Contractual Date of Delivery: T (months) Actual Date of Delivery: 11/12/2014 Olivier Julien (ENAC)

Transcription

1 MULTIPOS D4.6 Version 1. Report on the state-of-the-art on GNSS receiver processing, urban GNSS signal integrity monitoring in urban environment, user case definition and user requirements Contractual Date of Delivery: T + 16 (months) Actual Date of Delivery: 11/1/14 Editor: Olivier Julien (ENAC) Author(s): Enik Shytermeja (ENAC) Participant(s): Axel Garcia-Peña (ENAC), Olivier Julien (ENAC) Work package: WP4 Version: 1. Total number of pages: 41 Page 1 (41)

2 1. Document Control Version Details of Change Review Owner Approved Date 1. First version inserting all contributions Olivier Julien x 11/1/14 from ESRs Page (41)

3 . Executive Summary This document describes the achievement of the ESR 4.4, Enik Shytermeja hosted by Ecolé National de l Aviation Civile (ENAC), contributing to the WP4 (Hybrid positioning technologies) of the MultiPos ITN consortium during his first year of research work. An important part of this research work was dedicated to the state-of-the-art study regarding the past and current work carried out by different research institutions or companies in the field of Integrity monitoring in urban constrained environments and the study of available GNSS users/system performance requirements and standards dedicated to urban-oriented GNSS applications. Several studies have addressed the problematic of integrity monitoring in urban environments, but neither proper methodologies nor urban user requirements and standards are publicly available in this field, therefore increasing the relevance of this PhD study in the domain of GNSS application in urban environment, characterized by a significant market growth, in terms of potential users and revenues but also in terms of new applications and services, such as the case of new Intelligent Transport Systems (ITS) services being ready for deployment. This report is organized as follows: Section 4 describes the general PhD context with an emphasis on the problematic in urban environment and more specifically the objectives of this research consisting in the development of innovative techniques capable of ensuring the robustness and integrity monitoring of an integrated GPS/Galileo receiver and Inertial Navigation System (INS) sensors in a constrained urban environment; Section 5 gives a summarized description of the state-of-the-art study on novel and robust GNSS receiver signal processing techniques and on the development of innovative GNSS integrity monitoring techniques suited to urban navigation constraints along with the identification of the targeted application; Section 6 is dedicated to the technical contributions of ESR 4.4 during the first year of the PhD research comprising the proposal and development of a novel step-by-step technique consisting of an integrated single frequency GPS/Galileo receiver + low-cost MEMS sensors, aided by a video Fisheye camera for Non Line-of-Sight (NLOS) satellites detection and finally implementing an urban-oriented integrity monitoring technique. The detailed description of this proposed approach was published in the conference ICL-GNSS 14, held in Helsinki, Finland on 4 6 June 14; Section 7 describes the definition of the targeted GNSS-based urban environment applications, along with their classifications from the intregrity requirements perspective, focusing on the performance requirements in GNSS-based Electronic Toll Collection (ETC) systems; In Sections 8 and 9, the main conclusions and future work goals are detailed, respectively; Section 1 provides a summarized table of all the events attended by ESR 4.4 in the framework of this PhD research, including: the ITN Marie Curie MULTIPOS training events, the academic and professional courses and workshops organized by ENAC or Institute National Polytechnique de Toulouse and the conferences/journals publications. In the Section 11 the references cited in this report are given in details. Page 3 (41)

4 Authors Partner Name Phone / Fax / ENAC Enik Shytermeja Phone: shytermeja@recherche.enac.fr ENAC Axel Garcia-Peña Phone: garcia-pena@recherche.enac.fr ENAC Olivier Julien Phone: ojulien@recherche.enac.fr Page 4 (41)

5 Table of Contents 1. Document Control.... Executive Summary List of Acronyms and Abbreviations ESR 4.4: General PhD Context The Problematic in Urban Environment State-of-the-Art Technical Contributions during the first year of PhD Fisheye Camera technique for Non Line-of-Sight (NLOS) GNSS signals rejection Vector Frequency/Delay Lock Loop (VDFLL) algorithm VDFLL Position State formulation via Extended Kalman Filter (EKF) EKF Time Update or A priori prediction equations EKF Measurement update equations VDFLL Pseudo-range state formulation via Extended Kalman Filter (EKF) Errors characterization of the MEMS Sensors GNSS/INS MEMS Hybridization techniques Tightly Coupled GNSS/INS MEMS Integration Tightly Coupled GNSS/INS implementation Final Remarks on the GNSS/INS MEMS Tight Coupling technique Ultra-tight GNSS/INS MEMS Coupling technique Coherent Deep integration GNSS/INS MEMS architecture Federated Coherent Deep GNSS/INS MEMS architecture Non-coherent Deep GNSS/INS MEMS architecture Final remarks on the Ultra-tight or Deep GNSS/INS integration Multipath Mitigation techniques Integrity Monitoring algorithm Receiver Autonomous Integrity Monitoring algorithm (RAIM) algorithm Isotropy-Based Protection Level (IBPL) technique Definition of targeted urban environment applications Performance Requirements in GNSS-based ETC systems Conclusions Future Work Events attended Page 5 (41)

6 11. References List of Acronyms and Abbreviations Abbreviations ENAC Ecole Nationale de l Aviation Civile GMV GMV Aerospace and Defense SA Unipersonal EC European Commission GSA European GNSS Agency FDE Fault Detection and Exclusion mechanism INS Inertial Navigation System FLL Frequency Lock Loop PLL Phase Lock Loop DLL Delay Lock Loop LS Least Squares solution KF Kalman Filter EKF Extended Kalman Filter IMU Inertial Measurement Unit SiS GNSS Signal-in-Space ABAS Aircraft-based Augmentation System SBAS Satellite-based Augmentation System GBAS Ground-based Augmentation System PL Protection Level LMSCM Land Mobile Multipath Satellite Channel Model DLR German Aerospace Centre (Das Deutsche Zentrum für Luft- und Raumfahrt) CIR Channel Impulse Response LOS Line-of-Sight NLOS Non-Line-of-Sight ITS Inetelligent Transport Systems CWI Continuous Wave Interference UHF Ultra-High Frequency VHF Very-High Frequency DVB-T Digital Video Broadcasting Terrestrial VDFLL Vector Frequency/Delay Lock Loop PVT Position, Velocity and Time solution MEMS Micro-Machined Electro-Mechanical System neml Narrow Early-Minus-Late ΔΔ Double Delta HRC High Resolution Correlator PAC Pulse Aperture Correlator ELS Early-minus-Late Slope MGD Multiple Gate Discriminator POCS Projection Onto Convex Sets Page 6 (41)

7 4. General PhD Context ESR 4.4: Enik Shytermeja (ENAC) Research Topic: GNSS Integrity Monitoring in Urban Environment Employer and PhD enrolment: Ecole Nationale de l'aviation Civile (ENAC), Toulouse, France Start Date: September 1 st 13 Planned secondment: GMV (6 months) The overall aim of this PhD thesis consists in the development of innovative techniques capable of ensuring the robustness and integrity monitoring of an integrated GPS/Galileo receiver and Inertial Navigation System (INS) sensors in a constrained urban environment. More specifically the objectives of this PhD research are the following: Identification of the targeted application and the determination of its performance requirements in terms of accuracy, integrity etc; Development of advanced receiver signal processing techniques capable of discarding erroneous measurements at the source prior to the position computation; Implementation of suitable GNSS/INS hybridization techniques; Application of innovative Integrity monitoring techniques performing the Fault Detection and Exclusion (FDE) mechanism for the provision of accurate confidence level on the position in urban environment. In the last decade, Global Navigation Satellites Systems (GNSS) have gained a significant position in the development of Urban Navigation applications and associated services. A major concern of the constant growth of GNSS-based urban applications is related to the quality of the positioning service, expressed in terms of accuracy, availability and continuity of service but also of integrity provision, ensuring that the application requirements are met [1]. In dense urban environments, such as city centres, traditional GNSS signal processing techniques are incapable of providing an accurate and reliable position solution due to the frequent blockage of the Line-Of-Sight (LOS) signals and the presence of diffractions/reflections of the transmitted signal (multipath). These effects severely affect the pseudo-range and Doppler measurements, used by a GNSS receiver for the position computation. Therefore, advanced GNSS signal processing techniques are necessary to mitigate the undesired effects introduced from the urban environment. It is thus preferable to go toward a multi-constellation GNSS (GPS + Galileo) receiver for measurements redundancy, coupled with the use of complementary sensors. However, this approach might only manage to provide an accurate positioning but still does not ensure a measure of trust of the positioning solution. GNSS integrity monitoring is defined as a measure of trust that can be placed in the correctness of the information supplied by the system, including the ability of providing timely and valid warnings or alerts to the user when the requirements are not assured to be met []. The concept of integrity has been initially developed in the framework of Civil Aviation, as being a Safety-of-Life (SoL) application, where very stringent navigation performance requirement should be met. GNSS integrity monitoring is not only strictly related to the civil aviation domain, but it is also applied to the GNSS-based urban navigation applications. Recently, a great attention of the European Commission (EC) and European GNSS Agency (GSA) has been given to the development of several research projects focused on the road transportation sector, as in [3], [4]. In this framework, the European Road Federation Union (ERF), based on the integrity requirement perspective, classifies road applications in two main categories such as [5]: Safety of Life (SoL) applications, where the main representatives are the Advance Driver Assistance Systems (ADAS) and Emergency Services Management (ESM) and Liability Critical (LC) applications including Road User Charging (RUC), Pay per use insurance pricing, On street parking pricing and so on. However, the integrity monitoring concept in Road User applications, was firstly introduced and developed within the framework of Liability Critical applications, where Electronic Toll Collection (ETC) constitutes its main representative. In ETC systems, an erroneous positioning leads to an incorrect user charging. Therefore, in order to meet the integrity requirements, GNSS has been recognized as the most flexible and cost-effective technology to be embedded in ETC systems. Several studies have addressed the problematic of integrity monitoring in urban environments but neither proper methodologies nor urban user requirements and standards are publicly available in this field. For this reason, the aim of this work conducted in the first year of the PhD research, was dedicated to the determination of the accuracy and integrity requirements of the ETC application, being our targeted urban Page 7 (41)

8 application and also, the proposal of an innovative step-by-step approach that is capable of providing integrity monitoring of a hybridized GNSS/MEMS/Video system in urban canyons. The logic behind our proposed innovative step-by-step approach, capable of providing integrity monitoring of a hybridized GNSS/MEMS/Video system in urban canyons, will be detailed in the technical contributions section The Problematic in Urban Environment The urban environment presents several challenges to GNSS signal reception and therefore, severely degrading the positioning accuracy. In our research study, the main identified problems arising from the urban environment conditions are the following: i. Multipath: defined as the reception of reflected or diffracted echoes (from the ground, buildings, foliage, lampposts and so on) of the desired Line-of-Sight (LOS) GNSS signal, as illustrated in Figure 4-1; ii. iii. Attenuation or blockage of the GNSS LOS signal: is a phenomenon arising due to the partial or total obstruction of the GNSS LOS from the urban environment characteristics. Interference: occurring due to the presence of a wide class of interfering signals, falling within the GNSS frequency bands. The dominant source of interference is related to the reception of continuous wave interference (CWI) signals, generated from Ultra-High Frequency (UHF) and Very-High Frequency (VHF) TV transmitters, Digital Video Broadcasting Terrestrial (DVB-T) system and so on. a) b) Figure 4-1 Illustration of: a) Multipath scenario through the reception of reflected echoes (in red) and direct LOS signal (in green); b) Attenuation or blockage of the GNSS LOS signal [9] The consequences of the above mentioned urban environment error sources either on the received signal or at the receiver correlator output w.r.t. the ideal reception of a GNSS signal are given next. The mitigation of these consequences constitutes the initial step of the proposed solution. a. Distortion of the receiver s correlation function: between the received multipath-contaminated signal and the receiver s locally generated replica. In the GNSS context, this is the main consequence of multipath, affecting the signal code and carrier tracking accuracies, and thus introducing large degradations to the pseudo-range accuracy and therefore producing an inaccurate position solution [1]. b. Only NLOS signals reception: occurs when the direct LOS GNSS signal is blocked and thus, only reflected signals are received. This results in a pseudo-range measurement error and consequently a decrease of the positioning accuracy. c. Incongruent GNSS pseudo-range measurements: occurring when a set of pseudo-range measurements, provided from one or more GNSS satellites, are not congruent with the other ones. This event is the outcome of the three error sources mentioned above. These severe urban conditions lead to large measurement errors and consequently to inaccurate positioning. In the worst case, the GNSS positioning capability can be unavailable. Therefore, it is evident that advanced signal processing techniques are necessary to mitigate these undesired effects in order to ensure the accuracy and availability of the position solution. Page 8 (41)

9 5. State-of-the-Art The first phase of this research project was dedicated to the state-of-the-art study on robust GNSS receiver signal processing techniques and on the development of innovative GNSS integrity monitoring techniques suited to urban navigation constraints along with the identification of the targeted application (pedestrian or vehicular user) and user platform consisting of an integrated GPS/Galileo receiver with additional inertial INS sensors. In this context, the state-of-the-art research was split into the following sub-phases: GNSS Receiver Signal Processing consisting of: o Study of the overall GNSS systems structure (such as GPS, GLONASS, Galileo, Compass) with an emphasis on the GPS and Galileo signals structures, modulations and modernization plan; o Analysis of the GNSS receiver architecture, including GNSS signals acquisition and code/carrier tracking procedure, focusing mostly on the structure and parameters description of the Frequency Lock Loop (FLL), Phase Lock Loop (PLL) and Delay Lock Loop (DLL); o Exploitation of multipath characteristics and models, mostly focusing on the study of multipath mitigation approaches relying on GNSS code correlation techniques. This is due to the fact that multipath constitutes one of the main positioning error sources in urban environment, introducing significant degradation of the positioning accuracy; o Examination of the possible interference sources in urban environment, notably Continuous Wave Interference (CWI), generated by the Digital Video Broadcasting Terrestrial (DVB-T) system and also the study of the frequently used interference mitigation techniques; o Mathematical description of the Least Square solution and the Kalman filter configuration, with the later one being the chosen approach that addresses the problem of states estimation of the discrete-time controlled GNSS positioning process; o Analysis of the Vector Tracking algorithm, representing an advanced GNSS signal processing technique due to its robustness exhibited in highly dynamics scenarios. In fact, the extensive study of this technique constituted the crucial part of this first state-of-theart sub-phase. Inertial Sensors and GNSS/INS Hybridization techniques: comprising the following tasks: o Description of Inertial Measurement Unit (IMU), capable of providing an independent position from GNSS systems and their propagation channels and consisting of accelerometers (measuring the specific force f of the vehicle along its sensitive axis) and gyroscopes (providing the body rotational motion ω across each sensitive axis); o Analysis of the Inertial Navigation System (INS) mechanization equations, resolving the accelerometer/gyroscope measurement from the INS body frame (b-frame) to the chosen navigation frame; o Error characterization of the Micro-Machined Electro-Mechanical System (MEMS) sensors, which represent the most widely used INS sensors for vehicular and pedestrian navigation due to their small size (in order of cm) and low production cost (price from 1 $); o Description of odometer sensors that are devices or instruments mounted on the wheels of the vehicles, providing positioning and overall motion of the vehicle and their deterministic and stochastic error modeling; o Video Fisheye camera technique implementation, capable of performing GNSS NLOS o rejection and erroneous GNSS measurements exclusion prior to the position solution; Detailed analysis of the GNSS/INS integration techniques, yielding many benefits due to the complementary nature of these two systems. The state and process model configuration of the three GNSS/INS hybridization techniques were evaluated: a. Loosely Coupled GNSS/INS system: where the GNSS and INS position and velocity estimates are compared and the resulting differences form the measurement are input to the Kalman filter; b. Tightly Coupled GNSS/INS system: for which, a comparison between the GNSS measurements of pseudo-range and pseudo-range rate and the INS estimates of these quantities, is conducted; c. Deep or ultra-tightly Coupled GNSS/INS system: where the GNSS signal tracking function and the GNSS/INS integration are combined in a single algorithm. GNSS Integrity Monitoring: ensuring a measure of trust of the navigation solution through the provision of timely alerts when the user requirements cannot be met, includes the following reviewed subjects: Page 9 (41)

10 o o o Panorama of the GNSS Integrity monitoring techniques implemented in the civil aviation domain such as ABAS, SBAS and GBAS, with a focus on GNSS Signal-in-Space (SiS) performance requirements and on the Fault Detection and Exclusion (FDE) mechanism; Analysis of RAIM (Receiver Autonomous Integrity Monitoring) algorithms, that are measurement rejection techniques, widely employed in civil aviation domain, run autonomously by the GNSS receiver. Our attention was dedicated to the adaption of the RAIM technique utilization in the GNSS/INS hybridized architecture in urban environment and to the protection levels (PL) computation; Examination of Isotropy-Based Protection Level (IBPL) integrity monitoring algorithm, specifically developed for the Liability Critical land applications and quietly differing from the other RAIM based integrity techniques. It is important to highlight the fact that RAIM and IBPL constitute the two potential candidate techniques for the final proposed integrity monitoring approach in urban environments. GNSS Propagation Channel in urban and sub-urban environments: dedicated to the treatment of GNSS signals reception over fading multipath channels by developing a statistical characterization of the GNSS channel through the Rayleigh and Rice fading distributions: o o Description of the possible types of GNSS fading channels statistical models along with their multipath intensity profile; Exhaustive analysis of the deterministic and statistic parameters of the wideband land mobile multipath channel model (LMSCM), developed in MATLAB by DLR [8], was performed in order to apprehend the logic behind the generation of complex time-variant multipath echoes. Definition of targeted applications and user platform: focused on the definition of the urban application and its operational needs, for which our proposed user integrity monitoring platform will be required: o o Detailed analysis of the road applications classification according to the integrity requirements perspective, where the main representative is constituted by the Electronic Toll Collection (ETC) system; An elaborated investigation of the relation between the GNSS-based ETC requirements and also and the integrity monitoring parameters, such as: integrity risk, probability of false alarm, probability of missed detection and so on; 6. Technical Contributions during the first year of PhD To overcome the urban environment constraints, strongly affecting the positioning performance and to guarantee a satisfying level of trust of the PVT solution, the development of a novel step-by-step technique consisting of an integrated GPS/Galileo receiver + low-cost MEMS sensors, aided by a video Fisheye camera and implementing an urban-oriented integrity monitoring technique is proposed. Figure shows the schematic structure of the proposed technique for the provision of GNSS positioning and integrity monitoring in dense urban environment. The rationale for the algorithm lies on the implementation of different sub-techniques, each aiming at the mitigation of the three major error sources in urban environments, identified in the previous section. The starting point of the approach is the inaccurate position solution as a consequence of the urban environment constraints, described in Section 6.1. In the next step, four different techniques are employed for each specific error source. Firstly, the Fisheye camera has been chosen to detect GNSS satellite masking and exclude the corresponding measurements from the position solution. Secondly, a simple and efficient multipath mitigation technique will be utilized to mitigate the multipath at the GNSS receiver correlator output. Then, Vector Delay/Frequency Lock Loop (VDFLL) is implemented as a robust technique using a centralized approach to conduct joint signal tracking and position determination. In parallel, GNSS/MEMS hybridization is performed for measurement redundancy and consistency checking, knowing that inertial low-cost MEMS are capable of providing an independent position from the GNSS system and propagation channel. The novelty of our approach consists in the integrity monitoring provision of a vectorised position solution, output of the VDFLL navigation filter. To provide a measure of trust on the position solution, two integrity monitoring techniques are taken into consideration, namely: the Receiver Autonomous Integrity Monitoring (RAIM) algorithm and Isotropy-Based Protection Level (IBPL) technique. Page 1 (41)

11 Figure 6-1 Schematic structure of the proposed step-by-step GNSS Integrity monitoring architecture in dense urban environment Fisheye Camera technique for Non Line-of-Sight (NLOS) GNSS signals rejection In dense urban environment, the main contribution to GNSS errors is related to the lack of reception of the LOS GNSS signal combined with the reception of only NLOS GNSS signals. As a direct consequence, a degraded position accuracy is observed due to the introduced error on the pseudo-range measurements. Many techniques have been developed and implemented to overcome this source of error, with the majority of them relying on signal processing techniques. In our project, the implementation of Video Fisheye camera technique to perform GNSS NLOS rejection and exclude the erroneous pseudo-range measurements at the source was proposed. The Fisheye camera, characterized by a large field of view (typically 18 o ), is mounted on the vehicle roof and oriented upwards to capture the sky images while the vehicle is moving along its trajectory. This technique, used for GNSS satellite detection and firstly presented in [6], is based on image processing techniques aiming as illustrated in Figure 4-. Figure 4- Block diagram of LOS GNSS satellites detection using the Fisheye camera. The Fisheye camera technique for GNSS satellite detection proposed in [6] is based on the following steps, which are illustrated in the block diagram in Figure 4-: 1. Image data acquisition: constitutes the starting point of the video Fisheye technique, in which the consecutive images from the Fisheye camera mounted on the vehicle roof are acquired;. Image processing phase consisting of four successive steps that perform the pixels classification in two clusters such as sky and non-sky (represented by buildings, vegetation, lampposts etc). Moreover, the reclassification of the uncertainty regions, which are regions considered as clear sky but located in a non-sky area (building or foliage region) and vice-versa, is carried out; 3. Satellites repositioning: representing the key phase of the video Fisheye technique, is achieved by overlapping or merging the GNSS satellites sky plot from the GNSS receiver on board of the vehicle, containing the GNSS satellite positions in terms of azimuth and elevation angles and the simplified Fisheye image. Page 11 (41)

12 In Figure 6-3, the Fisheye image processing steps based on the LOS/NLOS criterion using the different color representation are illustrated, where [6]: In green: satellites providing direct LOS signals and therefore their measurements are accepted for the position solution; In red: satellites providing blocked signals; In orange: satellites providing reflected signals; In our proposed solution, both satellites providing blocked and reflected GNSS signals will be excluded from the tracking and position computation algorithm. 4. Identification of LOS/NLOS satellites: is the output of this technique, where the identification of the GNSS NLOS satellites is performed and followed by the exclusion from the position calculation of the measurements provided by these satellites. This will significantly reduce the number of corrupted GNSS measurements present in the tracking loop and therefore, providing a simplification of the GNSS integrity monitoring algorithm. Figure 6-3 Results of the image processing (left to right: acquired image, classified image into two classes (sky and non-sky) with satellites projection and the calculated horizon line) [6] 6.. Vector Frequency/Delay Lock Loop (VDFLL) algorithm Vector Tracking algorithm, first introduced in [11], represents an advanced GNSS signal processing technique due to its high performance in lower carrier-to-noise power density (C/N o) ratios and in higher dynamics scenarios w.r.t. traditional GNSS tracking loops [1]. As previously stated in the previous section, NLOS pseudo-range measurements and multipath errors are a direct and main consequence of urban environment. Therefore, traditional GNSS signal tracking techniques, which track the GNSS signals independently (scalar mode), sometimes fail to cope with these severe cases as tracking is possible. This is the reason why, in our approach, we propose the implementation of a VDFLL, capable of performing a joint GNSS signal tracking. In comparison to traditional receivers, where all the received GNSS signals are processed by parallel independent blocks, in the vector tracking technique they are collectively processed and the navigation filter outputs are used as a feedback loop to pilot the code and carrier tracking loops. The simplified block diagram for the scalar and vector tracking architecture, is shown in Figure 6-4. In the basic scalar-tracking architecture, shown in Figure 6-4 a), the down-converted and filtered GNSS received signal samples are passed to each tracking channel in parallel mode and further input to a signal processing function where Doppler removal and correlation tasks are performed. The correlator outputs are then passed to an error determination function consisting of code, frequency and phase discriminators and loop filters. Finally, the filtered error estimates enter in the local signal generator for the generation of the estimated Doppler frequency and local code replica. The outputs of each channel tracking loop, are fed into the navigation filter to perform the position, velocity and time solution. Page 1 (41)

13 a) b) Figure 6-4 Simplified block diagram of the: a) Basic Scalar-Tracking architecture and b) Basic Vector-Tracking Architecture [13] The benefits of scalar-tracking technique are the implementation s simplicity and the provision of high level of robustness that is gained by not having one tracking channel corrupt another tracking channel. However on the downside, the fact that the signals are inherently related via the receiver s position and velocity is completely ignored. Furthermore, the possibility for one tracking channel to aid another channel is unfeasible. On the contrary, in the vector-tracking architecture the individual tracking loops are eliminated and effectively replaced by the navigation filter, as depicted in Figure 6-4 b). In this architecture, the code and phase NCOs are controlled by calculating code phase, code rate and Doppler frequency of the tracked satellite based on the most recent PVT solution. Based on the correlation output, the code and frequency discriminators estimate the code phase and Doppler frequency difference between the true GNSS signals parameters w.r.t. to the predicted ones. In [11], it is stated that the vector tracking approach exploits the coupling between the receiver s dynamics and the dynamics seen by the tracking loops. Moreover in VDFLL, the signal tracking and navigation solution tasks are combined in a single step through the use of Least Square (LS) or Extended Kalman Filter (EKF) to simultaneously track the PRN code delays and the carrier frequencies. There are two possible ways to design the navigation filter in the Vector Tracking approach, as illustrated in Figure 6-5: Position-state formulation configuration: where the states of the filter are the receiver s position, velocity, and clock states. Pseudo-range-state formulation: where the states of the central filter are the pseudo-ranges and pseudo-range rates of the available satellites. In Figure 6-5, for each channel 1 to M, the pseudo-range and pseudo-range-rate discriminators output, denoted by ρ and ρ -, respectively, are fed to the central navigation (EKF) filter. Figure 6-5 Block diagram of VDFLL tracking and navigation filter implementation with two possible configurations of the EKF filter Page 13 (41)

14 The feedback to the code and carrier Numerical Control Oscillators (NCOs), for the two given configurations, is obtained from the EKF-computed pseudo-ranges and pseudo-range rates based on the most recent receiver s position and velocity estimate. In the proposed algorithm, the chosen implementation is the position-state formulation [1] due to its feasibility for further extension of VDFLL to ultra-tight (deep) integration GNSS/MEMS. This can be achieved by replacing the navigation filter with an integrated GNSS/INS filter and also adding the MEMS error states. The advantages and drawbacks of VDFLL technique with respect to scalar tracking are summarized in Table 6-1. In the tight and ultra-tight coupled integration, the vector states will consist of inertial sensor (in our case MEMS) position, velocity error states along with GNSS clock offset and drift biases. The performance assessment of VDFLL implementation in ultra-tight coupling was investigated in [13]. Table 6-1 VDFLL performance characteristics w.r.t. the scalar tracking technique VDFLL Performance Characteristics Advantages Disadvantages Robustness to momentary blockages (tracking performed even under no received signal energy condition) ; No signal re-acquisition performed when the signals energy is re-presented; Signal tracking achieved with less signal energy (C/N); Tracking improvement in weak-signal and jamming environments; Robust architecture to high receivers dynamics; Performance improvement due to: o o Exploitation of over-determined system of equations; Channels coupling and accumulative signal power; Feasibility to ultra-tight GNSS/INS integration. Increased receiver s design complexity; Not feasible for of shelf GNSS receivers (no access to the correlators outputs). Initialization from Scalar tracking is a necessary requirement; Channel fault coupling; Higher processing load and complexity; VDFLL Position State formulation via Extended Kalman Filter (EKF) The states of the central Kalman filter in this configuration are the receiver s position and clock states. For the VDLL, only the position and clock bias states are required, while for the VDFLL in addition the velocity and clock drift states are required. In the model described below, an EKF will be employed to estimate user position, velocity, clock bias and drift, which will feed the code and carrier NCO blocks to drive the code and carrier generation, respectively. The standard Kalman equations can be subdivided into two blocks. The first one named time update or a priori prediction is responsible for predicting the user position knowing the receiver transition model; the second block named as measurement model is in charge of correcting the predictions by exploiting measurement information. The final optimal estimate is obtained through a weighted mean of the a priori estimate and the measurement correction; depending on the filter gain, either the prediction or the correction are considered more in the final estimation [11] EKF Time Update or A priori prediction equations In the EKF, in comparison to the Kalman filter, the distributions (or densities in the continuous case) of the various random variables are no longer normal after undergoing their respective nonlinear transformations. The EKF is simply an ad hoc state estimator that only approximates the optimality of Bayes rule by linearization. The time update equations of the EKF filter are given below: X i = F i 1 X i 1 + B i w i P i = F i P i 1 F T T i + W i Q i 1 W i (6-1) The estimated position, velocity and clock terms are predicted over time T sec using the following equation: Page 14 (41)

15 X i = F i 1 X i 1 + B i w i (6-) Where: X i is the a priori estimate of the state at the current time step or known as the filter state vector ; F i represents the system transition matrix describing the dynamics of the user platform and clock; X i 1 is the a posteriori estimate of the state (from a previous time step i - 1); w i is the Gaussian random driving variable or the uncertainties affecting the model. The states of the central Kalman filter in the position-state formulation differ depending on the architecture and the application scenario, where in dynamic scenarios, for the VDFLL, velocity along the three axes and clock drift is included in the states vector. The vector states of the EKF are [1]: X i = δx i δy i δz i δb i,clk [ δx i δy i δz i ] δb i,clk = Position Error, X axis Position Error, Y axis Position Error, Z axis Clock Bias Velocity Error, X axis Velocity Error, Y axis Velocity Error, Z axis [ Clock Drift ] (6-3) The transition matrix is given as: 1T 1T 1T F i = 1T [ 1] (6-4) Where: b is the bias in [m] due to the clock misalignment between receiver and satellites; b is the clock drift in [m/s]; T = t i t i 1 is the time interval between two consecutive estimations The process noise in the system comes from two sources, receiver dynamics and the clock [1]. w i = w x w y w z w b [ w d ] (6-5) and T T T 1T B i = [ 1] (6-6) Where: Page 15 (41)

16 w x w dyn = [ w y ] receiver s noise vector and w clk = [ w b w ] error of the local oscillator (6-7) w d z The changing dynamics of the receiver are modeled by the noise vector w dyn. The noise sources (w x,w y,w z) drive their respective velocity states corresponding to a continuous Wiener process velocity model. The terms (w b, w d) in w clk represent the clock phase and frequency error of the user s local oscillator, expressed in units of meters and meters per second, respectively. Noise vector w i is a Gaussian noise with zero mean and variance Qi. The statistics for the two main components of the overall noise vector w i are expressed in Eq (6-7) Eq (6-13) [1]. For the noise vector w dyn, the expectance or mean and variance are as follows: E{w dyn } = [ ] (6-8) and σ x T Q dyn = E{w dyn w dyn } = [ σ y ] (6-9) σ z While for the noise vector w clk, the statistics are: And E{w clk } = [ ] (6-1) Q clk = E{w clk w T clk } = [ σ b σ ] (6-11) d Thus, we can express the statistics of the overall noise vector from the two noise contributions described above, as follows: E{w i } = [ ] (6-1) And the variance as: Q i = E{w i w i T } = σ x σ y [ σ z σ b σ d ] (6-13) The values for σ x, σ y and σ z are chosen based on the expected level of receiver dynamics, while on the other hand σ b, σ d take into consideration the clock oscillator errors, as detailed in the Appendix C. Returning to the second statement of the time update EKF equations, we have: Where: P i = F i P i 1 F i T + W i Q i 1 W i T (6-14) P i is the a priori estimate error covariance matrix at the time step i; P i 1 is the a posteriori estimate error covariance matrix at time step i-1; W i is the Jacobian matrix of partial derivates of f with respect to the w process noise at step i; Q i 1 is the process noise covariance matrix at step i The discrete time process noise covariance matrix for the receiver dynamics process noise is shown in Eq. (6-15): Page 16 (41)

17 Where: p Q dyn Q x Q y = [ ] (6-15) Q z σ x T3 Q x = 3 [ σ x T σ y T3 Q y = 3 [ σ y T σ z T3 Q z = 3 [ σ z T σ x T σ x T ] σ y T σ y T ] σ z T σ z T ] The position noise spectral densities terms σ x, σ y and σ z are all set equal to a value of 4 m s 4. Varying the magnitude of the process noise from to 5 m/s4 had a negligible affect on the results of the covariance analysis [1]. The discrete time process noise covariance matrix for the clock process noise is shown in Eq. (6-16): Where: Q p clk = [ ] (6-16) Q c Q c = [ σ b T + σ d T3 3 σ d T σ d T σ d T ] EKF Measurement update equations It is important to highlight the fact that the position and velocity error states are in the ECEF frame and the clock bias and drift errors are in the units of meters and m/sec, after dividing by the speed of light c. In this approach, the actual estimates of the user s states are maintained outside of the EKF algorithm. At each measurement update, the errors in the states are estimated using the pseudo-range and pseudo-range-rate residuals supplied by each channel. The estimated state errors are then added to the state estimates outside the filter [1]. Afterwards, the state vector is reset to zero. The EKF measurement update equations are as follows: K i = H i T (H i P i H i T + V i R i V i T ) 1 x i = x i + K i (z i Hx i ) P i = (I K i H i )P i (6-17) Where: K i is the Kalman gain matrix at time step i; P i is the a priori estimate error covariance at time step i; R i is the measurement noise covariance matrix at time step i; V i is the Jacobian matrix of partial derivates of the non-linear function h in the measurement equation w.r.t to the measurement noise v i Page 17 (41)

18 As can be easily seen from Eq (6-17), the first task during the measurement update is the computation of the Kalman gain, K i, which is chosen in order to minimize the a posteriori error covariance. An obvious drawback of EKF compared to the LS solution is related to the difficulty in determining the process noise covariance Q, as we typically do not have the ability to directly observe the process that we are estimating. As described above, the pseudo-range and pseudo-range-rate residuals are used in the measurement model. At the end of every integrate and dump operation, the correlator outputs are used by the code phase and frequency discriminator to produce a code phase and Doppler frequency residual. The code phase error is scaled to convert it to units of meters and similarly, the Doppler frequency residual is scaled to convert it to units of meters per second. The scaled code phase error represents the error in the predicted line-of-sight range from the satellite to the receiver plus the receiver clock bias (pseudo-range residual) and the scaled Doppler frequency is the error in the predicted line-of-sight velocity from the satellite to the receiver plus the receiver clock drift (pseudo-range-rate residual). The states of the filter are updated with the residuals from each channel. The relationship between the states of the filter and the pseudo-range and pseudo-range-rate residuals is as follows: Where: z i = H i x i + v i (6-18) z i is the Nx1 vector of the available measurements as follows: z i = [δρ 1,, δρ n, δρ 1,, δρ n ] T H i is the measurement model matrix; v i is the observation noise process; a x,1 a y,1 a z,1 1 a x, a y, a z, 1 H i = a x,n a y,n a z,n 1 [ a x,n a y,n a z,n 1] (6-19) In Eq (6-19), the variables a x,n, a y,n and a z,n are the components of the line-of-sight unit vector from the user to the N-th satellite [1]. The statistics for the measurement noise vector v are shown in Eq (6-): E{v} = Nx1 E{vv T } = R v (6-) After processing the residuals, the pseudo-ranges and pseudo-range-rates are predicted for the next integration interval using the updated state estimates. Eq (6-) shows that in the position-state VDFLL formulation the satellite signals are coupled together through the states of the filter. Errors in the predicted pseudo-ranges and pseudo-range-rates are corrected by applying corrections to the states of the filter [1]. The variance of the corrections to the predicted pseudo-ranges is given by Eq. (6-1) [1]: E{( ρ E{ ρ })( ρ E{ ρ }) T = σ v W N N (6-1) T W N N = H N 4 (H N 4 H N 4 ) 1 T H N 4 The variance of the corrections is found by multiplying the measurement noise variance (σ v ) by the diagonal elements of the matrix W. It is assumed that variance of the measurement noise (σ v ) is related to C/N by the formula shown in Eq. (6-) [Crane, 7]: Where: (c f σ chip ) v = (T 1 (C/N )/1 ) + (c f chip) (6-) 4T 1 (C/N )/1 c is the speed of light in (m/s); f chip is the GNSS signal carrier frequency in Hz; Page 18 (41)

19 T is the measurement update time set to ms, equal to the correlation time interval; C/N is the satellite channel carrier-to-noise ratio. The variances of the estimated pseudo-ranges from the scalar tracking method are equal to the variance of the measurement noise (σ v ). For the vector tracking method, the variance of the estimated pseudo-ranges is: σ ρ = (T 1 ( C N 1 ) + T 1 C N 1 ) ( c πf c T ) (6-3) The formula in Eq. (D.3) is strictly related to the choice of the frequency lock loop (FLL) discriminator employed, which in our case is the non-coherent Early minus Late (EML) VDFLL Pseudo-range state formulation via Extended Kalman Filter (EKF) As previously described, the states of the EKF in this configuration are the pseudo-ranges and pseudorange-rates for all available satellites and the error states of the EKF are as follows: The state dynamics of the filter are as follows: δρ 1 δρ 1 = SV 1 Pseudorange Error SV 1 Pseudorange rate Error δρ N [ δρ N] SV N Pseudorange Error [ SV N Pseudorange rate Error] (6-4) X i = AX i 1 + B ρ dyn w dyn + B ρ clk w clk (6-5) Where: k x x A = [ x k ] and k = [ 1 x ] (6-6) x x k ρ B dyn a x,1 a y,1 a z,1 = [ a x,n a y,n a z,n] w x and w dyn = [ w y ] (6-7) w z I x B ρ clk = [ ] and w dyn = [ w b w ] (6-8) I d x The noise terms in Eq (6-8) are the same as those shown in the Position state formulation. The states of the filter are updated with the residuals from each channel. The relationship between the states of the filter and the pseudo-range and pseudo-range-rate residuals is shown below: z i = I NxN x i + v i (6-9) It can be noted that the signals from different satellites are not coupled through the state transition matrix or the measurement update equations but through the process noise. However, the steady state covariance matrix of the prediction errors for both formulations of the VDFLL are identical. Thus, the two algorithms yield the same performance with respect to the pseudo-range and pseudo-range-rate prediction errors Errors characterization of the MEMS Sensors Page 19 (41)

20 In challenging environments, such as urban canyons, GNSS receivers suffer from the reception of incongruent, multipath- and interference-contaminated GNSS measurements. Therefore, our proposed solution relies on the integration of the GNSS system with the MEMS sensors, capable of supplying an independent position from GNSS systems and their propagation channels. In the past years, MEMS have been rapidly developing to be the most widely used INS sensors for positioning and navigation due to their small size (in order of cm), reduced production cost (price from 1 $), related to the silicon fabrication process. MEMS sensors are provided in different formats, such as: MEMS accelerometers (measuring the specific force f of the vehicle along its sensitive axis), MEMS gyroscopes (measuring the body rotational motion ω, across each sensitive axis, w.r.t.. the inertial reference frame) or MEMS Inertial Measurement Unit (IMU) containing both - or 3-axes accelerometers and gyroscopes along with the magnetometers measuring the heading of the vehicle. Therefore, a standalone position from the MEMS sensor can be provided from the use of two gyroscopes and one accelerometer. This will be reflected in a simplification of the EKF state vector, containing less bias states. MEMS low performance, as investigated in [7], makes them unsuitable to be used autonomously as a primary mean for positioning and navigation. Therefore, GNSS/MEMS integration yields many benefits, due to the complementary nature of these two systems, expressed in the following terms: MEMS are characterized by a short-term accuracy while on the other hand, GNSS system provides long-term positioning accuracy; In contrast to GNSS, MEMS performance is not affected from the surrounding environment and propagation channel; Contrary to the GNSS system, MEMS INS can be considered as an offline system immune toward interference and jamming. In the framework of GNSS/MEMS hybridization, MEMS errors characterization is of great interest. This is related to the fact that the inertial sensor biases will be integrated in the state vector of the Kalman filter and are a necessary requirement for the integrity monitoring algorithm. The single-axis MEMS gyroscope measurement models, consisting of both deterministic and random errors components, is expressed in the following form [14]: where: ω = ω + b cons + b run to run + b in run + (S cons + S random )ω + Nω + ε(ω) (6-3) ω denotes the single-axis gyroscope measurement; ω denotes the gyroscope true angular rate in ( o /s); b cons is the constant portion of the bias removed by the calibration process in units of ( o /s); b run to run is a deterministic bias express in ( o /s), slightly increasing its value every time the sensor is switched on; b in run is a stochastic bias occurring due to the changing environment conditions and in mostly modelled as a Gauss Markov process noise; S cons and S random are the constant and random portions of the MEMS gyroscope scale factor errors, which are the ratio of a change in output to the change in the intended input to be measured. S const = (s const,x, s const,y, s const,z ) is the vector mathematically denoting the deterministic part of the scale factor bias, expressed in parts per million (ppm) or % unit; N representing the non-orthogonalities or cross-misalignment errors, expressed in ppm or %; ε(ω) is a stochastic bias representing the MEMS sensor noise and its modeling is strictly datasheet related (e.g. Random Walk, First-Order Gauss Markov noise etc). Similarly, the MEMS accelerometer measurement model, is given by: f = f + b cons + b random + S f + (S cons + S random )ω + Nf + δg + ε(ω) (6-31) Page (41)

21 where: f denotes the single-axis accelerometer measurement; f denotes the accelerometer true specific force in (m/s ); b cons is the constant portion of the bias removed by the calibration process in units of (m/s ); S cons and N represent the same error sources as in (6-3); b random is the remaining random portion of the bias modelled as a Random Walk noise; S denotes the nonlinear scale factor bias in (ppm or %), being referred to as the anisoelastic bias (or g dependent bias) expressed in (m s g ) and has a minor contribution to the overall accelerometer bias; δg denotes the anomalous gravity deviation from its theoretical value, expressed in (m/s ). Recalling the MEMS sensor measurement model given in (6-3) and (6-31), it is possible to classify MEMS error contribution based on their nature into deterministic and random biases (errors). This classification is very helpful for a better understanding of the possible types of MEMS errors affecting our measurements and also to identify the best procedures or models to minimize and preferably remove their contributions from the position solution, as summarized in Table 6-. MEMS Errors (Biases) Table 6- MEMS sensors Error modelling and Removal procedure Symbol Unit Errors Nature Minimization or Removal procedures Deterministi Random Deterministi Random Constant bias b cons Gyro: o /s Accelero: m/s Run-to-run bias In-Run stability bias Scale factor bias c x b run to run Gyro: o /s Accelero: m/s x x b in run 1σ value x Gyro: o /s Accelero: m/s S cons ppm or % x x S random 1σ value x (negligible ) N ppm or % x x Nonorthogonalities or crossmisalignment bias Anisolastic S m s g x x bias Gravity δg m/s x x deviation Sensor Noise ε 1σ value x x c x x x (negligible ) Page 1 (41)

22 6.4. GNSS/INS MEMS Hybridization techniques The main reason of GNSS/INS integration yields on the benefits of their mutual operation, due to the fact that these systems are complementary to each-other in many aspects, described below: GNSS provides a high long-term position accuracy with bounded errors, while on the other hand, INS provides a short-term position accuracy with unbounded long-term errors due to the integration process [9]; GNSS solution availability is vulnerable toward unintentional and intentional interference (jamming and spoofing); while on the other hand INS can be treated as an offline system and thus immune toward interference; GNSS contain mostly high-frequency errors, whereas INS errors are larger at low frequency (related to the fact that the integration performed by the mechanization equations is, effectively, a low-pass filter); GNSS positioning accuracy is affected from several factors such as: satellite geometry, atmospheric effects, changing in propagation conditions, user clock instability, multipath, interference that lead to GNSS signal s interruptions especially when operating in urban environments [7]. Three main classes of GNSS/INS integration techniques can be defined, such as [1]: A Loosely Coupled GNSS/INS system in which the GNSS and INS position and velocity estimates are compared and the resulting differences form the measurement inputs to the Kalman filter; A Tightly Coupled GNSS/INS system in which a comparison between the GNSS measurements of pseudo-range and pseudo-range rate and the INS estimates of these quantities is conducted; A deep or ultra-tightly Coupled GNSS/INS system in which the GNSS signal tracking function and the GNSS/INS integration are combined in a single algorithm. Our attention is focused on the detailed comparison between the tight and ultra-tight coupled GNSS/INS integration techniques, outperforming the former loose coupled approach especially in low C/N and dynamic urban environment. Emphasis will be given toward the analysis of the three possible and different Ultra-tight coupled GNSS/MEMS INS hybridization approaches, due their feasibility of implementation after the VDFLL vector tracking module Tightly Coupled GNSS/INS MEMS Integration In the Tightly Coupled integration, all the processing is realized centrally in a single Kalman filter and thus this technique is referred to as the centralized integration architecture [4]. In the Tightly Coupled scheme, the separated GNSS and INS filters are not anymore present but all the raw GNSS measurements are passed directly to the combined GNSS/INS Kalman filter. The Tightly Coupled GNSS/INS integration architecture is depicted in Figure. Page (41)

23 Figure 6.7 Tightly Coupled GNSS/INS integration architecture [4] From the figure above, we can note the presence of a single centralized Kalman filter, whose inputs are the pseudo-ranges and pseudo-range rates obtained from the GPS receiver and the predicted ones computed using the GNSS satellite positions and velocities from the ephemeris and user s position and velocity from the INS measurements. The outputs of the Kalman filter are the INS error estimates, which in the next step are combined with the position, velocity and attitude information derived from the INS navigation processor. The last step of the Tightly Coupled algorithm is the feedback loop, depicted in the dashed red line, which consists in sending back the INS error estimates from the KF to the INS unit with the objective of correcting the INS states vector. The advantages and disadvantages of the Tightly Coupled technique compared to the Loosely Coupled one, will be detailed in the last sub-section Tightly Coupled GNSS/INS implementation As described in the previous section, a unique Kalman filter is present in the Tightly Coupled scheme, which processes the GNSS raw pseudo-ranges and pseudo-range rates (or Doppler measurements) along with INS observations. The goal of the GNSS/INS filter is to provide the estimation of the INS system errors, aiming to the correction of the INS solution and compensation of the INS errors. The same approach for the definition of the states vector, as in the case of Loosely Coupled technique, will be followed. However, since in the Tightly Coupled architecture all the processing is centralized in the GNSS/INS filter, the state vector is augmented with two more parameters representing the receiver clock states [4]. GNSS/INS EKF Process Model As for the Loosely Coupled integration, we can still distinguish three possible ways of writing the INS state vector. The only difference relies in the fact that in the Tightly Coupled case, we should augment the INS state vector with the two receiver clock states. Thus, we can write the following relations: 9 states Loose coupling 11 states Tight coupling 15 states Loose coupling 17 states Tight coupling 7 states Loose coupling 9 states Tight coupling * In fact, 7 states in the Loose coupling (or 9 states in Tight coupling) are reduced into 1 and 3 states, for the respective cases; due to the fact that the turn-on bias is constant during a run and thus can be neglected (6-3) The receiver clock states dynamics can be written as follows: δ(c δt offset) = δ(c δt drift ) + η offset (6-33) Page 3 (41)

24 δ(c δt drift) = η drift Where: η offset is the clock offset driving noise with spectral density q offset ; η drift is the clock drift driving noise with spectral density q drift. The clock errors spectral densities are calculated, as follows [4]: q offset = c h q drift = c π h (6-34) where h and h represent the Allan variance parameters describing the clock errors. For simplicity, only the 3-states process model of the GNSS/INS EKF for the Tightly Coupled technique, obtained by just adding the two receiver clock states w.r.t. the EKF model in the Loose coupling method. δr e δv e ε e δb a δb g δs a = δs g δ(cδt offset) [ δ(cδt drift) ] 3 3 I e N 3 3 (Ω ie ) 3 3 e F (Ω ie e ) (R e b ) (R e b ) ( 1 τ a ) ( 1 τ g ) ( 1 τ sa ) [ δr e δv e ε e δb a δb g δs a δs g δ(cδt offset ) [ δ(cδt drift ) ] ( 1 τ sg ) (R e b ) (R e b ) I [ I I I ] η 3 1 a 3 1 η 3 1 g 3 1 η ba η bg η sa η sg η offset 1 [ η drift ] 1 ] Where: δx e = [δr e δv e ε e ] T is the state vector consisting of: o Position errors δr e = [δφ δλ δh] T ; o Velocity errors δv e = [δv E δv N δv U ] T in East-North-Up coordinates; o Attitude errors ε e = [ε E ε N ε U] T in East-North-Up coordinates; S a and S g are the accelerometer s and gyroscope s scale factor errors, respectively; δt offset is the GNSS receiver clock offset, expressed in [sec]; δt drift is the GNSS receiver clock drift, expressed in [sec ]; (6-35) Page 4 (41)

25 F rr F rv F rε F = [ F vr F vv F εr F εv F vε ] is the dynamic matrix; F εε e R b is the rotation matrix from body frame to ECEF frame; e is the skew symmetric matrix of the Earth rotation rate relative to the inertial space; Ω ie 3 1 G = [ R e b δf b ] is the shaping matrix; R e b δw b w = [δf b δw b ] T is the forcing vector, consisting of errors in the measured specific forces and angular rates, respectively; δx n = e e [δr δv ε e ] T, where the dots denote the time derivatives, while the superscript e and b denote the ECEF frame and body frames, respectively; η a = [η ax η ay η az ] T are the accelerometer noises for the x, y and z axes respectively with spectral density vector q a ; η g = [η gx η gy η gz ] T are the gyroscope noises for the x, y and z axes respectively with spectral density vector q g. η sa = [η sax η say η saz ] T are the accelerometer scale factor bias terms for the x, y and z axes respectively, modelled as a first-order Gauss-Markov process with spectral density vector q sa ; η sg = [η sgx η sgy η sgz ] T are the gyroscope scale factor terms for the x, y and z axes respectively, modelled as a first-order Gauss-Markov process with spectral density vector q sg. τ ai = [τ ax τ ay τ az ] T are the accelerometer s bias correlation time intervals for the x, y and z axes respectively; τ gi = [τ gx τ gy τ gz ] T are the gyroscope s bias correlation time intervals for the x, y and z axes respectively; τ sai = [τ sax τ say τ saz ] T are the accelerometer s scale factor bias correlation time intervals for the x, y and z axes respectively; τ gi = [τ sgx τ sgy τ sgz ] T are the gyroscope s scale factor bias correlation time intervals for the x, y and z axes respectively; GNSS/INS EKF Measurement Model The measurement model of the GNSS/INS EKF filter in the Tightly Coupled has the following form: Where: δz = H δx + η (6-36) δz is the measurement vector consisting of the differences between the GNSS and INS pseudoranges and pseudo-range rates, as follows: δz = [ PR GNSS PR INS ] (6-37) PR GNSS PR INS o o PR GNSS and PR GNSS denote the pseudo-ranges and pseudo-range rates, respectively, obtained by using the GNSS information; PR INS and PR INS denote the predicted pseudo-ranges and pseudo-range rates, respectively, obtained by using the INS-derived information; δx is the INS error state vector augmented with the two receiver s clock states; H is the measurement matrix, relating the pseudo-ranges and pseudo-range rate errors to the error states expressed as follows: H = [ H(ρ) H(ρ ) ] (N 1 +N ) 8 (6-38) o o N 1 and N denote the number of available pseudo-ranges and pseudo-range rates, respectively; H(ρ) is the matrix relating the pseudo-range observations to the error states and is given as: Page 5 (41)

26 H(ρ) = ρ (1) ρ (1) ρ (1) 1 r x r y r z ρ (N 1) ρ (N1) ρ (N1) 1 [ r x r y r z ]N1 8 (6-39) o H(ρ ) is the matrix relating the pseudo-range observations to the error states and is given as: (1) ρ (1) ρ (1) (1) (1) (1) ρ ρ ρ ρ 1 r x r y r z v x v y v z H(ρ ) = (N ρ ) (N ρ ) (N) (N) ρ ρ (N ρ ) (N ρ ) 1 [ r x r y r z v x v y v z ]N 8 (6-4) Where: - - r x,y,z v x,y,z is the partial derivate with respect to the position error vector; is the partial derivate with respect to the velocity error vector; ρ = (x u x s ) + (y u y s ) + (z u z s ) + c δt offset + ε ρ Where: - (x u, y u, z u ) represent the user s position in ECEF coordinates; - (x s, y s, z s ) represent the satellite s position in ECEF coordinates; - δt offset represents the GNSS receiver clock bias; - ε tot represents all the errors affecting the pseudo-range measurement; ρ = (x u x s ) (x u x s) + (y u y s ) (y u y s) + (z u z s ) (z u z s) + c (x u x s ) + (y u y s ) + (z u z s ) δt offset + ρ Where: - (x u, y u, z u ) represent the user s position in ECEF coordinates; - (x s, y s, z s ) represent the satellite s position in ECEF coordinates; - δt offset = δt drift represents the GNSS receiver clock drift; - ρ represents all the errors affecting the pseudo-range rate measurement; Final Remarks on the GNSS/INS MEMS Tight Coupling technique In the Tight Coupling architecture, GNSS pseudo-range and pseudo-range rates denoted as the GNSS observables and INS measurements, are merged together in a unique filter to provide a single navigation solution. Recalling the Loosely Coupled scheme, the principle of operation in the Tight Coupling architecture is quite different, related to the fact that in Loosely Coupled integration the PV estimation for both GNSS and INS measurements was computed separately and prior to the GNSS/INS EKF blending filter. On the contrary, in the Tightly Coupled architecture, there is not a Position and Velocity computation made by the GNSS and INS filters, but only a merging of raw data, such as pseudo-range and pseudorange rates from the GNSS receiver with the INS measurements. This is the reason why, the Loose Coupling techniques is mostly referred in literature as the decentralized GNSS/INS hybridization technique [4], [41]. Advantages of Tight Coupling 1. Increased positioning accuracy and availability: on the contrary to the Loose Coupling technique, a reliable positioning is provided even when the number of satellites in view is less than four. This is related to the redundancy of information provided from the GNSS and INS measurements merged together in a single KF filter, thus mutually aiding each-other for the user s position Page 6 (41)

27 computation. This is the main reason why Tight Coupling is widely used for positioning in urban environments;. Continuous signal tracking in high-dynamic scenarios: due to the aid provided to the GNSS code and carrier tracking loops through the feedback of the position and velocity information from the central EKF filter [5]. 3. Increased system s robustness toward interference and jamming: related to the narrowing of the tracking loop bandwidths and thus reducing the noise and increasing the system s robustness toward interference and jamming [5]; 4. Decreased process noise: due to the presence of a unique Kalman filter KF in this architecture, the process noise is added only once. While in the Loose Coupling scheme with two separate filters, the process noise was added twice; 5. Superior GNSS fault detection and exclusion (FDE): relies on redundancy of information provided from the two sensors GNSS and INS, thus increasing the reliability of the test statistic. Disadvantages of Tight Coupling 1. Increased complexity and slower processing time: this disadvantage is linked to the presence of a single centralized filter merging the information provided from the two GNSS and INS sensors with an increased nr of states. This leads to a slower processing time with respect to the Loose Coupling architecture;. Increased fault influence: related to the dependency of the GNSS and INS units, where a fault present in one of the sensors, will affect the other sensor s performance [5]. In the implementation of Tight Coupling technique for land user navigation, we should take into consideration velocity and height constraints, specified in greater detail in [5], [6] Ultra-tight GNSS/INS MEMS Coupling technique The architecture and principle of operation of ultra-tight or deep coupled GNSS/INS integration technique quietly differs from the other previously mentioned integration architectures, since in the Deep Coupling the GNSS signal tracking and INS/GNSS integration functions are combined in a single estimation filter [45]. The closed-loop deep GNSS/INS integration architecture is depicted in Figure 6.8. Figure 6.8 The closed-loop deep GNSS/INS integration architecture [7] Page 7 (41)

28 In the Deep Coupling architecture in Figure 6.8, we can distinguish that the key role in the deep coupling algorithm is played from the INS/GNSS Integration Kalman filter and the GNSS NCO control algorithm. The closed-loop ultra-tight GNSS/INS integration algorithm steps are as follows: 1. GNSS receiver performs the correlation between the incoming GNSS signals and the internally generated GNSS signal replicas. The code and carrier Is (In phase) and Qs (Quadrature) correlators outputs are fed to the central integration Kalman filter [7];. GNSS/INS Integration Kalman filter: merges the GNSS measurements, constituted by the Is and Qs correlator outputs with the INS measurements, consisting in the position, velocity, attitude and INS sensor biases provided from the IMU unit. The outputs of the Kalman filter are the GNSS estimates sent to the GNSS NCO block for the generation of the NCO commands and the INS corrections fed to the INS block through a closed feedback loop. A detailed description of the Kalman filter process and measurement model will be the objective of the following section; 3. GNSS NCO control algorithm: the aim of this module is the generation of the NCOs control commands, expressed in the form of code and carrier frequency offsets, using the satellite ephemeris parameters, satellite and receiver clock error estimates, ionosphere and troposphere delay estimates along with the corrected INS solution. Based on the processing approach of the Is and Qs correlator outputs, Deep GNSS/INS algorithms can be divided in two main categories: Coherent algorithm: separated in two subdivision such as centralized and federated coherent algorithms. In the coherent algorithms, the GNSS correlator outputs Is and Qs are fed directly to the Kalman filter as measurements; Non-coherent algorithm: where the GNSS correlator outputs Is and Qs are firstly passed to code and carrier discriminator functions before being sent to the Kalman filter Coherent Deep integration GNSS/INS MEMS architecture Taking into consideration the GPS data channels and that the correlator outputs Is and Qs are directly fed to the Kalman filter, it is thus a necessary requirement the generation of Is and Qs at 5 Hz equal to the navigation data bits rate [7]. The centralized coherent deep integration GNSS/INS architecture is shown in Erreur! Source du renvoi introuvable.. Figure 6.9 The Centralized Coherent Deep GNSS/INS integration architecture In this approach, the reference and received signal carrier frequencies must be synchronized to maintain signal coherence within the receiver s correlators during the integration interval [7]. However, the reference-signal carrier phase offsets are estimated as Kalman filter states, thus enabling the carrier phase tracking without the necessity to keep aligned the reference and received signal phase. The main disadvantages of the coherent deep GNSS/INS integration taking use of a centralized Kalman filter are the following: Page 8 (41)

29 High processing load due to the large measurement vector with 6 inputs/signal, namely IE, IP, IL, QE, QP, QL per tracked channel. Reference signal carrier phase offsets need to be estimated as Kalman filter states; Fast update rate related to the fact that in the case of GNSS data channels, the Is and Qs correlators outputs need to be updated at the same rate as the navigation bits at 5 Hz. These represent the main reasons why a coherent deep integration algorithm using a centralized Kalman filter is not mostly used, thus moving toward the use of a federated Kalman filter, as described in the following subsection Federated Coherent Deep GNSS/INS MEMS architecture The federated coherent deep integration architecture, show in Erreur! Source du renvoi introuvable., takes use of a bank of tracking Kalman filters receiving as inputs the Is and Qs measurements at a 5 Hz rate. Figure 6.1 The Federated Coherent Deep GNSS/INS integration architecture The data flow in the federated coherent deep GNSS/INS integration is described in the following steps: 1. One pre-filter for each tracked signal, performing the following tasks: a. Inputs the six dimension measurement vector from the GNSS receiver containing (I E, I P, I L, Q E, Q P, Q L); b. Outputs the two dimension vector containing the pseudo-range and pseudo-range rate innovations obtained from the carrier-frequency and code phase tracking error estimates at 1- Hz rate.. GNSS/INS integration Kalman filter: taking as inputs the pseudo-range and pseudo-range rate innovations. This process is nearly the same as the one used in tight-coupling. The main problem occurring in the federated coherent approach, closely related to its architecture, is the problem s flow from the tracking filters to the integration Kalman filter. However, this problem can be avoided by zeroing the code-phase and carrier frequency estimates when the measurements are output to the integration filter. This approach is referred to as the federated zero-reset (FZR) integration [7]. The main disadvantages of the coherent deep GNSS/INS integration taking use of a centralized Kalman filter are the following: 1. Knowledge of the reference-received signal carrier phase offset: needed to extract the code information from the I and Q measurements [7];. Low tracking capability in low C/N environments: due to the fact that carrier-phase tracking cannot be maintained at lower C/N environment (the lower C/N threshold is 15 db/hz). Page 9 (41)

30 Non-coherent Deep GNSS/INS MEMS integration architecture The main difference between the coherent and non-coherent deep integration, is the presence of carrier and code discriminators in the data flow of the second approach, as depicted in Erreur! Source du renvoi introuvable.. Figure 6.11 The Federated Coherent Deep GNSS/INS integration architecture The data flow in the non-coherent deep GNSS/INS integration approach is summarized in the following steps: 1. Code and carrier frequency discriminators: compute the code and carrier discriminator outputs from the IS and QS samples. As in the case of the coherent algorithm, the input rate of the IS and QS measurements is at least equal to the navigation data rate in the case of GNSS data channels [7];. Summation and scaling: the averaging operation is used for two main reasons: a. Reduce the Kalman filter output rate: the measurement update rate is reduced from 5 Hz to 1-1 Hz; b. Reduce the measurement noise. While, the scaling operation performs the conversion from the code and carrier tracking errors to pseudo-range and pseudo-range rate estimation, through the Kalman filter s measurement matrix H. In weak signal environments, it is common to use a hybridized combination scheme of coherent and noncoherent deep integration algorithm. In this case, a switching function between the two modes needs to be defined. The main feature of the deep or ultra-tight integration algorithm, is the use of the I S and Q S correlators outputs to estimate the INS errors during the measurement process in the GNSS/INS Kalman filter. Though it is crucial to define the states measurement relationship, obtained from the relation between the I and Q estimations with the INS Position and Velocity data, through the frequency and phase errors. Navigation EKF Process Model The process model of the Kalman filter (KF) in the ultra-tight integration is identical to the one of the tight integration, described in Eq (6-41) - (). The state vector of the Kalman filter is composed of 3 states: 1 states for the INS quantities and states for the GNSS quantities, as shown in Table. In most applications, the INS scaling factor biases can be neglected, thus the states vector in Table 6-3 is now composed of 17 states. The state propagation matrix F along with the system noise covariance matrix Q are the same as for the tight coupling case, expressed in Eq (6-41) - (). Page 3 (41)