Figure 4.10: Trajectory results of ultra-tight integration of assisted-gnss with coherent integration time of 100 ms and DR system in the urban canyon test. The blue line is the reference trajectory; the red line is the ultra-tight integration result from GSNRx-hs-dr Figure 4.11: Trajectory results of ultra-tight integration of assisted-gnss with coherent integration time of 100 ms and DR system using the signal power based multipath mitigation algorithm in the urban canyon test. The blue line is the reference trajectory; the red line is the result without the signal power based multipath mitigation algorithm; and the green line is the result using the signal power based multipath mitigation algorithm Figure 4.12: RMS position and velocity errors in different directions by using bit aiding and ML bit decoding based bit wipe-off from ultra-tight receiver in the urban canyon test xi

12 Figure 4.13: Trajectory results of standalone ultra-tight receiver using the coherent integration time of 100 ms from ML bit decoding in the urban canyon test. The blue line is the reference trajectory; the red line is the result from standalone ultra-tight receiver Figure 5.1: Demonstration of bit boundaries alignment among all satellites within the receiver Figure 5.2: Cross-correlation output of one navigation data bit in collective bit synchronization Figure 5.3: Field test trajectory near the University of Calgary Figure 5.4: Dense foliage environment in the field test Figure 5.5: C/N0 of satellites in the field test estimated by GSNRx Figure 5.6: Performance of collective bit synchronization as a function of signal strength for different numbers of satellites when using one data bit at a time Figure 5.7: Performance of collective bit synchronization as a function of signal strength for different numbers of satellites when using ten data bits at a time Figure 5.8: Sensitivity improvement as a function of SSR for different number of satellites when using ten data bits at a time Figure 5.9: Performance of traditional ML bit synchronization as a function of signal strength for different navigation data bit numbers in the hardware GNSS simulator test Figure 5.10: Successful synchronization rate for all satellite when using the collective bit synchronization with different numbers of data bits Figure 5.11: Performance comparison of traditional ML bit synchronization and collective bit synchronization for the strong signal satellite (PRN-09) Figure 5.12: Performance comparison of traditional ML bit synchronization and collective bit synchronization for the weak signal satellite (PRN-25) xii

13 List of Abbreviations and Symbols Abbreviations AWGN BER BPSK C/A C/N 0 CAF CDMA DGPS DLL DR EKF FLL GNSS GPS GSNRx GSM HOW I IF IMU INS Additive White Gaussian Noise Bit Decoding Error Rate Binary Phase-Shift Keying Coarse/Acquisition Carrier to Noise Ratio Cross Ambiguity Function Code Division Multiple Access Differential Global Navigation Satellite System Delay Locked-Loop Dead Reckoning Extended Kalman Filter Frequency Locked-Loop Global Navigation Satellite System Global Positioning System GNSS Software Navigation Receiver Global System For Mobile Communication Hand-over Word In-phase Correlator Output Intermediate Frequency Inertial Measurement Unit Inertial Navigation System xiii

14 LAAS LKF LOS MEMS ML MMSE NCO NI NLOS NTP OCXO OS PLAN PLL PRN PVT Q RF RMS SAS SDR SIS SPAN Local Area Augmentation System Linearized Kalman Filter Line-of-Sight Micro Electro-Mechanical Systems Maximum-Likelihood Minimum Mean Square Error Numerically Controlled Oscillator National Instruments Non-Line-of-Sight Network Time Protocol Oven-Controlled Crystal Oscillator Open Service Position, Location And Navigation Phase Locked-Loop Pseudorandom Noise Position, Velocity and Time Quadra-phase Correlator Output Radio Frequency Root Mean Square Steering Angle Sensor Successful Decoding Rate Signal in Space Synchronized Position Attitude Navigation xiv

15 SSR TCP/IP TCXO TDMA TLM TTFF WAAS WSS VA Successful Synchronization Rate Transmission Control Protocol/Internet Protocol Temperature Compensated Crystal Oscillators Time Division Multiple Access Telemetry Word Time-To-First-Fix Wide Area Augmentation System Wheel Speed Sensors Viterbi Algorithm xv

16 Symbols A Signal Amplitude b a y Longitudinal acceleration error in body frame b b y Navigation message Longitudinal accelerometer bias b m Possible bit value vector c C Ranging code or speed of light Cross-correlation function d G Gyroscope drift dt d i Receiver s clock bias Error in predicted pseudorange E b Transmitted signal energy per bit N 0 Specified noise spectral density T co Coherent integration time f d Doppler frequency f IF Intermediate frequency f RF Radio frequency F G H I m Dynamics matrix Shaping matrix Design matrix Inner product xvi

17 I K l b Identity matrix Kalman gain Bit boundary L M i Length of the data bit sequence to be decoded Millisecond integer ambiguity in the range N P d Number of bits Probability of successful decoding P e,coh BER in coherent decoding P e,diff BER in non-coherent decoding P Q Q Covariance matrix Process noise matrix Complementary cumulative distribution function r () t Signal in space at the input of a GNSS receiver RF rn () n r R R S S Locally generated signal Position error vector in navigation frame Covariance matrix of the observations Correlation function Sum of the absolute values of cross-correlation Scale factor error vector of wheel speed sensors t ( ) tx n Transmit time t () rx n Receiver time xvii

18 T b Length of one navigation data bit T c Period of ranging code T s Sampling rate of the digitalization process v Error vector in an observation function b V y Longitudinal velocity error in body frame w W x x ˆ sv i Vector of zero-mean and unity variance white noise Window function State vector in a system model Estimated satellite position ˆ Rx x Estimated position of the user X yn ( ) z z x Vector of variable for bit synchronization Down-converted signal at IF Measured sub-millisecond pseudorange Observation vector in an observation function Reciprocal of time constant in first order Gauss-Markov s Pitch error Azimuth error Steering angle error Code phase Carrier phase Transition Matrix xviii

19 μ Variance of observations Mean vector Measurement errors ( n) Noise at IF Pseudorange Covariance matrix xix

20 Chapter One: Introduction Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS) can provide users with accurate navigation and timing services worldwide. They are vital for applications such as aircraft auto-piloting, automobile en-route guidance, pedestrian positioning, etc. Recently, processing weak GNSS signals has been receiving growing attention because of the increased demand for navigation in signal challenged environments, e.g., indoors, under dense foliage canopies, in urban canyons, etc. This thesis work presents an innovative standalone high-sensitivity GNSS receiver architecture that is able to process weak GNSS signals and provide reliable navigation solutions in the signal challenged environments. 1.1 Background The GNSS line-of-sight (LOS) signals are already very weak, e.g., GPS L1 C/A signal is designed to arrive on the ground at about dbw (i.e., dbm). In signal challenged environments, the signals are further attenuated as they propagate through the blockages. GNSS navigation in such environments is a major challenge, and this puts increasing demand on GNSS receiver design, e.g., improving sensitivity, processing weak GNSS signals, mitigating multipath, etc Navigation Challenges in Signal Challenged Environments The early explorers navigated using the idea that a position could be estimated relative to the departure point by keeping track of the direction and traveled distance. The name of this 1

21 technique is dead reckoning (DR). However, positioning errors in the DR system will accumulate over time without corrections. The satellite radio waves based GNSS are able to provide positioning accuracy ranging from meter-level (using civil ranging code) to centimeterlevel (using carrier phase). The advantages of GNSS technique for positioning and navigation include: Global coverage; High accuracy compared to other wireless navigation systems; Errors are bounded (i.e., not accumulated with time). However, the disadvantages of the satellite radio systems are also obvious: Sensitive to the propagation path (i.e., atmosphere delay), system errors (i.e., clock and orbit errors) and receiver noise; Vulnerable in signal challenged environments (e.g., signal attenuation, blockage, multipath, etc.). The differential GPS (DGPS) systems such as Local Area Augmentation System (LAAS) and Wide Area Augmentation System (WAAS) can mitigate the system errors in GPS measurements. However, they cannot help to solve the signal attenuation and distortion (by multipath) problems that are widely existed in harsh environments. Because GNSS LOS signals are already very weak, the risk of standard GNSS receivers is that the tracking loops may lose lock when the signal power is further attenuated to (Gleason & Gebre-Egziabher 2009): 2

22 -140 dbm: A Costas loop has difficulties following the signal; -155 dbm: Delay locked-loops (DLL) and frequency locked-loops (FLL) have difficulties following the signal. To process weak GNSS signals using standard GNSS receivers may either generate large biases as shown in Figure 1.1 from O Driscoll et al (2011) or limited navigation outputs as shown in Figure 1.2 from Xie (2013). Both of the GNSS data were collected in the Calgary downtown area, and Figure 1.3 shows a general picture of Calgary downtown. Figure 1.1: Trajectories obtained from the commercial receivers in urban navigation (from O Driscoll et al 2011) 3

23 Figure 1.2: Position performance of the standard GNSS receiver in urban navigation by employing least squares (from Xie 2013) Figure 1.3: A general picture of Calgary downtown (Downtown Calgary, by Kirk Cumming, Panoramio, Web. April 5, 2007 < 4

24 So in such harsh environments, high-sensitivity GNSS receivers with weak GNSS signal processing techniques are usually necessary. However, compared to standard GNSS receivers, high-sensitivity GNSS receivers have specific requirements dealing with modulated navigation messages Requirements of high-sensitivity GNSS Receiver High-sensitivity GNSS receivers are preferred for the improved acquisition and tracking capabilities under degraded signal environments. Currently the state-of-art high-sensitivity receivers are capable of providing satellite measurements for signals attenuated by approximately 35 db (Media Tek 2014 and u-blox 2014). For high-sensitivity GNSS receivers, extending integration time coherently is optimal for obtaining higher sensitivity, mitigating multipath and cross-correlation false locks, and avoiding squaring loss. Further details about high-sensitivity GNSS receivers and benefits of long coherent integration time can be found in (Pany et al 2009). However, longer coherent integration time is primarily limited by the navigation message data bit, if present. A brief introduction about the impact of the modulated data bit is presented as following. The purpose of a GNSS receiver is to estimate the code phase and Doppler of the incoming GNSS signals, thus allowing for the determination of the pseudorange and pseudorange rate to each satellite. The pseudoranges and pseudorange rates are then used to calculate the receiver s position, velocity and time (PVT) parameters. To accomplish this, the code phase and Doppler is estimated for each satellite from a cross ambiguity function (CAF) (Misra & Enge 2006), which is the cross-correlation between the received signal and the locally generated signal. Bit sign transition affects the CAF evaluation especially when the coherent integration time is longer than 5

25 the bit period ( T b ) (Jeon et al 2011, and Sun & Lo Presti 2010). In particular, bit sign transitions modify the shape of the CAF envelope and result in a drop in received signal power. So before extending the coherent integration time, two necessary steps are usually required. First, use bit synchronization to locate the bit boundaries; second, use bit decoding to wipe off the bits modulated on the carrier ( bit wipe-off ). Complete bit wipe-off requires knowledge of bit boundaries and bit values. The process of determining the location of the bit boundaries and extracting the bit values is herein called bit synchronization and bit decoding respectively. As shown in Figure 1.4, the bit sign transitions may even divide the central peak of CAF in frequency domain into two split side lobes if the bit synchronization error is too large, e.g., 4 ms or larger for the GPS L1 C/A signal. 6

26 Figure 1.4: Normalized correlator output as a function of Doppler errors for different bit synchronization errors There are two kinds of ways to achieve bit synchronization and decoding in the GNSS receiver design. The first is utilizing assistance information from external sources (e.g., Pany et al 2005, Van Diggelen 2009, O Driscoll et al 2010, Li 2012, and Xie 2013), and the second is the use of estimation-based algorithms (e.g., Van Dierendonck 1996, Kokkonen & Pietila 2002, Ziedan & Garrison 2003, Soloviev et al 2009, and Ren & Petovello 2014a). By implementing these two methods, a GNSS receiver s architecture will be classified as assisted-gnss receiver design or standalone GNSS receiver design, respectively. The certain types of assisted-gnss are able to provide timing information for bit synchronization (Pany et al 2005), and provide instant navigation data bits for bit wipe-off (O Driscoll et al 2010) via a secondary wireless network. 7

27 The details about assisted-gnss and relevant receivers will be introduced in the following section before moving to the main focus of this thesis standalone GNSS receivers Assisted-GNSS Assisted-GNSS improves on standard GNSS performance by providing information, through an alternative communication channel, that the GNSS receiver would ordinarily have received from the satellites themselves (Van Diggelen 2009). Assisted-GNSS simplifies the signal processing from the satellites, makes obtaining position and velocity solution easier, and minimizes the amount of information required from the satellites and reduces the time needed to obtain it. Compared to an unassisted receiver, the assisted-gnss receiver is able to make measurements from the satellites quickly with weak signals. Typically, assisted-gnss can obtain the following information from a secondary wireless network (Van Diggelen 2009 and Pany et al 2005): Navigation message, such that decoding those messages (e.g., ephemeris) from satellite signals is no longer necessary; Coarse estimation of user s position, which can help reduce search space size in the signal acquisition stage, and speed up the signal detection process; Timing information such that the location of bit boundaries can be obtained directly without requiring a bit synchronization process if the accuracy of the timing is within a half period of ranging code (e.g., 0.5 ms for GPS L1 C/A signal); Instantaneous navigation data bits, which enable the real-time bit wipe-off process. 8

28 Given Ephemeris data from wireless network and code phase estimates from five or more satellites, if a user s coarse position error is less than 100 km and the user s clock error is less than 1 min, Van Diggelen (2009) showed that the user s position can be resolved by a five state equation. This process is named coarse-time navigation. Bit synchronization and transmit time extraction from the navigation message are unnecessary in coarse-time navigation, and this speeds up GNSS time to first fix (TTFF) compared to conventional GNSS receivers. However, the receiver s sensitivity in coarse-time navigation is still limited due to limited coherent integration without bit wipe-off. Apart from the coarse-time navigation, Pany et al (2005) mentioned that if user s accurate position and clock error information is available from networks, the GNSS receiver is able to predict the precise transmit time. If the accuracy of the predicted transmit time is better than +/- half period of ranging code, the location of bit boundaries can be obtained directly without bit synchronization process. This means the wireless networks used for timing assistance should be synchronized with GPS time. However, Van Diggelen (2001) mentioned that certain code division multiple access (CDMA) networks (e.g., US-CDMA) are synchronized to GPS time, but other cellular networks, e.g., global system for mobile communication (GSM), W-CDMA, and time division multiple access (TDMA), are not synchronized to GPS time. For the systems that do not maintain such stringent synchronization to GPS time, Djuknic & Richton (2001) mentioned that the implementation of sensitivity assistance and assisted-gps technology in general will require novel approaches to satisfy the timing requirements. The standardized solution for GSM and TDMA adds time calibration receivers in the field (e.g., location measurement units) that can monitor both the wireless-system timing and GPS signals used as a timing reference. 9

29 By using the navigation data bit aiding and frequency aiding from an external source, Akos et al (2000) showed that during acquisition, signals with carrier to noise-density ratios (C/N 0 ) of 32, 22, 17, and 12 db-hz can be detected if the coherent integration time is at least 8, 200, 400, and 800 ms respectively. The coherent integration time of 800 ms means bit wipe-off of 40 data bits. In Pany et al (2009), the broadcast navigation data bits are transferred over a Transmission Control Protocol/Internet Protocol (TCP/IP) based link. O Driscoll et al (2010) proposed a bit aiding based high-sensitivity GNSS receiver architecture, shown in Figure 1.5. This highsensitivity GNSS receiver implemented a conventional bit synchronization process unit, and used an external network to provide the bit aiding service. Details of this receiver s inside architecture will be further discussed in Section Figure 1.5: Architecture of a high-sensitivity GNSS receiver with external bit aiding 10

30 1.1.4 Bit Synchronization and Bit Decoding In contrast to the assisted-gnss concept, standalone high-sensitivity GNSS receivers are the focus of this thesis. This is because the assisted-gnss receiver loses its autonomy and cannot avoid a corresponding increase in complexity and cost in receiver design. In order to achieve bit wipe-off and extend coherent integration time, a standalone highsensitivity GNSS receiver usually estimates the location of bit boundaries and the bit values from GNSS signals from bit synchronization and bit decoding process, respectively. There are several ways of performing bit synchronization. In theory bit boundaries can be directly viewed (by detecting the sign changes of two adjacent samples) from in-phase outputs in a Costas phase lock loop. However, the reliability and the sensitivity of this approach are low and it is only valid in strong signal environments. In order to improve the reliability, the Histogram bit synchronization method (Van Dierendonck 1996) determines bit boundaries by counting the sign changes between adjacent correlator outputs, and comparing the count against two thresholds. The performance of Histogram bit synchronization depends on the C/N 0 and setting of the two thresholds. In order to improve the sensitivity, the Maximum-Likelihood (ML) bit synchronization (Kokkonen & Pietila 2002) determines bit boundaries by calculating the absolute sum of the correlator output for each possible bit edge position and choosing the edge that maximizes the sum. The performance of ML bit synchronization depends on the C/N 0 and the data duration. Kokkonen & Pietila (2002) showed the ML bit synchronization outperforms the Histogram bit synchronization for weak GNSS signals. There are also several ways of performing bit decoding. In strong signal environments, bit values can also be directly viewed (by detecting the sign of samples) from in-phase outputs in a Costas 11

31 phase lock loop. Bit synchronization and bit decoding by using the Viterbi Algorithm (VA) (Macchi & Scharf 1981) with an extended Kalman filter (EKF) is introduced in Ziedan & Garrison (2003). Given a set of observations, VA is used to estimate the most likely sequence of data by performing an optimal recursive search process using dynamic programing (Cormen et al 1990). Dynamic programing can be applied when the optimal solution to the problem consists of optimal solutions to its sub-problems, and the optimal solution can be expressed in a recursive form (Ziedan & Garrison 2003). The ML bit decoding introduced in Soloviev et al (2009) uses a batch-based search of the bit combination that maximizes the signal energy accumulated coherently over the correlation integration interval. Both VA bit decoding and ML bit decoding showed a low bit decoding error rate (BER) for 15 db-hz signals by utilizing the characteristic of repeated GPS sub-frames in every 30 seconds. Given the consideration of performance and processing complexity, ML bit synchronization and ML bit decoding are chosen as the research focus in this thesis. In Ren et al (2012), the requirements of ML bit synchronization and ML bit decoding were further analyzed in terms of the number of data bits required for bit synchronization and the number of data bits that can be decoded at a time for bit decoding. The performance of ML bit synchronization and ML bit decoding rely heavily on the signal tracking performance of the receiver (i.e., estimation errors of code phase and Doppler of GNSS signals, and the tracking threshold). The tracking threshold is particularly critical, e.g., Gleason & Gebre-Egziabher (2009) mentioned that a Costas phase-locked loop (PLL) had difficulties following the signal at about 35 db-hz, and below which the process of bit synchronization and bit decoding are invalid. 12

32 1.1.5 Advanced Tracking Algorithms In this thesis work, focus is given to standalone high-sensitivity GNSS receiver design. The standalone approach requires the analysis of factors that impact the performance of ML bit synchronization and ML bit decoding. Furthermore, it is expected to see the benefits of utilizing the advanced tracking algorithms and collective signal processing techniques. The advanced tracking algorithms are aimed to improve ML bit decoding performance. The collective signal processing techniques are expected to improve ML bit synchronization performance. The collective signal processing techniques will be introduced in Section The conventional tracking architectures (e.g., PLL/DLL, FLL/DLL, Kalman filter tracking, etc.) have been discussed in many GNSS receiver design works, e.g., Ward et al (2006), Borre et al (2007), Petovello et al (2008a), Psiaki & Jung (2002), Lashley (2006), etc. However, the conventional tracking architectures have limited ability in tolerating signal attenuation and multipath fading (Satyanarayana 2011). So in order to achieve navigation data bit wipe-off in signal challenged environments, the advanced tracking algorithms should be utilized. The advanced tracking algorithms implemented and investigated in this thesis work include: vector tracking (e.g., Spilker 1996, Pany & Eissfeller 2006, Petovello & Lachapelle 2006, Lashley et al 2009, and Won et al 2010), openloop tracking (e.g., Van Graas et al 2005, Van Diggelen 2001, and Soloviev et al 2011) and ultratightly coupled (tracking) architecture (e.g., Soloviev et al 2004a, Soloviev et al 2011, Landis et al 2006, Ohlmeyer 2006, Petovello & Lachapelle 2006, and Petovello et al 2008b). Ultra-tightly coupled architecture is the integration of GNSS and vehicle/inertial sensors, since several field tests in this thesis work focus on the land vehicle navigation in urban canyons. 13

33 Vector Tracking The first advanced tracking algorithm used in thesis work is vector tracking. Vector tracking is the process of using the receiver s estimate of position and velocity to update the GNSS channel estimates of the Doppler frequency and code phase. In contrast to scalar tracking, which is always implemented in the conventional tracking designs, the individual tracking loops in vector tracking are eliminated and replaced by the vector-based navigation filter (Spilker 1996). Pany & Eissfeller (2006) showed that a 10 db-hz signal can be detected and tracked in vector tracking, and signals above a selectable threshold of 25 db-hz are satisfactory for the positioning update. Lashley et al (2010) showed vector tracking algorithms have an improvement in tracking threshold from 2.4 db to 6.2 db depending on the number and geometry of satellites tracked. Lashley et al (2009) showed that the vector delay/frequency lock loop can operate with 8 G coordinated turns (i.e., turns with significant dynamics occurred in two axes) at a C/N 0 ratio of 19 db-hz. Though the margins of improvement are different according to different designs and applications, compared to conventional scalar tracking, vector tracking is definitely an advanced tracking algorithm that can effectively extend the tracking threshold Ultra-Tightly Coupled Architecture An ultra-tightly coupled GNSS receiver is a system that integrates GNSS measurements with inertial and/or other sensor outputs, and uses the integrated estimate of position and velocity to update the GNSS channel estimates of the Doppler frequency and code phase. The ultra-tightly coupled architecture can be seen as an extension to the vector tracking algorithm, because it not only updates the GNSS channel estimates from the predictions of the navigation filter, but also integrates inertial sensors to measure actual user motion, thus providing a more robust and accurate navigation solution and, by extension, improved signal tracking. Generally, compared to 14

34 a GNSS only solution, the advantages of integrating GNSS and inertial sensors ultra-tightly include improved accuracy, smoother trajectories, availability of an attitude solution, reduced susceptibility to interference and increased sensitivity (Soloviev et al 2004, Petovello & Lachapelle 2006, and Petovello et al 2008b). Specifically, Soloviev et al (2004b) demonstrated the reacquisition and continuous carrier phase tracking of 15 db-hz GPS signals in flight test with simulated noise; Petovello & Lachapelle (2006) showed that an ultra-tightly coupled GPS and inertial navigation system (INS) architecture is able to track the carrier phase under foliage with a GPS signal attenuation of 15 db and still maintains a velocity solution accurate to a few centimeters per second. Petovello et al (2008b) demonstrated that the ultra-tight receiver provided about 7 db of sensitivity improvement over the standard receivers. INS has two prevalent dead reckoning (DR) models, namely the traditional INS mechanizations (e.g., Soloviev et al 2004a, Petovello & Lachapelle 2006, and Petovello et al 2008b), and the vehicle/inertial sensor based DR algorithm (e.g., Li 2012, Noureldin et al 2013, and Fouque et al 2008). The former approach obtains velocities by integrating accelerometer outputs, and position increments by integrating the velocities. The latter DR algorithm usually used in land vehicle navigation directly obtains velocity information from wheel speed sensors or odometers. The main benefit of DR algorithm over the traditional INS mechanization is the accuracy of DR algorithm degrades with the travelled distance rather than with time (Li 2012). This thesis work only utilizes the ultra-tight integration of GNSS and the vehicle/inertial sensor based DR algorithm, and investigates the benefits of such system to improve ML-based bit wipe-off and the whole navigation solution. 15

35 Open-Loop Tracking The last advanced tracking algorithm used in this thesis work is open-loop tracking. In contrast to closed-loop tracking that normally only uses early, late and prompt correlaters, multiple correlators (typically tens, hundreds or thousands correlators) are used in open-loop tracking to generate the CAF at every epoch, and loop filters are effectively removed. The open-loop tracking is similar to signal acquisition but uses different searching space and grid size to reduce computational load and mitigate noise and cross correlation between different satellites. The open-loop tracking can avoid the stability problem caused by long coherent integration in normal closed-loop tracking (Ward et al 2006). This architecture is necessary for building the correlator output measurements with longer coherent integration. In addition, Xie (2013) demonstrated that multipath could be separated in frequency domain with open-loop tracking. Soloviev et al (2011) showed an open-loop tracking with Doppler aiding scheme under dense foliage canopy available at 15 db-hz. The detailed benefits of open-loop tracking can be found in Van Graas et al (2005). The open-loop tracking in this work is combined with the vector tracking or the ultra-tightly coupled architecture and not assessed independently Collective Signal Processing Using Multiple Satellites In order to improve the performance of ML bit synchronization, an innovative algorithm called collective bit synchronization is proposed in this thesis. The inspiration comes from the collective signal processing techniques using multiple satellites. Different from the other telecommunication receivers that are designed for communication purpose, GNSS receivers can provide precise position and velocity information from the time of arrival (TOA) technique, which links all (satellite tracking) channels via spatial correlation. This 16

36 spatial correlation among all channels validates the collective signal processing scheme that can provide extra processing gain. Vector tracking and ultra-tightly coupled architecture use a receiver s position and velocity to improve tracking performance. In addition, the concept has been used in the collective detection of weak GNSS signals. Axelrad et al (2012) showed a rapid acquisition scheme by combining satellite correlograms, which could reduce the required signal power from a particular satellite by about 10 to 20 db. Instead of searching in a code phase/doppler domain, the collective acquisition search is performed in a position/clock space that directly yields the navigation solution. Along this vein, this thesis work proposes a novel collective bit synchronization approach for weak GNSS signals using multiple satellites. This is one of the original contributions of this thesis work. Rather than doing bit synchronization in each individual channel as in conventional methods, collective bit synchronization combines multiple satellites together to provide extra processing gain, and improve the detection rate of bit boundary positions. The details will be further discussed in Chapter Five. 1.2 Limitations of Previous Works After previously introducing the background and the general ideas of this thesis, this section discusses the limitations of previous works that need to be avoided or overcome. Many standard GNSS receiver designs (e.g., Akos 1997, Braasch & Van Dierendonck 1999, Krumvieda et al 2001, Ward et al 2006, and Borre et al 2007) only implemented and analyzed coherent integration time periods ranging between one ranging code period and one navigation 17

37 data bit period (e.g., between 1 ms and 20 ms for GPS L1 C/A signal). It is noted that there are some benefits in reducing the complexity of the GNSS receiver design by using short integration time. However, Akos et al (2000) showed that the GNSS signals with C/N 0 values of 32, 22, 17, and 12 db-hz may be hardly detected if the coherent integration time is not equal to or longer than 8, 200, 400, and 800 ms respectively. Furthermore, the coherent integration time of 1 ms can only be used to acquire GNSS signals with the attenuation not more than 5 db (ibid.). This indicates that short coherent time is not sufficient for the high sensitivity applications which have to deal with weak signals in harsh environments. The C/N 0 required for tracking is approximately 3 db lower than the above, the exact value depending upon the tracking loop configuration (Lachapelle 2004). However, given the certain coherent integration time, lower tracking threshold is usually achieved by decreasing tracking loop bandwidth. Low loop bandwidth will result in a tracking loop losing lock easily in high dynamic environments. The limitation of standard GNSS receiver was shown in Section Non-coherent integration (e.g., Ward et al 2006, Borio et al 2009, and Pany et al 2010), by summing the power of the correlator outputs, has been shown to be capable of avoiding the impact of navigation bit transitions without bit wipe-off and effectively improve the receiver s sensitivity. Pany et al (2010) showed a 17 db-hz GPS signal can be detected by applying a 16 ms coherent integration time and 200 non-coherent integrations. However, compared to the coherent integration, the squaring loss is the main concern for the non-coherent integration. In addition, the non-coherent integration loses the advantage in mitigating multipath and crosscorrelation false locks (Pany et al 2009). For these reasons, the non-coherent integration will not be further discussed in this thesis work. 18

38 Diversity techniques (e.g., Dehghanian et al 2010 and Dehghanian 2011) based on combining uncorrelated or partially correlated signals have proven to be effective for improving the reliability of a message signal by using two or more communication channels with different characteristics. However, multiple communication channels will increase system complexity and cost. The current mainstream high-sensitivity GNSS receiver design (e.g., Media Tek 2014, u-blox 2014, and O Driscoll et al 2010) utilizes assisted-gnss to improve performance. However, the assistance source cannot be always considered as available and the cost of additional communication channels is often a requisite concern. Paonni et al (2011) mentioned about drawbacks of obtaining coarse time reference from network assistance: from the loss of the GNSS receiver standalone capability, to the required additional costs for the cellular network and to the requirement of having always five or more satellites in view. Actually the system time reference used to compute the pseudorange cannot be easily retrieved from external sources or previously stored data, because this parameter is strictly related to the specific send time of the received signal in space. Van Diggelen (2001) mentioned that US-CDMA is synchronized to GPS time, but other cellular networks, e.g., GSM, W-CDMA, and TDMA, are not synchronized to GPS time. Since the systems do not maintain such stringent synchronization to GPS time, some extra efforts, e.g., adding time calibration receivers to monitor both the wireless-system timing and GPS signals, are usually required. Paonni et al (2011) mentioned that the precision of the user plane (e.g. Network Time Protocol (NTP) over TCP/IP) used in Android mobile-phones for time synchronization is far from being useable for GPS C/A code ambiguity resolution (i.e., bit synchronization). 19

39 Standalone high-sensitivity GNSS receiver design requires bit synchronization and bit decoding for modulated bit wipe-off. Among the mainstream bit synchronization algorithms, to view bit boundaries directly from in-phase outputs (i.e., detect the sign changes of two adjacent samples) in a Costas loop is only suitable for strong signals and its reliability is poor. Histogram bit synchronization is designed to improve the reliability of bit boundaries detection, but its sensitivity is limited. This is because the coherent integration time of the consecutive correlator outputs used to determine the sign change is only equal to the ranging code period. The performance of ML bit synchronization shown in Kokkonen & Pietila (2002) confirms the ML bit synchronization outperforms the Histogram bit synchronization for weak GNSS signals. However, the conventional ML bit synchronization omits the signal spatial correlation in different channels via the receiver s position and velocity. Among the mainstream bit decoding algorithms, to view bit values directly from in-phase outputs (i.e., detect the sign of the samples) in a Costas loop is still only suitable for strong signals and its performance is poor. Both VA bit decoding and ML bit decoding have shown convincing performance for signal power as low as 15 db-hz. However, those results are based on utilizing the characteristic of repeated GPS sub-frames in every 30 seconds to improve the bit decoding rate. In real applications, especially for dynamic positioning, e.g., land vehicle navigation, to wait several rounds of 30 seconds is not always a feasible solution. Soloviev et al (2009) stated that the batch processing routine used in ML bit decoding is more efficient than a sequential estimation routine. However this conclusion is yet to be justified. There are some other approaches proposed for bit cancellation. Jeon et al (2011) developed a bit cancellation mechanism by summing two correlator outputs with half a data bit period 20

40 discrimination in bit boundaries. Sun & Lo Presti (2010) proposed a two-step GNSS acquisition method to mitigate the CAF peak impairments caused by bit transitions. However, this method is limited to certain GNSS signal structures, e.g., Galileo E1 OS signal, where the period of ranging code equals to the length of data bit. In order to detect weak signals, Pany et al (2010) implemented a combination of a 16 ms coherent integration time and 200 non-coherent integrations. It mentioned that a bit transition during the coherent integration time reduces the correlation peak and causes a bias in the carrier Doppler estimation, but those losses become tolerable and the bias vanishes after applying many non-coherent integrations. However, the above bit cancellation algorithms usually aim to mitigate the problem caused by bit transitions instead of directly decoding bit values, and thus these algorithms cannot be used for bit wipe-off and extending coherent integration time. ML bit synchronization and ML decoding have benefits in weak signal processing. However, a systematic analysis of their performance and the validity of the ML-based bit wipe-off are still missing. As a result, investigating the performance of ML bit synchronization and ML bit decoding algorithms, in terms of the received signal strength and the tolerance to Doppler error is of importance for extending coherent integration time. With regard to carrier tracking for high-sensitivity GNSS receivers, the conventional PLL is limited by its relatively insufficient ability to improve tracking sensitivity. Among the closedloop structures, the Kalman filter tracking is widely used in challenged signal environments. The simulation works, e.g., Psiaki (2001), Psiaki & Jung (2002) and Ziedan & Garrison (2004), showed a tracking threshold of 15 db-hz in static scenarios by using an oven-controlled crystal oscillator (OCXO). However, the field test result, e.g., Petovello et al (2008b), showed there are 21

41 still severe limitations in tracking GNSS signals of C/N 0 below 24 db-hz. Soloviev et al (2011) showed an open-loop tracking with Doppler aiding scheme under dense foliage canopy available at 15 db-hz. However, this scenario requires large quantities of correlators to acquire GPS signals at every epoch and uses a navigation/tactical-grade inertial measurement unit (IMU) (not low cost) for Doppler aiding. The open-loop architecture outperforms the conventional tracking loops in weak signal environments. However, the open-loop tracking in previous works, e.g., Van Diggelen (2001) and Van Graas et al (2005), usually uses the full search space in every epoch to search the whole code phase and/or all possible Doppler frequencies. The accuracy of the navigation solution in this scheme can be improved when a strong signal is received, but the drawbacks are also obvious, e.g., the moderate computation load, and excessive noise due to the absence of a loop filter. To this end, the appropriate design of open-loop tracking for the interest of ultra-tight integration, and the assistance from vector tracking, open-loop tracking and inertial/vehicle sensors to improve the performance of ML bit synchronization and decoding is potentially of great consequence. 1.3 Objective and Contributions The ultimate objective of this thesis is to design a standalone high-sensitivity GNSS receiver. In order to fulfill this goal, several tasks need to be achieved: Understand the ML bit synchronization and ML bit decoding algorithms through a systematic performance analysis; Determine the benefits of using the advanced tracking algorithms in standalone mode to improve ML bit decoding, and further determining if the estimated data bit values can be 22

42 used to extend coherent integration via the ML-based bit wipe-off, and then assessing the accuracy and reliability of the whole system in the navigation domain; Improve ML bit synchronization by implementing the newly proposed collective bit synchronization algorithm, and evaluate its performance in signal challenged environments. In order to achieve these tasks, this thesis work is divided into three parts. First, a systematic performance analysis of ML bit synchronization and ML bit decoding is performed. The contributions of the first part of the thesis work are three-fold: It systematically assesses the performance of ML bit synchronization and ML bit decoding as a function of the number of data bits, the effect of Doppler error and received signal power in phase-locked mode and frequency-locked mode by using Monte Carlo test; It develops theoretical performance models of ML bit synchronization and ML bit decoding based on statistical theory, and the models can be used to predict the performance given certain parameters; It gives and compares different implementation schemes in a software-based GNSS receiver in weak signal environments. One can consider these contributions to be important to current GNSS research because they provide answers to various queries such as: What kind of performance can be expected from ML bit synchronization and decoding? What is the prerequisite for a standalone high-sensitivity GNSS receiver to extend coherent integration based on the ML algorithms? How to configure a high-sensitivity GNSS receiver design given a signal strength and Doppler frequency error level? 23

43 What are the bounds of Doppler frequency error tolerance? The answers to these questions are of great value for the designers of high-sensitivity GNSS receivers. Second, this thesis work presents an analysis on the utilization of the vector tracking and the ultra-tightly coupled architecture for ML bit decoding and navigating with extended coherent integration in signal challenged environments. The vector tracking and the ultra-tight coupled architecture are able to improve the signal tracking performance, reduce the tracking errors and extend the tracking threshold in harsh environments. The results from the second part of the thesis work determine the benefits of using a vector tracking and the ultra-tightly coupled GNSS receiver in standalone mode to improve bit decoding, and subsequently to determine if this improves the ability to extend coherent integration time and finally improves the navigation solution. The field test for this part of work is a vehicular navigation performed in the dense foliage and urban canyon environments. The contributions of the second part of the thesis work are four-fold: It evaluates the performance of ML bit decoding in vector tracking and ultra-tightly coupled GNSS receiver; It assesses the navigation performance with extended coherent integration time after bit wipe-off; It gives two strategies for extending coherent integration time in a software-based GNSS receiver in weak signal environments; It gives a strategy for mitigating multipath impacts. Third, this thesis work demonstrates a collective bit synchronization approach for weak GNSS signals using multiple satellites. The new approach is one of the original contributions of this 24

44 thesis work. In addition, the benefits of using collective bit synchronization to improve the detection rate of bit boundary positions are analyzed using a software GNSS receiver. The collective bit synchronization algorithm using 11 satellites provides 8 db sensitivity improvement over the traditional ML bit synchronization method, and are more than 200 times faster than the traditional ML bit synchronization for weak signals. All the algorithms in this thesis are implemented and assessed in a software-based GNSS receiver platform called GSNRx. The GSNRx platform is developed in C++ by the PLAN group, University of Calgary. 1.4 Innovations This thesis work presents several original contributions that are considered important for the high-sensitivity GNSS receiver design. The key innovations in this work include: The development of performance models of ML bit synchronization and decoding (Ren & Petovello 2014a). The performance models are derived by using the statistical theory and validated by Monte Carlo simulations in the various signal power environment. The performance models can be beneficial for settings required in the high-sensitivity GNSS receiver without storing any empirical data in memory, given the signal environment, the configuration of tracking mode, and any other parameter needed to consider before performing ML bit synchronization and decoding. The determination of upper bound of Doppler errors (i.e., maximum Doppler error tolerance) for ML bit decoding (Ren & Petovello 2014a). The upper bound of ML bit decoding is derived from theoretical inference and then validated by Monte Carlo 25

45 simulations. Finally the tolerance of Doppler errors is used as the criterion to assess the optimal configuration of ML bit decoding. The development of the standalone high-sensitivity approach (Ren et al 2013 and Ren et al 2014), in which bit wipe-off is achieved and coherent integration time is extended by using ML estimation based algorithms, rather than the bit aiding method, which usually requires aiding source from external networks. The development of the scheme using advanced tracking algorithms (e.g., vector tracking, open-loop tracking, and ultra-tight integration) to improve bit decoding, extend coherent integration time and improve navigation solutions (Ren et al 2013 and Ren et al 2014). The scheme is validated using several field tests in signal challenged environments such as dense foliage and urban canyon environments. The development of the strategies for selecting suitable correlator outputs for input into the ML bit decoding algorithm, to handle the high BER problem when extending coherent integration time in the signal challenged environments (Ren et al 2013). The first strategy is to select correlators based on a satellite s elevation angle, and the second is to select correlators based on the estimated C/N 0 values. The idea of the both strategies is to separate signals of different qualities, and then decide if ML bit decoding and bit wipe-off should be performed. Finally the approach of generating observations (e.g., pseudorange and pseudorange rate) with variable coherent integration time is proposed in this work, and validated in various field tests. The development of the collective bit synchronization approach, which combines multiple satellites together (rather than doing bit synchronization in each individual channel as in conventional methods) to provide extra processing gain, and improve the 26

46 detection rate of bit boundary positions (Ren & Petovello 2014b). The collective bit synchronization approach is implemented in the GNSS software receiver and validated in Monte Carlo simulations, GNSS simulator test, and vehicular field test. 1.5 Thesis Outline The structure of this thesis is summarized in the following paragraphs. Chapter Two provides a detailed and systematic analysis on the performance of ML bit synchronization and decoding algorithms. The GNSS signal model and the methodology of ML bit synchronization and decoding are introduced. Furthermore, the theoretical performance models of ML bit synchronization and decoding are proposed and verified. The performance results of ML bit synchronization and decoding are then presented and discussed. The performance results are listed as a function of different configurations, e.g., different number of bits (i.e., length of data period), in phase-locked or frequency-locked, and different values of Doppler errors. The test scenarios include the Monte Carlo simulation and a Spirent GNSS simulator test. The test results are analyzed using a software GNSS receiver. Chapter Three evaluates the benefits of a vector tracking architecture in GNSS-only mode to improve ML bit decoding, and the accuracy of the land vehicle navigation system with extended coherent integration time. This chapter starts with an introduction of the vector-based GNSS receiver. Then the strategies dealing with the high BER problem in extending coherent integration time are presented. The test scenarios include land vehicle field tests in dense foliage and in urban canyon (i.e., downtown Calgary). Finally, the test results are presented and analyzed. 27

47 Chapter Four evaluates the benefits of ultra-tightly coupled architecture in the standalone mode to improve ML bit decoding, and the accuracy of the land vehicle navigation system with extended coherent integration time. This chapter starts with an introduction of the ultra-tightly coupled GNSS receiver and the vehicle sensor configuration. Then a signal power based multipath mitigation algorithm is presented. A land vehicle field test is directly performed in the urban canyon environment, and the test results are presented and discussed. Chapter Five provides a collective bit synchronization approach for weak GNSS signals using multiple satellites. Three test scenarios are included: the Monte Carlo simulation, a Spirent GNSS simulator test, and a land vehicle field test in the dense foliage environment. Finally, the benefits of using collective bit synchronization to improve the detection rate of bit boundary positions are presented and analyzed. Chapter Six summarizes the work presented in this thesis, the conclusions are provided along with suggestions for future work. 28

48 Chapter Two: Systematic Analysis of ML Bit Synchronization and Decoding In this chapter, the performances of ML bit synchronization and ML bit decoding are systematically assessed as a function of the number of data bits (i.e., length of data period), the effect of Doppler error and received signal power in phase-locked mode and frequency-locked mode. In addition, the theoretical performance models of ML bit synchronization and ML bit decoding are developed based on statistical theory. The performance models and analyses are validated by a Monte Carlo simulation test. In addition, the performances of ML bit synchronization and ML bit decoding are assessed by using Monte Carlo simulation and a Spirent GNSS simulator test. All algorithms used in this systematic analysis are implemented and analyzed by using a software GNSS receiver. 2.1 Methodology This methodology section starts with the introduction of the general GNSS signal structure and then gives a brief overview of the ML algorithms for bit synchronization and ML bit decoding used in this thesis work. In the context of this thesis, the performances of bit synchronization and bit decoding are directly assessed in terms of the successful synchronization rate (SSR) with the navigation data bit (i.e., correct identification of the bit boundaries) and the successful decoding rate (SDR) of bit values. The proposed algorithms are derived for a generic binary phase shift keying (BPSK) GNSS signal, but are assessed using GPS L1 C/A signals only Signal Model The GNSS signal transmitted through an additive white Gaussian noise (AWGN) channel and received at the antenna of a GNSS receiver in the radio frequency (RF) band is represented by 29

49 N sv y ( t) r ( t) n ( t) (2.1) RF RF, i RF i1 Specifically, it is the sum of Nsv line-of-sight (LOS) signals ( rrf, i() t ) from Nsv satellites in view, plus a noise term n () t. In general, the Signal in Space (SIS) at the input of a GNSS receiver RF from the i th satellite has the following structure RF, i i i i i i RF d, i RF, i r ( t) Ab ( t ) c ( t )cos 2 f f t (2.2) where A i is the amplitude of the i th received signal; bt ( ) is the navigation message usually containing satellite ephemeris and almanac i i data, where each binary unit is called bit in the BPSK modulated structure; c( t ) is the ranging code (spreading code), e.g., GPS L1 C/A code used in this work; i i i is the code phase delay introduced by the transmission from the satellite to the receiver f RF is the GNSS carrier frequency which depends on the specified GNSS signals and, for the GPS L1 signal, f MHz ; RF f di, is the Doppler frequency shift of the i th received signal; RF, i is the carrier phase offset at the input of a GNSS receiver. 30

50 In this thesis, the period of ranging code is defined as T c, and the length of one navigation data bit is defined as T b. For the GPS L1 C/A signal, T c is equal to 1 ms and contains 1,023 chips, and the chip period is roughly 1 µs; T b is equal to 20 ms. After being down-converted in the receiver s front-end, signals from different satellites are approximately orthogonal so that i index can be dropped, and the carrier frequency is changed from f RF to f IF. f IF is the nominal intermediate frequency (IF) of the down-converted signal, and usually its magnitude is in the range of several mega-hertz. Then each signal sampled and digitized can be written separately as y( n) r( n) ( n) Ab( n T ) c( n T )cos 2 f f T n ( n) s s IF d s (2.3) where T s is sampling rate of the digitalization process. At this stage, the purpose of a GNSS receiver is to estimate and f d, thus allowing for the determination of the pseudorange and pseudorange rate to each satellite, which is then used to calculate the receiver s PVT parameters. To accomplish this, each and f d is estimated from a CAF, which is the cross-correlation between the received signal and the locally generated signal, and is given by 31

51 Tc Ts1 R(, f ) y( n) r ( n) d n0 Tc Ts1 y( n) c( n T )cos 2 f f n n0 s IF d (2.4) where rn () is the locally generated signal;, f d and are the locally-generated signal parameters used to generate rnusing () (2.3). Finally, the ML estimate of and f d is given by ˆ, fˆ arg max R(, f ) (2.5) d, fd d As will be shown later in Section 2.1.3, the input to the ML bit synchronization algorithm is several cross-correlation outputs, each computed using a coherent integration time equal to the ranging code period. After obtaining the ML estimate of and f d, the locally generated signal and relative parameters can be represented as r ( t) rˆ ( t), ˆ and f fˆ. If there is an error d d in ˆ and f ˆd compared to true and f d, i.e., ˆ and fˆd f d f d, the th k crosscorrelation output over the period T c (i.e., the cross-correlation output from the signal period of ( k 1) T c to kt c ) is given by kt c s R ( ˆ, fˆ ) y( n) rˆ ( n) k d T n( k1) Tc Ts A R ( ) b sinc( f T )exp j 2f kt R, k C, k lb, k d c d c I, Q (2.6) 32

52 where A Rk, is the amplitude of the cross-correlation output; R, ( ) is the normalized (i.e., divided by maximum value) ranging code correlation Ck function with the code phase error of the cross-correlation amplitude;, which results in a triangle shape attenuation in b is the modulated data bit with the boundary located at a integer value l b, which lb, k means each bit transition occurs at lt b relative to the start of the processing period, which is itself equal to the bit period T b ; c fd is the Doppler frequency error, which results in a sinc-shaped attenuation in the cross-correlation amplitude and a rotating carrier phase; is the initial carrier phase error. Since the right hand side of (2.6) is only a function of notation is adopted to make this more explicit and fd, the following shorthand R ( ˆ, fˆ ) R (, f f ) R (, f ) (2.7) k d k d d k d Acquisition and Tracking Equation (2.5) is of importance in GNSS signal processing, and the procedures of detecting GNSS signals and keeping track of the code phase, the Doppler and the carrier phase values are acquisition and tracking respectively. 33

53 Acquisition The purpose of acquisition is to detect visible satellites and obtain coarse values of code phase and Doppler offset of the satellite signals. Like general CDMA signals, the different satellites can be distinguished by different pseudorandom noise (PRN) sequences. For a specified PRN number, GNSS signal acquisition is a search process, which requires replica of both ranging code and the carrier to acquire the satellite signal. As shown in Figure 2.1, the successful signal detection in (2.6) requires a two dimensional parameter match. The code phase (i.e., range) dimension is associated with the replica code. The Doppler dimension is (primarily) associated with the replica carrier. The code phase is the time alignment of the PRN code, and only when the local code phase is perfectly aligned with the incoming code (PRN codes have the highest correlation for zero lag), the latter can be removed from the signal. The carrier frequency is associated to the known IF plus a Doppler offset, which is caused by the line-of-sight velocity of the satellite with respect to the receiver plus oscillator effects. For typical applications, the worst-case Doppler offset can deviate up to ±10 khz (Borre et al 2007). It is important to know the carrier frequency of the incoming signal to be able to generate a local replica, which is used to remove the incoming carrier from the signal. The probability of detecting a signal is associated with a configurable threshold, and the threshold is usually calculated as a function of dedicated false alarm rate, C/N 0 and integration time. Details about setting the threshold can be found in Ward et al (2006). 34

54 Figure 2.1: CAF output in the acquisition stage for a 42 db-hz signal with 1 ms coherent integration time Tracking In the acquisition stage, the signals are detected but only rough estimates of code phase and the Doppler parameters are provided. The purpose of tracking is to refine these values, keep tracking and estimating these values to build the observations (i.e., pseudorange and pseudorange rate), and demodulate the navigation data. A basic demodulation scheme suggested by Borre et al (2007) is shown in Figure

55 Figure 2.2: Basic navigation data demodulation scheme The incoming signal is first multiplied with a carrier replica. This is used to wipe off the carrier wave from the signal. Then the signal is multiplied with a code replica, and the output of this multiplication in (2.6) gives the navigation message. The continuous tracking of the carrier wave and the ranging code usually requires the combination of two tracking loops, e.g., DLL/PLL, DLL/FLL, etc. Details about different tracking loops and their combinations can be found in Ward et al (2006). The cross-correlation output in (2.6) is a complex value, and its real and imaginary parts are usually defined as the prompt in-phase (I) and quadrature (Q) respectively. Finally, in the tracking stage, a demonstration of the prompt I and Q components of correlator output from the combination of PLL and DLL is shown as a function of time in Figure 2.3. The figure shows that the energy of correlator output in PLL is accumulated in I, and Q only contains mostly noise. This feature of PLLs, compared to the tracking loop that does not lock carrier phase but only carrier frequency (i.e., an FLL), has benefits in bit synchronization and decoding that will be further discussed in Section and Section

56 Figure 2.3: Correlator output (I/Q) from PLL/DLL as a function of time in the tracking stage ML Bit Synchronization After properly tracking the incoming signal, the bit synchronization process is necessary for detecting the bit boundaries, decoding bit values and determining the transmit time. The process of extracting the transmit time and building observations will be discussed in Section A diagram of the modulated bits in correlator outputs is shown in Figure

57 Figure 2.4: Demonstration of modulated bits in correlator output ML bit synchronization is the process of detecting bit boundary locations using a likelihood function. Since the bit period and ranging code period are not necessarily the same but are known to be synchronized with each other (i.e., bit transitions always occur at ranging code rollovers), there are Tb T c possible bit locations ( l b ) of the bit boundary that needs to be searched. A window function, which has a total length of T b is given by W 1,( k 1,2,..., T / T ) (2.8) k b c For simplicity, it is assumed there is no error in the code phase estimation (the impact of be further discussed in Section 2.2.), i.e., 0, such that (2.7) can be rewritten as will R (, f ) R ( f ) (2.9) k d k d The matched filter output that is the cross-correlation between Rk( fd) in (2.9) and Wk is given by T T b c C ( f ) R ( f ) W,( n 0,1,..., N 1) (2.10) lb, n d k d k( nm lb) k1 38

58 where l b is the estimated shift of the window function relative to the start of the current data bit; N is the total number of bits ( NT b is the data duration) used for ML bit synchronization. The ML estimate of the bit boundary locations can be found by selecting the bit boundary location that maximizes the sum (over time) of the absolute values of cross-correlation from (2.10) (Kokkonen & Pietila 2002). The sum of the absolute values of cross-correlation is given by N 1 1 S ( f ) C ( fd) (2.11) l d b lb, n N n0 and the ML estimate of bit boundaries is correspondingly obtained as lˆ arg max S ( f ) (2.12) b lb [1: M] lb d To summarize, the ML bit synchronization process is given by the following: Track the GNSS signals using either a PLL or FLL; Perform correlations using T c coherent integration intervals; Accumulate the correlator output samples coherently over the data bit interval, T b, N times as in (2.10); Add the absolute of individual accumulations (this removes the need for a PLL); 39

59 Shift the stored sequence of correlator outputs by one sample as in (2.10) and repeat the above two steps; repeat this for all possible bit boundaries and identify the shift that yields the maximum output value ML Bit Decoding Bit decoding is the process of determining bit values after the bit synchronization has been completed. The likelihood function used in the ML algorithm is the inner product between T b seconds worth of prompt correlator outputs starting from a bit boundary (so as to avoid integrating over a boundary) and locally generated bit combinations. If trying to decode N bits at a time, the number of possible bit combinations is equal to 2N 1, and the correct bit combination is supposed to have the maximum energy. It is noted that the energy based ML bit decoding method detects the bit transition instead of the actual bit values (i.e., there is a sign ambiguity), but this is sufficient for data wipe-off for extending integration time within the receiver. The ML bit decoding algorithm described in Soloviev et al (2009) is summarized here. The bit value combination matrix B (2 N 1 N) is defined as B (2.13)

60 Referring to (2.6), the cross-correlation starts from a bit boundary and over the period T b (i.e., the cross-correlation output from the signal period of ( k 1) T b to kt b ) is given by ktb Ts R ( f ) y( n) rˆ ( n) T b,k d n( k1) Tb Ts A b sinc( f T )exp j 2f kt RT b, k k d b d b I, Q (2.14) where A is the amplitude of the cross-correlation over the period T b. R, k T b For an N bit sequence, the inner product between R ( fd ) RT 1( f ), 2 ( ),...,, ( ) b d RT f b d RT b N f N,, d (an N length vector containing the prompt correlator outputs, each accumulated over T b ) and the vector b m from the mth row of B is given by I f R f b m (2.15) N 1 m( d ) N( d ) m,( 1,2,...,2 ) The ML estimate of bit values can be found by maximizing the energy of the inner product. The ML estimate of bit values is obtained as bm[ ] b ˆ arg max I f ; b (2.16) m d m Building Observations and Navigation Solution This chapter is focused on the performance of ML bit synchronization and decoding. However, for the completeness of the GNSS receiver design, here a brief introduction about building observations (i.e., calculating pseudorange and pseudorange rate) and calculating navigation 41

61 solution using lease-squares estimation and Kalman filter is given. The implementation details will be discussed when the vector-based GNSS receiver and the ultra-tightly coupled GNSS receiver are introduced in Chapter Three and Chapter Four. Building Observations GPS L1 C/A signal transmits navigation data message at 50 bits per second. It takes 1500 bits or 30 seconds to transmit a message frame. Each frame is formatted into five sub-frames. Each subframe is 300 bits or 6 seconds long. The first two words (30 bits) of each sub-frame are special words: Telemetry word (TLM) and Hand-over word (HOW). A fixed 8-bit preamble in TLM is designed for the purpose of frame synchronization. Then the transmit time can be decoded from the HOW word, the offset to the last bit boundary, and the code phase. Finally, the pseudorange of the i th satellite at the th n epoch can be calculated as i rx tx, i ( n) c t ( n) t ( n) (2.17) where c is the speed of light, equal to 299,792,458 m/s; t () n is the receiver time at the rx th n epoch; t ( ), n is the transmit time of the i th satellite at the tx i th n epoch. The pseudorange rate of the i th satellite at the th n epoch can be calculated as (2.18) 42

62 where f ( ), n is the Doppler value of the i th satellite at the di tracking loops. th n epoch, obtained directly from the Least-squares Estimation After obtaining the pseudorange and the pseudorange rate, the continuous position and velocity solutions can be calculated by using least-squares or a Kalman filter (e.g., Grewal & Andrews 2011). The least-squares estimation will be introduced first as follows. In the least-squares estimation, usually an observation function is given by z = Hx v (2.19) where z is the observation vector, e.g., pseudoranges and/or pseudorange rates from all satellites; x is the state vector, e.g., position in three directions and receiver clock bias, and/or velocity in three directions and receiver clock drift; H is the design matrix, reflecting the relation between the observation vector and the state vector; v is the error vector, containing the errors from the observation vector, and the leastsquare estimation is unbiased if the mean of v equals to zero, i.e., v 0. The definition of least-squares is to estimate x by minimizing the loss function 43

63 2 T e = z Hx z Hx (2.20) which gives the normal equations ˆ T T H Hx = H z (2.21) Or T 1 T x ˆ = H H H z (2.22) In addition, the covariance matrix of ˆx is 1 P = H H (2.23) 2 T xˆ 0 where 2 0 is the variance of observations. The above process is based on the assumption that the observations are equally weighted and the observation model is linear. This means the covariance matrix of the observations ( R ) can be defined as the product of 2 0 and the identity matrix ( I ), i.e., 2 R 0 I. When the covariance matrix of the observations is not a diagonal matrix, or it is diagonal but the variances of observations are not identical, i.e., 2 R 0 I, Equation (2.22) needs to be reformed to be a general form as 1 T 1 T 1 x ˆ = H R H H R z (2.24) 44

64 Meanwhile a general form of the covariance matrix of ˆx is given by xˆ T 1 1 P = H R H (2.25) When the observation model is non-linear like the case in GNSS the general form of observation function is given by z = h x v (2.26) In such situations, linearization is performed using a Taylor series expansion as follows z = h x v ˆ x x xxˆ xxˆ x 2 dh 1 d h 2 hxˆ x xˆ 2 x xˆ... v dx 2! dx dh hxˆ x xˆ v dx z h x H x v xxˆ (2.27) where x x x ˆ represents the error in the state vector; dhx H dx represents the design matrix after the linearization, where only the first order term is maintained in the Taylor series expansion. Finally, by re-arranging Equation (2.27), the observation function after linearization is given by ˆ z h x H x v z Hx v (2.28) 45

65 where z is called the (measurement) misclosure vector. Then the (navigation) solution after linearization is similar to (2.22) and given by 1 T 1 T 1 x ˆ = H R H H R z (2.29) T 1 Meanwhile the covariance matrix of x ˆ remains the same as (2.25), i.e., P = H R H 1. xˆ Kalman Filter Least-squares estimation is an effective method to estimate navigation solutions by using GNSS observations. However, it omits the temporal correlation in user s dynamic (state) vector, e.g., the position difference can be obtained by accumulating velocity between two epochs (of solution outputs), and the velocity difference can be obtained by accumulating the acceleration value. For example, the third order dynamics model can be given by (2.30) where p, v and a are the position, the velocity and the acceleration respectively in the state vector; F () t is the dynamics matrix. 46

66 Usually a random process is included in the system model to represent noise and the uncertainty of the dynamics model (represented by F () t ), and a general form of (2.30) is given by x( t) F( t) x( t) G( t) w ( t) (2.31) where The term G( t) w ( t) is called process noise; G () t is the shaping matrix; w () t is a vector of zero-mean, unity variance white noise. In practice, (2.31) is always implemented in the discrete form, and the discrete system model is given by x x w (2.32) k1 k, k1 k k In addition to the system model, a discrete measurement model similar to that used in leastsquares is assumed, namely z H x v (2.33) k k k k Unlike least-squares estimation, the Kalman filter estimate at one measurement epoch usually consists of two steps; prediction and measurement update. These two steps are alternately performed. The prediction process is performed as xˆ x ˆ (2.34) k 1 k, k 1 k 47

67 After the measurement update, the state vector will be marked with the superscript +, otherwise with the superscript -. The initial (i.e., first) solution, i.e., x ˆ 0, can be obtained either from past recorded information or from least-squares estimation. As such, the covariance matrix of ˆx has similar concept and is given by P P Q (2.35) T k 1 k, k 1 k k, k 1 k where Q k is the process noise matrix, and T k k k Q w w. After the measurement update, the state vector x ˆ k is given by xˆ xˆ K z H x ˆ (2.36) k k k k k k where given by K k is the Kalman gain at the k th epoch, which needs to be updated in each epoch and is T 1 K P H H P H R (2.37) T k k k k k k k The Kalman gain K is chosen to achieve minimum mean square error (MMSE) in P k, which is k the covariance matrix after the measurement update and given by k k k k P I K H P (2.38) 48

68 When the observation model is non-linear, a linearization process similar to the linearization process in least-squares estimation is necessary. If the Taylor series expansion is based on the nominal trajectory, which is a priori estimation of the trajectory, this Kalman filter is called linearized Kalman filter (LKF). If the Taylor series expansion is based on the most recent estimate of the state vector, the Kalman filter is called an extended Kalman filter (EKF). In real applications, EKF is more popular than LKF because the increasing perturbations in LKF may result in large errors by neglecting the higher order terms in Taylor series. The update process in EKF is a bit different from (2.36) and given by xˆ xˆ K z (2.39) k k k k where x ˆ k is a null vector, i.e., xˆ k 0, when the estimation errors are compensated in each epoch. Finally, the complete state is updated as xˆ xˆ xˆ k k k xˆ xˆ K z k k k k (2.40) Other steps in EKF are similar to those in the standard Kalman filter. 49

69 2.2 Theoretical Performance Model This section gives the theoretical performance models for bit synchronization and bit decoding. The theoretical performance models are the models to assess the performance of bit synchronization and bit decoding. Before looking at the mathematical details, it is noted that ML bit synchronization and ML bit decoding algorithms can work either in the phase-locked mode or in the frequency-locked mode. Generally, the tracking loop with carrier phase estimates (i.e., using a PLL) can provide more precise carrier phase and frequency estimates, but tracking only the carrier frequency using an FLL can tolerate higher user dynamics and frequency errors (Ward et al 2006). However, from Equation (2.6), the main impact of carrier tracking is the frequency error in the sinc function, which only serves to attenuate the power passing through the tracking loop. In addition, the ML bit synchronization and ML bit decoding processes require that the ranging code be locked using a DLL such that the loss in signal power is negligible. To this end, a tracking error of better than 0.5 chips will lose a maximum of 6 db. That said, the assumption of zero code tracking error (i.e., 0) in this work makes the SSR independent from tracking methods and parameters. In other words, the results of SSR as a function of C/N 0 can be seen as the upper bound in real applications, and the worst case has 6 db attenuation in power Theoretical Performance Model of ML Bit Synchronization Consider the sum of the absolute values of cross-correlation in (2.11) when there is no Doppler error S S f 0 lb lb d, where Figure 2.5 shows S with the parameters of a GPS L1 C/A lb signal, that is T b = 20 ms, T c = 1 ms and M = 20. In this case, the bit transition location is set at 50

70 the middle of a bit, that is 10 ms, and the correlator outputs are integrated for T c in (2.6) have been normalized. The probability of successful synchronization is given by M P P S S s lb lb lb1, lblb M 1 P S S lb 1 lb lb lb (2.41) where S is the output at the estimated bit boundaries; lb l b is the difference between the estimated, l b, and the real, l b, bit boundary location b b b l l l. A successful bit synchronization requires the output at the true bit boundaries to be higher than any other outputs which are not at the true bit boundaries. When M is odd, the cross-correlation outputs are symmetric on the left and right side of S l b, the probability of successful synchronization equals to the square of the single-side probability of successful synchronization, and (2.41) can be written as P P S S M s l b lb lb lb 1 (2.42) 51

71 When M is even, as with GPS L1 C/A signals, the number of correlators outputs to the left and right of S l b in Figure 2.5 (relative to the true boundary) are not equal. However, the crosscorrelation outputs are nearly symmetric on the left and right side of S l b and thus the probability of successful synchronization approximately equals to the square of the single-side probability of successful synchronization, and (2.41) can be written as P P S S M 2 2 s l b lb 1 lb lb (2.43) A vector can be created containing the differences between the absolute value of crosscorrelation at the bit boundaries and the non-bit boundaries as Sl S b lb1 Sl S b lb2 X... (2.44) Sl S b lbm 2 Then the probability of successful synchronization is given by Ps P 2 ( X0 ) (2.45) 52

72 Figure 2.5: Cross-correlation output of one navigation data bit in ML bit synchronization In order to obtain the probability of successful synchronization in (2.45), the probability density function of X should be known. X is a vector of variables containing the differences between the absolute values of cross-correlations at the bit boundaries and the non-bit boundaries. The crosscorrelation output in (2.10) is Gaussian distributed (Misra & Enge 2006) according to the signal model shown in (2.4). If the amplitude (mean) of the cross-correlation outputs, S lb, are sufficiently large and their standard deviations are sufficiently small, the sum of their absolute values is also approximately Gaussian. This is illustrated in Figure 2.6 which shows normal distributions with different means and standard deviations along with the corresponding distributions if the absolute values are used. Obviously, for zero mean distributions (right hand plots), the distribution of the absolute values is not Gaussian. In contrast, if the mean is large (left hand plots) the distribution of the absolute values become more Gaussian. Moreover, as the 53

73 standard deviation of the original distribution decreases (top left plot vs. lower left plot), the Gaussian approximation becomes more accurate. Of course, since the normal distribution has infinite support, the distribution of the absolute values is never exactly Gaussian. With this in mind, equation (2.45) is concerned with the correct bit locations, that is, when l b lb. When this is true, the amplitude of lb S is comparatively larger than when lb lb M /2 (see Figure 2.5 where lb lb is the peak value). More importantly, however, is that the magnitude of Slb needs to be large with respect to the noise that is present. However, this is a minimal condition to have any reasonable chance of achieving bit synchronization in the first place (i.e., if the signal is buried in noise bit synchronization will surely fail). In other words, for the purpose of assessing the (non-zero) probability of successful bit synchronization, assuming X to be a multivariate Gaussian distribution should be reasonable and this assumption is thus adopted herein. It is nevertheless acknowledged that this approximation will become less valid for sufficiently low C/N 0 values, but as shown later in Figure 2.7, the approximation appears to be reasonable down to C/N 0 values of about db-hz. Furthermore, if the number of bits increases continuously, i.e., N, the approximation becomes accurate again because of the central limit theorem. This is also reflected in Figure 2.7, as discussed later. 54

74 Figure 2.6: Probability density functions of Gaussian distribution for different chosen parameters. Upper-left: mean is 10 and standard deviation is 1. Upper-right: mean is 0 and standard deviation is 1. Lower-left: mean is 10 and standard deviation is 5. Lower-right: mean is 0 and standard deviation is 5. The probability density function of multivariate Gaussian distribution is mathematically expressed as follows: f x,..., x X 1 M exp M T 1 X μ X μ (2.46) where 55

75 μ is the mean vector; is the covariance matrix. With a normalized value (equal to one) of correlator output of T c, the mean vector μ and the covariance matrix can be given by 2 4 μ (2.47) 2( M 2) ( M 2 1) 2( M 2 1) 2 4 2( M 2 1) 2( M 2) (2.48) where σ 2 is the variance of the correlator outputs of T c. Finally, the probability of successful synchronization in (2.45) can be written as Ps 0 μ 2 Q μ 2 Q (2.49) where 56

76 Q( ) is the complementary cumulative distribution function (Sklar 1988, and Haykin 2001) In order to verify the theoretical performance model developed above, Monte Carlo simulations have been used to estimate the performance of ML bit synchronization quantified by SSR (i.e., the simulated probability of successful synchronization from tests). The simulation is based on the signal model given in (2.6), and includes a bit sequence in which the bit transition happens for every bit. The square wave sequence is only used here to test the performance model. The performance model is developed based on the amount of data quantified in terms of the number of bit transitions rather than units of time, as this scenario links the number of bit transition and the data duration together. The GPS L1 C/A signal parameters are used here and 10,000 trials were simulated for each C/N 0 value in Matlab. This is the setting for all the following Monte Carlo simulations unless otherwise stated. It can be seen in Figure 2.7 that a good agreement between theoretical and simulation results can be achieved if the C/N 0 is higher than 20 db-hz, where the theoretical results are obtained based on (2.49). This suggests that the theoretical model developed previously is indeed valid. In particular, it suggests that the Gaussian assumption for the sum of the absolute values of the correlators outputs is reasonable for the C/N 0 values considered. It is acknowledged, however, that when the C/N 0 is lower than about 20 db-hz, the disagreement between the theoretical and simulation models increases with increasing numbers of navigation data bits. In this scenario, the standard deviation of the correlator outputs will increase meaning the Gaussian assumption is less correct, but only slightly based on the results shown. Furthermore, when the number of bits is continuously increased, the disagreement tends to decline at higher number of bits, e.g.,

77 bits, because of the central limit theorem as discussed before. Actually, the performance of ML synchronization is primarily determined by the number of bit transitions instead of the number of bits processed (i.e., the data duration), though this test links these two factors together. The detailed relationship among the SSR, the number of bits and the number of bit transitions will be discussed in Section Figure 2.7: Theoretical and simulated performance of ML bit synchronization as a function of signal strength. Different numbers of navigation data bits are considered. Ten thousand trials were simulated for each C/N 0 value. Generally, longer coherent integration time periods such as 2 s (100 bits) would have concerns about oscillator stability and code Doppler. However, it is important to note that the ML bit synchronization process analyzed here only sums the correlator output samples coherently to the length of the window function in (2.8) (i.e., the length of 1 bit, which equals to 20 ms for GPS 58

78 L1-C/A signals), followed by non-coherent accumulation to 2 s. Therefore, the oscillator stability and code Doppler will not have obvious impact on ML bit synchronization Theoretical Performance Model of ML Bit Decoding The BER of coherent decoding (e.g., from PLL) for BPSK signal is given by (Sklar 1988, Haykin 2001, and Proakis & Salehi 2007) P e,coh 2E b Q N 0 0.1CN0 Q 210 T co (2.50) where E b is the transmitted signal energy per bit; N 0 is the specified noise spectral density; T co is the coherent integration time and set as the bit length here. Bit decoding is uncorrelated between bits in coherent decoding, and the probability of successful decoding the entire sequence in phase-locked mode is given by P L d, PL e,coh, k k 1 1P (2.51) where P is the BER of the kth data bit in coherent decoding; e,coh, k L is the length of the data bit sequence to be decoded. 59

79 It is important to note that this equation does not specify how the bits are to be decoded. In other words, if the bits are decoded one at a time, pair-wise, N at once (N L), the probability of successfully decoding all L bits correctly is the same in all cases. This is because decoding of each bit is independent. For the ML bit decoding approach, the number of bits to be decoded at a time (i.e., N) is chosen arbitrarily. Ultimately, therefore, the performance of ML bit decoding in phase-locked mode is insensitive to the number of bits to be decoded at a time. The BER of non-coherent decoding (i.e., differential decoding, e.g., from FLL) for BPSK signal is given by (Sklar 1988, Haykin 2001, and Proakis & Salehi 2007) P e,diff 1 E exp 2 N 1 exp CN0 b 0 T co (2.52) Given the above, the probability of successful decoding for two bits to be decoded at a time in frequency-locked mode is given by P d,fl, N 2 e, diff 1 P (2.53) A rigorous theoretical performance model for more than two bits to be decoded at a time has not been developed yet. Assuming bit decoding is uncorrelated between bits in non-coherent decoding, and this means that the performance of ML bit decoding in frequency locked mode is insensitive to the number of bits to be decoded at a time (i.e., N), an approximate form can be given based on (2.53) as 60

80 P d,fl L 1Pe,diff,k (2.54) k 1 where P e,diff,k is the BER of the kth two bits to be decoded at a time in non-coherent decoding. Later the effectiveness of (2.54) will be confirmed with a multiple-trial test. Equations (2.51), (2.53), and (2.54) represent the first known relationship between the probability of successful decoding and the BER and are collectively one of the main contributions of this work. Monte Carlo simulations are used to estimate the performance of ML bit decoding quantified by SDR (i.e., the simulated probability of successful decoding from tests). The simulation is based on the signal model given in (2.6) in Section As shown in Figure 2.8 and Figure 2.9, a good agreement between the theoretical results of (2.51) and (2.53) and the simulation results has been found, suggesting the validity of the theoretical performance model. The approximate result of (2.54) also fits the Monte Carlo simulation curves, although discrepancies are present. This means that the performance of ML bit decoding in frequency-locked mode is nearly insensitive to the number of bits being decoded at a time. 61

81 Figure 2.8: Theoretical and simulated performance of ML bit decoding in the phase-locked mode. Different numbers of navigation data bits are considered. 62

82 Figure 2.9: Theoretical and simulated performance of ML bit decoding in the frequency-locked mode. Different numbers of navigation data bits are considered. 2.3 Other Factors Impacting the Performance of ML Bit Synchronization and ML Bit Decoding The development of the performance models help to analyze ML bit synchronization and ML bit decoding. The analysis has been completed in Section 2.2. In this section, the other factors that may impact the performance of ML bit synchronization and ML bit decoding will be further discussed. Those factors include the number of bit transitions (for ML bit synchronization only), the phase-lock mode and the frequency-locked mode, and carrier Doppler errors. Monte Carlo simulation results assessing the performance of ML bit synchronization and ML bit decoding under different conditions are reported. In addition, all algorithms have been assessed in the software-based GNSS receiver GSNRx. A dataset with various signal power levels were generated using a Spirent GS7700 GNSS simulator. Approximately 1 hour of data was collected 63

83 using a National Instruments PXI-5600 front-end (Austin, TX, USA) which includes an OCXO. The front-end parameters are shown in Table 2.1. Table 2.1: Front-end parameters used for collecting GNSS data for the performance test of ML bit synchronization and ML bit decoding Parameter Value (MHz) Intermediate Frequency 0.42 Sampling Rate (I/Q) 3.0 Bandwidth Factors Impacting ML Bit Synchronization Number of Bits vs. Number of Bit Transitions The Monte Carlo simulation results in Figure 2.10 show that the performance of ML bit synchronization improves with higher number of bits used. This is true only when the actual number of transitions increases as the number of bits considered increases. To assess performance for different bit sequences, three kinds of bit sequences are implemented and tested: first, a bit transition is present at every bit (i.e., a square wave ); second, a bit transition is present at every other bit; third, bit transitions occur randomly with a probability equal to 50%. Note that in the first case, a minimum of 2 bits need to be considered; similarly, a minimum of 4 bits need to be considered for the second case. The last test is a good emulation of real GNSS messages, and the number of bits considered will normally be greater than two (herein a minimum of four is considered) and then the probability of a bit transition will be sufficiently high. 64

84 Considering ML bit synchronization in phase-locked mode, Figure 2.10 shows that the performance of the first and the second kind of bit sequence are nearly similar and only differ slightly at low C/N 0 values. The reason is because both sequences have the same number of bit transitions even though they use a different number of bits. This result confirms the former assumption that generally the performance of ML bit synchronization is determined by the number of bit transitions and not the absolute number of bits. The reason bit transitions are significant is because without them, the result in (2.11) will be approximately constant for all possible shifts considered, to within the level of the noise. In other words, without any bit transitions, the decision of the bit synchronization process would be based solely on noise. In Figure 2.10, a disagreement can be noticed between the solid line (when the bit transition happens every 2 bits) and the dashed line (when the bit transition happens every bit) when C/N 0 is low. This confirms that using longer bit sequences without any additional bit transitions can degrade bit synchronization performance when C/N 0 is low. 65

85 Figure 2.10: Simulated performance of ML bit synchronization as a function of signal strength. Different numbers of navigation data bits with different kinds of bit sequences are considered. Without a priori knowledge about the navigation message contents, the bit values/transitions in real GNSS data cannot be predicted. This coincides with the third kind of bit sequence. Figure 2.10 also shows the results between the second and the third kind of bit sequence are almost similar if the number of bits is larger than 20. The following simulations will only use the third kind of bit sequence unless otherwise stated. A separation between the theoretical model and the simulation result when the number of bits is low (e.g., red lines/dots in Figure 2.10) is observed. This is due to a lack (absence) of bit transitions when the number of bits is low. 66

86 Comparison in Phase-locked Mode and Frequency-locked Mode The performance results related to ML bit synchronization discussed in Section are based on phase-locked mode. This subsection presents a comparison between the phase-locked and the frequency-locked mode. Figure 2.11 summarizes the results of the Monte Carlo simulation and the Spirent GNSS data processing. Compared to the phase-locked mode a small degradation in the frequency-locked mode can be viewed with the simulation data. Moreover, the simulator test results processed by GSNRx are also included in Figure In the simulator test, thousands of trials have been performed in the receiver by intentionally restarting the bit synchronization process (without a priori information) every time a bit synchronization result is obtained (regardless of the outcome). With the coherent integration time of 1 ms, the receiver in the Kalman filter tracking mode can track the signal power to 28 db-hz in a static scenario. The Kalman filter tracking model and parameters used here are same as Petovello et al (2008a). With the coherent integration of 20 ms, the receiver of the same mode can track the signal power to 23 db-hz. 67

87 Figure 2.11: Simulated and real performance of ML bit synchronization as a function of signal strength. Different numbers of navigation data bits are considered in phase-locked mode and frequency-locked mode. The longer coherent integration can help to extend the tracking threshold. It is also noticed that the coherent integration of 20 ms can have a better estimation of Doppler, as shown in Figure

88 Figure 2.12: RMS errors of Doppler estimation as a function of signal strength. Two different coherent integration times are considered. These results indicate the necessity of extending coherent integration time. Without knowledge of bit boundaries, it is impossible to extend coherent integration time to 20 ms, and the 20 ms result in Figure 2.11 is only for assessing the performance of ML bit synchronization in low C/N 0 environment. However, the tracking threshold can be extended by advanced tracking methods, e.g., vector tracking, Doppler aiding, and ultra-tight integration with inertial sensors. These schemes will be further discussed in Chapter Three and Chapter Four. For the receiver results shown in Figure 2.11, the trend seems coincident with the former conclusion that a higher number of bits results in better performance. However, the receiver results appear a bit worse than the simulation results. This is because the simulator set the reserved words to all zeroes. The ML bit synchronization might totally fail without any bit transition. It can be seen in Figure

89 that the plus ones last longer than 3 s in the data set. This causes the ML bit synchronization with 100 bits to fail once and those with 20 bits to fail seven times even without noise. Figure 2.13: In phase correlator output in phase-locked mode. Based on the results discussed above, there are three recommended schemes for implementing the ML bit synchronizer in a GNSS receiver. First, choose different numbers of bits for synchronization according to current signal power and the possible Doppler errors (the effect of Doppler errors will be introduced in the next section). This scheme is efficient to achieve bit synchronization, but the trade-off is that it is vulnerable to the bit sequence without bit transitions. A method detecting if bit transitions existed was reported in Kokkonen & Pietila (2002) by a hypothesis testing. The bit boundary will be declared if the ratio between the cross-correlation output from the candidate of the boundary position (maximum value) and the output from the candidate shifted by 10 ms (supposed minimum value) passes a certain threshold. Second, choose a relatively large number of bits for synchronization no matter the values of signal power 70

90 and other parameters. This scheme is the easiest to be implemented but is less efficient,requires longer time for bit synchronization, and has no verification mechanism. Third, choose the number of bits either according to current parameters (e.g., estimated C/N 0 ) or fixed as one trial, but do not declare the position of the bit boundaries unless the certain number of continuously successful trials is achieved. This scheme can increase the reliability of synchronization results but also increases the system complexity as a trade-off Effect of Doppler errors Any Doppler tracking errors will adversely affect the synchronization performance for two reasons: a reduction in power (refer to Equation (2.6) in Section 2.1.1), and the frequency error will induce a changing phase error. To illustrate this, a series of Monte Carlo simulations were conducted and different frequency errors were included in the correlator outputs. The Monte Carlo simulation results of 20 and 100 bits with the Doppler error from 0 to 26 Hz are shown in Figure 2.14 and Figure Three phenomena can be viewed: first, the increased Doppler errors degrade the synchronization performance; second, the performance degradations are not significant if the Doppler error is within 5 Hz; third, the SSR decreases rapidly if the Doppler error is equal or higher than 25 Hz. The third phenomenon happens because the bit synchronizer cannot distinguish a real bit transition and a perceived bit reversal caused by frequency errors if the error is equal or higher than 25 Hz. The detailed derivation of the Doppler error upper bound can be found in Kokkonen & Pietila (2002). 71

91 Figure 2.14: Simulated performance of ML bit synchronization with 20 bits. Different Doppler errors are considered. 72

92 Figure 2.15: Simulated performance of ML bit synchronization with 100 bits. Different Doppler errors are considered Factors Impacting ML Bit Decoding The performance of ML bit decoding being assessed in this work assumes that successful bit synchronization has been achieved Comparison in Phase-locked Mode and Frequency-locked Mode With the case of two bits to be decoded at a time, a comparison between the results from the Monte Carlo simulation and the simulator test in the phase-locked mode and the frequencylocked mode is shown in Figure The results from the simulator test fit the Monte Carlo simulation curves though a small discrepancy can be noticed at about 23 db-hz. This is due to the fact that the receiver loses lock around 23 db-hz, and the insufficient samples may result in the biased results in the simulator test. 73

93 Figure 2.16: Simulated and real performance of ML bit decoding as a function of signal strength. 2 bits to be decoded at a time are considered in phase-locked mode and frequency-locked mode Effect of Doppler Errors In Section 2.2.2, it was concluded that the performance of ML bit decoding is insensitive and nearly insensitive to how many bits to be decoded at a time in coherent and non-coherent decoding, respectively. However, the impact of Doppler errors has not been taken into account in that analysis. The existence of the Doppler errors contaminates the bit decoding performance. Consider the case of two bits to be decoded at a time. In this case, with reference to (2.15), the inner product between the vector of prompt correlator outputs with coherent integration time of T b and the possible bit value vector b m is given by 74

94 I ( f ) R ( f ) b, ( m 1,2) m d N d 2 R ( f ) b, ( m 1,2) k1 m Tb, k d m, k (2.55) where N is the length of data bit sequence, which equals to 2 here; fd is the Doppler error; b mk, is the kth element in vector b m. Now the maximum allowable Doppler error will be determined in ML bit decoding without considering the effect of the noise. Substituting (2.14) into (2.55) and omitting noise gives 2 I ( f ) A b sinc( f T )exp j 2f kt b m d RT b, k k d b d b k1 m,1 m,2 A sinc( f T )exp j2f T b b b b exp j2f T Tb d b d b 1 2 d b mk, (2.56) The sinc function reduces the amplitude of the inner product in (2.56) but does not impact the upper bound directly, because it is always same no matter what b mk, is chosen and it does not cause a perceived bit reversal because the product of the frequency error ( D f d ) is nearly constant over the integration period. So the sinc function and the irrelevant phase term j f T can be absorbed by, which equals to A sinc( f T )exp j2 f T simplified result is obtained as Tb d b d b 2 d b. Then a m d T 1 m,1 2 m,2 b d b I ( f ) A b b b b exp j2 f T (2.57) 75

95 and the ML bit decoding result in (2.16) is only affected by b b,1 b b,2 j f T 1 m 2 m exp 2 d b. For comparison, for the case without Doppler error, the corresponding equation is b b b b 1 m,1 2 m,2. Correspondingly, as will be shown immediately below, for a 2-bit sequence the Doppler error can make the process fail if 2fT 2 d b f d 1 4T b (2.58) The reason for this is that the likelihood function I f ; b magnitude of the sum of two vectors 1 m,1 in (2.16) is determined by the m d m bb and b b,2 j f T 2 exp 2 and any phase error m d b 2 ft d b in the second vector will reduce the tolerance of noise. More specifically, as shown in Figure 2.17, when the phase error increases, the magnitude resulting from the incorrect bit sequence will increase, and this reduces the tolerance space of noise. But if the phase error is less than π/2, the magnitude resulting from the incorrect bit sequence is still less than the magnitude obtained with the true bit sequence without noise. However, as shown in Figure 2.18, when the phase error is equal or larger than π/2, the magnitude resulting from the incorrect bit sequence will be equal or greater than the magnitude obtained with the true bit sequence even without noise, and this will result in a totally failed test. So without considering the effect of the noise, the upper bound of Doppler error for ML bit decoding with a 2-bit sequence for the GPS L1 C/A signal is 12.5 Hz (T b = 20 ms). Of course, receiver noise will make the transition between frequency errors greater or smaller than 12.5 Hz more gradual. 76

96 Figure 2.17: Vector diagram when the phase error is less than π/2 77

97 Figure 2.18: Vector diagram when the phase error is larger than π/2 The Monte Carlo simulation result of ML bit decoding with a 2-bit sequence is shown in Figure Four phenomena can be observed: first, the increased Doppler errors degrade the bit decoding performance; second, the performance degradations are not significant if the Doppler error is within 2 Hz (less than 2%); third, the SDRs increase with C/N 0 if the Doppler error is equal or less than 12 Hz; fourth, the SDR is about 50% if the Doppler error is equal to 12.5 Hz, meaning that the value of the likelihood function in (2.16) is the same whether a bit transition exists or not; fifth, the SDR decreases rapidly with increasing C/N 0 if the Doppler error is larger than 12.5 Hz. These results validate the theory developed above. It confirms that the upper bound of Doppler error with a 2-bit sequence is indeed 12.5 Hz. 78

98 Figure 2.19: Simulated performance of ML bit decoding with a 2-bit sequence. Different Doppler errors are considered. For the sake of comparison, the simulation result of ML bit decoding with a 5-bit sequence is shown in Figure The SDR is very low (around 20%) when C/N 0 increases if the Doppler error is equal to 5 Hz. This indicates the tolerable Doppler error with a 5-bit sequence (about 4 Hz) is much lower than for a two bits sequence (12.5 Hz). 79

99 Figure 2.20: Simulated performance of ML bit decoding with a 5-bit sequence. Different Doppler errors are considered. It is shown in Section that the performance of ML bit decoding is insensitive/nearly insensitive to how many bits to be decoded at a time if there is no Doppler error. However, based on the analysis above, the bit sequence with more bits to be decoded at a time has lower ability to tolerate Doppler error. So the configuration with a 2-bit sequence (the minimum number of bits in ML bit decoding) is the optimum scheme. 2.4 Summary In this chapter, a systematic analysis of the performance of ML bit synchronization and decoding is presented. The performance is assessed as a function of the number of data bits, the effect of Doppler error and received signal power in the context of stand-alone GNSS receivers containing different tracking modes, namely phase-locked mode and frequency-locked mode. In addition, 80

100 the theoretical performance models of ML bit synchronization and decoding are developed based on statistical theory. These models are being reported for the first time. The performance models and analysis have been experimentally validated. Finally, the other factors which impact the performance of ML bit synchronization and ML bit decoding are analyzed. Generally the performance of ML bit synchronization is determined by the number of bit transitions, not the absolute number of bits. For the most common case that bit transitions happen with a probability equal to 50%, a higher SSR, a lower C/N 0 and a higher Doppler frequency error all require more data bits. For GPS L1 C/A signals, by using 100 data bits, the SSR can reach to about 100% with C/N 0 as low as 20 db-hz with no Doppler error. The performance degradation caused by Doppler error is not significant if the Doppler error is within 5 Hz. The maximum tolerance of Doppler error is 25 Hz. Without Doppler error the performance of ML bit decoding is insensitive/nearly insensitive to how many bits are being decoded at a time in phase-locked mode and frequency-locked mode, respectively. The bit sequence with more bits to be decoded at a time is more sensitive to Doppler error. So, in the presence of Doppler errors, the optimum configuration is the 2-bit sequence, which is the minimum number of bits available in ML bit decoding. For GPS L1 C/A signals, the SDR of the two bits sequence can reach to about 100% with C/N 0 as low as 25 db- Hz with no Doppler error. The performance degradation caused by Doppler error is not significant (within 2%) if the Doppler error is within 2 Hz. Both theoretical and simulation results show that the upper bound of Doppler error for a 2-bit sequence is 12.5 Hz. 81

101 Chapter Three: Improving ML Bit Decoding and Navigation Performance in Vector-Based High-Sensitivity GNSS Receiver In the last chapter, the performances of ML bit synchronization and ML bit decoding are assessed under different C/N 0, Doppler errors, data duration, and different tracking modes. Bit synchronization only needs to be achieved once at the beginning of data processing. However bit wipe-off requires bit values to be decoded continuously, and that means the bit decoding process is more critical for extending coherent integration time. The performance of ML bit decoding relies heavily on the signal tracking performance and the tracking threshold (below which the process of bit decoding cannot be performed). Therefore, in this chapter, the effectiveness of using vector tracking to improve the tracking performance and extend the tracking threshold will be evaluated, and subsequently to determine if this improves the bit decoding and the ability to extend coherent integration time and ultimately improves the navigation performance with GNSS only solution. In addition, two innovative strategies are proposed to select the suitable correlator outputs to extend coherent integration time, and without them the falsely decoded bits may impair the navigation performance. After adopting all the ideas, a vector-based standalone high-sensitivity GNSS receiver is proposed in this chapter. The new receiver design is validated in several vehicular field tests. Similar to Chapter Two, the performance of bit decoding in the context of this chapter is assessed in terms of the SDR of bit values. 3.1 Different GNSS Receiver Architectures This section describes the different GNSS receiver architectures and tracking schemes used in this chapter for data processing, and then the newly proposed vector-based standalone highsensitivity GNSS receiver is introduced. 82

102 3.1.1 Scalar-Based Software GNSS Receiver GSNRx There are three software GNSS receivers used in this chapter. The first one is a scalar-based GNSS receiver called GSNRx, which includes a closed-loop tracking structure. The scalarbased GNSS receiver is also called the standard GNSS receiver, and it has been used for data processing in Chapter Two. The scalar-based GNSS receiver is shown in Figure 3.1. It contains independent local tracking loops/channels dedicated to providing independent pseudorange and/or pseudorange rate measurements for the PVT calculations. The scalar-based GNSS receiver is used as a reference to compare the bit decoding and navigation improvement from other receivers. Figure 3.1: Architecture of a scalar-based GNSS receiver, GSNRx Vector-Based Assisted-GNSS High-Sensitivity Receiver GSNRx-hs The second receiver is a vector-based high-sensitivity GNSS receiver called GSNRx-hs, as shown in Figure 3.2. The difference between a scalar-based GNSS receiver and a vector-based GNSS receiver is that the latter sets the numerically controlled oscillators (NCOs) inside the 83

103 local signal generator from navigation filter outputs rather than from local channel filter outputs. In addition, a vector-based GNSS receiver requires knowledge about ephemeris data when updating the channel parameters. To this end, long term ephemeris (e.g., Garrison and Eichel 2006) could be used to calculate satellite orbits without requiring an aiding source. The vector-based receiver usually requires the first position and velocity fix from the scalar mode. GSNRx-hs is configured to use the scalar tracking to obtain the first position and velocity, and then switch to the vector tracking mode. Another advantage of GSNRx-hs is that it contains an open-loop tracking structure, which can avoid the stability problem caused by long coherent integration in normal closed-loop tracking (Ward et al 2006 and Kazemi 2008). The open-loop is preferred for building the correlator output measurements with long coherent integration. In addition, the open-loop tracking structure can mitigate the multipath impacts in navigation solutions by distinguishing a LOS signal and nonline-of-sight (NLOS) signals in the frequency domain (Xie & Petovello 2011). The other benefits of open-loop tracking can be found in Van Graas et al (2005). 84

104 Figure 3.2: Architecture of an assisted-gnss high-sensitivity GNSS receiver, GSNRx-hs Vector-Based Standalone High-Sensitivity Receiver GSNRx-hs-sa It is noted that the original version of GSNRx-hs extends the coherent integration time by bit aiding method (O Driscoll et al 2010), which requires an external network and is not a standalone approach. Therefore, a modified version of the receiver was developed in this thesis work that uses ML bit decoding to extend integration time. The architecture of new GSNRx-hs is shown in Figure 3.3. This modified version is a vector-based standalone high-sensitivity GNSS receiver named GSNRx-hs-sa. Both GSNRx-hs and GSNRx-hs-sa are used to process the vehicular field data, assess the performance of ML bit decoding in a vector-based receiver in signal challenged environments, verify effectiveness of the strategies for selecting the suitable correlator outputs for longer coherent integration, and evaluate the performance of this standalone high-sensitivity approach with extended coherent integration time in land vehicle navigation. 85

105 Figure 3.3: Architecture of a standalone high-sensitivity GNSS receiver with ML bit decoding, GSNRx-hs-sa All of the receivers used for ML bit decoding test assume the bit synchronization has already been achieved. The collective method to improve bit synchronization will be discussed in Chapter Five. 3.2 Correlator Outputs Selecting Strategies for Extending Coherent Integration Time For high-sensitivity GNSS receivers, extending integration time coherently is optimal for obtaining higher sensitivity, mitigating multipath and cross-correlation false locks, and avoiding squaring loss. However, if the signal power as determined by C/N 0 is low, the BER will increase accordingly. High BER will result in falsely decoded bits in ML bit decoding and distort the shape of CAF by using ML-based bit wipe-off to extend coherent integration time. Finally, compared to extending coherent integration time without bit wipe-off, the incorrect bit wipe-off has similar problems as mentioned in Section Soloviev et al (2009) proposed using the data bit repeatability in the navigation message to decrease the BER. However, for the case of 86

106 the GPS L1 C/A signal, data bits repeat no sooner than every 30 s, which is considered too long for real time applications. Other signals would have similar limitations. In order to handle the high BER problem, two strategies are proposed in this thesis to select suitable correlator outputs for ML bit decoding and then used for extending coherent integration time. The general idea is to set a certain criteria that, when satisfied only the coherent integration time of a bit period is used, and when not satisfied ML-based bit wipe-off and further extended coherent integration time is applied Strategy I: Selecting Correlators Based on Satellite s Elevation Angle Strategy I is to select correlators based on a satellite s elevation angle. The idea is that in areas such as under dense foliage and surrounded by trunks and houses, the signals from low elevation angle satellites are more attenuated than high elevation angle satellites because of signal shadowing and multipath fading. By setting an angle mask threshold and ignoring those satellites below the threshold, the impact of high BER is expected to be greatly reduced. It is noticed that this strategy can only be used in signal challenged environment containing blockage from ground to a certain elevation, e.g., dense foliage and urban canyon, but is not suitable for indoor environments Strategy II: Selecting Correlators Based on Estimated C/N 0 Strategy II is to select correlators based on the estimated C/N 0 values. This method is suitable for all environments but relies on C/N 0 estimate algorithms. In this work, the C/N 0 estimation was implemented by separately calculating the signal power and noise power spectral density and then computing their ratio. 87

107 3.3 Test Description In order to assess the performance of ML bit decoding in vector tracking and the performance of the vector-based standalone high-sensitivity GNSS receiver, three tests are performed. The three tests include one vehicular field test under dense foliage, and two vehicular field tests in urban canyons. The GNSS receivers were started in open-sky to finish acquisition and bit synchronization processes before the vehicle ran into the signal challenged envrironments. In all cases, only the GPS L1 C/A code signal was used Dense Foliage Test for ML Bit Decoding and Navigation The first test is a vehicular field test conducted in a signal challenged environment, namely under dense foliage in an area near the University of Calgary. The test was performed on August 16, The test trajectory is shown in Figure 3.4 and images captured along the test trajectory are shown in Figure 3.5 and Figure 3.6. As can be seen, there are portions of the test where sky visibility is highly restricted. Figure 3.4: Field test trajectory near the University of Calgary 88

108 Figure 3.5: Dense foliage environment in the field test Figure 3.6: Dense foliage environment facing vertically upwards 89

109 The sky plot in the dense foliage test is shown in Figure 3.7. The C/N 0 values estimated by GSNRx-hs of all satellites in view in the dense foliage test are shown in Figure 3.8, in which the signal power values fluctuate markedly (a cumulative histogram is also shown later in Figure 3.26). Some attenuations of C/N 0 are higher than 25 db. Figure 3.7: Sky plot in the dense foliage test 90

110 Figure 3.8: C/N 0 of all satellites in view in the dense foliage test estimated by GSNRx-hs Urban Canyon Test I & II for ML Bit Decoding and Navigation The second and third tests are vehicular field tests conducted in an urban canyon environment, namely downtown Calgary. Both tests were performed on August 16, 2012 and named Urban Canyon Test I and Urban Canyon Test II respectively. The trajectories of Urban Canyon Test I and Urban Canyon Test II are different. The trajectory of Urban Canyon Test I is shown in Figure 3.9 and images captured along the test route are shown in Figure As can be seen, there are portions of the test where sky visibility is highly restricted. 91

111 Figure 3.9: Field test trajectory in Urban Canyon Test I Figure 3.10: Urban canyon environment in Urban Canyon Test I 92

112 The sky plot in Urban Canyon Test I is shown in Figure The C/N 0 values estimated by GSNRx-hs of all satellites in view in Urban Canyon Test I are shown in Figure 3.12, in which the signal power values fluctuate markedly. Some attenuations of C/N 0 are higher than 35 db. Figure 3.11: Sky plot in Urban Canyon Test I 93

113 Figure 3.12: C/N 0 of all satellites in view in the Urban Canyon Test I estimated by GSNRx-hs The Urban Canyon Test II is similar to the Urban Canyon Test I, and both of the tests are performed in downtown of Calgary but in different route. The route of Urban Canyon Test II is shown in Figure 3.13, and the data from inertial/vehicle sensors were collected simultaneously with GNSS data. 94

114 Figure 3.13: Field test trajectory in Urban Canyon Test II Images captured along the test trajectory are shown in Figure As can be seen, the environment is similar to the environment in Urban Canyon Test I, and there are portions of the test where sky visibility is highly restricted. 95

115 Figure 3.14: Urban canyon environment in Urban Canyon Test II The sky plot in Urban Canyon Test II is shown in Figure The C/N 0 values estimated by GSNRx-hs of all satellites in view in the urban canyon test are shown in Figure As shown, the signal power values fluctuate markedly. 96

116 Figure 3.15: Sky plot in Urban Canyon Test II Figure 3.16: C/N 0 of all satellites in view in in Urban Canyon Test II estimated by GSNRx-hs 97

117 The main purpose of Urban Canyon Test II is to test the ML bit decoding and navigation performance in an ultra-tightly coupled architecture in Chapter Four. That said, the trajectory results are also shown in this chapter Field Test Equipment and Configuration A reference system consisting of a NovAtel SPAN SE units (which contains a NovAtel OEMV receiver and a, LCI tactical-grade IMU ( LCI )) was used to provide the reference trajectory and dynamics. The estimated 1 accuracy of the reference system (per axis) is 0.2 m for position and 0.02 m/s for velocity. The land vehicle with a NovAtel GPS-702-GG antenna and a LCI IMU on top and a National Instruments PXI-5600 front-end inside is shown in Figure

118 Figure 3.17: The land vehicle with navigation systems for field data collection. The upper-left picture shows a NovAtel GPS-702-GG antenna and a LCI IMU on top of the vehicle. The upperright picture shows a National Instruments PXI-5600 front-end inside the vehicle. The lower picture shows the land vehicle. In all tests, the data were collected using the National Instruments PXI-5600 front-end which includes an OCXO. The front-end parameters are shown in Table 3.1. The front-end has a 16 bit quantization level, although for the data collected typically only 3-4 bits are necessary (i.e., only 3-4 bits are non-zero). 99

119 Table 3.1: Front-end parameters used for collecting GNSS data in three tests Parameter Value (MHz) Intermediate Frequency 0.42 Sampling Rate (I/Q) 10.0 Bandwidth 5.0 The reference data bits (i.e., bit aiding source) in three tests are obtained from an antenna located on the roof of the CCIT building at the University of Calgary. The navigation filter used in the software receivers is a Kalman filter, and velocity random walk is used in the stochastic model. The spectral density of velocity driving noise in each axis is set as 4.0 m/s 2 / Hz, and the standard deviation of pseudorange measurement is set as 5.0 meters and the standard deviation of Doppler measurement is set as 0.2 Hz. 3.4 Dense Foliage Test Result The dense foliage test assesses the benefits of a vector tracking structure for ML bit decoding with field data. It uses the estimated data bits to extend coherent integration using bit wipe-off and then assesses the accuracy of the navigation solution of this standalone approach Performance of ML Bit Decoding in Dense Foliage Test First of all, a comparison of estimated C/N 0 from the scalar-based receiver GSNRx and the vector-based receiver GSNRx-hs-sa is shown in Figure PRN 14 is selected for comparison purpose and the results are typical for other satellites. It is noticed that the signal can 100

120 be tracked using vector-tracking although the signal power is quite low (between about 15 db-hz and 35 db-hz). In scalar tracking, however, during most of time the signal is not tracked (indicated by a C/N 0 value equal to zero). Figure 3.18: C/N 0 of PRN 14 in scalar tracking and vector tracking in the dense foliage test The SDRs of ML bit decoding as a function of signal strength in the scalar-based receiver and the vector-based receiver are shown in Figure The SDR results in all tests were obtained by setting the open-loop search space uncertainty as 40 meters (for pseudorange errors) by 10 Hz (for Doppler errors). This is an empirical setting, and preferred when processing GNSS signals in signal challenged environments. The statistics of bit decoding as a function of C/N 0 are calculated using bins with a width of 2.5 db. Compared to the results in scalar tracking, a marked performance improvement of ML bit decoding in the vector tracking is noticed. This shows the benefits of vector tracking for ML bit decoding, which improves the SDR by 3% 35% 101

121 depending on the signal strength. The improvement comes from reduced Doppler errors in vector tracking, as shown in Figure PRN 14 is selected again for comparison purpose and the results are typical for other satellites. Though the real Doppler value is unknown, it can be observed clearly that the jitter of estimated Doppler in vector tracking is far less than scalar tracking. In Figure 3.19, it can be observed that in scalar tracking, the SDR is close to 50% at about 25 db-hz, and this shows the scalar-based receiver lost signal lock there. Compared with the Monte Carlo results (the settings were introduced in Section 2.2.1), the difference in SDR between vector tracking and Monte Carlo simulations is due to the non-white noise present in the field tests that is not present in the simulation (i.e., multipath). Figure 3.19: Performance of ML bit decoding as a function of signal strength in scalar tracking and vector tracking in the dense foliage test 102

122 Figure 3.20: Estimated Doppler values of PRN 14 in scalar tracking and vector tracking in the dense foliage test Figure 3.21 shows the SDR from each satellite in the entire field test. Compared to scalar tracking, the improvement of the SDR resulting from vector-tracking ranges from 2% (PRN 04) to 40% (PRN 14). The average C/N 0 of different satellites in the dense foliage test is shown in Table 3.2. By comparing the C/N 0 of PRN 04 (the strongest) and the C/N 0 of PRN 14 (the weakest) in Figure 3.8, it can be concluded that vector tracking improves the ML bit decoding of weak signals more significantly. 103

123 Figure 3.21: Performance of ML bit decoding in scalar tracking and vector tracking in the dense foliage test Table 3.2: Average C/N 0 of different satellites in the dense foliage test PRN Average C/N 0 [db-hz] Benefits of Extended Coherent Integration Time in Assisted-GNSS In order to verify the benefits of longer coherent integration time, the navigation solutions obtained in GSNRx-hs by implementing different coherent integration times are assessed first. The root mean square (RMS) position and velocity errors obtained using 20 ms, 60 ms, 100 ms and 200 ms in the dense foliage test are shown in Figure The bit wipe-off of long coherent 104

124 integration here was achieved from the bit aiding method, and it is considered perfect and no error or loss is included. The result shows the RMS position and velocity errors decrease when the coherent integration time is extended from 20 ms to 100 ms. Interestingly, the RMS velocity errors show a slight increase when the coherent integration time is further extended to 200 ms. This suggests longer coherent integration time does not always provide better navigation performance, likely because the tolerance of Doppler errors decrease with longer coherent integration time. Correspondingly, it is important to extend coherent integration time to a suitable value. These results imply that in the dense foliage environment, a coherent integration time of around 100 ms provides the best results. Actually, as mentioned in Gleason & Gebre-Egziabher (2009), due to the oscillator s stability, the maximum available coherent integration time for temperature compensated crystal oscillators (TCXO) is about 100 ms. So in this thesis work, though a higher quality OCXO clock was used for data collection (see Section 3.3.3), for the purpose of generality, only the maximum coherent integration of 100 ms is considered unless otherwise stated. 105

125 Figure 3.22: RMS position and velocity errors with different coherent integration times in the bit aiding mode in the dense foliage test The position and velocity errors as a function of time for different coherent integration times in the dense foliage test are shown in Figure 3.23 and Figure It can be viewed that generally position and velocity errors decrease by extending coherent integration time from 20 ms to 100 ms. Another phenomenon is that when the vehicle is in the open sky and the light foliage area (left side of the dash line in Figure 3.23 and Figure 3.24), the navigation results using different coherent integration time are very similar. This means in open sky or light foliage environments where the signal attenuation and multipath are not severe, the benefits of extending coherent are not obvious. However, the advantage of longer coherent integration time appears when the land vehicle enters the dense foliage environment (right side of the dashed line). 106

126 Light Foliage Dense Foliage Figure 3.23: Position errors in north, east and up as a function of time for different coherent integration times in the bit aiding mode in the dense foliage test 107

127 Light Foliage Dense Foliage Figure 3.24: Velocity errors in north, east and up as a function of time for different coherent integration times in the bit aiding mode in the dense foliage test The above analysis showed that, for this data set, and having perfect bit information, the optimal coherent integration time is around 100 ms. Now the question is: Is it possible to achieve the same or similar performance by using the ML-based bit wipe-off to extend coherent integration time to 100 ms in the standalone mode? 108

128 3.4.3 Extending Coherent Integration Time Using Estimated Data Bits in Dense Foliage Test In Section 3.2, two strategies to select suitable correlator outputs for ML bit decoding and extending coherent integration time are introduced. First it is expected to see, without any of these strategies, compared to coherent integration time of one bit period (20 ms), whether the navigation (position and velocity) performance is improved by extending coherent integration time to 100 ms using ML-based bit wipe-off. The third (yellow) bar in each plot in Figure 3.25 shows the RMS position and velocity errors from GSNRx-hs-sa in the horizontal and vertical directions without applying any correlator output selection strategy. Compared to the navigation results using 20 ms (the dark blue bar in each plot), the 100 ms results using ML-based bit wipeoff without any strategy have larger position errors. By applying Strategy I and employing the elevation angle mask of 15 degrees, the 20 ms and 100 ms measurements are alternately used to calculate the navigation solution. The 100 ms measurements can avoid using most of the degraded signals arising from passing tree trunks, houses and other blockages along the test road. With Strategy I, the degraded signals can still be used to build the 20 ms measurements, and this helps to avoid the high BER problem without losing any useful observation. Finally, the RMS position and velocity errors from GSNRx-hs-sa in the horizontal and vertical directions obtained with Strategy I are shown as the fourth (red) bar in each plot in Figure The results are very close to the 100 ms results using bit aiding in GSNRx-hs (the second (light blue) bar in each plot in Figure 3.25), and the latter is the ideal case. This shows the feasibility of ML-based bit wipe-off when combined with Strategy I. Overall, the position and 109

129 velocity accuracy has been improved about 50% after extending coherent integration time from 20 ms to 100 ms in the standalone high-sensitivity GNSS receiver. Figure 3.25: RMS position and velocity errors in different directions by using Strategy I in the dense foliage test The validity of Strategy I can be further confirmed by viewing the cumulative C/N 0 plots of all satellites in the dense foliage test, which is shown in Figure There are three satellites (dashed lines) below 15 degrees of elevation whose signal C/N 0 are noticeably weaker than those satellites above 15 degrees (solid lines). This elevation angle mask strategy helps ML bit decoding distinguish the good and bad candidates. It is noticed that the value of the elevation angle mask 15 degrees in this work should vary according to different field environments. 110

130 Usually it is a trade-off between the number of observations with longer coherent integration and the tolerance of BER values. Figure 3.26: Cumulative C/N 0 plots of all satellites in the dense foliage test Strategy II can also help to select the right correlator outputs to extend coherent integration time and avoid the high BER problem. Strategy II uses C/N 0 as the threshold, because the high BER problem is directly linked to the low C/N 0 situation. With Strategy II, the coherent integration time is extended to 100 ms if the current C/N 0 exceeds the threshold, and the coherent integration time stays at 20 ms if the C/N 0 is below the threshold. The corresponding RMS position and velocity errors are shown in Figure Four different threshold values (denoted as Th in the following figures) in GSNRx-hs-sa were chosen for comparison, namely 25, 30, 35, 40 db-hz. The results can be used to evaluate different thresholds, and in this case the overall results (i.e., 3D error) are the best when applying a 111

131 threshold of 35 db-hz, and the position results with a threshold of 30 db-hz are the best in the horizontal channels. The 100 ms results using ML-based bit wipe-off with a threshold of 35 db-hz are comparable to the ideal 100 ms results from GSNRx-hs using bit aiding (the second bar in each plot in Figure 3.27). Compared to Strategy I, the 100 ms position results using ML-based bit wipe-off with a threshold of 35 db-hz are a bit worse in height. However, the optimal elevation angle mask value is highly dependent on the test environments. The optimal threshold in Strategy II is based on C/N 0 and should be applied in various kinds of environments. The optimal threshold of around 35 db-hz obtained in this test will be further verified in the following urban canyon test. Figure 3.27: RMS position and velocity errors in different directions by using Strategy II in the dense foliage test 112

132 Finally, by setting the threshold as 30 db-hz (best in horizontal), the resulting trajectory from the scalar-based GNSS receiver GSNRx and the vector-based standalone high-sensitivity GNSS receiver GSNRx-hs-sa are shown in Figure The results confirm the validity of extended coherent integration time and Strategy II, with which the navigation solution from the standalone GSNRx-hs-sa using 100 ms coherent integration time is very close to the reference trajectory in the dense foliage test. In contrast, there are obvious errors in the position results from GSNRx. It is noted that the vehicle speed here is from 0 to 50 km/h, and the navigation performance can be different in other dynamics or other applications, e.g., pedestrian navigation. The performance may also vary using different oscillators. Reference trajectory GSNRx-hs-sa TM, 100 ms, Th = 30 db-hz GSNRx TM, 20 ms, scalar tracking Figure 3.28: Trajectory results by using Strategy II in the dense foliage test 113

133 3.5 Urban Canyon Test I Result The Urban Canyon Test I assesses the benefits of a vector tracking structure for ML bit decoding with field data in an urban canyon environment. Similar to the configuration in the dense foliage environment, this scheme utilizes the estimated data bits to extend coherent integration using bit wipe-off and then assesses the accuracy of navigation solution Performance of ML Bit Decoding in Urban Canyon Test I The ML bit decoding results as a function of signal strength in the scalar-based receiver GSNRx and the vector-based receiver GSNRx-hs-sa are shown in Figure Compared to the results in scalar tracking, a marked performance improvement of ML bit decoding in the vector tracking is noticed. This shows the benefits of vector tracking for ML bit decoding, which improves the SDR by 2% 30% depending on the signal strength in the urban canyon environment. This result is generally consistent with the improvement in the dense foliage environment as shown in Figure

134 Figure 3.29: Performance of ML bit decoding as a function of signal strength in scalar tracking and vector tracking in the Urban Canyon Test I Figure 3.30 shows the SDR from each satellite in the entire field test. Compared to the results in scalar tracking, a marked performance improvement of ML bit decoding in the vector tracking for different satellites is noticed. This confirms the benefits of vector tracking for ML bit decoding, which improves the SDR by 20% 25% depending on the different satellites in the urban canyon environment. The average C/N 0 of different satellites in the dense foliage test is shown in Table

135 Figure 3.30: Performance of ML bit decoding in scalar tracking and vector tracking in Urban Canyon Test I Table 3.3: Average C/N 0 of different satellites in Urban Canyon Test I PRN Average C/N 0 [db-hz] Benefits of Extended Coherent Integration Time in Assisted-GNSS In the Dense Foliage Test, the coherent integration time of around 100 ms is confirmed as optimal in the dense foliage environments. It is desirable to verify whether 100 ms of coherent integration is also optimal in the urban canyon environments. 116

136 Similar to the analysis in Section 3.4.2, the navigation solutions obtained by implementing different coherent integration times are assessed first using GSNRx-hs. The RMS position and velocity errors by using 20 ms, 60 ms, 100 ms and 200 ms in the Urban Canyon Test I are shown in Figure The bit wipe-off of long coherent integration here was achieved from the bit aiding method. The result shows the RMS errors decrease when the coherent integration time is extended from 20 ms to 100 ms, then the RMS errors start to increase when the coherent integration time is further extended to 200 ms. This indicates, in the urban canyon environment, the coherent integration time around 100 ms provides the best results. This result is consistent with the conclusion from the Dense Foliage Test. So it can be concluded that the optimal coherent integration time for land vehicle navigation in the signal challenged environments is around 100 ms. It is noted that this optimal coherent integration time is subject to the receiver architecture and the quality of front-end. A front-end driven by an OCXO is used in this thesis work, and the optimal coherent integration time will likely decrease if a lower-end oscillator is equipped. 117

137 Figure 3.31: RMS position and velocity errors with different coherent integration times in the bit aiding mode in the Urban Canyon Test I The position and velocity errors as a function of different time for different coherent integration times in Urban Canyon Test I are shown in Figure 3.32 and Figure It can be viewed that both position and velocity errors decrease by extending coherent integration time from 20 ms to 100 ms. Similar to the results obtained in the Dense Foliage Test, when the vehicle is in the open sky (left side of the first dash line and right side of the second dash line in Figure 3.32 and Figure 3.33), the navigation results using different coherent integration time are very close; however, the advantage of longer coherent integration time appears when the land vehicle enters the downtown area (between two dash lines). 118

138 Open Sky Downtown Open Sky Figure 3.32: Position errors in north, east and up as a function of time for different coherent integration times in the bit aiding mode in the Urban Canyon Test I 119

139 Open Sky Downtown Open Sky Figure 3.33: Velocity errors in north, east and up as a function of time for different coherent integration times in the bit aiding mode in the Urban Canyon Test I Extending Coherent Integration Time Using Estimated Data Bits in Urban Canyon Test I In this urban canyon test, when using the coherent integration time of around 100 ms, the best position and velocity results are obtained. Then it should be verified compared to the bit aiding method if similar performance can be achieved by using the standalone ML bit decoding based bit wipe-off algorithm. 120

140 The third light (blue) bar in each plot in Figure 3.34 shows RMS position and velocity errors from GSNRx-hs-sa in the horizontal and vertical directions without applying any correlator outputs selecting strategy. Similar to the result obtained in the Dense Foliage Test, compared to the navigation results using 20 ms (the first (dark blue) bar in each plot), the 100 ms results using ML-based bit wipe-off without any strategy have larger position errors. In the Urban Canyon Test I, only Strategy II is used to deal with the high BER problem because the signal power based selecting strategy can directly mitigate the impact in ML-based bit wipeoff from high BER. However, Strategy I employs the elevation angle mask which is not suitable for urban canyon environments. When the land vehicle is running, the satellite signals will frequently pop up when there is a slot and drop out when they are blocked by skyscrapers. The elevation angle mask based strategy is totally unfit in this environment. RMS position and velocity errors in the horizontal and vertical directions obtained with Strategy II are shown in Figure The coherent integration time is extended to 100 ms if the current C/N 0 exceeds the threshold, and the coherent integration time stays at 20 ms if the C/N 0 is below the threshold. Three different threshold values were chosen for comparison, namely 30, 35, 40 db-hz. It is shown in Figure 3.34 that the position and velocity results with the threshold of 35 db-hz are the best in both horizontal and vertical directions. This is consistent with the conclusion from the Dense Foliage Test, that the threshold of 35 db-hz is optimal. 121

141 Figure 3.34: RMS position and velocity errors in different directions by using Strategy II in the Urban Canyon Test I Finally, by setting the threshold as 35 db-hz, the trajectory results from GSNRx-hs-sa are shown in Figure The reference trajectory and the results from GSNRx-hs using the coherent integration time of 20 ms and 100 ms are included for comparison. An improvement in the trajectory results by extending coherent integration time from 20 ms to 100 ms can be easily observed. The results confirm the validity of ML-based bit wiped-off combined with Strategy II, and the position result of standalone GSNRx-hs-sa using 100 ms coherent integration time is close to GSNRx-hs with bit aiding, and the difference in RMS position error is less than 5 meters in horizontal. 122

142 Reference trajectory GSNRx-hs TM, 20 ms GSNRx-hs TM, 100 ms, bit aiding GSNRx-hs-sa TM, 100 ms, ML bit decoding, Th = 35 db-hz Figure 3.35: Trajectory results by using Strategy II in the Urban Canyon Test I 3.6 Limitations of GNSS Only Solution An obvious improvement can be viewed in Figure 3.35 when the coherent integration time is extended from 20 ms to 100 ms in GSNRx-hs-sa. However, the position results with 100 ms from both GSNRx-hs and GSNRx-hs-sa still contain large biases. Unfortunately, the performance of standalone receiver GSNRx-hs-sa can only approach ideal assisted-gnss receiver GSNRx-hs. With GNSS only solutions, the performance of the standalone approach cannot be further improved if the accuracy of the ideal assisted approach (i.e., bit aiding method) is limited. In order to verify if the GNSS only solution is limited in urban canyon environments, the data collected in Urban Canyon Test II is used here. Only trajectory results are included here and other ML bit decoding results will be introduced in Chapter Four. The position results from GSNRx-hs and GSNRx-hs-sa by extending the coherent integration time to 100 ms are shown in Figure First, the results re-confirm the validity of the standalone approach, with 123

143 which the performance of standalone receiver GSNRx-hs-sa is very close to the assisted- GNSS receiver GSNRx-hs. However, the figure also shows noticeable biases in GNSS only solutions (marked by yellow circles) from both GSNRx-hs and GSNRx-hs-sa. In order to achieve a better solution, it is important to integrate other available vehicle sensors with GNSS for land vehicle navigation in urban canyon environments. The scheme and the relevant analysis will be presented in the next chapter. Reference trajectory GSNRx-hs TM, 100 ms, bit aiding GSNRx-hs-sa TM, 100 ms, ML bit decoding, Th = 35 db-hz Figure 3.36: Trajectory results in GNSS only mode by using Strategy II in the Urban Canyon Test II 3.7 Summary This chapter proposes a vector-based standalone high-sensitivity GNSS receiver, assesses the performance of ML bit decoding in vector tracking, presents an analysis of the navigation performance with extended coherent integration time after ML-based bit wipe-off, and gives two 124

144 strategies to select the suitable correlator outputs for ML-based bit wipe-off in signal challenged environments. The ML bit decoding and the standalone approach with extended coherent integration time using ML-based bit wipe-off are analyzed in vehicular navigation tests in dense foliage and urban canyon environments. The results in dense foliage show vector tracking can improve the SDR by 3% 35% depending on the signal strength. The results in an urban canyon environment show vector tracking can improve the SDR by 2% 30% depending on the signal strength. The navigation results show that extended coherent integration can help to improve the navigation performance in signal challenged environments. The position and velocity accuracy has been improved about 50% in the standalone approach after extending coherent integration time from 20 ms to 100 ms in the vehicular navigation test. The coherent integration time of 100 ms is found to give the best navigation performance for both dense foliage and urban canyon environments. Two newly proposed strategies have helped to overcome the high BER problem in ML-based bit wipe-off. The two strategies select the suitable correlators for ML-based bit wipe-off based on a satellite s elevation angle and estimated C/N 0 respectively. It is shown that after implementing either strategy, the navigation results in dense foliage with extended coherent integration time from the standalone receiver are close to those from the assisted-gnss receiver, and the latter are considered as containing no bit errors and expected to give the best results. Only the estimated C/N 0 based correlator selection strategy is fit for applications in urban canyon environments. After applying this strategy, the navigation results in urban canyon with extended 125

145 coherent integration time from the standalone receiver are close to those from the assisted-gnss receiver, and the difference in RMS position error is less than 5 meters in horizontal. 126

146 Chapter Four: Improving ML Bit Decoding and Navigation Performance in Ultra-Tightly Coupled High-Sensitivity GNSS Receiver In the last chapter, a vector-based GNSS receiver was demonstrated to extend the tracking threshold, improve the ML bit decoding. Then a vector-based, standalone, high-sensitivity GNSS receiver with ML-based bit wipe-off for extending coherent integration time was proposed. The standalone approach was validated in the vehicular tests under dense foliage and in an urban canyon. However, in urban canyon environments, even with extended coherent integration is done with the ideal bit aiding method, GNSS only solution is still not satisfactory. In this chapter, it will be evaluated if the tracking threshold can be further extended by using the ultra-tight integration of GNSS and vehicle/inertial sensors, and then assess the benefits of this ultra-tightly coupled architecture in improving ML bit decoding and navigation solution with extended coherent integration time. The ultra-tightly coupled architecture is also a standalone approach, and it does not require any assistance information from external networks. Similar to the previous chapters, the performance of bit decoding in the context of this chapter is assessed in terms of the SDR of bit values. 4.1 Standalone Ultra-Tightly Coupled High-Sensitivity GNSS Receiver GSNRx-hsdr-sa I compared different GNSS only receivers and proposed a vector-based standalone highsensitivity receiver GSNRx-hs-sa in Section 3.1. In this section, an ultra-tightly coupled assisted-gnss high-sensitivity receiver GSNRx-hs-dr is introduced. 127

147 The architecture of GSNRx-hs-dr is shown in Figure 4.1. This ultra-tightly coupled receiver is the integration of GNSS and DR system. This DR system directly obtains velocity information from wheel speed sensors, which is different from and has benefits over the traditional INS mechanizations (shown in Figure 4.2). The main benefit of DR system over the traditional INS mechanization is the accuracy of DR algorithm degrades with the travelled distance rather than with time. Figure 4.1: Architecture of a conventional ultra-tight receiver with external bit aiding, GSNRxhs-dr 128

148 Figure 4.2: Architecture of ultra-tight integration of GNSS and traditional INS mechanizations Except for the integrated vehicle sensors and DR based navigation filter, the GNSS receiver signal processing part in GSNRx-hs-dr is similar to GSNRx-hs. Similar to the drawbacks in GSNRx-hs, the conventional GSNRx-hs-dr is an assisted-gnss approach and extends the coherent integration time by bit aiding method, which requires an external network. In order to achieve a standalone ultra-tight approach, the conventional ultra-tight receiver is modified in this thesis work using ML bit decoding to extend integration time, as shown in Figure 4.3. This modified version can be considered as the design of a standalone ultra-tightly coupled highsensitivity GNSS receiver, namely GSNRx-hs-dr-sa. 129

149 Figure 4.3: Architecture of a new ultra-tight receiver with ML bit decoding, GSNRx-hs-dr-sa 4.2 Vehicle Sensor Configuration The DR algorithm uses the vehicle sensors output as measurements to update the system rather than the mechanization approach used in conventional INS. As mentioned before, the ultratightly coupled system in this work employs four wheel speed sensors, a steering angle sensor, a longitudinal accelerometer and a vertical gyroscope (WSS/SAS/1A1G). This setup is similar to the one used in Li (2012) and the system model is given by n n r r 0 b b 0 Vy Vy b b a w y a y a w 0 F w S S w W b w y by A d w G d G G w s s S (4.1) 130

150 where The position error vector is in navigation frame (i.e., local level frame or East-North-Up (ENU) frame); b V y is the longitudinal velocity error in body frame; b a y is the longitudinal acceleration error in body frame, modeled as random walk with the driving noise w a ; is the pitch error, modeled as first order Gauss-Markov process with the driving noise w ; is the azimuth error; is the yaw rate error, modeled as random walk with the driving noise w ; S is the scale factor error vector of wheel speed sensors, modeled as first order Gauss- Markov process with the driving noise w W ; b y is the longitudinal accelerometer bias, modeled as first order Gauss-Markov process with the driving noise w A ; d G is the gyroscope drift, modeled as first order Gauss-Markov process with the driving noise w G ; s is the steering angle error, modeled as first order Gauss-Markov process with the driving noise w S. Besides, F is the dynamics matrix and given by 131

151 0 R1 0 R2 R sin cos cos W A G S 2 F (4.2) where x is the reciprocal of the time constant in each first order Gauss-Markov process (e.g., when x represents ). In addition, the detailed system model relevant to n r is given by r n re r N r U b V y R V b y R1 R3 R2 b b b sin cos Vy cos cos V y sin sin V y b b cos cos Vy sin cos Vy cos sin b sin 0 Vy cos (4.3) 132

152 4.3 Test Description of Urban Canyon Test II for ML Bit Decoding and Navigation The Urban Canyon Test II has been introduced in Section It is the vehicular field test conducted in downtown Calgary. The data from inertial/vehicle sensors were collected simultaneously with GNSS data. The built-in vehicle sensors including wheel speed sensors, inertial sensors and steering angle sensors originally equipped in the vehicle to improve the safety and operational stability, are used in this work to build the DR system. Wheel speed sensors are used as a low cost solution to measure the vehicle s speed. A steering angle sensor is used to measure the wheel turning angle with respect to the neutral position (Li 2012). With the steering angle sensor, the front wheel speed sensors can provide the in-track velocity and yaw rate estimation. The built-in reduced micro electro-mechanical systems (MEMS) IMUs including a longitudinal accelerometer and a vertical gyroscope (1A1G) are used to measure acceleration and angular velocity. The in-run variability of the gyroscope is 113 deg/hr and the angular random walk is 1044 deg/hr/ Hz (Li 2012). 4.4 Urban Canyon Test II Result The urban canyon test assesses the benefits of the proposed standalone ultra-tightly coupled architecture for ML bit decoding with field data. It uses the estimated data bits to extend coherent integration using bit wipe-off and then assesses the accuracy of the navigation solution Bit Decoding Performance in Ultra-Tight Receiver First of all, a comparison of estimated C/N 0 from the scalar-based receiver GSNRx and the ultra-tight receiver GSNRx-hs-dr-sa is shown in Figure 4.4. PRN 25 is selected for comparison purpose but the results are typical for other satellites. It is noticed that the signal can 133

153 be tracked in the ultra-tight receiver although the signal power is quite low (between about 10 and 30 db-hz). In the scalar-based receiver, however, during more than half of time the signal is not tracked (indicated by a C/N 0 value equal to zero). Figure 4.4: C/N 0 of PRN 25 in scalar-based receiver and ultra-tight receiver in the urban canyon test The SDRs of ML bit decoding as a function of signal strength in the scalar-based receiver GSNRx and the ultra-tight receiver GSNRx-hs-dr-sa are shown in Figure 4.5. The number of bits to be decoded at one time here is two (i.e., N = 2), which is the optimal number for tolerating Doppler errors as shown in Section The statistics of bit decoding as a function of C/N 0 are calculated using bins with a width of 2.5 db. Compared to the results in the scalar-based receiver, a marked performance improvement of ML bit decoding in the ultra-tight receiver is noticed. This shows the benefits of the ultra-tight 134

154 receiver for ML bit decoding, which improves the SDR by 1% 30% depending on the signal strength. Compared with the Monte Carlo results (the settings were introduced in Section 2.2.1), the difference in SDR between the ultra-tight receiver and Monte Carlo simulations is due to the non-white noise factor resulting from multipath, as well as the inherent tracking errors that are present within the receiver. An interesting phenomenon can also be viewed in Figure 4.5. Specifically, the SDRs from the ultra-tight receiver and from the vector-based receiver are quite close. This implies in the urban canyon test the abilities of the ultra-tight receiver and the vectorbased receiver to track signal code phase and Doppler are quite close. Figure 4.5: Performance of ML bit decoding as a function of signal strength in scalar-based receiver and ultra-tight receiver in the urban canyon test Figure 4.6 shows the SDR from each satellite during the entire field test. Compared to scalar tracking, the improvement of the SDR resulting from the ultra-tight receiver ranges from 2% to 135

155 30%. Figure 4.7 shows the cumulative C/N 0 plots of all satellites in the urban canyon test, and, when cross-referenced against Figure 4.6 it is noted that ultra-tight receiver improves the ML bit decoding of weak signals more significantly. It can also be viewed in Figure 4.6, compared to the vector-based receiver, the SDR from the ultra-tight receiver only has a slight improvement. This suggests in the urban canyon test the SDR cannot be further improved if the signal is blocked by skyscrapers, even if the navigation solution has been improved in the ultra-tight receiver. The results of the navigation solution will be discussed later. Figure 4.6: Performance of ML bit decoding in scalar-based receiver, vector-based receiver and ultra-tight receiver in the urban canyon test 136

156 Figure 4.7: Cumulative C/N 0 plots of all satellites in the urban canyon test The SDR results in Figure 4.6 were obtained by an empirical setting, where the open-loop search space uncertainty was set as 40 meters (for pseudorange errors) by 10 Hz (for Doppler errors). Figure 4.8 shows the SDR resulting from the ultra-tight receiver with different search space sizes. The result shows that the SDR has no obvious change with different search space settings. This confirms the former conclusion that the SDR cannot be further improved if the signal is blocked. 137

157 Figure 4.8: Performance of ML bit decoding with different search space in ultra-tight receiver in the urban canyon test Performance of Assisted-GNSS and DR only solution Before integrating GNSS and DR system, the performance of GNSS only solution and DR only solution are assessed first. The GNSS only solution is obtained from the vector-based receiver GSNRx-hs with the optimal coherent integration time of 100 ms. In GSNRx-hs, the bit wipe-off is achieved by the ideal bit aiding method. The trajectory results from of DR only and GNSS only solution are compared to the reference trajectory in Figure 4.9. The trajectory of DR only solution (green line in Figure 4.9) looks smooth but has accumulated position errors; the GNSS only solution (red line in Figure 4.9) has no accumulated bias but is noisy due to signal blockage and heavy 138

158 multipath in the urban canyon. Especially, a large spike error (in the yellow circle) can be easily viewed in Figure 4.9. Figure 4.9: Trajectory results of GNSS only solution and DR only solution in the urban canyon test. The blue line is the reference trajectory; the red line is the result of GNSS only solution with the coherent integration time of 100 ms by bit aiding; and the green line is the result of DR only solution Ultra-Tight Integration of Assisted-GNSS and DR System From results in Figure 4.9, in order to obtain a better solution, it is necessary to integrate GNSS and DR together. The red line in Figure 4.10 shows trajectory result of the ultra-tight integration of assisted-gnss with coherent integration time of 100 ms and DR system. Compared to the results in Figure 4.9, it is noticed that the result from ultra-tight integration is fairly smoothed and contains no obvious accumulated errors. It can also be viewed that the large spike error, which was in the yellow circle area in Figure 4.9, has disappeared. This result demonstrates the effectiveness of integrating GNSS and DR system. 139

159 Figure 4.10: Trajectory results of ultra-tight integration of assisted-gnss with coherent integration time of 100 ms and DR system in the urban canyon test. The blue line is the reference trajectory; the red line is the ultra-tight integration result from GSNRx-hs-dr. The RMS position and velocity errors of GNSS only, DR only and ultra-tight integration are summarized in Table 4.1. From both Figure 4.10 and Table 4.1, although the ultra-tight integration has provided marked improvement over the GNSS-only solution and DR only solution, the navigation result in urban canyon is still not quite satisfactory. The RMS position error in the horizontal plane is larger than 10 meters. This is because, in urban canyon environments, there are massive reflecting surfaces from normal buildings and skyscrapers, and thus multipath can severely deteriorate the navigation solutions (up to 150 meters for GPS L1 C/A signals (Lachapelle 2004). 140

160 Table 4.1: RMS position and velocity errors in GNSS only solution, DR only solution, and ultratight integration. RMS Position Error [m] System North East Up GNSS Only, GSNRx-hs, 100 ms DR Only Ultra-Tight Integration, GSNRx-hs-dr, 100 ms RMS Velocity Error [m/s] System North East Up GNSS Only, GSNRx-hs, 100 ms DR Only Ultra-Tight Integration, GSNRx-hs-dr, 100 ms Signal Power Based Multipath Mitigation In order to mitigate the effect of multipath, this thesis work proposes a signal power as determined by the estimated C/N 0 based observation selection strategy for selecting suitable GNSS pseudorange and Doppler measurements in the navigation filer. A signal power threshold can be used to mitigate multipath. From Xie (2013), reflected signals rarely exceed 42 db-hz in such environments. As such, if a satellite s C/N 0 is higher than this, all of its measurements are used. Otherwise, only the Doppler measurement is used. Although signal power threshold chosen here is 42 db-hz, it would ideally be an environment-dependent value. 141

161 The reason for only using Doppler measurement in a LOS and NLOS mixed signal channel is twofold. First, the correct Doppler measurement can be extracted in the open-loop tracking if the LOS signal and the NLOS signals can be separated in the frequency domain (Xie & Petovello 2011). The Doppler error caused by NLOS signal is limited if the LOS signal cannot be separated from NLOS signals. In other words, the Doppler bias from NLOS signals should be small especially with extended coherent integration time if LOS signal and NLOS signals are overlapped in the frequency domain. Second, the vehicle sensors can correct the system velocity with a higher update rate and mitigate errors introduced by GNSS measurements. However, in this case, there is no direct position update from vehicle sensors or DR algorithm, and any position error caused by inaccurate GNSS pseudoranges will remain until the next accurate GNSS update. In other words, the ultra-tight receiver is more vulnerable to pseudorange errors than Doppler errors. After implementing the signal power based multipath mitigation algorithm, the trajectory result from ultra-tight receiver GSNRx-hs-dr is shown in Figure 4.11 (green line). Compared to the ultra-tight result without the signal power based multipath mitigation algorithm (red line in Figure 4.11), a marked improvement can be viewed in Figure The green line is almost overlapped with the reference trajectory (blue line in Figure 4.11). 142

162 Figure 4.11: Trajectory results of ultra-tight integration of assisted-gnss with coherent integration time of 100 ms and DR system using the signal power based multipath mitigation algorithm in the urban canyon test. The blue line is the reference trajectory; the red line is the result without the signal power based multipath mitigation algorithm; and the green line is the result using the signal power based multipath mitigation algorithm. The RMS position and velocity errors of GNSS only, DR only and ultra-tight integration without the signal power based multipath mitigation algorithm, and ultra-tight integration using the signal power based multipath mitigation algorithm are summarized in Table 4.2. It can be viewed that the ultra-tight receiver with the signal power based multipath mitigation algorithm outperforms the other systems or settings. The RMS position error in horizontal is less than 5 meters. It is noted that the signal power based multipath mitigation algorithm was not used in the GNSS only receiver because the reduction in the number of observations caused by the algorithm usually results in too few observations remained to compute a solution, and that leads to poor navigation performance. The algorithm is not reliable for GNSS-only solution. 143

163 Table 4.2: RMS position and velocity errors in GNSS only solution, DR only solution, ultra-tight integration, and ultra-tight integration with the multipath mitigation algorithm RMS Position Error [m] System North East Up GNSS Only, GSNRx-hs, 100 ms DR Only Ultra-Tight Integration, GSNRx-hs-dr, 100 ms Ultra-Tight Integration, GSNRx-hs-dr, 100 ms, with Signal Power Based Multipath Mitigation Algorithm RMS Velocity Error [m/s] System North East Up GNSS Only, GSNRx-hs, 100 ms DR Only Ultra-Tight Integration, GSNRx-hs-dr, 100 ms Ultra-Tight Integration, GSNRx-hs-dr, 100 ms, with Signal Power Based Multipath Mitigation Algorithm Navigation Results in Standalone Ultra-Tightly Coupled High-Sensitivity GNSS Receiver with ML Bit Decoding In the previous sections, the performance of ML bit decoding has been assessed, the navigation performance of assisted-gnss only solution, DR only solution and ultra-tight integration of assisted-gnss and DR, and the navigation solution of ultra-tight integration with a signal power based multipath mitigation algorithm. In Section 4.1, by using ML-based bit wipe-off, a standalone ultra-tightly coupled highsensitivity GNSS receiver GSNRx-hs-dr-sa is proposed. In this section, the navigation 144

164 performance of this standalone approach will be assessed, and to verify if it is able to achieve a similar performance compared to the ultra-tight integration of ideal assisted-gnss and DR. In Section 4.4.3, a signal power based multipath mitigation algorithm is proposed in this thesis. The field test results show that it is always necessary to include this algorithm in urban canyon environments to avoid large errors caused by multipath. So in the standalone approach, it will be considered that this algorithm is a default configuration. The navigation results using 100 ms from GSNRx-hs-dr with bit aiding and GSNRx-hs-drsa with ML bit decoding are shown in Figure For comparison, the navigation results using 20 ms from GSNRx-hs-dr are also included. The position and velocity accuracy has been markedly improved (more than 40%) after extending coherent integration time from 20 ms to 100 ms in both bit aiding approach and ML bit decoding approach. In Section and Section 3.5.3, the results from Figure 3.25, Figure 3.27 and Figure 3.34 showed that usually in standalone approach it is necessary to include a strategy to select suitable correlators for ML bit decoding and ML-based bit wipe-off. This is due to the high BER problem associated with low C/N 0 values. Otherwise, the navigation results with 100 ms from ML bit decoding could be even worse than the 20 ms results. However, no strategy to select suitable correlators in the standalone ultra-tight approach was implemented, and as shown in Figure 4.12, for the coherent integration time of 100 ms, the results from the standalone ultra-tight approach are very close to ultra-tight bit aiding approach. In other words, the strategy to select suitable correlators for ML bit decoding and ML-based bit wipe-off does not offer any significant benefits here. This implies that ultra-tight receivers are more immune to the high BER problem 145

165 (because they do not require any strategy to suitably select correlator outputs and mitigate high BERs), and are thus better able to extend coherent integration time compared to the vector-based receiver. In ultra-tight receivers, the DR system can mitigate the errors caused by the high BER problem. In the standalone ultra-tight receiver with 100 ms from ML bit decoding, i.e., GSNRxhs-dr-sa, the RMS position error in horizontal and vertical is less than 5 m and 10 m respectively, and the RMS velocity error in horizontal and vertical is both less than 0.2 m/s. Figure 4.12: RMS position and velocity errors in different directions by using bit aiding and ML bit decoding based bit wipe-off from ultra-tight receiver in the urban canyon test 146

166 Finally, the trajectory results from the standalone ultra-tightly coupled high-sensitivity GNSS receiver GSNRx-hs-dr are shown in Figure With the coherent integration time of 100 ms from ML bit decoding, the navigation solution is very close to the reference trajectory in the urban canyon test. Figure 4.13: Trajectory results of standalone ultra-tight receiver using the coherent integration time of 100 ms from ML bit decoding in the urban canyon test. The blue line is the reference trajectory; the red line is the result from standalone ultra-tight receiver. 4.5 Summary The work in this chapter proposes a standalone ultra-tightly coupled high-sensitivity GNSS receiver. In addition, it assesses the performance of ML bit decoding in an ultra-tightly coupled GNSS receiver, presents an analysis of the navigation performance with extended coherent integration time after ML-based bit wipe-off, and gives a signal power based multipath mitigation algorithm for selecting the pseudorange and/or Doppler measurements in the standalone software-based ultra-tightly couple high-sensitivity GNSS receiver in weak signal environments. 147

167 The SDR of ML bit decoding in an ultra-tight receiver is assessed as a function of received signal power. In the context of GPS L1 C/A signals, the field test results show that an ultra-tight receiver can improve the SDR by 1% 30% over scalar-based receiver depending on the signal strength. The ultra-tight receiver is also shown to be more robust than the vector-based receiver, that it is more immune to the high BER problem and does not require any correlator outputs selection method in extending coherent integration time. The ultra-tight navigation results show that extended coherent integration with ML based bit wipe-off method can help to improve the navigation performance in signal challenged environments. In both the bit aiding approach and the standalone approach, the position and velocity accuracy has been improved more than 40% after extending coherent integration time from 20 ms to 100 ms in the vehicular navigation test. The navigation results with extended coherent integration time from ML bit decoding are close to those from bit aiding, and the latter are considered as containing no bit errors and expected to give the best results. A newly proposed signal power based multipath mitigation algorithm has helped to overcome the inaccurate GNSS measurements problem existing in heavy multipath (fading) areas. It is shown that after implementing the strategy in the standalone ultra-tight receiver with 100 ms from ML bit decoding, the RMS position error in horizontal and vertical is less than 5 m and 10 m respectively, and the RMS velocity errors in horizontal and vertical both are less than 0.2 m/s. This confirms the feasibility of the standalone ultra-tight approach. 148

168 Chapter Five: Collective Bit Synchronization In the last two chapters, the benefits from the vector-based receiver and the ultra-tight receiver were determined for improving ML bit decoding, extending coherent integration time and, subsequently, improving the navigation solution in the vehicular tests under dense foliage and in urban canyon. However, without the knowledge of the location of the bit boundaries, ML-based bit wipe-off cannot be performed effectively even if bit values are known. This means, in order to extend the coherent integration time, bit synchronization should be achieved first. In this chapter, a novel collective bit synchronization method that can help to improve bit synchronization performance in signal challenged environments is demonstrated. The novel collective bit synchronization approach combines multiple satellites together rather than doing bit synchronization in each individual channel as in conventional methods to provide extra processing gain and improve the detection rate of bit boundary positions. The collective bit synchronization approach is another original contribution of this thesis work. The benefits of using collective bit synchronization to improve the detection rate of bit boundary positions are analyzed using the standard software GNSS receiver GSNRx. In the context of this chapter, the performance of bit synchronization is directly assessed in terms of the SSR with the navigation data bit (i.e., correct identification of the bit boundaries). 5.1 Methodology of Collective Bit Synchronization As shown in Chapter Three, vector tracking is able to improve tracking performance by using a receiver s position and velocity. Furthermore, similar to vector tracking concepts, the collective detection method can reduce the required signal power by searching weak GNSS signals in a 149

169 position/clock space (instead of searching in a code phase/doppler domain) that directly yields the navigation solution (Axelrad et al 2012). Along this vein, a novel collective bit synchronization approach is proposed in this thesis for weak GNSS signals using multiple satellites. The idea of collective bit synchronization is: given approximate information about satellite ephemeris (or almanac) as well as the receiver s position and time, the relative bit boundary positions between satellites can be determined by the pairwise differences of predicted pseudoranges (themselves computed from the available receiver and satellite positions). If the relative bit boundaries are determined successfully, the bit boundaries for all satellites can be aligned within the receiver and bit synchronization can be done using all information at once. So, rather than doing bit synchronization in each individual channel as in conventional methods, collective bit synchronization combines multiple satellites together to provide extra processing gain, and improve the detection rate of bit boundary positions. The requirements for the receiver s initial position and time are not overly stringent, as will be discussed below, and is achievable in many practical applications. A demonstration of bit boundary alignment at the receiver among all satellites is shown in Figure 5.1. The figure shows the transmission of the n th to the (n+2) th navigation data bits for various satellites. By design, the beginning of all data bits from all satellites are broadcast simultaneously (to within the satellite clock error), but are received at different times by the receiver due to the different distances to each satellite this is shown as time-shifted versions of the data bits between the satellites. These time shifts can be determined if pseudoranges are known, but pseudoranges cannot be calculated without knowledge of bit boundaries. However, if the relative distances to the satellites are known, these time shifts can still be compensated. In the figure, the 150

170 data bit sequence from Satellite i is shifted and denoted as Satellite i. As shown in more detail below, the magnitude of the time shift is a function of the integer number of code periods (i.e., milliseconds for GPS L1 C/A) between the receiver and satellite and the sub-code period portion that is available from the tracking loop. Figure 5.1: Demonstration of bit boundaries alignment among all satellites within the receiver In order to determine the relative bit boundary positions between satellites, the millisecond integer ambiguities in the predicted pseudoranges need to be resolved. An effective way to solve the millisecond integer ambiguities has been shown in Van Diggelen (2009) in the context of coarse-time navigation and is summarized below. First, the predicted pseudorange of the satellite is given by th i sv Rx ˆ xˆ xˆ c dt i i i d i c M z c dt d i i i i (5.1) 151

171 where x ˆ sv i is the estimated satellite position; ˆ Rx x is the estimated position of the user; c is the speed of light; dt is the receiver s clock bias; sv Rx d is the error in xˆ x ˆ caused by the error in the a priori position and time; i i M i is the millisecond integer ambiguity in the range between the i th satellite and the user; z i is the measured sub-millisecond pseudorange (i.e., it is related the tracking loop s code phase estimate); i is the measurement errors (including atmospheric errors and thermal noise). In this thesis work, the 1 st satellite is arbitrarily chosen as the reference and its millisecond integer ambiguity is calculated by making cm1 z1 close to 1 ˆ, and thus it is estimated as Mˆ round ˆ z c (5.2) Then the pairwise differences of the millisecond integer ambiguities (between, say, the satellite and the 1 st satellite) can be determined by th i c M i zi c M1 z1 cdt d cdt d ˆi i i ˆ1 1 1 (5.3) Finally the millisecond integer ambiguity of the i th satellite can be estimated as 152

172 i 1 1 i i 1 M ˆ round c M z z ˆ ˆ c (5.4) The experience from coarse-time navigation suggests that the relative millisecond integer ambiguities can always be solved if the errors of the initial receiver position and clock are less than 100 km and 1 min respectively (Van Diggelen 2009), which should be possible in many cases After aligning the data bits from the satellites, the proposed collective bit synchronization algorithm is a process to combine some or all satellites likelihood functions (the sum of the absolute values of cross-correlation used for conventional ML bit synchronization) in (2.11) and detect navigation bit boundary positions together. Hence, the collective bit synchronization algorithm can also be named as collective ML bit synchronization. Assuming the millisecond integer ambiguities have been solved using the process described above, the relative bit boundary positions between the i th satellite and the 1 st satellite can be determined by the pairwise differences of the integral part of the predicted pseudoranges (i.e., millisecond integer ambiguities). As such, the bit boundary position of the i th satellite is given by mod b, i b,1 i 1 b c l l M M T T (5.5) This means all satellites likelihood functions can be shifted to align with the bit boundary position of the 1 st satellite. By shifting and summing all satellites likelihood function, the bit boundary position of the 1 st satellite can be obtained from Nsv ˆ lb,1 arg max S f l d,i b,i Mi M (5.6) 1 lb, 1[1: M] i1 153

173 where S f is the likelihood function in (2.11) shifted by M i M1 lb,i M d,i i M1 points. Figure 5.2 shows a demonstration of the process using only two satellites, where the correlation output function from equation (2.11) of the i th satellite needs to be shifted left six milliseconds (points), in order to align with the 1 st satellite. Once this is done and the two likelihood functions are summed a new likelihood function for collective bit synchronization is obtained. Finally the bit boundary position of the i th satellite can be obtained by shifting back from the bit boundary position of the 1 st satellite, and is thus estimated by b, i b,1 i 1 b c lˆ lˆ M M mod T T (5.7) As noted above, the time shifts in Figure 5.1 are also a function of the relative sub-code periods of the satellites. However, these values do not appear explicitly in the above equations because, by definition, the correlator outputs in (2.6) are output at code boundaries where the sub-code period portion is effectively zero (to within the sample period). 154

174 Figure 5.2: Cross-correlation output of one navigation data bit in collective bit synchronization 5.2 Tests Description In order to assess the performance of collective bit synchronization, three tests are used. In all cases, only the GPS L1 C/A code signal was used Monte Carlo Simulation The first test is Monte Carlo simulations based on the signal model given by Equation (2.6). A total of 10,000 trials were performed to generate the ideal results for assessment. The Monte Carlo simulations assume no tracking errors in the correlator outputs (i.e., 0, 0 ), and that the bit transitions happen with a probability of 50%. The Monte Carlo simulations are used to assess the theoretically ideal performance of collective bit synchronization. f d 155

175 5.2.2 GNSS Simulator Test The second test is the same dataset introduced in Section 2.3. The GNSS simulator was configured to generate one hour of data with various power levels. There are totally 12 satellites in view in this test, and each satellite was assigned a specific power in the range of 15 db-hz to 40 db-hz (repeated for convenience in Table 5.1). No multipath was simulated. Although somewhat contrived, this scenario, which contains a mix of weak signals and strong signals, approximates the case under dense foliage or in an urban canyon. Table 5.1: Signal power assigned to each satellite in the GNSS simulator test (signal power remained constant throughout the test) Satellite No. C/N 0 [db-hz] Satellite No. C/N 0 [db-hz] Field Test The third test is a vehicular field test conducted under dense foliage near the University of Calgary. The dataset is same as the one introduced in Section The test trajectory is repeated for convenience in Figure 5.3 and an image captured along the test route is shown in Figure 5.4. The C/N 0 estimated by GSNRx of all satellites in view in the dense foliage test are shown in Figure 5.5, in which some signal power values fluctuate markedly. 156

176 Figure 5.3: Field test trajectory near the University of Calgary Figure 5.4: Dense foliage environment in the field test 157

177 Figure 5.5: C/N 0 of satellites in the field test estimated by GSNRx In both GNSS simulator and field tests, the data were collected using the National Instruments PXI-5600 front-end driven by an OCXO. Table 5.2: Front-end parameters used for collecting GNSS data in two tests Value (MHz) Parameter GNSS Simulator Dense Foliage Test Intermediate Frequency Sampling Rate (I/Q) Bandwidth Monte Carlo Test Result As shown in Equation (5.6), by shifting and summing all satellites likelihood function, the collective bit synchronization algorithm is expected to improve the SSR. Given a signal power 158

178 value (i.e., C/N 0 ) and the number of bits (i.e., data duration) used for generating the crosscorrelation in (2.11) of each satellite, the processing gain of the collective bit synchronization approach is only a function of the number of satellites. To this end, Figure 5.6 shows the performance of collective bit synchronization as a function of signal strength for different numbers of satellites, where all satellites are assumed to have the same received power. These results are generated by considering only 20 ms of data (i.e., equivalent to one data bit). From the results, it is noticed that even for high C/N 0 values, the SSR tends to 50%. This makes sense because the probability of having a bit transition in any 20 ms period is 50% (as per the simulation parameters), and if there are no bit transitions present, the algorithm will fail (i.e., it will not detect a bit transition). In other words, for a single satellite, the collective bit synchronization algorithm degenerates to the normal ML bit synchronization. However, by combining four satellites in collective bit synchronization, a marked improvement in SSRs can be viewed over the one satellite case. By further increasing the number of satellites, e.g., to 11 in Figure 5.6, the SSRs are further improved. These results confirm the validity of the collective bit synchronization algorithm. It can also be concluded that more combined satellites with same data period will result in a higher processing gain. Assuming all satellites are identical in power levels, the benefits coming from the increment of combined satellites are similar to those by increasing the number of bits for each satellite. However, whereas this requires the traditional approach to use more data, the collective bit synchronization does not have this drawback, and this will be further discussed later. 159

179 Figure 5.6: Performance of collective bit synchronization as a function of signal strength for different numbers of satellites when using one data bit at a time. Figure 5.7 shows the performance of collective bit synchronization when using ten bits (i.e., 0.5 s of data). For all satellite combinations, the ten-bit scenario shows improvement in SSR over the one-bit scenario in Figure 5.6. Given a SSR value, e.g., 90%, collective bit synchronization with 11 satellites has 8 db sensitivity improvement over the single satellite case. A detailed sensitivity improvement as a function of SSR for different number of satellites is shown in Figure 5.8. As the desired SSR increases, the sensitivity improvement with 11 satellites also increases, from around 8 db to 25 db. 160

180 Figure 5.7: Performance of collective bit synchronization as a function of signal strength for different numbers of satellites when using ten data bits at a time. 161

181 Figure 5.8: Sensitivity improvement as a function of SSR for different number of satellites when using ten data bits at a time 5.4 GNSS Simulator Test Result In the Monte Carlo simulation test, only the combination of satellites with same signal power levels was discussed. However, in real signal challenged environments, weak signal and strong signal are usually mixed. This should provide greater advantage for collective bit synchronization used in such environments, because the performance will be improved by the presence of stronger signals. As such, it is unnecessary for weak signals to increase the number of bits used in bit synchronization. In order to process the simulator data, the collective bit synchronization algorithm was implemented in the software-based GNSS receiver platform GSNRx. In order to assess bit synchronization performance, the receiver was configured to restart the bit synchronization 162

182 process as soon as it completed its previous attempt. All of the bit synchronization outcomes (i.e., success or failure) are recorded (true data bits are available from the simulator). Using one hour of data, there are about 2,000 and 500 bit synchronization attempts when using 100 bits (two seconds) and 400 bits (eight seconds) of data, respectively. As summarized in Table 5.1, the GNSS simulator was configured to generate signals from 12 satellites with various power levels. Figure 5.9 shows the performance of traditional ML bit synchronization (i.e., single-satellite detection) as a function of signal strength for different numbers of data bits in the hardware GNSS simulator test. Compared to Figure 5.7, it is noted that the performance can be worse than the Monte Carlo simulation results due to the imperfect tracking of code phase and carrier Doppler in this case. Details about the impacts of code phase and carrier Doppler errors on bit synchronization can be found in Ren & Petovello (2014a). It is shown in Figure 5.9 that in order to achieve an SSR close to 100%, an 18 db-hz signal needs at least 400 bits (eight seconds) for synchronization. However, as shown in Figure 5.10, the collective bit synchronization by combining 12 satellites together only requires two bits (i.e., one bit transition, or 40 milliseconds) and provides an SSR of 100% for all satellites (C/N 0 ranges from 15 db-hz to 40 db-hz). This is considered as a major benefit of collective bit synchronization, which is in the mixed signal power channel, the bit synchronization can be achieved for the signal as low as 15 db-hz within 40 milliseconds. 163

183 Figure 5.9: Performance of traditional ML bit synchronization as a function of signal strength for different navigation data bit numbers in the hardware GNSS simulator test 164

184 Figure 5.10: Successful synchronization rate for all satellite when using the collective bit synchronization with different numbers of data bits 5.5 Field Test Result After assessing the performance of collective bit synchronization as a function of different signal power levels in the GNSS simulator test, this section directly evaluates collective bit synchronization for different satellites in a vehicular field test. In order to do this, two satellites (PRN-09 and PRN-25) are analyzed here. The elevation angles of PRN-09 and PRN-25 are 42 and 10, respectively. Correspondingly, the latter s signal is more easily blocked and attenuated in the dense foliage environment. The estimated mean power of PRN-09 is in the midst of five strongest satellites (averaged C/N 0 = 43.8 db-hz), therefore it is chosen as the representative of satellites with relatively strong signals, and PRN-25 is a relatively weak signal satellite (averaged C/N 0 = 26.8 db-hz). 165

185 Figure 5.11 shows the performance comparison of traditional ML bit synchronization and collective bit synchronization for the strong satellite PRN-09 when using different durations of data bits. It can be viewed that in order to achieve an SSR close to 100% using the traditional ML bit synchronization approach, at least 25 bits should be used. However, the collective bit synchronization with only two bits of each satellite can achieve an SSR of 100%. This means for a relatively strong signal satellite the collective bit synchronization can detect bit boundary positions 10 times faster than the traditional ML bit synchronization, on average. Figure 5.11: Performance comparison of traditional ML bit synchronization and collective bit synchronization for the strong signal satellite (PRN-09) Figure 5.12 shows the performance comparison of traditional ML bit synchronization and collective bit synchronization for the weak signal satellite PRN-25. It can be viewed that the SSR is only about 65% even when 400 bits have been used in the traditional ML bit synchronization. 166

186 However, the collective bit synchronization with only two bits of each satellite can achieve an SSR of 100%. This means for a relatively weak signal satellite the collective bit synchronization can detect bit boundary positions more than 200 times faster than the traditional ML bit synchronization. This also indicates collective bit synchronization improves the bit synchronization of weak signal satellites more significantly. Figure 5.12: Performance comparison of traditional ML bit synchronization and collective bit synchronization for the weak signal satellite (PRN-25) 5.6 Summary This chapter proposes a collective bit synchronization approach for weak GNSS signals using multiple satellites. The validity of collective bit synchronization has been confirmed using Monte Carlo simulation, a GNSS simulator test and a vehicular field test under dense foliage in suburban areas. 167