GNSS Multi-Receiver Vector Tracking

Transcription

1 1 GNSS Multi- Vector Tracking Yuting Ng, Student Member, IEEE and Grace Xingxin Gao, Senior Member, IEEE Abstract Accurate, reliable and robust localization is desirable for many navigation applications. Unfortunately, it is challenging for a single receiver to always provide accurate positioning solutions. In urban environments, intermittent signal availability leads to degraded signal tracking and position estimation of the single receiver. In addition, equipment malfunction of the single receiver results in inaccurate navigation solutions. This paper presents a deeply-coupled Multi- Vector Tracking (MRVT) architecture that improves the reliability and robustness of signal tracking and position estimation. MRVT jointly tracks signals received by multiple receivers, mitigating signal tracking disruptions, improving the reliability of localization in periods of intermittent signal availability. In addition, the MRVT receiver is more robust to equipment malfunctions than the single receiver. We implemented a MRVT receiver using commercial radio frequency front ends and our PyGNSS software. We experimentally validated the reliability of our MRVT receiver in periods of intermittent availability experienced in downtown San Francisco. Our MRVT receiver exhibited consistent signal tracking and position estimation as compared to vector tracking. In addition, we experimentally validated the robustness of our MRVT receiver to the failure of a single receiver. Index Terms Global positioning system (), global navigation satellite systems (GNSS), multiple receivers, vector tracking I. INTRODUCTION receivers, providing absolute position coordinates under all weather, platforms and visual conditions, are increasingly relied upon for urban navigation [1]. Unfortunately, a single receiver suffers from intermittent signal availability in urban environments, leading to signal tracking disruptions and position estimation challenges [2]. In addition, equipment malfunction of the single receiver results in inaccurate position solutions. To improve the reliability and robustness of localization, existing approaches include sensor fusion [3] with vision [4] and inertial measurements [5]. Instead of augmenting the single receiver with additional sensors, there is inherent potential in leveraging multiple receivers [6]. A. Related Work Existing approaches using multiple receivers include loosely-coupled and tightly-coupled architectures. A wellknown example with both loosely-coupled and tightly-coupled implementations is Differential (D) [7]. The looselycoupled implementation uses position differences while the tightly-coupled implementation uses pseudorange differences. The authors are with the Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. s: yng5@illinois.edu, gracegao@illinois.edu. Loosely-coupled/ tightly-coupled receiver architecture measurements / coordinates Nav Filter PVT no feedback, no improvement to signal tracking Antenna array processing of a controlled radiation pattern antenna precise calibration/ significant additional processing PVT Fig. 1. Existing approaches using multiple receivers and antennas: loosely-coupled or tightly-coupled receiver architecture that integrates at the coordinate or measurement level; antenna array processing of a controlled radiation pattern antenna. Adding to the vast work on tightly-coupled architectures, our prior work included integration of pseudorange measurements from multiple receivers using an Extended Kalman Filter (EKF) [8], an Unscented Kalman Filter (UKF) [9] and Probabilistic Graphical Models (PGM) [10], [11]. Tightlycoupled architectures, while improving the robustness of the final navigation solution, do not improve the performance of signal tracking within the individual receivers, as shown in Fig. 1. Disruptions in signal tracking lead to degraded measurements, adversely affecting the final navigation solution. To improve the reliability and robustness of signal tracking, other existing approaches used antenna array processing of controlled radiation pattern antennas (CRPA) [12]. Antenna array processing exploits the accurately known antenna array geometry to beamform [13] [15], increasing the signalto-noise ratio (SNR) of visible satellites, creating a combined signal equivalent to the output of a single high quality antenna. Antenna arrays, however, require precise calibration [16] or additional processing with significantly higher computational loads [17], as shown in Fig. 1. Bias errors would otherwise be introduced into the combined signal [16]. B. Our Approach and Contributions We propose Multi- Vector Tracking (MRVT) to improve the reliability and robustness of signal tracking and position estimation. MRVT is a deeply-coupled receiver architecture that jointly tracks the signals received by multiple receivers. Our MRVT receiver architecture is different from existing approaches in two ways. Unlike loosely-coupled and tightly-coupled architectures, our MRVT receiver architecture jointly tracks multiple receivers using feedback to vector tracking loops within individual receivers. MRVT is thus a deeply-coupled architecture that augments signal tracking. Unlike antenna arrays, our MRVT receiver does not

2 2 Multi- Vector Tracking (MRVT) deeply-coupled receiver architecture fuse information from multiple receivers Nav Filter PVT feedback for joint signal tracking Fig. 2. Our Multi- Vector Tracking (MRVT) architecture. Different from loosely-coupled or tightly-coupled architectures, MRVT jointly tracks signals received by multiple antennas. Unlike antenna arrays, MRVT does not require precise calibration nor significant additional processing. require precise calibration nor significant additional processing. An illustration comparing MRVT to existing approaches is shown in Fig. 2. Prior to this paper, our first iteration of MRVT [18] used an average navigation solution from multiple receivers as feedback. In addition, vector tracking within each receiver was implemented using an EKF with a constant acceleration motion model and a constant, heuristically specified process noise covariance. The coherent processing interval was 1 millisecond. Experiments were conducted in an opensky environment, using 4 Universal Software Radio Peripherals (USRPs), with timing signals split from 1 Chip Scale Atomic Clock (CSAC). Our second iteration of MRVT [19], [20] used a Minimum Mean Square Error (MMSE) combination of navigation solutions as feedback. In addition, the EKF implementation within each receiver was improved with a time-varying process noise covariance that addressed vehicle accelerations as process noise. The coherent processing interval was extended to 20 milliseconds. Additional sub-sample time synchronization was implemented in our PyGNSS software receiver. Using the previous experimental data, navigation solutions with reduced noise, increased reliability, and robustness was demonstrated. In this paper, we improve upon previous iterations and combine navigation solutions from multiple receivers using an EKF [21], [22]. Following navigation estimation in the individual receivers, we concatenate the states and state error covariances from multiple receivers into an overall measurement input vector and an overall measurement noise covariance input matrix for the overall EKF. We then use the state of the overall EKF as feedback to augment vector tracking within the individual receivers, closing the overall MRVT loop. We conducted further experiments using different equipment configurations and different experiment scenarios to evaluate our MRVT receiver architecture. We defined reliability and robustness as key performance criteria: consistent and accurate signal tracking and position estimation in periods of intermittent signal availability, signals Multi- Vector Tracking Vector Tracking Channel EKF Time Measurement Navigation Filter EKF Time Measurement PVT Fig. 3. MRVT block diagram showing joint signal tracking and position estimation using multiple receivers. Incoming signals on the left are jointly processed by the MRVT receiver architecture to produce an overall navigation solution on the right. Shown above is the improved architecture implemented in this paper. tolerant to equipment malfunctions resulting in degradation of the received signal, such as attenuation. The rest of this paper is organized as follows. We begin by detailing the MRVT receiver architecture in Section II. In Section III, we discuss our implementation and experiment results. Section IV summarizes the paper. II. MULTI-RECEIVER VECTOR TRACKING The MRVT receiver architecture consists of multiple receivers and an overall navigation filter, as shown in Fig. 2. Implemented within each receiver in the MRVT architecture is vector tracking. In vector tracking, multiple channels are jointly tracked through shared receiver states, typically via an EKF [23]. In MRVT, the receiver states of multiple receivers, estimated in the EKF measurement update, are fused to estimate shared multi-receiver states. The shared multireceiver states are also estimated using an EKF. Using an EKF improves the reliability of MRVT in periods of intermittent signal availability, while mitigating the effects of degraded receiver states on the joint signal tracking and navigation effort in the event of equipment malfunction. The shared multi-receiver states are then used as feedback to the EKF time update of multiple receivers, closing the MRVT loop. MRVT is thus a deeply-coupled joint signal tracking and position estimation architecture. Information integration and redundancy from multiple receivers lend MRVT its reliability and robustness [24]. A block diagram is given in Fig. 3. Section II-A describes vector tracking within individual receivers while Section II-B describes the deeply-coupled MRVT receiver architecture. In addition, Section II-C describes modifications to the MRVT receiver architecture when using unsynchronized receiver front ends. A. Vector Tracking Within Individual s Implemented within each receiver in the MRVT architecture is vector tracking, as shown in Fig. 4. We used the non-coherent Vector Delay and Frequency Lock Loop (VDFLL) [25], [26] with the following state vector: X : state vector of an individual receiver (1) = [ x, y, z, cδt, ẋ, ẏ, ż, c δt ] T

3 3 signal Correlator Code and Carrier Discriminators Channel Code and Carrier Phase Accumulations LOS Projections EKF Time Measurement PVT Fig. 4. Block diagram of the vector tracking sub-architecture within an individual receiver in the MRVT receiver architecture. where x, y, z and cδt are the three-dimensional (3D) position coordinates and clock bias in (m); ẋ, ẏ, ż and cδt are the 3D velocity coordinates and clock drift in (ms 1 ). The speed of light c is given as (ms 1 ). Other state notations used within this paper: X i : state vector of i th satellite, with N satellites in view X ECEF : state vector expressed in ECEF X ECI X x,y,z Xẋ,ẏ,ż X cδt X c δt : state vector expressed in ECI : position component of state vector : velocity component of state vector : clock bias component of state vector : clock drift component of state vector ECEF : Earth-Centered-Earth-Fixed reference frame ECI : Earth-Centered-Inertial reference frame The navigation filter is an EKF [27], [28], with a 2-step update process: measurement update producing receiver state corrections at epoch boundaries and time update predicting new receiver states, used to update the channel parameters, for the next epoch boundary. For the measurement update at epoch k, the input to the EKF is derived from code phase and carrier frequency residuals ( Φ code (chips), f carr (Hz)) measured by the code and carrier discriminators. These measurements, coming from multiple channels, are first scaled into pseudorange and pseudorangerate residuals ( ρ(m), ρ(ms 1 )), then concatenated to form the error input vector e to the EKF. The EKF measurement update equations at epoch k: e : error input vector (2) = [ ρ 1... ρ N, ρ 1... ρ N ] T W : error noise covariance input matrix (3) = diag{σ 2 ρ 1... σ2 ρ N, σ2 ρ 1... σ2 ρ N } ρ : pseudorange error (m) (4) = c Φ code f C/A ρ : pseudorangerate error (ms 1 ) (5) = c f carr f L1 : code phase residual (chips) Φ code f carr : carrier frequency residual (Hz) f C/A : C/A code frequency, (chips s 1 ) f L1 : L1 carrier frequency, (Hz) The code and carrier discriminator functions are the normalized early-minus-late amplitude and the four quadrant arc-tangent [29], [30]. The measurement noise variances are estimated using 20 past discriminator outputs. The coherent processing interval and EKF update interval T is the same and set to 20 milliseconds [31] [33]. We perform navigation bit wipe-off in our PyGNSS software to allow coherent processing across navigation bit boundaries. The EKF measurement update equations at epoch k to estimate the current state X k continues as follows: K : Kalman gain matrix (6) = ˆΣ k H T (H ˆΣ k H T + W ) 1 X ECI : state error vector in ECI coordinates (7) = Ke ˆΣ k : predicted state error covariance matrix H : geometry matrix in ECI coordinates (8) [ ] Hlos = H los los 1 x los 1 y los 1 z 1 H los = los N x los N y los N z 1 los i x,y,z : line of sight vector in ECI coordinates = Xi x,y,z,eci X x,y,z,eci Xx,y,z,ECI i X x,y,z,eci X k : corrected state vector (9) = ˆX k + X Σ k : corrected state error covariance matrix (10) I 8 8 = (I 8 8 KH)ˆΣ k : 8 8 identity matrix For the EKF time update to predict the next state ˆX k+1, we use a constant acceleration motion model and a dynamic process noise model [34], [35] that addresses vehicle accelerations as process noise. The equations for the EKF time update at epoch k + 1 are thus given as: ˆX k+1 : predicted state vector (11) = F X k ˆΣ k+1 : predicted state error covariance matrix (12) = F Σ k F T + Q k F : state propagation matrix (13) T T T 0 = T

4 4 Q k : state process noise covariance matrix (14) = F σẋ 2 k F T σẏ 2 k σż 2 k σ 2 cδt where the process noise due to vehicle accelerations in the x, y and z directions are assumed to be the same and predicted using a saturation function [36] as: σ 2 ẋ k : process noise due to vehicle accelerations (15) in a constant acceleration motion model = /(min(max( Xẋ,ẏ,ż 2, 5 2 ), 25 2 )) The above process noise function is small when the receiver s speed is large and large when the receiver s speed is small, capturing the intuition that it is more difficult for a vehicle s velocity to change when its speed is large as compared to when its speed is small. The coefficients were determined from a least squares fit to acceleration time data of a generic vehicle by [36]. The process noise of the front end oscillator is calculated from the Allan deviation as: σ 2 c δt σ τ : process noise of front end oscillator = (c σ τ ) 2 : Allan deviation of front end oscillator The Allan deviation σ τ of a front end oscillator is a measure of frequency stability [37], [38]. It can be estimated from past navigation solutions and also obtained from the manufacturer s datasheet, such as [39]. The predicted state error covariance matrix ˆΣ is initialized using 20 past state vectors. The equations for the frequency and phase updates, within the individual channels, after the EKF time update: f i carr,k : corrected carrier frequency (16) f IF of the i th satellite = f IF + fdcarr,k i : intermediate frequency (IF), (Hz) f i dcarr,k : corrected carrier doppler frequency (17) of the i th satellite = f L1 ( los i x,y,z (Xẋ,ẏ,ż,ECI c Xẋ,ẏ,ż,ECI) i + (X c δt Xi cδt )) fcode,k i : corrected code frequency of the i th satellite (18) = f C/A + 1 T (Φi code,k ˆΦ i code,k) + f C/A fdcarr,k i f L1 Φ i code,k : corrected code phase of the i th satellite (19) = f C/A ( Xx,y,z,ECI Xx,y,z,ECI i c +(X cδt Xcδt)) i ˆΦ i code,k+1 : predicted code phase of the i th satellite (20) = Φ i code,k + f i code,k T ˆΦ i carr,k+1 : predicted carrier phase of the i th satellite (21) = Φ i carr,k + f i carr,k T B. Deeply-Coupled MRVT Architecture In MRVT, the state vector X of multiple receivers are jointly tracked through the shared multi-receiver state vector X m. X m : multi-receiver state vector (22) = [ x, y, z, cδt, ẋ, ẏ, ż, c δt ] T where X m contains the shared position and velocity referenced to the geometric center of the multi-receiver configuration and the shared clock bias and clock drift referenced to a single front end oscillator. The MRVT update process is described as follows, with the superscripts and + differentiating between the individual receiver states before and after the MRVT update. The individual receiver EKF measurement update is first performed to obtain the individual receiver corrections to the state vectors and error noise covariance matrixes. X are concatenated to form the multi-receiver error input vector e m ; Σ are concatenated to form the multi-receiver error noise covariance input matrix W m. We then perform the MRVT EKF measurement update. The updated joint multi-receiver state vector X m is used as feedback, replacing the individual receiver state vectors with a more robust estimate X +. The MRVT EKF time update is subsequently performed together with the EKF time update of the individual receivers. The MRVT EKF measurement update equations for M receivers are given as: X j,k X + j,k : state vector of jth receiver : MRVT augmented (23) state vector of j th receiver = X m,k e m : multi-receiver error input vector (24) X 1,k ˆX m,k X = 2,k ˆX m,k... X M,k ˆX m,k W m : multi-receiver (25) : error noise covariance input matrix = diag{σ 1,k, Σ 2,k,..., Σ M,k } K m : multi-receiver Kalman gain matrix (26) = ˆΣ m,k Hm(H T m ˆΣm,k Hm T + W m ) 1 H m : multi-receiver geometry matrix (27) = H 1 H 2... H M

5 5 H j : geometry matrix element (28) = I 8 8 X m,k : multi-receiver state error vector (29) = K m e m X m,k : corrected multi-receiver state vector (30) = ˆX m,k + X m,k Σ m,k : corrected multi-receiver (31) : state error covariance matrix = (I 8 K m H m )ˆΣ m,k The predicted multi-receiver state error covariance matrix ˆΣ m is initialized using past multi-receiver state vectors X 1,... calculated using weighted least squares. The MRVT EKF time update is performed together with the EKF time update of the individual receivers. The equations are the same and given in Eq. (11) to Eq. (15). Through MRVT, shared multi-receiver states jointly track the states of multiple receivers which jointly track the states of multiple channels, achieving deeply coupled multi-receiver signal tracking. Joint tracking increases signal availability while leveraging information redundancy for robustness. This is possible for multiple receivers installed in close proximity, on a rigid body and sharing the same front end oscillator [6], [24]. Section II-C describes modifications to the MRVT architecture for unsynchronized front ends. C. Modifications for Unsynchronized Front Ends For the case of unsynchronized front ends, additional clock bias and clock drift states are appended to X m. X m = [ x, y, z, cδt 1, ẋ, ẏ, ż, cδt 1, cδt 2, cδt 2, ] T The rest of the MRVT equations are updated accordingly: [ X 1,k e m = ˆX ] m,x,y,z,cδt1,ẋ,ẏ,ż,cδt 1,k X 2,k ˆX m,x,y,z,cδt2,ẋ,ẏ,ż,c [ Σ1,k Σ2,k] δt 2,k W m = [ ] H1 H m = H H 1 = H 2 = X + 1,k = X m,x,y,z,cδt 1,ẋ,ẏ,ż,c δt 1,k X + 2,k = X m,x,y,z,cδt 2,ẋ,ẏ,ż,c δt 2,k The MRVT EKF time update equations are also modified: ˆX m,k+1 ˆΣ m,k+1 F m Q m,k σ 2 c δt j : predicted multi-receiver state vector = F m X m,k : predicted multi-receiver state error covariance matrix = F m Σ m,k Fm T + Q m,k : multi-receiver state propagation matrix T T T T 0 0 = T : multi-receiver state process noise covariance matrix σ 2 ẋ k σ ẏ 2 k σ ż 2 k σ 2 cδt σ 2 cδt 2 : process noise of j th front end oscillator F m III. IMPLEMENTATION AND EXPERIMENT RESULTS We implemented 3 different MRVT receiver configurations and conducted 3 different experiments to evaluate the performance of our MRVT receiver architecture. Section III-A describes an experiment in downtown San Francisco using 2 unsynchronized radio frequency (RF) front ends with lower RF sensitivity and lower oscillator stability. This experiment validates the reliability of our MRVT receiver architecture in periods of intermittent signal availability while using only 2 receivers. The total cost of this setup purchased in the year 2015 is approximately $630. Section III-B describes an experiment in our University of Illinois at Urbana-Champaign campus using 4 synchronized RF front ends with higher RF sensitivity and higher oscillator stability. This experiment validates the reliability of our MRVT receiver architecture in periods of limited signal availability while using more receivers, and of higher quality. The total cost of this setup purchased in the year 2014 is approximately $ F T m

6 6 TABLE I E XPERIMENT SETUPS Experiment Location A. Urban Environment with 2 s Downtown San Francisco Number of receivers RF front end Sampling frequency Sampling precision Bandwidth Oscillator Oscillator frequency Phase noise Frequency bias Allan deviation Synchronized 2 SiGe GN3S Sampler v MHz 2-bit 2.2 MHz TCXO MHz 80 dbc/hz ± 100 Hz s s 1 No Remarks validate reliability in periods of intermittent signal availability lower RF sensitivity lower oscillator stability unsynchronized oscillators B. Suburban Environment with 4 s University of Illinois at Urbana-Champaign 4 USRP N210 2 MHz 14-bit 8 MHz CSAC 10 MHz 50 dbc/hz ± Hz s s 1 Splitter validate reliability more receivers in architecture higher RF sensitivity higher oscillator stability synchronized oscillators C. Equipment Malfunction (1 of 2 s Malfunctioning) University of Illinois at Urbana-Champaign 2 USRP N210 5 MHz 14-bit 8 MHz CSAC 10 MHz 50 dbc/hz ± Hz s s 1 MIMO cable validate robustness to equipment malfunction higher RF sensitivity higher oscillator stability synchronized oscillators Section III-C describes an experiment using 2 synchronized receivers where we physically loosened the antenna connection of 1 receiver, resulting in an SNR degradation of 15 db per channel for that receiver. This experiment validates the robustness of our MRVT receiver to equipment malfunctions of a single receiver. Table I provides an overview of the 3 experiment setups. A. Experiment in Urban Environment With 2 s We implemented a 2-receiver MRVT architecture using 2 sets of RF components: 2 ANT-555 magnetic mount active patch antennas [40] and 2 SiGe GN3S version 3 samplers [41], as shown in Fig. 5. The 2 patch antennas and SiGe samplers have lower RF sensitivities as compared to configurations described in subsequent sections. This configuration is thus more susceptible to reduced signal availability. In addition, the SiGe samplers have independent, unsynchronized oscillators, introducing additional clock bias and clock drift parameters into the shared multi-receiver state vector. Referenced against the time solution, the SiGe samplers had inherent clock drifts that were 200 Hz apart. Using this MRVT receiver configuration, with 2-bit complex sampling and a sampling frequency of MHz, we collected a 10-minute data set in downtown San Franciso. The signals were first processed using vector tracking in our PyGNSS software. The densely located buildings in downtown San Francisco provided rich signal obstruction, resulting in frequent signal disruptions. The navigation results from vector tracking, as plotted on Google Maps [42], are shown in Fig. 6. The blue and red curves correspond to vector tracking results using signals received by patch antennas installed on the left and right edges of the vehicle s roof. The blue receiver lost track at a location with a particularly tall building on the left, as shown in Fig. 6. The red receiver lost track at a location with a particularly tall building on the right, as shown Fig. 6 (c). Both vector tracking receivers did not manage to lock back onto the received signals after the initial loss of lock. Fig. 5. Experiment setup in downtown San Francisco using 2 receivers. Implementation using 2 patch antennas and 2 SiGe GN3S version 3 samplers. Vector tracking (VT) results VT left (L) VT right (R) street-view where left (L) receiver lost track street-view where right (R) receiver lost track (c) Fig. 6. Navigation results from vector tracking (VT) of the 2 receivers, plotted using Google Maps [43]. The blue and red receivers lost track at the locations indicated by blue and red triangles. Google street view [44] of the location where the blue receiver lost track, a particularly tall building is on the left. (c) Google street view of the location where the red receiver lost track, a particularly tall building is on the right.

7 7 (c) (c) (d) (d) Fig. 7. Signal acquisition results using a 25 db SNR threshold, discontinuities represent signal outages. Since the 2 receivers are closely located on the roof of the same road vehicle, most signal disruptions are concurrent. On the other hand, periods where the 2 receivers did not concurrently experience signal disruptions exist. These are opportunities for joint signal tracking via MRVT. Acquired carrier doppler frequency of PRN 3; acquired code phase of PRN 3; acquired carrier doppler frequency of PRN 32; acquired code phase of PRN 32. The above plots have been processed to reject outliers. Fig. 8. Signal tracking errors referenced to signal acquisition. MRVT accurately and consistently tracked the received signals. In comparison, vector tracking using the blue received resulted in large signal tracking residuals at the times indicated by the blue arrows. Carrier doppler frequency residual of PRN 3; code phase residual of PRN 3; carrier doppler frequency residual of PRN 32; code phase residual of PRN 32. Acquisition performed using coarse 0.5 chip intervals and fine frequency estimation. On the other hand, a plot of signal visibility in Fig. 7 showed that signals received by the blue and red receivers were not always disrupted and the disruptions were not always simultaneous. Opportunities for MRVT to improve the reliability of signal tracking and position estimation exist. Using MRVT, we jointly processed the signals received by both the blue and red receivers. The signal tracking errors, referenced to signal acquisition, is shown in Fig. 8. MRVT accurately and consistently tracked the received signals. In comparison, vector tracking using the blue receiver lost track at the times indicated by the blue arrows. The navigation results using MRVT are plotted in Fig. 9. MRVT effectively mitigated signal tracking disruptions of the individual receivers through joint signal tracking across multiple receivers. MRVT leveraged multiple receivers to increase the reliability of localization, consistently providing accurate positioning solutions even when the performance of vector tracking was degraded. MRVT results MRVT Fig. 9. MRVT accurately and consistently positioned the vehicle in downtown San Francisco, demonstrating reliable signal tracking and position estimation in periods of intermittent signal availability. In comparison, vector tracking of the blue and red receivers lost track at the locations indicated by the blue and red triangles within the orange box, as shown in Fig. 6. Results were plotted using Google Maps [42].

8 tracking was noisy and lost track. Vector tracking; MRVT. Plots were generated using Google Maps [42]. visibility was limited and the number of visible satellites was less than 4. MRVT reliably estimated the position of the stationary vehicle while vector Fig. 12. Positioning of a stationary vehicle in the parking lot of an apartment complex. Due to partial obstruction by the apartment building, satellite Vector tracking; MRVT. Results from vector tracking, loosely-coupled using an EKF (VT combined), are also plotted for comparison. Above map buildings. The vehicle is moving from west to east. MRVT demonstrated improved reliability with smoother tracks on the correct side of the road; 8 VT 1 VT 2 VT 3 VT 4 Fig. 10. Experiment setup in our University of Illinois at Urbana-Champaign campus using 4 receivers. was generated using Google Maps [42]. B. Experiment With 4 s We implemented a 4-receiver MRVT architecture using 4 sets of RF components: 4 AntCom 3GNSSA4-XT-1 GNSS antennas [45] and 4 Ettus Research N210 Universal Software Radio Peripherals (USRPs) [46], each equipped with a DB- SRX2 daughterboard [47], as shown in Fig. 10. Compared to the patch antennas and SiGe samplers in the previous configuration, the AntCom antennas and USRPs have increased sensitivity to weak signals. In addition, the USRPs were synchronized using timing signals from a common external oscillator, a Microsemi Quantum SA.45s Chip Scale Atomic Clock (CSAC) [39]. Compared to the previous configuration, this configuration is synchronized, with a stable front end oscillator. We conducted 2 experiments on our University of Illinois at Urbana-Champaign campus to validate the reliability of MRVT in periods of intermittent and limited signal availability. The first experiment was conducted on Green St, a suburban environment with tall buildings. Vector tracking results are shown in Fig. 11 ; where the 4 receivers are distinguished using 4 different colors. MRVT results, in black, are shown in Fig. 11. In addition, we plotted an EKF combination of the vector tracking results, considered a loosely-coupled architecture, in orange. In comparison to vector tracking and combined vector tracking, MRVT demonstrated improved reliability with consistently smoother tracks on the correct side of the road. The second experiment was conducted in the parking lot of an apartment complex. Due to partial obstruction by the apartment building, the number of satellites in view from the stationary vehicle was less than 4. Vector tracking results are shown in Fig. 12 ; MRVT results are shown in Fig. 12. While vector tracking lost track of the stationary vehicle, MRVT reliably estimated the position of the stationary vehicle. I II Fig. 11. Navigation results on Green St, a suburban environment with tall III C. Experiment With Equipment Malfunction In many critical systems, redundancy, the multiplication of crucial components, aids in increasing robustness to equipment malfunction. Using MRVT of multiple receivers, we are able to mitigate the effects of a single malfunctioning receiver, increasing the robustness of localization. We thus demonstrate in this experiment, the robustness of MRVT to equipment malfunction of a single receiver. We implemented a 2-receiver MRVT configuration using 2 patch antennas and 2 USRPs. In addition to the CSAC, we synchronized the USRPs using a MIMO cable provided by the manufacturer, Ettus Research. We then physically loosened

9 idated the reliability of our MRVT receiver in periods of in 3 different experiment scenarios, we experimentally val- position estimation. Using 3 different MRVT implementations leveraged multiple receivers for joint signal tracking and MRVT is a deeply-coupled multi-receiver architecture that tion, we proposed Multi- Vector Tracking (MRVT). To increase the reliability and robustness of localiza- may lead to inaccurate positioning solutions. which malfunctions, equipment to vulnerable also is receiver single the addition, In environments. urban in availability signal intermittent to due degradation positioning and tracking signal to susceptible is receiver single A systems. navigation many to integral is localization CONCLUSION IV. receiver. single a of malfunction equipment to robustness demonstrating weakened, severely was architecture receiver MRVT the in 9 (c)

10 10 [11], Robust MAV state estimation using an M-Estimator augmented sensor fusion graphs, in Proceedings of the 28th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2015), Tampa, Florida, 2015, pp [12] I. S. Reed, J. D. Mallett, and L. E. Brennan, Rapid convergence rate in adaptive arrays, IEEE Transactions on Aerospace and Electronic Systems, vol. AES-10, no. 6, pp , Nov [13] J. K. Ray, M. E. Cannon, and P. Fenton, code and carrier multipath mitigation using a multiantenna system, IEEE Transactions on Aerospace and Electronic Systems, vol. 37, no. 1, pp , Jan [14] C. C. Counselman, Multipath-rejecting antennas, Proceedings of the IEEE, vol. 87, no. 1, pp , Jan [15] A. Brown and N. Gerein, Test results of a digital beamforming receiver in a jamming environment, in Proceedings of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION 2001), Salt Lake City, UT. ION, 2001, pp [16] A. J. OBrien and I. J. Gupta, Mitigation of adaptive antenna induced bias errors in GNSS receivers, IEEE Transactions on Aerospace and Electronic Systems, vol. 47, no. 1, pp , January [17] Y.-H. Chen, J.-C. Juang, J. Seo, S. Lo, D. M. Akos, D. S. De Lorenzo, and P. Enge, Design and implementation of real-time software radio for anti-interference /WAAS sensors, Sensors, vol. 12, no. 10, pp , [18] Y. Ng and G. X. Gao, Multi-receiver vector tracking based on a Python platform, in Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, California, 2015, pp [19], Advanced multi-receiver vector tracking for positioning a land vehicle, in Proceedings of the 28th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2015), Tampa, FL, 2015, pp [20], Advanced multi-receiver position-information-aided vector tracking for robust time transfer to PMUs, in Proceedings of the 28th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2015), Tampa, FL, 2015, pp [21] Q. Gan and C. J. Harris, Comparison of two measurement fusion methods for Kalman-filter-based multisensor data fusion, IEEE Transactions on Aerospace and Electronic Systems, vol. 37, no. 1, pp , Jan [22] H. Qi and J. B. Moore, Direct Kalman filtering approach for /INS integration, IEEE Transactions on Aerospace and Electronic Systems, vol. 38, no. 2, pp , Apr [23] J. J. Spilker and B. W. Parkinson, Progress in Astronautics and Aeronautics: Global Positioning System. American Institute of Aeronautics and Astronautics, 1996, ch. Fundamentals of signal tracking theory, pp [24] I. Klein, I. Rusnak, and Y. Bar-Shalom, A joint filter for formation tracking, IEEE Transactions on Aerospace and Electronic Systems, vol. 51, no. 4, pp , Oct [25] S. Bhattacharyya, Performance and integrity analysis of the vector tracking architecture of GNSS receivers, Ph.D. dissertation, University of Minnesota, [26] J. J. Brewer, The differential vector phase-locked loop for global navigation satellite system signal tracking, Ph.D. dissertation, Air Force Institute of Technology, [27] R. E. Kalman et al., Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana, vol. 5, no. 2, pp , [28] R. E. Kalman, A new approach to linear filtering and prediction problems, Journal of Basic Engineering, vol. 82, no. 1, pp , [29] P. W. Ward, J. W. Betz, and C. J. Hegarty, Understanding : Principles and Applications Second Edition. Artech House, Boston, 2006, ch. Satellite signal acquisition, tracking, and data demodulation, pp [30] P. Misra and P. Enge, Global Positioning System: Signals, Measurements and Performance Second Edition. Lincoln, MA: Ganga-Jamuna Press, [31] P. W. Ward, Performance comparisons between FLL, PLL and a novel FLL-assisted-PLL carrier tracking loop under RF interference conditions, in Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION 1998), Nashville, TN, 1998, pp [32] P. W. Ward and T. D. Fuchser, Stability criteria for GNSS receiver tracking loops, NAVIGATION, Journal of The Institute of Navigation, vol. 61, no. 4, pp , [33] C. O Driscoll, M. G. Petovello, and G. Lachapelle, Choosing the coherent integration time for Kalman filter-based carrier-phase tracking of GNSS signals, solutions, vol. 15, no. 4, pp , [34] F. D. Busse, J. P. How, and J. Simpson, Demonstration of adaptive extended Kalman filter for low-earth-orbit formation estimation using CD, NAVIGATION, Journal of The Institute of Navigation, vol. 50, no. 2, pp , [35] D. Simon and T. L. Chia, Kalman filtering with state equality constraints, IEEE Transactions on Aerospace and Electronic Systems, vol. 38, no. 1, pp , Jan [36] Mathworks. (2015, jun) State estimation using time-varying kalman filter. [Online]. Available: [37] D. W. Allan, Statistics of atomic frequency standards, Proceedings of the IEEE, vol. 54, no. 2, pp , Feb [38] J. Rutman and F. L. Walls, Characterization of frequency stability in precision frequency sources, Proceedings of the IEEE, vol. 79, no. 7, pp , Jul [39] Microsemi Corporation. (2012, jun) Quantum SA.45s chip scale atomic clock (CSAC). [Online]. Available: document-portal/doc download/ quantum-sa-45s-csac [40] On Shine Enterprise Co. Ltd. (2012, jun) ON SHINE G.P.S. antenna ANT-555. [Online]. Available: /www/ant pdf [41] K. Borre, D. M. Akos, N. Bertelsen, P. Rinder, and S. H. Jensen, A software-defined and Galileo receiver: a single-frequency approach. Springer Science & Business Media, [42] Google Inc. (2016, jan) Google Maps. [Online]. Available: https: // [43] Google Developers. (2016, jan) Google Maps Javascript API. [Online]. Available: javascript/ [44]. (2016, jan) Google Street View Image API. [Online]. Available: [45] Antcom Corporation. (2014, jun) 3.5in dia. GNSS antenna for global navigation satellite systems (GNSS) applications P/N: 3GNSSA4-XT-1 (front/back fixed mount). [Online]. Available: documents/catalogs/page/3gnssa4-xt-1 GNSSAntennas1.pdf [46] Ettus Research. (2012, jun) USRP N200/N210 networked series. [Online]. Available: Ettus N DS Flyer HR 1.pdf [47]. (2012, jun) DBSRX MHz Rx. [Online]. Available: Yuting Ng received her B.S. degree in electrical engineering and her M.S. degree in aerospace engineering from the University of Illinois at Urbana- Champaign, Illinois, USA in 2014 and Her research interests are in machine learning, radar signal processing, GNSS signal tracking, navigation and time synchronization. Grace Xingxin Gao received her B.S. degree in mechanical engineering and her M.S. degree in electrical engineering from Tsinghua University, Beijing, China in 2001 and She received her PhD degree in electrical engineering from Stanford University in From 2008 to 2012, she was a research associate at Stanford University. Since 2012, she has been an assistant professor in the Aerospace Engineering Department at University of Illinois at Urbana-Champaign. Her research interests are systems, signals, control, and robotics. She is a senior member of IEEE and a member of ION.