UNIVERSITY OF CALGARY. Performance of GPS and Partially Deployed BeiDou for Real-Time Kinematic Positioning in. Western Canada. Jingjing Dou A THESIS

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1 UNIVERSITY OF CALGARY Performance of GPS and Partially Deployed BeiDou for Real-Time Kinematic Positioning in Western Canada by Jingjing Dou A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER SCIENCE GRADUATE PROGRAM IN GEOMATICS ENGINEERING CALGARY, ALBERTA JANUARY, 215 Jingjing Dou 215

2 Abstract China has completed the development of the first phase of its BeiDou satellite navigation system, which contains fourteen operational satellites at of the end of 212. This thesis implements the Real-Time Kinematic (RTK) positioning using the integrated GPS and BeiDou system in comparison to the GPS-only system to evaluate whether current BeiDou, which is designed to provide regional coverage in the Asia-Pacific region, can augment the GPS system in North America. Three types of measurements, L1-only, L1 and L2, and Wide-lane combination, were tested over short (1 m), medium (2 km), and long (4 km) baselines to give a comprehensive performance analysis in terms of RTK positioning. The signal quality and measurement precision of BeiDou are presented and compared with those of GPS. The availability and geometry, float and fixed positioning accuracy, convergence time of float ambiguities, Time To First-Fix (TTFF) the ambiguities, and the actual success rate of the ambiguities for the GPS/BeiDou system and the GPS-only system are compared to analyze the improvements brought by the current BeiDou system. Results reveal that BeiDou measurements have the same level of precision as GPS. Adding BeiDou improves the float positioning accuracy and accelerates the convergence time of the ambiguities over three different baselines. The actual success rates are improved and the TTFFs are reduced by inducing BeiDou in the L1-only and L1 and L2 cases. The use of the wide-lane combination brings great improvements in the ambiguity resolution particularly over longer baselines. With the additional BeiDou measurements, the actual success rates do not improve since they all maintain at 1%, but the TTFFs are reduced greatly over the three baselines. ii

3 Acknowledgements I would like to show my deep gratitude to all those who have directly or indirectly encouraged me, helped me, and guided me through the MSc program. Explicit appreciation goes to the following persons for their invaluable contributions to this thesis. First and foremost, my parents: Their endless love, trust, support, and encouragement over the years give me the most motivation to go each step closer to success. Thank my mom for being positive and supportive whenever life is up and down. Thank my dad for always encouraging me to achieve more of my potentials. Your passing makes me more determined to grow into a daughter whom you would be proud of. My supervisor, Professor Kyle O Keefe: Thanks for guiding me through to the right path with your knowledge and encouragement all the time. Your positive suggestions have given me constant confidence in this research, my MSc defense, and the ION conferences. I would not have made these successes without your wisdom and support. The financial sponsorship from you is also appreciated. Those individuals who work at PLAN Group: Particular thanks are extended to Vimal Bhandari, Rakesh Kumar, and Ali Jafarnia for helping me collect RTK data, which are the most significant sources of this research. I would also like to thank Zhe He for offering great discussions about BeiDou characteristics, Srinivas Bhaskar for patiently answering my questions about carrier phase positioning, and Erin Kahr for tutoring me to use Trimble Business Centre at the risk of iii

4 being besieged by your students. Besides, I would never forget to appreciate the company from Sergey Krasovski, Paul Verlaine Gakne, Elmira Amirloo, Mohammad Mozaffari, Chandra Tjhai, Lingran Li, and all other group members, without whom studying at PLAN Group would not have been as pleasant and exciting. My friends, Bei Huang, Hongfu Sun, Yihe Li, and Wenxin Yang: Thanks for encouraging me all the time and pulling me out of difficulties using your kindness, humor, and Chinese food. Your friendship is very precious for me. iv

5 Table of Contents Abstract... ii Acknowledgements... iii Table of Contents...v List of Tables... vii List of Figures... ix List of Symbols and Abbreviations...xv CHAPTER 1 : INTRODUCTION Background Literature Review Objectives and Contribution Thesis Outline...1 CHAPTER 2 : BEIDOU SYSTEM OVERVIEW The Development of BeiDou System BeiDou Constellation BeiDou Coordinate System The Definition of BeiDou coordinate system The difference between CGCS2 and WGS BeiDou Time System BeiDou Signal Structure BeiDou Navigation Message Orbit model Clock offsets and group delay Ionosphere model...26 CHAPTER 3 : RTK POSITIONING RTK Technology Overview Double Differential Error Sources Satellite Orbital Error Tropospheric Error Ionospheric Error Multipath and Noise Phase Measurements and Combinations Ambiguity Resolution...35 CHAPTER 4 : GPS/BDS RTK TESTS Data Sources Test Scenarios Scenario A Scenario B Scenario C True Coordinates...49 v

6 4.3 Hardware Characteristics Signal Tracking Information Measurement Precision Navigation Methodology: PLANSoft TM Analysis Methodology...72 CHAPTER 5 : RESULTS AND ANALYSIS Results of Scenario A Availability Position Accuracy Ambiguity Resolution Results of Scenario B Availability Position Accuracy Ambiguity Resolution Results of Scenario C Availability Position Accuracy Ambiguity Resolution CHAPTER 6 : CONCLUSIONS AND RECOMMEDATIONS Conclusions Recommendations REFERENCES APPENDIX A APPENDIX B APPENDIX C vi

7 List of Tables Table 2.1 BeiDou-II navigation system launch status (May 214) Table 2.2 Frequency bands of BeiDou satellite Table 2.3 The Gravitional coefficient and the Earth rotation rate of GPS and BDS ephemeris models Table 3.1 Magnitude of Spatially Correlated Double Differencing Errors... 3 Table 3.2 Carrier Phase Combinations Table 3.3 Comparison of GPS L1 and WL Errors Table 3.4 F-test Thresholds from central F-distribution (significance level 2%)... 4 Table 4.1 The details of the test Scenarios Table 4.2 The True Baseline Precision for all Scenarios... 5 Table 4.3 Signal Tracking of Scenario A - 1 m baseline Table 4.4 Signal Tracking of Scenario B 2 km baseline Table 4.5 Signal Tracking of Scenario C - 4 km baseline Table 4.6 Code and Phase Uncertainty Table 5.1 Median position errors from float solutions Scenario A - 1 m baseline using a15 o mask Table 5.2 RMS position errors from float solution (cm) Scenario A - 1 m baseline using a 15 o mask Table 5.3 Median Errors from Correctly fixed positions Scenario A - 1 m baseline using a 15 o mask Table 5.4 RMS Errors from Correctly fixed positions Scenario A - 1 m baseline using a 15 o mask Table 5.5 Actual Success Rate Probability Scenario A - 1 m baseline using a 15 o mask Table 5.6 Median position errors from float solution (cm) Scenario B - 2 km baseline using a 15 o mask Table 5.7 RMS position errors from float solution (cm) Scenario B - 2 km baseline using a 15 o mask vii

8 Table 5.8 Median Errors from Correctly fixed positions Scenario B - 2 km baseline using a 15 o mask Table 5.9 RMS Errors from Correctly fixed positions Scenario B - 2 km baseline using a 15 o mask Table 5.1 Actual Success Rate Probability Scenario B - 2 km baseline using a 15 o mask Table 5.11 Median position errors from float solution (cm) Scenario C - 4 km baseline using a 15 o mask Table 5.12 RMS position errors from float solution (cm) Scenario C - 4 km baseline using a 15 o mask Table 5.13 Median and RMS errors of the fixed positions using wide-lane Scenario C - 4 km baseline using a 15 o mask viii

9 List of Figures Figure 2.1 The Orbits of BeiDou-II GEO and IGSO (December, 212) Figure 2.2 CGCS2 Coordinate System Figure 4.1 The MGEX network (December 13, 214) Figure 4.2 Trimble R1 Receiver Figure 4.3 Data Collection, Scenario A - 1 m baseline Figure 4.4 The Test Scenario of 2 km baseline Figure 4.5 Data Collection, Scenario B - 2 km baseline Figure 4.6 Test Scenario of 4 km baseline Figure 4.7 Data Collection, Scenario C 4 km baseline Figure 4.8 L1/B1 C/N versus Elevation of Trimble Net R9 (base receiver) Figure 4.9 L2/B2 C/N versus Elevation of Trimble Net R9 (base receiver) Figure 4.1 L1/B1 C/N versus Elevation of Trimble R1 (rover receiver) Figure 4.11 L2/B2 C/N versus Elevation of Trimble R1 (rover receiver) Figure 4.12 DD Code and Phase Errors Scenario A - 1 m baseline using a 5 o mask... 6 Figure 4.13 DD Code and Phase Errors Scenario A - 1 m baseline using a 15 o mask Figure 4.14 DD Code and Phase Errors Scenario B - 2 km baseline using a 5 o mask Figure 4.15 DD Code and Phase Errors Scenario B - 2 km baseline using a 15 o mask Figure 4.16 DD Code and Phase Errors Scenario C - 4 km baseline using a 5 o mask Figure 4.17 DD Code and Phase Errors Scenario C - 4 km baseline using a 15 o mask Figure 4.18 The flow chart of GPS/BDS RTK in PLANSoft TM... 7 Figure 4.19 GPS/BDS RTK Analysis Methodology Figure 5.1 BDS Sky Plot of Scenario A - 1 m baseline using a 5 o mask Figure 5.2 GPS Sky Plot of Scenario A - 1 m baseline using a 5 o mask Figure 5.3 Elevation of BDS Satellites, Scenario A - 1 m baseline using a 5 o mask... 8 ix

10 Figure 5.4 Elevation of GPS Satellites, Scenario A - 1 m baseline using a 5 o mask Figure 5.5 Number of Visible Satellites, Scenario A - 1 m baseline using a 5 o mask Figure 5.6 EDOP, NDOP and UDOP, Scenario A - 1 m baseline using a 5 o mask Figure 5.7 Number of Visible Satellites, Scenario A - 1 m baseline using a 15 o mask Figure 5.8 EDOP, NDOP and UDOP, Scenario A - 1 m baseline using a 15 o mask Figure 5.9 Single-frequency (L1) Float Position Errors Scenario A - 1 m baseline using a 15 o mask Figure 5.1 Dual-frequency (L1 and L2) Float Position Errors Scenario A - 1 m baseline using a 15 o mask Figure 5.11 Wide-Lane combination Float Position Errors Scenario A - 1 m baseline using a 15 o mask Figure D view of position errors, Scenario A - 1 m baseline using a 15 o mask Figure D view of fixed position errors, Scenario A - 1 m baseline using a 15 o mask Figure 5.14 DD L1 float ambiguities of GPS satellites with PRN pair (2-21) using Single frequency measurements Scenario A 1 m baseline using a 15 o mask Figure 5.15 DD L1 float ambiguities of GPS satellites with PRN pair (5-21) using Dual frequency measurements Scenario A 1 m baseline using a 15 o mask... 1 Figure 5.16 DD float ambiguities of GPS satellites with PRN pair (2-21) using Wide-lane measurements Scenario A 1 m baseline using a 15 o mask Figure 5.17 DD float ambiguities of BDS satellites using Wide-lane measurements Scenario A 1 m baseline using a 15 o mask Figure 5.18 Time To First-Fix (TTFF) the ambiguities Scenario A - 1 m baseline using a 15 o mask Figure 5.19 BDS Sky Plot of Scenario B - 2 km baseline using a 5 o mask Figure 5.2 GPS Sky Plot of Scenario B - 2 km baseline using a 5 o mask Figure 5.21 Elevation of BDS Satellites, Scenario B - 2 km baseline using a 5 o mask Figure 5.22 Elevation of GPS Satellites, Scenario B - 2 km baseline using a 5 o mask Figure 5.23 Number of Visible Satellites, Scenario B - 2 km baseline using a 15 o mask Figure 5.24 EDOP, NDOP and UDOP, Scenario B - 2 km baseline using a 15 o mask x

11 Figure 5.25 Single-frequency (L1) Float Position Errors Scenario B - 2 km baseline using a 15 o mask Figure 5.26 Dual-frequency (L1 and L2) Float Position Errors Scenario B - 2 km baseline using a 15 o mask Figure 5.27 Wide-lane combination Float Position Errors Scenario B - 2 km baseline using a 15 o mask Figure D view of position errors, Scenario B - 2 km baseline using a 15 o mask Figure D view of fixed position errors, Scenario B - 2 km baseline using a 15 o mask Figure 5.3 DD L1 float ambiguities of GPS satellites with PRN pair (2-5) using Singlefrequency measurements Scenario B 2 km baseline using a 15 o mask Figure 5.31 DD L1 float ambiguities of GPS satellites with PRN pair (2-5) using Dualfrequency measurements Scenario B 2 km baseline using a 15 o mask Figure 5.32 DD float ambiguities of GPS satellites with PRN pair (2-5) using Wide-lane measurements Scenario B 2 km baseline using a 15 o mask Figure 5.33 Time To First-Fix (TTFF) the ambiguities Scenario B - 2 km baseline using a 15 o mask Figure 5.34 BDS Sky Plot of Scenario C - 4 km baseline using a 5 o mask Figure 5.35 GPS Sky Plot of Scenario C - 4 km baseline using a 5 o mask Figure 5.36 Elevation of BDS Satellites, Scenario C - 4 km baseline using a 5 o mask Figure 5.37 Elevation of GPS Satellites, Scenario C - 4 km baseline using a 5 o mask Figure 5.38 Number of Visible Satellites, Scenario C - 4 km baseline using a 15 o mask Figure 5.39 EDOP, NDOP and UDOP, Scenario C - 2 km baseline using a 15 o mask Figure 5.4 Single-frequency (L1) Float Position Errors Scenario C - 4 km baseline using a 15 o mask Figure 5.41 Dual-frequency (L1 and L2) Float Position Errors Scenario C - 4 km baseline using a 15 o mask Figure 5.42 Wide-lane combination Float Position Errors Scenario C - 4 km baseline using a 15 o mask Figure D positioning errors using correctly fixed wide-lane ambiguities Scenario C 4 km baseline using a 15 o mask xi

12 Figure 5.44 DD L1 float ambiguities of GPS satellites with PRN pair (5-7) using Single frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure 5.45 DD L1 float ambiguities of GPS satellites with PRN pair (5-7) using Dual frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure 5.46 DD float ambiguities of GPS satellites with PRN (3-5) using Wide-lane measurements Scenario C - 4 km baseline using a 15 o mask Figure 5.47 DD float ambiguities of BDS satellites using Wide-lane measurements Scenario C 4 km baseline using a 15 o mask Figure 5.48 Time To First-Fix (TTFF) the ambiguities Scenario C - 4 km baseline using a 15 o mask Figure A.1 GPS L1 DD float ambiguities using GPS Single frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.2 GPS L1 DD float ambiguities using GPS/BDS Single frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.3 BDS B1 DD float ambiguities using GPS/BDS Single frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.4 GPS L1 DD float ambiguities using GPS Dual frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.5 GPS L2 DD float ambiguities using GPS Dual frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.6 GPS L1 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.7 GPS L2 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.8 BDS B1 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.9 BDS B2 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario A - 1 m baseline using a 15 o mask Figure A.1 GPS DD float ambiguities using GPS Wide-lane measurements Scenario A - 1 m baseline using a 15 o mask Figure A.11 GPS DD float ambiguities using GPS/BDS Wide-lane measurements Scenario A - 1 m baseline using a 15 o mask xii

13 Figure A.12 BDS DD float ambiguities using GPS/BDS Wide-lane measurements Scenario A - 1 m baseline using a 15 o mask Figure B.1 GPS L1 DD float ambiguities using GPS Single frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.2 GPS L1 DD float ambiguities using GPS/BDS Single frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.3 BDS B1 DD float ambiguities using GPS/BDS Single frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.4 GPS L1 DD float ambiguities using GPS Dual frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.5 GPS L2 DD float ambiguities using GPS Dual frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.6 GPS L1 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.7 GPS L2 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.8 BDS B1 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.9 BDS B2 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario B - 2 km baseline using a 15 o mask Figure B.1 GPS DD ambiguities using GPS Wide-lane measurements Scenario B - 2 km baseline using a 15 o mask Figure B.11 GPS DD ambiguities using GPS/BDS Wide-lane measurements Scenario B - 2 km baseline using a 15 o mask Figure B.12 BDS DD ambiguities using GPS/BDS Wide-lane measurements Scenario B - 2 km baseline using a 15 o mask Figure C.1 GPS L1 DD float ambiguities using GPS Single frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure C.2 GPS L1 DD float ambiguities using GPS/BDS Single frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure C.3 BDS B1 DD float ambiguities using GPS/BDS Single frequency measurements Scenario C - 4 km baseline using a 15 o mask xiii

14 Figure C.4 GPS L1 DD float ambiguities using GPS Dual frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure C.5 GPS L2 DD float ambiguities using GPS Dual frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure C.6 GPS L1 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure C.7 GPS L2 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure C.8 BDS B1 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure C.9 BDS B2 DD float ambiguities using GPS/BDS Dual frequency measurements Scenario C - 4 km baseline using a 15 o mask Figure C.1 GPS DD ambiguities using GPS Wide-lane measurements Scenario C - 4 km baseline using a 15 o mask Figure C.11 GPS DD ambiguities using GPS/BDS Wide-lane measurements Scenario C - 4 km baseline using a 15 o mask Figure C.12 BDS DD ambiguities using GPS/BDS Wide-lane measurements Scenario C - 4 km baseline using a 15 o mask... 2 xiv

15 List of Symbols and Abbreviations Symbol Definition a Semi-major axis of the CGCS2 ellipsoid b length of baseline c speed of light d ionospheric delay iono d tropospheric delay dt dt ê e F N P trop s sv rx sb, Q â satellite clock errors receiver clock errors phase residuals based on the float ambiguities phase residuals based on the fixed ambiguities ratio test threshold integer ambiguities predicted success rate of the integer least square P predicted success rate of the integer bootstrapping Q y R () () variance-covariance matrix of the float ambiguities variance-covariance matrix of the phase measurements geometric range between receivers single differencing double differencing measurement noise and multipath carrier wavelength approximate distance from the receivers to the satellites phase measurement Abbreviations Definition BDS BeiDou Navigation Satellite system BDT BeiDou navigation satellite system Time CDMA Code Division Multiple Access CGCS2 China Coordinate System 2 DLR German Space Agency FASF Fast Ambiguity Search Filter GEO Geostationary Orbit GNSS Global Navigation Satellite Systems GPS Global Positioning System ICD Interface Control Document IERS International Earth Rotation and Reference System Service IGSO Inclined Geosynchronous Satellite Orbit xv

16 ILS Integer Least-Squares IRP Reference Pole ITRF97 International Terrestrial Reference Frame 1997 LAMBDA Least-Square Ambiguity Decorrelation Adjustment MEO Medium Earth Orbit MGEX Multi-GNSS Experiment RDSS Radio Determination Satellite Service RTK Real-Time Kinematic TTFF Time To First-Fix UTC Coordinated Universal Time WGS84 World Geodetic System 1984 WL wide-lane measurement combination xvi

17 CHAPTER 1 : INTRODUCTION Satellite positioning and navigation is playing an ever-increasing role in today s society. The applications include commercial aircraft positioning, precise surveying for mapping, automobile positioning for instantaneous bus scheduling and so on, ranging from military to civil users. However, the availability and reliability can be impaired greatly under some challenging environments such as urban canyons, mountain valleys, and deep open-pit mines. Therefore, the integration of the emerging Global Navigation Satellite Systems (GNSS) and the existing Global Positioning System (GPS) is implemented to improve the current GPS system. For this reason, as the fourth GNSS system, the BeiDou Navigation Satellite System (BDS) has received tremendous attention especially on carrier phase-based applications, for instance, Real Time Kinematic (RTK) satellite navigation, which can give centimetre-level positioning accuracy. All of this prior work has focused on either the theoretical performance of the fully deployed system, or on the actual performance of the first phase of the system in its Asia-Pacific service area. This thesis focuses on the performance of the new-built BDS and the augmentation it brings to GPS in terms of RTK positioning in North America where only a limited number of BeiDou satellites are currently visible. 1.1 Background China is now developing its own independent global navigation satellite system which is called the BeiDou Navigation Satellite System. The Interface Control Document (ICD) was published in December 212 and the deployment of the first phase of BeiDou global navigation satellite system (BeiDou-II/COMPASS) consisting of fourteen satellites has been completed. The 1

18 BeiDou regional navigation satellite system is also known as the first phase of the BeiDou global navigation satellite system which is public to the users all over the world. Further to this, since BDS adopts similar design to GPS, the operation of dual positioning system (i.e., GPS and BDS) can be easily implemented. Given these, a considerable amount of research has been conducted to evaluate the performance of the BeiDou system. According to current BDS ephemerides, in the Asia Pacific region, ten BDS satellites are typically visible at any given time. Globally, for instance, in North America, two or three Medium Earth Orbit (MEO) satellites and one or two Inclined Geosynchronous Satellite Orbit (IGSO) satellites can be simultaneously tracked during limited time. However, most of the investigations of BDS are only limited within the Asia Pacific region, which is the main coverage area of the Geostationary Orbit (GEO) satellites and the IGSO satellites. Considering the design purpose of BDS is to provide global positioning service, it is valuable to compensate the current research through investigating the performance of BDS outside of the Asia Pacific area. Among these investigations on BDS, RTK positioning, as a commonly used high-precision positioning technology, has received increasing attention since many applications require or could benefit from such high positioning accuracy (i.e., centimetre-level). The applications of RTK positioning include precise land surveying, precision agriculture, structural monitoring, deforming monitoring, petroleum exploration, unmanned aerial vehicles shipboard landing and so on. Therefore, this thesis implements GPS and BDS RTK to evaluate whether partially deployed BDS can contribute to augmenting GPS RTK positioning in North America. 2

19 1.2 Literature Review The investigations on BDS were initiated from simulations and extended to real data. Since China announced the development of the BeiDou Navigation Satellite System, tremendous research has been conducted to illustrate the performance of the BDS by simulating its measurements. The results can be found in Greilier et al. (27a), Huang and Tsai (28), Cao et al. (28), Chen et al. (29), Zhang et al. (21), Guo et al. (211), Verhagen and Teunissen (213). These simulations demonstrated that the average number of visible satellites can be more than sixteen in China and neighborhood regions. In addition, in terms of relative positioning, BDS may have poorer performance of ambiguity resolution comparing with GPS and Galileo on the basis of an assumption that BDS signals had larger noise level. Since the BDS satellites share many common features with GPS, investigations of the transmitted signals started immediately after the launch of the COMPASS-M1 (MEO) experimental satellite in 27. The analysis was presented in Greilier et al. (27b), De Wilde et al. (27), Gao et al. (29), Septentrio (21), and Hauschild et al. (211). These papers indicated that the signal strength of the experimental BDS satellite was larger than GPS, while the range accuracy was comparable to GPS. Further, the satellite clock solution demonstrated unexpectedly high temporal variations, which might be due to the instability of the onboard clock that may have rapid frequency offset variations. Positioning was impossible at that time because only one MEO satellite was available. Because of the deployment of the BeiDou Regional Satellite System (i.e., first phase of BeiDou Global Satellite System) and the publication of the Interface Control Document (ICD) of BDS in 3

20 December 212, extensive investigations became possible with the increasing number of visible BDS satellites. Several researchers provided preliminary positioning analysis of BDS using data collected in China, as the main coverage region of GEO and IGSO satellites is China. The first positioning analysis of the BDS in the world was published in Shi et al. (212a) using GEO and IGSO measurements collected in Wuhan, China. The visibility of satellites and validity of measurements, carrier-to-noise density ratio and code noise were analyzed. The analysis of multipath combinations showed that the noise level of BDS code measurements was higher than that of GPS. For the standalone BDS solutions, an accuracy of within 1.5 m horizontal and 3. m vertical was obtained, using dual-frequency code only measurements for a short baseline. The precise relative positioning using code and phase together for the short baseline can reach better than 4 cm, which can improve the accuracy of GPS alone by 2% at least when integrated with GPS. In the same year, when two more MEO satellites were added to the BeiDou constellation, results of precise orbit determination, static PPP and kinematic RTK positioning with BDS were given by the same group in Shi et al. (212b), which revealed that the radial accuracy of precise orbit determination for BDS satellites was better than 1 cm; the accuracy of static PPP, relative baseline positioning, and kinematic RTK positioning can achieve centimetre-level, millimetrelevel, and 5-1 cm accuracy respectively, able to satisfy the high accuracy needs within China. Similarly, the accuracy analysis of precise orbit determination and timing for BeiDou-II 4 GEO, 5 IGSO and 4 MEO constellation can be found in Zhou et al. (213). Later, single-epoch BeiDou carrier phase ambiguity resolution using three civil frequencies, using a third frequency provided by Radio Determination Satellite Service (RDSS), was firstly proposed by Qu et al. (212). With increasing focus on precise relative positioning, the first results of the short baseline singleepoch RTK positioning based on dual-frequency for the combined BDS/GPS were presented in 4

21 He et al. (213), which showed that the fixed rate and reliability of ambiguity resolution for the BDS/GPS was remarkably improved as compared to that of GPS-only and the single-epoch dualfrequency RTK positioning accuracy for BDS/GPS was improved by 23% and 4% relative to the GPS-only case with two short baseline tests respectively. The results also showed that the BDS/GPS RTK required initialization for several seconds. In addition, the first single-epoch dual-frequency RTK positioning for BDS-only case was shown in Li et al. (213a) in which the full constellation of BeiDou regional satellite system was used. The results indicated that the accuracy of BeiDou RTK positioning was slightly worse than that of GPS at that time, but it had reached to millimetre to centimetre level over very short and short baselines. Afterwards, the same group published more complete assessment of BDS including the satellite visibility, the precision of code and carrier phase measurements, the accuracy of single point positioning and differential positioning in Yang et al. (213). The research demonstrated that the fixed rate and reliability of single-epoch and dual-frequency ambiguity resolution was comparable to those of GPS and the accuracy of BDS carrier phase differential positioning was better than 1 cm for a very short baseline and 3 cm for a short baseline. However, the accuracy of BDS code differential positioning was worse than that of GPS, which may result from large code multipath errors of BDS GEO satellite measurements. Besides, some attention was paid to the analysis of the code multipath and the geometry of GEO satellites. There have also been a limited number of results published by researchers outside China, although only within Asia Pacific region. The first analysis of BeiDou-II using real data outside China was given in Montenbruck et al. (212), which was based on nine GEO and IGSO satellites using data collected at some monitoring stations in Asia Pacific region. The signal 5

22 quality and tracking performance were described and special attention was given to the availability of three frequencies. Besides, first results of a short baseline relative positioning from BDS were presented, showing a consistency of about 1 cm comparing to GPS. Immediately following the above research, a further research was given in Montenbruck et al. (213), which illustrated the quality of code and phase measurements of up to three frequencies. The performance of the onboard Rubidium frequency standards was evaluated and shown to be well competitive with other GNSS satellite clocks. Precise orbit and clock solutions were obtained and used in point positioning for BDS alone. More importantly, it illustrated the benefit of triplefrequency measurements and extra-wide-lane ambiguity resolution for relative positioning on short baselines. The receiver relative positioning results based on code measurements with three frequencies for short baselines were shown in Odolinski et al. (214a). The standard deviations reached around.5 m horizontally and 1 m vertically for BDS alone system. Also, the results of single-frequency and multi-frequency single point positioning were presented in the same research. As to high precision positioning, Steigenberger et al. (212, 213) analyzed the orbit determination and PPP of BeiDou-II and the analysis of the combined GPS/BDS RTK positioning was reported by Odolinski et al. (213a, b) for single-epoch and single-frequency RTK using B1 and L1 in Australia. As the BDS became operational in the Asia Pacific region, Teunissen et al. (213) and Odolinski et al. (214b) demonstrated the capabilities that a combination of BDS with GPS brought to positioning. Single epoch, single-frequency and dualfrequency RTK positioning were conducted with an extra focus on the cut-off elevations. The meaning of ADOP and bootstrapped success rate of ambiguity resolution is explained mathematically in depth. For the first time, the comparison between multi-frequency and multisystem ambiguity resolution was conducted with real-data and showed that the single-frequency 6

23 combined system had an ambiguity resolution performance that was similar to that of a dualfrequency single system, but the positioning capability outperformed that of the dual-frequency single system especially for large cut-off elevations. Shortly after that, Odolinski et al. (214c) presented the long baseline RTK results using GPS/BDS/Galileo/QZSS, in which the ionosphere-float strategy were used to model the slant ionospheric delays. In industry, almost all Chinese navigation companies (i.e., South, Hi Target, ComNav, Unicorecomm, Unistrong) have produced hardware receivers that can perform BeiDou RTK positioning. Some companies outside China, including, but not limited to, Trimble, NovAtel, Leica and U-blox have receivers that can track BeiDou signals and provide positioning results. Trimble and Leica have products that support BeiDou RTK. 1.3 Objectives and Contribution The RTK positioning using GPS/BDS or even BDS alone has proven very successful. However, as stated before, all of the work done so far has only been focusing on the Asia Pacific region, which can benefit from the regional augmentation of GEO and IGSO satellites. For global common GNSS users outside of the regional coverage area, only MEO satellites and sometimes very low elevation IGSO satellites are observable according to the design of the BDS constellation. Therefore, the performance analysis based on the Asia Pacific Region only considers the augmented BDS system, failing to give a fair evaluation of BDS, which is supposed to be a global system. Given these, the main objective of this thesis is to assess the performance of BDS outside of the Asia Pacific region (i.e., North America) and investigate 7

24 whether the current regional BDS can improve the current GPS system in terms of RTK positioning. Under the scheme of investigating BDS RTK positioning in North America, some other attention regarding the RTK technology has also been paid to compensate the current research. In the context of differential positioning, the spatially related errors including the satellite orbital errors, ionospheric errors, and tropospheric errors have increasing effects on the RTK positioning due to the separation of the base and rover receivers. It is more desirable if an RTK system can allow a longer base-to-rover baseline. However, almost all the research of BDS RTK to date has focused on very short baseline or short baseline (i.e., no longer than 1 km). Odolinski et al. (214b) mentioned long baseline RTK positioning using GPS/BDS, but the long baseline was defined as the necessity to model the ionospheric delays and no specific baseline lengths were given in the paper. Therefore, another objective of this thesis is to evaluate how BDS performs in the integrated GPS/BDS system when implementing standard RTK positioning (without ionospheric modelling) over different baselines (i.e., about 1 m, 2 km, and 4 km) where the currently accepted operational range of RTK without modelled ionospheric delays is around 2 km. In RTK positioning, inter-frequency carrier phase combinations can bring many benefits such as greater baselines, reduced or eliminated ionospheric impact, reduced noise level and so on. The BDS provides the possibility for the frequency combinations with its two open service frequencies. Therefore, BDS RTK positioning using carrier phase combinations deserves some attention. Even though some dual-frequency RTK positioning using BDS has been investigated by Li et al. (213a), Yang et al. (213), Teunissen et al. (213, 214), and Odolinski et al. 8

25 (214b), these investigations were geared at evaluating the performance with an extra observation of a second frequency, failing to discuss and demonstrate the benefits of frequency combinations. This was because that much of the work was with very short baseline and short baseline, which can hardly represent the contribution brought by the frequency combinations. Considering that the investigation of long baseline is included in this thesis, it is therefore meaningful to investigate how frequency combination (i.e., wide-lane combination) could affect the RTK performance especially with longer baselines. Carrier phase ambiguity resolution is a key procedure in RTK positioning. The instantaneous (i.e., single-epoch) ambiguity resolution is the most challenging case to investigate and the advantage is that the results of instantaneous ambiguity resolution will be insensitive to the carrier phase cycle slips. Hence, all the exiting research of BDS RTK positioning had been done was based on the single-epoch measurements. However, the single-epoch solution is not practically used in real applications due to its poor accuracy and reliability induced by code noise and multipath. Since the carrier ambiguities remain constant over time if no cycle slip is detected, the ambiguities can be estimated using measurements over multiple epochs to smooth out the multipath to a certain extent. In this light, this thesis also aims to analyze the most realistic performance of BDS RTK positioning by implementing ambiguity resolution over multiple epochs. The contribution of this thesis is firstly presenting the BDS RTK performance in North America. The signal quality, the measurement precision, the availability, and the geometry of BDS were comprehensively analyzed. The float and fixed positioning accuracy were given and interpreted 9

26 in details. The ambiguity resolution was evaluated in terms of the convergence time, the actual success rate and the Time To First-Fix (TTFF). At the same time, the baseline length of about 2 km and 4 km was firstly attempted and the RTK positioning was implemented using the singlefrequency (i.e., L1, B1), dual-frequency (i.e., L1/L2, B1/B2), and combined wide-lane measurements. To accomplish the above, PLANSoft TM, which was developed by the Positioning, Location And Navigation (PLAN) Group at the University of Calgary, was modified and further developed by including the new BDS system to the current GPS and GLONASS. Three different field tests were conducted under open sky scenarios over 1 m, 2 km, and 4 km baselines. The results were compared between the GPS-alone solutions and the integrated GPS/BDS solutions. The work presented in this thesis had been presented in two conference papers (Dou and O Keefe 213; Dou and O Keefe 214) in the proceedings of the Institute of Navigation GNSS Meetings. 1.4 Thesis Outline This thesis consists of six chapters. Chapter One introduces the motivations and objectives of this thesis. The work and limitations of previous research are reviewed and discussed. Finally, the scope and objective of the research are defined. Chapter Two presents an overview of BeiDou Navigation Satellite System. The error sources of BeiDou system are discussed in detail. The transmitting signals and broadcasting ephemeris is evaluated and their role in RTK positioning is discussed. 1

27 Chapter Three presents the technology of RTK positioning. GNSS RTK positioning and the sources and levels of double differential measurements errors are described. The ambiguity estimation and ambiguity resolution algorithm are also introduced. Chapter Four describes the testing, data processing and analysis methods. Three types of baselines are proposed: 1) very short baseline; 2) medium baseline; 3) long baseline. The characteristics of the utilized hardware are tested and analyzed. The various strategies for incorporating measurements into the RTK solutions are outlined, and the methods and visual displays used to analyze the GPS/BeiDou RTK performance are also defined. The results of the different baselines testing are presented in Chapter Five. This chapter investigates the impact of BeiDou and dual-frequency measurement combinations on the availability of satellites, the performance of ambiguity resolution, as well as the float and fixed ambiguity positioning accuracy. The causative and related factors of ambiguity are then investigated in details, including the convergence time of the float ambiguities, the actual success rate, and the Time To First-Fix the ambiguities. These are illustrated to visually facilitate interpretation. Chapter Six concludes this thesis and presents the major findings from the previous chapters. Recommendations for future research in this area are finally made. 11

28 CHAPTER 2 : BEIDOU SYSTEM OVERVIEW 2.1 The Development of BeiDou System In a quest for independence, China has been pursuing the build-up of a proprietary national satellite system for more than a decade. Named after the constellation of the Great Bear, BeiDou Navigation Satellite System is called BeiDou System for short, with the abbreviation as BDS (CSNO 212). The BeiDou system will eventually provide global coverage with positioning, navigation and time services by 22 according to its own development plan (CSNO 213a). The development of BeiDou system follows the three-step strategy, which is, the Demonstration system, Regional system and Global system. The demonstration system which is called BeiDou-I was completed in 23. BeiDou-I was a regional system consisting of two geostationary satellites and one backup satellite that used 4-way ranging and data relay from ground stations and a different signal structure than the regional and global systems. Following the successful deployment and operation of the Demonstration system, the BeiDou-II (also known as Compass) was initiated in 27 with the first launch of a first navigation satellite (Compass-M1) into the Medium Earth Orbit (Montenbruck et al 213). The BeiDou-II system includes two phases. The first phase is the BeiDou regional system. One MEO and one GEO satellite were launched respectively in 27 and 29. Its implementation was speeded up later, and five satellites (three GEO and two IGSO) were launched in 21, three IGSO satellites in 211, and six satellites (two GEO and four MEO) in 212. By the end of 212, the first phase of BeiDou-II system has been completed along with the release of the version 1. of the Signal-in- 12

29 Space Interface Control Document. A start of regional positioning, timing and short message services for users throughout Asia and Australia was declared at the same time (CSNO 213a). The satellites list of the first phase of BeiDou-II is presented in Table 2.1 (Multi-GNSS Experiment Constellation 214). By October 25 th, 212, a total of sixteen BeiDou-II navigation satellites have been launched. Presently, an apparent clock problem has been reported for the M1 satellite, which inhibits its use for navigation despite a continued signal transmission. Furthermore, the G2 is no longer transmitting signals and performs an uncontrolled vibration motion around the stable geostationary point (Montenbruck et al, 213). The remaining five GEO satellites, five IGSO satellites and four MEO satellites are fully operational. The second phase of BeiDou-II aims to provide global service. From 214, additional satellites will be launched, while regional service performances will be advanced and expanded to the worldwide scope. Approximately forty BeiDou navigation satellites in total will have been launched by about 22, and the system with global coverage will be fully established (CSNO 213a). 13

30 Table 2.1 BeiDou-II navigation system launch status (May 214) Sat PRN Launch Date Orbit Type Longitude (degrees) Status M1 C MEO Not in use G2 N/A GEO Not in use G1 C GEO 14 o E In use G3 C GEO 11.5 o E In use I1 C IGSO 12 o W In use G4 C GEO 16 o E In use I2 C IGSO 12 o W In use I3 C IGSO 12 o W In use I4 C IGSO 95 o W In use I5 C IGSO 95 o W In use G5 C GEO o E In use M3 C MEO In use M4 C MEO In use M5 C MEO In use M6 C MEO In use G6 C GEO 8.3 o E In use In order to enable users obtain a better understanding of BDS and to make BDS serve the users better, China Satellite Navigation Office (CSNO) published the BeiDou Navigation Satellite System Signal In Space Interface Control Document Open Service Signal B1I (BeiDou ICD 14

31 V1.) on December 27 th, 212 and BeiDou Navigation Satellite System Signal-In-Space Interface Control Document Open Service Signal (BeiDou ICD V2.) on December 27 th, 213. The BeiDou ICDs (i.e., V1. and V2.) specify the interface relationship between the satellites and user terminals to use the BDS open service signal B1I and B2I. They identify the coordinate framework and time reference of BDS, specify the signal structure, basic characteristics and parameters, and ranging code specifications related to B1I and B2I signals, define navigation message. BeiDou Navigation Satellite System Open Service Performance Standard (version 1.) was also published together with the BeiDou ICD V2.. It describes the BDS overall structure, Signal-In-Space characteristics and performance specifications, system open service performance characteristics and specifications in details. With the publication of these documents, BDS becomes the first global navigation satellite system which possesses two civil signal frequencies and has already provided service capability. Based on these documents, domestic and international enterprises can develop dual-frequency, high-precision BeiDou receivers, to enable the users achieve navigation services with higher accuracy. According to the development and current status of BeiDou Satellite System, the research of this thesis is completely based on the first phase of BeiDou-II system with fourteen satellites in operation. For clarification, the second phase of BeiDou-II Satellite System will be referred to as BDS or BeiDou system interchangeably for short in the following chapters. 2.2 BeiDou Constellation In contrast to other GNSSs, the constellation of BeiDou system consists of three types of orbits, which are MEO, GEO, and IGSO. By 22 when the system is fully operational, twenty-seven 15

32 MEO satellites, five GEO satellites, and three IGSO satellites will be in orbit. The MEO has an altitude of 21,528 km, with a period of 12h53m and an inclination of 55 o to the equatorial plane. The GEO satellites, which have an altitude of 35,786 km, are operating at almost constant positions in an Earth fixed system. The IGSO has the same altitude and inclination as GEO with an eccentricity less than.3 and a period of 23h56m, which results in a daily repeat ground track shaped like a symmetric figure of eight (CSNO 212). Figure 2.1 gives the orbits of GEO and IGSO satellites (Chen 213). It can be observed that the main purpose of GEO and IGSO is regional augmentation. The current constellation was finished at the end of 212 and includes four MEO, five GEO and five IGSO satellites as stated before. 16

33 Figure 2.1 The Orbits of BeiDou-II GEO and IGSO (December, 212) 2.3 BeiDou Coordinate System The Definition of BeiDou coordinate system According to the BeiDou ICD V1., the BeiDou system uses the China Coordinate System 2 (CGCS2) as shown in Figure 2.2. CGCS2 is referred to the International Terrestrial Reference Frame 1997 (ITRF97). The origin is located at the mass center of the earth. The Z-axis is in the direction of the IERS (International Earth Rotation and Reference System Service) Reference Pole (IRP) and the X-axis is directed to the intersection of IERS Reference Meridian 17

34 (IRM) and the plane passing the origin and normal to the Z-axis. The Y-axis, together with Z- axis and X-axis, constitutes a right handed orthogonal coordinate system (CSNO 212). Figure 2.2 CGCS2 Coordinate System The origin of the CGCS2 is also the geometric center of the CGCS2 ellipsoid, and the Z- axis is the rotation axis of the CGCS2 ellipsoid. The basic parameters of the CGCS2 ellipsoid are: 1) Semi-major axis: a m 2) Geocentric gravitational constant (mass of the earth atmosphere included): GM m s 3) Flattening: f 1/ ) Rate of earth rotation: rad / s 18

35 2.3.2 The difference between CGCS2 and WGS84 Since GPS uses World Geodetic System 1984 (WGS84) coordinate reference system while BDS uses CGCS2 system, a question should be considered when GPS and BDS are integrated: whether the coordinate frames transformation is needed? To answer this question, it is necessary to compare the difference between these two coordinate systems. The definitions of the CGCS2 and WGS84 coordinate system are consistent. The origin, scale, and orientation are all defined the same. The reference ellipsoids using by these two systems are very close to each other. Among the four parameters of the ellipsoid (i.e., a, f, GM, ), the semi-major axis a, the geocentric gravitational constant GM, and the rate of earth rotation are equivalent. Slight differences exist in the flattening f : f WGS 84 f CGCS 2 1/ / (2.1) According to the above equation, the flattening difference is: df f f 11 CGCS 2 WGS (2.2) The flattening difference df will make the coordinates of the same position different in these two coordinate systems. The changes of the geodetic latitude B, longitude L, and height H are shown in Equation (2.3). dl 2 2 M 2 (2 f f )sin B db sin B cos Bdf 1 f M 1 f dh 1 (2 f f )sin B sin Bdf (2.3) 19

36 where M is the radius of curvature in meridian. From Equation (2.2) and Equation (2.3), the changes of the geodetic latitude B, longitude L, and height H can be summarised as follows: 1) df does not change the latitude o 2) df makes the longitude change from mm (on the Equator) to.15 mm ( B 45 ) 3) df make the height change from mm (on the Equator) to.15 mm (at the Poles) At Calgary (N 51 o ), the changes of latitude and height are about.13 mm and.61mm respectively. Depending on the discussion above, the differences of the coordinates in CGCS2 and WGS84 caused by the different flattenings for each reference ellipsoid are very slight. The CGCS2 and WGS84 were realized from a set of monitor stations, whose coordinates were derived from successive refinements to agree with ITRF. The accuracy of the current realizations for both systems can be at the centimetre level. Therefore, the two systems are consistent within their accuracies. For most of the applications, the difference between these two coordinate systems in both the definition level and realization level can be ignored. 2.4 BeiDou Time System The BeiDou system uses the BeiDou navigation satellite system Time (BDT) as the time reference. As for the GPS time system, BDT is a continuous timekeeping system, with its length of second being an international system of units (SI) second, without leap seconds. The zero time of BDT stated at :: on January 1st, 26 of Coordinated Universal Time (UTC). The offsets of BDT and GPS with respect to UTC are controlled within 1 ns (CSNO 212) and 25 2

37 ns (IS-GPS-2 212) respectively, which are donated as C B and C G herein. The relations between the systems are: GPST UTC tls C BDT UTC tls C G B (2.4) Therefore, the relation between GPST and BDT is: where GPST BDT tls C C (2.5) G B tls is the leap second of UTC. The leap seconds are broadcast in navigation message: tls tls s 14s (2.6) The RTK algorithm of this thesis was implemented in the GPS time system so that the BDT was transformed into GPST and 14 seconds of leap seconds were used herein. The effects of the remaining part in Equation (2.5), CG CB, can be eliminated by double differencing. 2.5 BeiDou Signal Structure The BeiDou system uses code division multiple access (CDMA) signals similar to those of the GPS system. Signals from BeiDou satellites are transmitted in three frequencies B1, B2, and B3. As shown in Table 2.2 (Steigenberger et al. 213), the B1 band is close to the GPS L1 frequency of MHz and the B2 frequency is identical to Galileo E5b. The B3 band is close to Galileo E6 with frequency of MHz. There is no overlap between the BDS frequencies and the GPS frequencies, and thus no Inter-system-bias parameterizations are needed when integrating GPS and BDS (Odijik and Teunissen 213a). 21

38 Table 2.2 Frequency bands of BeiDou satellite Band Frequency (MHz) Comment B Close to GPS L1 B Same as Galileo E5b B Close to Galileo E6 According to the latest BeiDou ICD, only B1 and B2 are open service signals. Tracking of the B3 signal to date is only possible due to knowledge about the signal structure and ranging codes obtained from analyses conducted with high-gain antennas (Gao et al. 29). The signals of B1 and B2 are the sum of channel I and Q, which are in phase quadrature of each other. In the research of this thesis, the signals from B1I and B2I are used for RTK positioning. 2.6 BeiDou Navigation Message The BeiDou system uses two types of navigation messages, which are D1 and D2, transmitted by the MEO/IGSO and GEO satellites, respectively (CSNO 212). The D1 navigation message is comparable to that of GPS, which is transmitted at the same data rate of 5 bits/s. The contents of D1 include the basic ephemeris data, and almanac information, and the inter-system time offsets for all the satellites. The D2 navigation message, which contains not only the information on D1 but also the pseudorange corrections and the ionosphere grid data for regional users, is transmitted with a data rate of 5 bits/s. Even though the data rate of D2 is ten times higher than D1, the basic ephemeris data of D2 are split across a sequence of ten pages, which results in the same repeat duration of 3 s as for these of D1. Therefore, the basic ephemeris data transmitted by MEO/IGSO and GEO are at the same data rate as GPS. 22

39 The specific choice of data bits and scaling factors for BeiDou ephemeris parameters was compared with those of GPS in Montenbruck and Steigenberger (213). The representation of all orbits related parameters matches that of GPS. A larger number of data bits are used for the clock offset polynomial, which allows for a better solution of the clock offset, the first and second order derivatives due to a high stability of the BeiDou Rubidium clock. This was demonstrated in Hauschild et al. (213). Receiver-level users need to take corresponding care discussed above when decoding the BeiDou ephemeris data. Since this is not in the scope of this thesis, the readers can refer to the research mentioned above for more details. As a positioning-level user to utilize the ephemeris output from the receivers, the following broadcast navigation models are investigated Orbit model The BeiDou constellation has three types of orbits (i.e., MEO, IGSO, and GEO). The orbit model is consistent with that of GPS and the same set of orbital parameters is defined for all types of satellites. However, two differences exist in the orbital model between GPS and BDS. The first is that the BDS uses different values of the Earth gravitational coefficient GM and the Earth rotation rate as shown in Table 2.3. The specific values should be used for the corresponding constellation to achieve better accuracy of the broadcast ephemeris. 23

40 Table 2.3 The Gravitional coefficient and the Earth rotation rate of GPS and BDS ephemeris models Constellation 3 2 GM ( m / s ) ( rad / s) GPS BDS The second difference is the final transformation of the satellite position from the orbital plane (i.e., x, y ) to the Earth-fixed coordinates (i.e., X, Y, Z ) for BDS GEO satellites. Usually the k k k k k transformation is conducted as a rotation about the x-axis by the inclination angle i and a subsequent rotation about the z-axis by the longitude of ascending node system: k in the Earth-fixed k e k e oe X x cos y cosi sin Yk xk sin k yk cosik cos k Zk yk sin ik k k k k k k t t (2.7) However, for GEO satellites, the model is modified by referring the inclination to an auxiliary plane with a 5 tilt relative to the Earth equator. The GEO satellite coordinates are firstly transferred into a user defined inertial system (i.e., XGK, YGK, Z GK ) and then to the Earth-fixed system: 24

41 t t k k e oe X x cos y cosi sin YGK xk sin k yk cosik cos k ZGK yk sin ik Xk XGK o Y k Rz ( etk ) RX ( 5 ) Y GK Z k Z GK GK k k k k k (2.8) This is done to avoid the fact that the Keplerian model is singular for satellites with an inclination angle of zero since the location of the ascending node is undefined for a satellite in an equatorial orbit. Since GEO satellites are not observable in North America, this will not be investigated further in this thesis. More details can be found in CSNO (212), and Montenbruck and Steigenberger (213) Clock offsets and group delay The BeiDou system uses the same clock model as that of GPS. The satellite clock offset is modelled as a sum of a second order polynomial in time and a periodic relativistic correction depending on the eccentric anomaly. However, the clock reference of BDS differs from that of GPS. The GPS satellite clocks of both the broadcast and precise ephemeris are referred to the ionosphere-free combination of the code measurements, and therefore, the group delays are cancelled in this combination. In contrast, the BDS satellite clocks of the broadcast ephemeris are referred to the code measurements of the B3 signal (Wu et al. 213). Hence, differential code biases (DCBs) need to be applied in B1 or B2 single-frequency positioning, B1/B2 dualfrequency positioning, and code ionosphere-free combination. For the carrier phase, a bias always exists in the measurements since the clocks are referred to the code measurements for 25

42 both GPS and BDS. And this carrier phase bias is assimilated in the estimated float ambiguities and it will affect the ambiguity fixing. In this thesis, these biases will not be a problem since they can be cancelled through between-receiver differencing when forming double differencing in the RTK positioning Ionosphere model BeiDou broadcast ephemeris provides a set of eight correction parameters for the ionosphere model to calculate the ionospheric path delays. The model is based on the well-known GPS Klobuchar model, but is formulated in the geographic coordinates rather than the geomagnetic coordinates, which are used by GPS. The variations of the vertical delays on the day side are modeled by a latitude-dependent and periodic function in the local time, and a constant delay of 5 ns is used on the night side (Montenbruck and Steigenberger 213). According to the research presented in Wu et al. (213), the parameters of the BDS ionosphere model are derived from monitoring stations in China and updated every hour. The corresponding results show that the BDS ionosphere model gives a better performance than the GPS Klobuchar model for the northern hemisphere users in the Asia-Pacific region but presents a degraded performance outside this region. 26

43 CHAPTER 3 : RTK POSITIONING 3.1 RTK Technology Overview Back in the 198 s when GPS was first used for surveying, the only way to obtain centimetrelevel positioning with GPS was via post-processing. In the early 199 s, Real-Time-Kinematic (RTK) was born and it allows the user to obtain centimetre level positioning accuracy in realtime. Surveying aside, RTK techniques have found a number of industrial applications in earth moving, dredging, mining, construction and agriculture (Misra and Enge 211). In RTK mode, the measurements and the corrections of the reference receiver (base station) are usually transmitted to the roving receiver on a radio link (i.e., UHF or spread spectrum radios) that is built specifically for wireless data transfer. Typically, the coordinates of the base station are known and the coordinates of the other station are estimated. The accurate corrections transmitted by the base station allow the rover to fix ambiguities and therefore determine its position at the centimetre level with respect to the reference station. Traditionally, RTK techniques are applied to short baselines involving one base station and one roving receiver, using double differencing and employing some ambiguity fixing techniques (Leick 24). In the RTK method using a single base station, the rover needs to work within a short range from the base station because of the spatial correlation of distance-dependent errors brought by the satellite orbital errors, ionosphere and troposphere. The operation range of RTK positioning is thus dependent on the existing atmospheric conditions and is usually limited to a distance of up to 1-2 km (EL-Mowafy 212). 27

44 3.2 Double Differential Error Sources The basic concept between RTK technology is the carrier phase-based relative positioning. Double differencing is used to eliminate the receiver and satellite clock errors, which are not discussed further herein. The other double differential error sources can be treated in two types: spatially correlated errors (i.e., satellite orbital errors, tropospheric errors and ionospheric errors) and spatially uncorrelated errors (i.e., multipath and noises). Double differencing reduces many of the spatially correlated errors, while the spatially uncorrelated errors cannot be reduced by double differencing Satellite Orbital Error The satellite positions are estimated using a set of Keplerian orbit, perturbation, and satellite clock parameters (Kaplan et al. 25). For most real-time applications, the broadcast ephemeris transmitted along with satellite navigation messages is used. The satellite orbital errors are induced by inaccurate predictions of satellite positions based on the ephemeris (Dao 25). The GPS satellite position calculated using broadcast ephemeris has an RMS error of approximately 1 m (IGS 213). The overall accuracy of BeiDou satellite positions for the MEO/IGSO broadcast ephemeris is better than 3 m (Montenbruck and Steigenberger 213). According to Leick (24), a rule of thumb for relating baseline accuracy and the satellite orbital accuracy is b (3.1) b 28

45 where b is the total error in the length of baseline b m, is the total error in the satellite coordinates (m), and is the approximate distance from the receivers to the satellites (m). Assuming the average satellite receiver distance of 22 km, the baseline error caused by a satellite position error of 3 m is less than 1.5 cm over a 1 km baseline Tropospheric Error The troposphere is a neutral atmosphere, which occupies about to 43 km above the surface of the earth. Instead of depending on the solar activity, the troposphere affects GNSS measurements due to its temperature, pressure and humidity (Skone 23). For example, the tropospheric error on GNSS measurements is generally larger in summer than in winter in Calgary due to the more humid troposphere in summer (de Jong et al 22). Generally, tropospheric effects on GNSS signals reach 2 m to 5 m for a satellite at zenith and up to approximately 25 m for a satellite at low elevation, for instance, in the range of 5 o (Skone 23). The tropospheric errors are spatially correlated so that they can be reduced to some extent by double differencing Ionospheric Error The ionosphere, formed by the ionization of the neutral atmosphere by ultraviolet radiation and X-ray radiation, is a very important error source in GNSS measurements (Skone 1998). The satellite signals may be attenuated when travelling through the ionosphere depending on the signal frequency, electron collisions and the election density along the travel path (Kaplan et al. 1996). The magnitude of ionospheric errors varies from day to night, and from one season to another. Diurnally, the ionospheric error usually reaches its peak at 14: local time and drops to the minimum before sunrise (Dao 24). Seasonally, the ionospheric errors are larger in winter 29

46 (October to March for Calgary) than summer (April to September for Calgary) due to the slower recombination process of free electrons caused by cold molecular nitrogen N 2 (Skone 23). The spatially correlated errors are correlated between the base and rover so that double differencing can reduce their effects. However, the extent of this correlation depends on the separation of the two receivers. Therefore, the above errors can be quantified in terms of partsper-million (ppm), where 1 ppm is equivalent to 1 mm of error per 1 km of receiver separation. Table 3.1 indicates the magnitude of spatially correlated errors mentioned above (Petovello 23). Table 3.1 Magnitude of Spatially Correlated Double Differencing Errors Error Magnitude Error Typical (RMS) Extreme Orbital.1 ppm (Ryan 22) N/A Troposphere <1 ppm (Zhang 1999) 1-3 ppm Ionosphere 1-3 ppm (Klobuchar et al. 1995; Fortes et al. 2, 21) >1 ppm (Lachapelle et al. 2) 3

47 3.2.4 Multipath and Noise Multipath happens when the antenna receives the direct signals and the reflected signals. The errors of multipath are not spatially correlated between two separated receivers. The effect of multipath depends on the reflector s properties, the antenna-reflector distance, the antenna gain pattern and the type of correlator used in a receiver (Ray 2). The primary way to reduce multipath is to locate the antenna away from reflectors. Typically, the multipath error in code measurements is from 1-5 m, or more in highly reflective environment. The corresponding errors in the carrier phase measurements are typically 1-5 cm because the phase measurement error can be no worse than a quarter cycle (Misra and Enge 211). Multipath errors in static measurements are not Gaussian and follow a sinusoidal trend (Dao 25). The receiver noises primarily arise from thermal noise, dynamic stress and oscillator stability in the tracking loop of the receiver (Lachapelle 29). The magnitude of receiver noise on pseudorange measurements is about 1-1 cm, while about.2-2 mm for carrier phase measurements. When double differential is implemented, the receiver noise is doubled in comparison to undifferentiated measurements. Aside of the noises brought by hardware, the measurement errors due to receiver noises vary with the signal strength, which in turn, varies with the satellite elevation (Misra and Enge 211). 3.3 Phase Measurements and Combinations The carrier phase measurement, in unites of metres, transmitted by a satellite can be written as R dr c( dt dt ) N d d (3.2) where 31 sv rx iono trop

48 is the phase measurement (metres) R is the geometric range (metres) dr is the satellite orbit errors (metres) dt sv is the satellite clock errors (seconds) dt rx is the receiver clock errors (seconds) N is the integer ambiguities (cycles) d iono is the ionospheric delay (metres) d trop is the tropospheric delay (metres) is the measurement noise and multipath (metres) c is the speed of light (metres/second) is the carrier wavelength (metres/cycle) The between receivers single differencing (SD-Rx) measurement is R dr c dt N d d (3.3) rx iono trop where represents between receivers single differencing. The satellite clock errors are eliminated by SD-Rx. The double differencing (DD) measurement is R dr N d d (3.4) iono trop where represents double differencing. The receiver clock errors are eliminated by DD. When the baseline length is less than 4 km (the focus in this thesis), it can be assumed that the double differential orbital errors, tropospheric errors, ionospheric errors, multipath errors and noise are small. Therefore, the DD measurement can be re-written as R N (3.5) 32

49 where includes the residual double differenced errors mentioned above. If the second frequency (i.e., L2 for GPS and B2 for BDS) is observable, liner combinations can be formed using the above carrier phase observations (Lachapelle 29). Where m and n are combination coefficients. m n (3.6) 1 2 is double differenced phase measurement in units of cycles. The wavelength mn, and the double differenced ambiguity N mn, of the above combination can be written as mn, 1 2 m n 2 1 (3.7) N m N n N (3.8) mn, 1 2 Many linear combinations can be formed using carrier phase measurements. The most common phase combinations are single-frequency L1, dual-frequency L1 and L2 observations, dualfrequency wide-lane (WL) and dual-frequency ionospheric-free. The first three strategies are investigated herein. The corresponding coefficients, wavelengths, observation equations and ambiguities are shown in Table 3.2. Table 3.2 Carrier Phase Combinations Measurement m n GPS mn, (cm) BDS mn, (cm), L1 only N1 L2 only N2 Wide-lane NWL N1 N2 N mn 33

50 Take GPS as an example, the comparison of L1 and WL errors are shown in Table 3.3 (Lachapelle 29). Table 3.3 Comparison of GPS L1 and WL Errors Error L1 Error (m) WL Error (m) Ratio WL/L1 Satellite orbital error Troposphere dr dr 1 dtropo dtropo 1 Ionosphere 1 WL( f1 f2) 1 I I I f cf f f f Multipath d MP 2 WL dmp Noise 2 WL From the above two tables, it can be observed that the ionospheric error, multipath and noise of L1 only are low in metres, but it is difficult to solve the integer ambiguities for long baselines or in periods of high ionospheric activity. When dual-frequency L1 and L2 observations are used, more system redundancy can be achieved, but L2 has a higher ionospheric error in metres than L1 and WL due to its lower carrier frequency. It is expected to suffer significantly from ionospheric error in periods of high ionospheric activity. The wide-lane measurement has larger ionospheric errors in metres than L1 and is more than six times noiser than L1 in metres, because of which noisy position estimates are expected. However, the advantage of using wide-lane is that it is easier to solve the integer ambiguities due to its larger wavelength (Lachapelle 29). 34

51 3.4 Ambiguity Resolution Resolving integer ambiguities is an essential process to achieve sub-centimetre level positioning using carrier phase measurements. In general, there are three classifications of ambiguity resolution methods (Kim and Langley 2): 1) Ambiguity resolution in the measurement domain, which uses pseudoranges directly to determine the ambiguities of the corresponding carrier phase observations. 2) Search technique in the coordinate domain, which uses only the fractional value of the instantaneous carrier phase measurement. 3) Search technique in the ambiguity domain, which are based on the theory of integer leastsquares (Teunissen 1993). The most common technique of ambiguity resolution is the third class, which is carried out in three steps (Teunissen 23): 1) estimate the float ambiguities and positions; 2) estimate the integer ambiguities; 3) adjust the estimate of the positions. It makes use of the variancecovariance matrix obtained from the float solution and employs different ambiguity search processes to estimate the integer ambiguities. The candidates in the search space are discriminated (according to some criteria) and the one corresponding to the best estimate of the integer ambiguities is chosen (Ong 21). There are two methods to estimate float ambiguities (O Keefe et al. 29): 1) Geometry-based method, which uses the differential measurements to estimate the position along with the ambiguities; 2) geometry-free method, which uses the differential measurements to estimate the corresponding differential range and ambiguities. 35

52 In kinematic applications, both code and phase measurements need to be used to estimate the ambiguities, which causes a limitation in ambiguity estimation due to the sub-metre level of code noise and multipath. In addition, when the measurements are significantly biased by residual ionospheric effects, tropospheric effects, and satellite orbital errors, a single epoch of measurements is not enough to estimate float ambiguities accurately. This problem can be overcome by using sequential measurements over multipath epochs because of the constant feature of the ambiguities. When the position (or range) and the ambiguities are estimated together in Kalman filter, the estimates of them converge to their true values as the measurement errors are smoothed out. Float estimation gives the initial search space for the integer ambiguities. The search method, Integer Least-Squares (ILS), searches for the best set of integer ambiguities that gives the smallest weighted sum of squared ambiguity residuals or the distance between the float and integer ambiguities (Teunissen 2). The following are some representative ILS methods: the Brute force, the Fast Ambiguity Search Filter (FASF), and the Least-Square Ambiguity Decorrelation Adjustment (LAMBDA). The most widely used method of these is LAMBDA, which decorrelates the ambiguities into a smaller search space by implementing a linear transformation of the ambiguities (Teunissen 1995). The estimation of the integer ambiguities involves a mapping of float ambiguities to integer ambiguities and needs to have sufficient confidence in the integer solution. Therefore, the reliability of the integer ambiguities is an important consideration. The predicted success rate is 36

53 used as one of the reliability tests in this thesis to determine whether an attempt to fix the ambiguities should be made. In addition, the fix validation is used to evaluate whether the most likely integer ambiguity should be accepted. The corresponding thresholds are adjusted to reject more incorrect integer ambiguities. Success rate is the rate of correct ambiguity solution or how often the ambiguities are correctly fixed. It is impossible to obtain the actual success rate instantaneously without a true reference of ambiguities. However, the success rate can be predicted according to the precision of the ambiguities. The ILS method has been demonstrated as the optimal search method in terms of maximizing the success rate in Teunissen (1999). However, it is complicated to predict the success rate of ILS. In this case, Verhagen (25) proposed to use the predicted success rate of integer bootstrapping as a lower bound for the ILS success rate, since exact and easy computation of this bootstrapping success rate is possible. This approximation of ILS success rate is acceptable because the integer bootstrapping, which is based on sequential rounding, is nearly optimal in terms of the success rate when LAMBDA is applied beforehand. The lower bound of the ILS success rate or the success rate of integer bootstrapping is as follows (Teunissen 1998, Verhagen 25): n 1 Ps Ps, B 2 1 i 1 2 i I (3.9) where P s is the predicted success rate of the ILS P sb, is the predicted success rate of the integer bootstrapping 37

54 is the standard deviation of the i th ambiguity obtained through a conditioning on i I the previous I 1,...,( i 1) ambiguities, and ( x) is the integral of the standard normal distribution from to x Only if the predicted success rate is close to 1, can the fixing procedure of the ambiguities be attempted. The success rate is predicted using the float ambiguity uncertainties before fixing the ambiguities. Since the float ambiguity uncertainties are assumed normally distributed when calculating the success rate, the non-gaussian differential errors, consisting of multipath, ionospheric errors, and tropospheric errors will affect how closely the predicted success rate follows the actual success rate (Ong 25). When the predicted success rate passes the threshold, which is usually close to 1, the fixing procedure of the ambiguities can be attempted. The Fix validation decides whether the most likely integer ambiguity is actually correct. The most likely integer ambiguity is determined in two steps according to some statistics of the measurement or ambiguity residuals. First, the most likely integer ambiguity should have the smallest statistic. Second, the most likely integer ambiguity should be sufficiently more likely than the second-most likely integer ambiguity. Some statistics have been developed to implement statistical hypothesis tests. Verhagen (24) defines three statistics based on the weighted sum of squared residuals (WSSR). ˆ T 1 eˆ Q ˆ y e T 1 e Qy e T R ( aˆ a) Q ( aˆ a) 1 aˆ (3.1) where 38

55 ê are the phase residuals based on the float ambiguities e are the phase residuals based on the fixed ambiguities Q y is the variance-covariance matrix of the phase measurements, and Q â is the variance-covariance matrix of the float ambiguities The differences between the float and fixed ambiguities, in the third equation, are defined as the ambiguity residuals. To identify which integer ambiguity estimates are most likely correct, a statistic based on the WSSR should both pass the following identification test and have the smallest value (Verhagen 24). R n K ˆ m n p (3.11) where m is the number of measurements n is the number of ambiguities p is the number of position states, and K is the identification test threshold Once the most likely integer estimates are identified, the ratio test can be conducted to discriminate whether the most likely estimates are sufficiently more likely than the others. A statistic of ratio test is shown below (Euler and Schaffrin 199): 39

56 R 2 F R (3.12) 1 where R 1 is calculated using the most likely integer estimates R 2 is calculated using the second most likely integer estimates, and F is the ratio test threshold If the null hypothesis that a correct integer ambiguity estimate cannot be determined is true, both R 1 and R 2 are distributed according to a central 2 distribution after simplification (Leick 24). Therefore, the ratio is distributed according to a central F distribution. A threshold based on the significance level of F distribution is used in this thesis. The significance level represents the probability of accepting an incorrect integer ambiguity estimate. The thresholds from central F distribution with a significance level of 2% are shown in Table 3.4. Table 3.4 F-test Thresholds from central F-distribution (significance level 2%) Number of Ambiguities F-test threshold Number of Ambiguities F-test threshold

57 CHAPTER 4 : GPS/BDS RTK TESTS This chapter will present the design of the RTK experiment. A brief description of the data sources and the setup of GPS/BDS RTK are introduced. The test scenarios and hardware characteristics are then explained in details, followed by the design of the software and the strategies for analysis. 4.1 Data Sources To implement GPS/BDS RTK experiment, two GNSS receivers (i.e., base and rover) that can track GPS/BDS dual-frequency signals are required to generate the base-to-rover vectors over different distances. The base station for the permanent reference receiver, UCAL, is set up at the University of Calgary. UCAL is a station operated by the German Space Agency (DLR) as a part of the Multi-GNSS Experiment (MGEX) (Dow et al. 29). MGEX has been set up by IGS to track, collate and analyze all available GNSS signals including GPS, GLONASS, BeiDou, Galileo, QZSS, modernized GPS, and any Space-Based Augmentation System (SBAS). It provides 24 hours real time observation data, precise orbit, and clock products. Analysis centers will attempt to estimate inter-system calibration biases, compare equipment performance, and further develop processing software capable of handling multiple GNSS observation data (Montenbruck et al. 214). Figure 4.1 shows the network of MGEX, which contains more than 1 stations in the world, with four stations in Canada, and one (i.e., UCAL) being located at the roof of the Calgary Center for Innovative Technology placed on August 21, 213. The UCAL station is using a Trimble Net R9 receiver, providing real-time data from GPS, GLONASS, Galileo, BeiDou, QZSS and SBAS. 41

58 Figure 4.1 The MGEX network (December 13, 214) Some commercial GNSS receivers like NovAtel OEM617 Receiver, Trimble R1 receiver, Unicore UR37 receiver, Leica GS15 receiver and ComNav M3 GNSS receiver can track GPS and BeiDou dual-frequency signals. Receivers from different companies may use different clocks and different multi-path eliminating strategies. Considering that a Trimble Net R9 has been chosen as the base station, another Trimble GNSS receiver (i.e., Trimble R1) is selected to serve as the rover in order to avoid some inter-receiver errors. The Trimble R1 receiver as shown in Figure 4.2, was set up as the rover receiver for each scenario. Trimble TSC3 controller was used to configure the Trimble R1 receiver. 42

59 Figure 4.2 Trimble R1 Receiver 4.2 Test Scenarios As stated in Chapter 3, the inter-station distance between the base and rover is a main limitation for RTK positioning. This is because of the strong dependence of the ionospheric error due to the separation of two receivers. Another distance-dependent error is the tropospheric residuals after differencing the measurements. Usually, the orbital errors of the broadcast ephemeris are sufficiently small and negligible. Therefore, the RTK system is considered more desirable if a longer base-rover distance is allowed (Feng et al., 28). To test the system performance over different baselines, three static data sets were collected under open sky environment with very short baseline, medium baseline, and long baseline respectively. 43

60 4.2.1 Scenario A A static data set of 2 one-second epochs was collected on March 18, 214 on the roof of CCIT building at the University of Calgary. The distance between the base and rover was 1.9 metres as shown in Figure 4.3. For simplicity, the length of baseline will be denoted as 1 m baseline in the following context. The measurement data were recorded at a rate of 1 Hz with a cutoff elevation of 5 degrees. The local time of the data collection was from 4:: am to 4:33: am. The K-index computed by the Canadian Geomagnetism Program for the Meanook observatory ( o N, o E), which is 45 km from Calgary, was around 1. (Space Weather Canada, 214). This level of K-index does not indicate strong ionospheric activity (USNOAA Space Weather Scales, 25). The true coordinates of the base station were known (Groot, 23), while the true coordinates of the rover station were determined using Trimble Business Center (TBC). 44

61 Figure 4.3 Data Collection, Scenario A - 1 m baseline Scenario B To test the GPS/BDS RTK performance over a medium baseline, a data set with 19.7 km baseline was collected on July 19 th, 214 at Calgary. For simplicity, the length of baseline will be denoted as 2 km baseline in the following context. Similarly to Scenario A, 2 one-second epochs were surveyed at a data rate of 1 Hz using a 5 o mask of elevation. The local time during this test was from 18:: pm to 18:33: pm. According to the magnetic indices released by the Meanook observatory, the K-index was. which shows that the ionospheric activity was quite low during the test. Figure 4.4 shows the baseline (red line) in Google Map. Again, the base station was the MGEX station, UCAL as shown in Figure 4.5 (left). A Trimble R1 receiver was set up as the rover station at 28 Rolling Heights Estates, which is in the North East of Calgary as shown in Figure 4.5 (right). The reference coordinates of the rover were calculated in Trimble Business Center using GPS and GLONASS measurements. 45

62 Figure 4.4 The Test Scenario of 2 km baseline Figure 4.5 Data Collection, Scenario B - 2 km baseline 46

63 4.2.3 Scenario C A long baseline of 42.1 km was surveyed on June 26, 214 as shown in Figure 4.6. For simplicity, the length of baseline will be denoted as 4 km baseline in the following context. 25 one-second epochs were collected at a rate of 1 Hz using an elevation mask of 5 o. As presented in Figure 4.7, the base station was the UCAL station (left) again, while the rover station (right) was set up in the North West of Calgary. The local time of this test was from 12:: pm to 12:41: pm. The K-index during that time was 1., which did not suggest strong ionospheric disturbances. Figure 4.6 Test Scenario of 4 km baseline 47

64 Figure 4.7 Data Collection, Scenario C 4 km baseline A summary of the details of the three test data is given in Table 4.1. Table 4.1 The details of the test Scenarios Scenario Date (local) Epochs Base Rover Baseline length (m) K-index A March 18, UCAL Trimble R B July 19, UCAL Trimble R1 19,715. C June 26, UCAL Trimble R