Advanced Multi-Receiver Vector Tracking for Positioning a Land Vehicle

Transcription

1 Advanced Multi-Receiver Vector Tracking for Positioning a Land Vehicle Yuting Ng, and Grace Xingxin Gao University of Illinois at Urbana-Champaign BIOGRAPHIES Yuting Ng is a Master s student in the Aerospace Engineering Department at the University of Illinois at Urbana- Champaign. She received her Bachelor s degree, graduating with university honors, from the Electrical and Computer Engineering Department at the same university in Grace Xingxin Gao is an assistant professor in the Aerospace Engineering Department at the University of Illinois at Urbana-Champaign. She obtained her PhD from Stanford University in She was a research associate at Stanford University from 2008 to ABSTRACT The novel Multi-Receiver Vector Tracking (MRVT) architecture for the joint tracking of multiple GPS receivers, presented in our prior work [1], is improved upon in this followup paper. Improvements include an augmented software platform, Python Software Defined Radio (Python SDR), which has, among its many enhancements, a variable coherent integration interval with navigation bit wipe-off. Dynamic process noise covariance matrix, attitude aiding and additional sub-sample timing synchronization between individual receivers. The main concept behind MRVT is still the same. The reduction in the overall search space, from the state vector of each individual receiver to a single reference state vector and attitude of the rigid body comprising the multi-receiver network, offers increased information redundancy which brings about increased accuracy, reliability and robustness to signal attenuation and multipath. In this paper, we begin by detailing the MRVT concept and implementation, followed by demonstrating with our experiments the enhanced performance of Advanced MRVT by showing increased accuracy in positions, altitudes, baselines and timing with respect to conventional vector tracking. I. INTRODUCTION GPS receivers are commonly used for navigation purposes [2] [4]. Examples are flying an unmanned aerial vehicle [5], [6] through skyscrapers for captivating aerial photography and operating a self-driving car in the city [7]. Such environments present challenges to the single conventional GPS receiver in the form of limited signal availability and multipath [8] [10]. To overcome such challenges, we aim to leverage upon the inherent potential of combining results from more than one The authors are with the Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. yng5@illinois.edu, gracegao@illinois.edu. GPS receiver for better performance in navigation solution estimation [1], [5], [11], [12]. The concept we proposed and preliminarily verified with experimental data is Multi-Receiver Vector Tracking (MRVT), which provides deep multi-receiver integration at the signal level [1]. MRVT can be thought of as an extension of Single-Receiver Vector Tracking (SRVT). In SRVT, the states of multiple Channels within a Receiver are jointly tracked through the states of one Receiver [13] [20]. The Receiver states are: position, clock bias, velocity and clock drift. Likewise, in MRVT, the states of the multiple Receivers within a Receiver Network are jointly tracked through the states of one Receiver Network. In this case, the Receiver Network is a rigid body on which multiple GPS receiving antennas have been installed. Since the antennas are installed on a rigid body, the relative geometry and baselines of the antennas remains unchanged, can be estimated in advance, and used as prior information. As such, the number of states required to describe the Receiver Network can be reduced to: reference position, clock bias, velocity, clock drift and attitude. Once the Receiver Network states have been estimated and filtered, this information is then used to augment the SRVT within each Receiver in the Receiver Network. In this manner, the overall search space is reduced to the states of the Receiver Network. This reduction in overall search space offers increased robustness due to information redundancy. This paper continues the development of the MRVT platform and specifically focuses on the following improvements. 1) Enhanced software platform - Python Software Defined Radio (Python SDR). 2) Variable coherent integration interval with navigation bit wipe-off, 3) Dynamic process noise covariance matrix, 4) Attitude aiding, 5) Determination of reference velocity and clock drift and 6) Additional sub-sample time synchronization. The above improvements were proposed for better accuracy, reliability and robustness as compared to the results presented in our prior work [1]. We demonstrate with our experiments the enhanced performance of Advanced MRVT. This paper is organized as follows: Section II describes the background, theory and implementation of Single Receiver Vector Tracking (SRVT) within each individual receiver. Section III describes the theory and implementation of MRVT. Outputs from the Single Receiver Vector Tracking Loop (STVTL) within each individual receiver is used to estimate the state of the MRVT Loop (MRVTL). The output from the MRVTL is used to augment the SRVTL of each individual receiver. Section IV describes the improvements made to the

2 The discriminator functions: Fig. 1. Single Receiver Vector Tracking (SRVT) architecture implemented within each individual Receiver in this paper. The quantities above and below the timeline are calculated within the navigation filter of the receiver and tracking channels respectively. The navigation filter is an Extended Kalman Filter (EKF) with a two-step update process: measurement update producing state corrections at epoch boundaries and time update predicting new states for the next epoch boundary. Python SDR. Section V describes the experiments that were conducted on a road vehicle. Finally, Section VI concludes the paper. II. BACKGROUND OF VECTOR TRACKING First proposed in 1996 as the Vector Delay Lock Loop (VDLL) by Spilker [13], there has been many variations to the concept of vector tracking [16] [20]. This paper implements a variation of the non-coherent Vector Delay and Frequency Lock Loop (VD/FLL) [14], [15] shown in Fig.1, within each individual receiver. The state vector of each individual receiver is given as (1): X : state vector (1) x y z = cδt ẋ ẏ ż cδt x, y, z : position (m) ẋ, ẏ, ż : velocity (ms 1 ) c : speed of light, , (ms 1 ) cδt : clock bias (m) cδt : clock drift (ms 1 ) The non-coherent vector tracking architecture is implemented in this paper. Thus, the error input vector e to the navigation filter is composed of the scaled discriminator outputs ( ρ, ρ) from each channel [15]. The VDLL s discriminator function is the normalized early-minus-late amplitude (2) and the VFLL s discriminator function is the four quadrant arc-tangent (3) [28]. The scaled discriminator output noise variances (σ ρ 2, σ2 ρ ) are estimated using 20 past discriminator outputs. The coherent integration period and measurement update interval, T, are the same and set to T = 0.020s. Channel and receiver updates are synchronous; the Python SDR performs navigation bit wipe-off such that the coherent integration period can straddle navigation bit boundaries. Φ code : DLL discriminator (chips) (2) = E L 2(E + L) E = ie 2 + qe 2 L = il 2 + ql 2 f carr : FLL discriminator (Hz) (3) = tan 1 ( cross dot ) 2π T cross = ip 0 qp 1 ip 1 qp 0 dot = ip 0 ip 1 + qp 0 qp 1 (ie, qe, ip, : coherent in-phase and quadrature-phase qp, il, ql) T early, prompt, late correlations : coherent integration period and measurement update interval, 0.020(s) The discriminator outputs ( Φ code (chips), f carr (Hz)), are scaled into pseudorange and pseudorangerate, ( ρ(m), ρ(ms 1 )) errors (6,7) before being concatenated into the error input vector e (4). Similarly, the discriminator output noise variances are scaled before being concatenated into the error noise covariance input matrix W (5). e : error input vector (4) = e( ρ 1... ρ N, ρ 1... ρ N ) = [ ρ 1... ρ N, ρ 1... ρ N ] T W : error noise covariance input matrix (5) = W (σ ρ σ2 ρ, N σ2 ρ 1...σ2 ρ ) N σ 2 ρ = 0 0 σ 2 ρ N σ 2 ρ σ 2 ρ N ρ : pseudorange error (m) (6) = c Φ code f C/A ρ : pseudorangerate error (ms 1 ) (7) = c f carr f L1 : frequency of C/A code, 1.023, (MHz) f C/A f L1 : frequency of L1 carrier, , (MHz) The navigation filter within each individual receiver is an Extended Kalman Filter (EKF) and thus have a two-step update process: measurement update and time update, as shown in Fig.1. To begin with, the measurement update produces the state error vector X k used to obtain the corrected state vector X k at epoch k. X k is naturally determined in Earth- Centered-Inertial (ECI) coordinates X k,eci as the range and range-rate equations are most easily solved in ECI coordinates (9). The measurement update of X k is then performed as such. The predicted state vector ˆXk is first transformed

3 from Earth-Centered-Earth-Fixed (ECEF) ˆXk,ECEF to ECI coordinates ˆX k,eci. X k,eci is then used to update ˆX k,eci as X k,eci = ˆX k,eci + X k,eci (11). The updated state vector X k is then transformed from ECI X k,eci back to ECEF coordinates X k,ecef. The EKF measurement update equations at time k are given as follows (8-12): K : Kalman gain matrix (8) = ˆΣ k H T (H ˆΣ k H T + W ) 1 X ECI : state error vector in ECI coordinates (9) = Ke ˆΣ k : predicted state error covariance matrix H : geometry matrix in ECI coordinates (10) los i x,y,z = H(Xx,y,z,ECI...X 1 x,y,z,eci, N ˆX x,y,z,eci ) ( los 1 x,y,z, 1) (0, 0, 0, 0) = ( los N x,y,z, 1) (0, 0, 0, 0) (0, 0, 0, 0) ( los 1 x,y,z, 1) (0, 0, 0, 0) ( los N x,y,z, 1) : line of sight vector in ECI coordinates = Xx,y,z i X x,y,z X k : corrected state vector (11) = ˆX k + X Σ k : corrected state error covariance matrix (12) = (I KH)ˆΣ k The EKF time update equations at time k + 1 are given as follows (13-18): ˆX k+1 : predicted state vector (13) = F X k ˆΣ k+1 : predicted state error covariance matrix (14) = F Σ k F T + Q k F : state propagation matrix (15) = F ( T ) T T T 0 = T The initial predicted state error covariance matrix ˆΣ 0 is estimated using 20 past state vectors X ECEF. The state process noise covariance matrix, Q k, is time-varying [21]. It is set using the 20 sample running average amplitude of the receiver s velocity v = ẋ, ẏ, ż [22] and the specification of the external clock [23]. The steps to estimate Q k is as shown in (16-18). Q k : state process noise covariance matrix (16) [ ] 0 0 = F F T 0 Q v,k Q v,k : velocity and clock drift component of Q k (17) f(v k ) = 0 f(v k ) f(v k ) (c 2.5e 10 ) 2 f(v k ) : saturation function for velocity v k (18) = /(min(max(v 2 k, 5 2 ), 25 2 )) While the navigation filter in the receiver performs the EKF measurement and time updates, the channels perform the frequency and phase updates. The equations for the frequency update, after the EKF measurement update, at time k are given as follows (19-22): f i carr,k : corrected carrier frequency (19) f IF of the i th satellite = f IF + fdcarr,k i : intermediate frequency (IF), 0(Hz) f i dcarr,k : corrected carrier doppler frequency (20) of the i th satellite = f L1 ( los i x,y,z (Xẋ,ẏ,ż,ECI c Xẋ,ẏ,ż,ECI) i + c(xδt Xi )) δt fcode,k i : corrected code frequency of the i th satellite (21) = f C/A + 1 T (Φi code,k ˆΦ i code,k) +f caid fdcarr,k i Φ i code,k : corrected code phase of the i th satellite (22) = mod( f C/A ( Xx,y,z,ECI Xx,y,z,ECI i c +c(x δt Xδt)), i 1023) The equations for the phase update, at the same time as the EKF time update, at time k + 1 are given as follows (23,24): ˆΦ i code,k+1 : predicted code phase of the i th satellite (23) = Φ i code,k + f i code,k T ˆΦ i carr,k+1 : predicted carrier phase of the i th satellite (24) = Φ i carr,k + f i carr,k T III. MULTI-RECEIVER VECTOR TRACKING In MRVT, the corrected state vector X of each receiver is used to determine the reference state vector X ref of the rigid body. The reference state vector X ref of the rigid body contains the reference position, clock bias, velocity, clock drift and attitude of the rigid body. After the reference state vector is determined, it is used to augment the VTL of the individual receivers as shown in Fig.2. Within the navigation filter of the Receiver Network, the reference clock bias is first determined. The state vector of

4 Fig. 2. MRVT architecture implemented in this paper. Fig. 4. Geometry of receiving antennas on the roof of a vehicle. East, North, Up (ENU) are local level coordinates. right, front, top are body coordinates. Each antenna is given a color label, referenced in the figures of the results, Fig.10. Fig. 3. MRVTL update implemented in this paper. each Receiver X is then propagated in time to match the reference clock bias, synchronizing the Receivers. The reference position, velocity and clock drift states of the reference state vector X ref is then determined. This can be done through various methods, such as simple averaging or Kalman filtering. For the results shown in the next section, a simple averaging was performed. Then, the attitude of the Receiver Network is determined. Similarly, the attitude may be determined through various methods. For the results shown in the next section, the attitude was obtained from the reference velocity. After the attitude is determined, the updated positions of each Receiver is fed back to the Receiver, aiding their VTL. See Fig.3. A. Attitude determination using reference velocity Attitude determination using reference velocity is based on the idea that the direction of the reference velocity is the front direction. When the vehicle is reversing, the f ront direction is taken as the opposite direction of the reference velocity. To obtain the attitude of the Receiver Network through the reference velocity, the reference velocity is first converted from the global ECEF to the local East-North-Up (ENU) coordinates. Following that, the velocity in the U p direction is set to 0 since the experiment is performed using a ground vehicle. Next, the velocity vector is normalized to produce a direction vector in the East-North plane. The f ront and right directions are then determined and used to form the baseline vectors. Lastly, the baseline vectors are transformed from the local ENU to the global ECEF coordinates then used to update the state vectors Xs of the individual receivers. B. Coordinate transformations: body and local coordinates The body coordinates is an arbitrary coordinate system used to describe the antenna geometry. In this paper, the origin of the body coordinates is set at the reference position of the rigid body, which is defined to be the geometric center of the four receivers. The x-axis points to the right, the y-axis points to the front and the z-axis points to the top of the rigid body, Fig.4. The yaw angle is defined an as the angle in the East-North plane, increasing in the counter-clockwise direction from the North axis to the front direction. The equations to convert the yaw angle into a direction vector in the East-North plane are given as follows (25,26): E : East component of f ront direction vector (25) = cos(yaw + π 2 ) N : N orth component of f ront direction vector (26) = sin(yaw + π 2 ) After the attitude is determined through either approach, the updated state vector X of each Receiver is reverse propagated in time, then fed back to the Receiver, aiding their VTL. The EKF time update step then follows in each Receiver. In this manner, the state vectors of the individual receivers are constrained, leading to a reduction in the overall search space, offering an increased robustness to signal attenuation and multipath. IV. IMPROVEMENTS TO PYTHON SDR To implement the MRVT architecture, we needed a research platform that allows for effective information sharing and deep integration between multiple receivers. The research platform should also be flexible, extensible, intuitive and free. As such, we developed Python SDR which is a Software Defined Radio (SDR), written using the Object-Oriented Programming (OOP) approach in the Python programming language. Python SDR heavily references [13], [26] [32]. Since Python SDR is an SDR, most of the receiver processing functions are performed in software, as shown in Fig.5. In the case of Python SDR, the frontend hardware components that it requires are a GPS antenna and an Analog-to-Digital

5 Fig. 5. Python Software Defined Radio (Python SDR). After the digitization of the received signal by the Analog-to-Digital Converter (ADC), the rest of the receiver processing functions are performed in software. Shown within the Python SDR box are some commonly used classes and their interconnections. converter (ADC), such as the SiGe sampler [37] or a Universal Software Radio Peripheral (USRP) [38], both of which it has been tested to work with. Python SDR also accepts simulated data, such as that from the NI GPS Simulator [39]. After the ADC, Python SDR takes in raw sampled voltages as input. Python SDR models real-world hardware receivers by having intuitive objects such as Channel, Correlator, Discriminator and LoopFilter, defined as classes and organized into modules. Since the previous iteration of Python SDR used in our prior work [1], we have revised the organization of the modules. The revised organization increases the ease of use, intuitiveness and effectiveness of the Python SDR. Fig.IV shows the revised organization of modules within Python SDR. We have also revised the interconnections between classes to enable new functionality. Classes are objects with the capacity to store relevant information, known as attributes or fields, and the ability to perform object-specific functions, also known as methods. For example, an instance of the Channel class would include the following attributes: a defining pseudorandom noise (PRN) code, Settings, Correlator, DLL Discriminator, F/PLL Discriminator, DLL LoopFilter, F/PLL LoopFilter, code and carrier frequency and phase, etc. It would also include the following methods: init (), cold start(),... and update(), where init () is the constructor that creates an instance of the Channel object. See Fig.6. The Python SDR is able to perform varying coherent integration periods in multiples of 1ms. Increased coherent integration periods allow for more robustness to SNR degradation Fig.7(c-e). The maximum coherent integration duration is limited by platform dynamics. Each iteration of Python SDR has been checked for accuracy, see Fig.7. For example, the parsed ephemerides, raw pseudorange and carrier phase measurements have been compared against the RINEX file of the Trimble NetR9 Receiver [33] located on the roof of Talbot Laboratory, University of Illinois at Urbana-Champaign. The calculated satellite positions and clock biases have been checked against IGS ephemerides [34]. The calculated satellite velocities and clock drifts have been checked against the time difference of the satellite positions and clock biases. The estimated positions Fig. 6. (a) Revised organization of the modules available within Python SDR, increasing the ease of use and intuitiveness. (b) scalar.channel.channel class showing its attributes, functions and interconnections with related classes. The Channel object is able to access essential information stored within related objects such as the Correlator object through having the Correlator object as one of its attributes. Similarly, the DLL Discriminator object is able to access information of the past correlations saved within the Channel object, enabling it to perform discriminations over longer coherent integration periods. (a) (b) (c) (d) (e) Fig. 7. Python SDR tracking accuracy. (a,b) Plots of in-phase prompt correlations against time. Navigation bits of 20ms duration are clearly visible. Ephemerides are also successfully decoded. (c,d,e) Code phase versus carrier doppler plot across various coherent integration periods: 5ms, 10ms, 15ms.

6 Fig. 8. Geometry of receiving antennas on the roof of the vehicle. Each antenna is given a distinguishing color label, referenced in the figures of the results Fig.10. (SRVT) (MRVT) (SRVT: altitude) (MRVT: altitude) (SRVT: baseline residual) (MRVT: baseline residual) (SRVT: cδt residual) (MRVT: cδt residual) Fig. 9. Data collection equipment in the backseat of the vehicle. and velocities have been compared against prior information. In addition, to ensure that the receiver maintains track of the received signal, the plots of SNR, in-phase prompt and quadphase prompt correlations have been checked. V. E XPERIMENTS ON A ROAD V EHICLE Experiments on road vehicles were conducted to evaluate the performance of the MRVT architecture. As a comparison against our prior results [1], the same experimental data was processed. In that experiment, four AntCom 3GNSSA4-XT-1 GNSS antennas [36] were installed at the four corners of a vehicles roof, as shown in Fig.4 and Fig.8. Each antenna was connected to an Ettus Research USRP N210, equipped with a DBSRX2 daughterboard [38], [40]. The complex GPS L1 raw signals were modulated to 0-IF, digitized at a sampling frequency of 2MHz and output as interleaved complex shorts. The output data were sent through an Ethernet switch and written directly onto the internal hard disk of a laptop running Ubuntu The Universal Software Radio Peripherals (USRPs) were triggered by the same Microsemi Quantum SA.45s Chip Scale Atomic Clock (CSAC) [41]. A power regulating circuit was built to power the equipment from a 12V sealed lead acid battery. The equipment were placed Fig. 10. Comparison of tracking results from SRVT and MRVT. Plots of altitude, baseline residual and clock bias cδt residual obtained immediately after EKF measurement update. SRVT on the left. MRVT on the right, with attitude aiding when the reference velocity is above a set threshold value of 0.5ms 1 (1.12mph). in the backseat of the vehicle, as shown in Fig.9. During data collection, the vehicle was initially parked head-in at the second parking lot from the bottom right corner. The vehicle then backed-out, turned onto the road and drove north. A comparison of the results from SRVT and MRVT is shown in Fig.10. Fig.10 shows the tracks traced by the antennas on My Maps - Google [35] and the altitudes, residual baseline distances and residual clock biases of the receivers.

7 The time taken to post-process the received signals from all four receivers, on an Intel Core i7-4700mq 2.40GHz x 8 running Ubuntu 14.04LTS, was approximately 15 minutes for each tracking scheme. As shown in Fig.10, MRVT provides more accurate results as compared to SRVT. It shows the individual MRVT positions tracing out smooth tracks in the expected direction while maintaining an expected distance apart, without crossovers, for a sustained period of time. On the other hand, the individual SRVT positions did not maintain the expected distance apart and had frequent cross-overs. It also shows more accurate altitudes and baseline distances when using MRVT. All tracking algorithms stabilized to a constant, non-drifting relative difference in clock bias, as expected of being triggered by the same external clock even though the clock bias states are not constrained in MRVT, unlike the position states. The experimental results demonstrated the vastly enhanced quality of Advanced MRVT over our prior work [1]. Advanced MRVT produced smooth tracks, more reliable antenna baseline distances and receiver clock timings. The key modifications that we have implemented since our prior work include (1) updating of code and carrier phase as appropriate, (2) variable increased coherent integration interval with navigation bit wipe-off, (3) dynamic process noise covariance matrix Q based on velocity information, (4) attitude aiding, (5) determination of reference velocity and clock drift and (6) additional subsample time synchronization through time propagation of the state vectors. Modification (1) smoothed out the code and carrier phase accumulator; modification (2) reduced the discriminator and EKF noise. Thus, modifications (1) and (2) aid in reducing the noise present in the results of our prior work. Modification (3) automatically tunes the bandwidth of the EKFs; modifications (4) and (5) introduced more constraints into the MRVT architecture. Thus, modifications (3), (4) and (5) aid in increasing stability, accuracy and robustness. VI. CONCLUSION In conclusion, we have proposed the MRVT architecture as an extension of SRVT. By reducing the search space from each individual Receiver to the Receiver Network, we have increased information redundancy which offers more accurate, reliable and robust results, especially under signal attenuation and multipath. Since our prior work [1], we have made significant improvements to our software platform - Python SDR; we have also proposed and implemented a few key improvements to the MRVT architecture. Finally, we have shown results of vast improvement compared to our prior work and validated the Advanced MRVT algorithm and Python SDR. ACKNOWLEDGMENT The authors would like to thank Ganshun Lim for encouragement. Mr. Phil Ward for guidance and advice. REFERENCES [1] Y. Ng, and G.X. Gao, Multi-Receiver Vector Tracking Based on a Python Platform, Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, California, January 2015, pp [2] G. Mintsis, S. Basbas, P. Papaioannou, C. Taxiltaris, and I. Tziavos, Applications of GPS technology in the land transportation system, European Journal of Operational Research, vol. 152, no. 2, pp , 2004 [3] C. R. Drane, and C. Rizos, Positioning Systems in Intelligent Transportation Systems. Norwood, MA, USA: Artech House, Inc., [4] S.T.S. Thong, C.T. Han, and T.A. Rahman, Intelligent fleet management system with concurrent GPS & GSM real-time positioning technology, Proceedings of the 7th International Conference on ITS Telecommunications (ITST 07), June 2007, pp. 1-6 [5] A. Shetty, and G.X. Gao, Measurement Level Integration of Multiple Low-Cost GPS Receivers for UAVs, Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, California, January 2015, pp [6] D. Chen, and G.X. Gao, Simultaneous State Estimation of UAV Trajectory Using Probabilistic Graph Models, Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, California, January 2015, pp [7] C. Urmson, J. Anhalt, D. Bagnell, C. Baker, R. Bittner, M.N. Clark, J. Dolan, D. Duggins, T. Galatali, C. Geyer, and others, Autonomous driving in urban environments: Boss and the urban challenge, Journal of Field Robotics, vol. 25, no.8, pp , 2008 [8] M. S. Braasch, Multipath effects, in Global Positioning System: Theory and Applications, B. Parkinson, J. Spilker, P. Axelrad, and P. Enge, Eds. Washington, DC: American Institute of Aeronautics and Astronautics, 1996, vol. I, pp [9] B. Eissfeller, and J.O. Winkel, GPS Dynamic Multipath Analysis in Urban Areas, Proceedings of the 9th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1996), Kansas City, MO, September 1996, pp [10] A. Soloviev, F. van Graas, Utilizing Multipath Reflections in Deeply Integrated GPS/INS Architecture for Navigation in Urban Environments, Proceedings of IEEE/ION PLANS 2008, Monterey, CA, May 2008, pp [11] E. Wycoff, and G.X. Gao, A Python Software Platform for Cooperatively Tracking Multiple GPS Receivers, Proceedings of the 26th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa FL, Sep [12] D. Chou, Y. Ng, and G.X. Gao, Robust GPS-Based Timing for PMUs Based on Multi-Receiver Position-Information-Aided Vector Tracking, ION International Technical Meeting 2015, Dana Point, California, January [13] Spilker Jr, J., Vector Delay Locked Loop in Global Positioning System: Theory and Applications, B. Parkinson, J. Spilker, P. Axelrad, and P. Enge, Eds. Washington, DC: American Institute of Aeronautics and Astronautics, 1996, vol. I, pp [14] S. Zhao, D. Akos, An Open Source GPS/GNSS Vector Tracking Loop - Implementation, Filter Tuning, and Results, Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011, pp [15] S. Bhattacharyya, Performance and Integrity Analysis of the Vector Tracking Architecture of GNSS Receivers. PhD Dissertation, , Retrieved August 1, 2014, from spotlight/bhattacharyya thesis final.pdf [16] M. Zhodzishsky, S. Yudanov, V. Veitsel, J. Ashjaee, Co-OP Tracking for Carrier Phase, Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998), Nashville, TN, September 1998, pp [17] J. Liu, X. Cui, Q. Chen, M. Lu, Joint Vector Tracking Loop in a GNSS Receiver, Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011, pp [18] J. Brewer, The Differential Vector Phase-Locked Loop for Global Navigation Satellite System Signal Tracking. PhD Dissertation, 22-40, Retrieved August 1, 2014, from AD=ADA [19] P. Henkel, K. Giger, and C. Gunther, Multifrequency, Multisatellite Vector Phase-Locked Loop for Robust Carrier Tracking, IEEE Journal of Selected Topics in Signal Processing, 3(4), , 2004 [20] P. Henkel, G.X. Gao, T. Walter, and C. Gunther, Robust Multi-Carrier, Multi-Satellite Vector Phase Locked Loop with Wideband Ionospheric Correction and Integrated Weighted RAIM, Journal of Italian Institute of Navigation, issue 190, December 2009 [21] F.D. Busse, J.P. How, J. Simpson, Demonstration of Adaptive Extended Kalman Filter for Low-Earth-Orbit Formation Estimation Using CDGPS, Navigation, vol. 50, no. 2, Blackwell Publishing Ltd, , pp , 2003.

8 [22] MathWorks, State Estimation Using Time-Varying Kalman Filter, Retrieved June 3, 2015, from control/getstart/estimating-states-of-time-varying-systems-using -kalman-filters.html [23] Microsemi, QUANTUM Chip Scale Atomic Clock Product Info, Retrieved June 3, 2015, from [24] Z. Dai, S. Knedlik, and O. Loffeld, Toolbox for GPS-based Attitude Determination: An Implementation Aspect INTECH Open Access Publisher, pp , [25] G. Lu, G. Lachapelle, M.E. Cannon, P. Kielland, Attitude Determination in a Survey Launch Using Multi-Antenna GPS Technology, Proceedings of the 1993 National Technical Meeting of The Institute of Navigation, San Francisco, CA, January 1993, pp [26] P. Misra and P. Enge, Global Positioning System: Signals, Measurements, and Performance, 2nd ed. Lincoln, MA: Ganga-Jamuna Press, 2006 [27] Y.-H. Chen, J.-C. Juang, J. Seo, S. Lo, D. M. Akos, D. De Lorenzo, and P. Enge, Design and implementation of real-time software radio for anti-interference GPS/WAAS sensors, Sensors, vol. 12, no. 10, pp , 2012 [28] E. Kaplan, C. Hegarty, P. Ward, and J. Betz, Chapter 5: Satellite Signal Acquisition, Tracking, and Data Demodulation, Understanding GPS: Principles and applications 2nd ed., pp , Boston: Artech House, [29] P.W. Ward, The Natural Measurements of a GPS Receiver, Proceedings of the 51st Annual Meeting of The Institute of Navigation, Colorado Springs, CO, June 1995, pp [30] P.W. Ward, Performance Comparisons Between FLL, PLL and a Novel FLL-Assisted-PLL Carrier Tracking Loop Under RF Interference Conditions, Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998), Nashville, TN, September 1998, pp [31] P.W. Ward, T.D. Fuchser, Stability Criteria for GNSS Receiver Tracking Loops, NAVIGATION, Journal of The Institute of Navigation, Vol. 61, No. 4, Winter 2014, pp [32] N. Ashby, and M. Weiss, Global Position System Receivers and Relativity, NIST Technical Note (Vol. 7385), Boulder, Colorado: National Institute of Standards and Technology, 1999 [33] Trimble, Trimble NetR9 Geospatial, Retrieved July 19, 2015 from [34] Internation GPS Service (IGS), IGS Product Availability, Retrieved July 19, 2015 from cb.html [35] Google, My Maps, Retrieved June 3, 2015 from com/mymaps [36] Antcom, P/N: 3GNSSA4-XT-1, Retrieved June 20, 2015 from 1 GNSSAntennas1.pdf [37] GNSS SDR, SiGe GN3S Sampler v2 USB front-end, Retrieved July 20, 2015 from [38] Ettus Research, USRP N210, Retrieved June 20, 2015 from [39] National Instruments, NI GPS Simulator, Retrieved July 20, 2015 from [40] Ettus Research, DBSRX MHz Rx, Retrieved June 20, 2015 from [41] Microsemi, QUANTUM Chip Scale Atomic Clock, Retrieved June 20, 2015 from