Investigation on the contribution of GLONASS observations to GPS Precise Point
Positioning (PPP)
THESIS
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University
By
Hilmi Can Deliktas, B.S.
Graduate Program in Civil Engineering
The Ohio State University
2016
Master's Examination Committee:
Dr. Charles Toth, Advisor
Dr. Dorota Grejner-Brzezinska
Dr. Alper Yilmaz
Copyright by
Hilmi Can Deliktas
2016
Abstract
The Global Navigation Satellite System (GNSS) is a generic term which embraces all satellite-based radio navigation systems that are currently operating or planned to operate globally (Hoffmann-Wellenhof, Lichtenegger & Wasle, 2008). This term includes the GPS (United States), GLONASS (Russia), GALILEO (European
Union), BEIDOU (China), QZSS (Japan), and IRNSS (India) systems. Although the latter two satellite-based radio navigation systems are regional systems, they are classified under the term GNSS. As of 2016, there are only two fully operational GNSS systems: the United States’ GPS and the Russian GLONASS. The GPS is a well- established GNSS system which has been widely used for high-accuracy Positioning,
Navigation, and Timing (PNT) solutions over the last 20 years. The GLONASS regained its Full Operational Capability (FOC) in 2011 after being inoperative for more than a decade, and became a second operational GNSS system which is not only an alternative but also a complementary utility to GPS in low satellite visibility areas. Besides the availability of the GPS and GLONASS systems, the development of new GNSS systems
(i.e. GALIEO and BEIDOU) brings the integration and interoperability issues that will allow users to take advantage of all available GNSS systems.
With the resurrection of GLONASS system, analyzing the feasibility of using
GLONASS observations along with GPS observations in global positioning with regard to accuracy and precision has drawn the researchers’ attention. In recent years, the ii
practicability of combined GPS/GLONASS observations has been especially investigated for Precise Point Positioning (PPP) method since the integration of two systems leads to considerable increase in the number of visible satellites worldwide, which is one of the crucial factors that may improve the positioning accuracy and precision obtained from
PPP. In addition, PPP’s potential as an alternative to precise relative positioning in terms of performance, time, and cost in remote areas has made it attractive to the GNSS community.
This thesis provides an evaluation of using combined GPS/GLONASS observations in post-processed static and kinematic PPP methods. In static PPP use, the benefits of combining GPS/GLONASS observations on accuracy and precision are investigated as a function of different latitude regions and observation duration by utilizing the data collected at three selected IGS stations with accurately known coordinates. Furthermore, the positioning accuracy of GPS and GPS/GLONASS static
PPP is compared under different sky view conditions by simulating various satellite visibility. The investigation includes the assessment of the contribution of combined
GPS/GLONASS observations to the convergence time of static PPP solutions.
In kinematic PPP method, the advantage of combined GPS/GLONASS observations to positioning accuracy is evaluated through three datasets collected in
Columbus Ohio. The assessment of the positioning accuracy of kinematic PPP is carried out by comparing the PPP solution against carrier phase based differential kinematic GPS solution which is considered as a ground truth. In addition, the effect of initialization time
iii
on positioning accuracy of kinematic PPP is examined by processing static observations of different duration along with kinematic observation.
With the analyses aforementioned, it has been demonstrated that combined
GPS/GLONASS observations could improve the 3D positioning accuracy of static PPP for the observations with a short duration (<= 4-hour) in high latitude and equatorial regions, and enhance the 3D positioning accuracy regardless of the observation duration in mid-latitude region. The percentage of improvement in the positioning accuracy increases with respect to the worsening sky view condition. It has also been determined that there is no meaningful positive effect of using combined GPS/GLONASS observations on the precision of static PPP. Lastly, it has been revealed that combined
GPS/GLONASS observations could significantly speed up the convergence time of static
PPP solutions.
As for kinematic PPP, it has been shown that up to a 48% improvement in 3D positioning accuracy could be achieved using the combined GPS/GLONASS observations depending on the quality of collected data. Regarding the impact of initialization time on positioning accuracy, it has been demonstrated that relatively short initialization (~ 20 minutes) with combined GPS/GLONASS observations could be adequate to improve 3D positioning accuracy by about 23%.
iv
Dedication
This document is dedicated to Can.
v
Acknowledgments
I would like to express my sincere thanks to my advisor, Dr. Charles Toth, for providing help and guidance throughout my study.
I would like to specifically thank Dr. Brzezinska and Dr. Yilmaz for being on my committee and reviewing my thesis.
vi
Vita
2006...... Fatih Sultan Mehmet High School
2012...... B.S. Geomatics Engineering, Istanbul
Technical University
August 2016 ...... M.S Geodetic Engineering, The Ohio State
University
Fields of Study
Major Field: Civil Engineering
vii
Table of Contents
Abstract ...... ii
Dedication ...... v
Acknowledgments...... vi
Vita ...... vii
Fields of Study ...... vii
Table of Contents ...... viii
List of Tables ...... xiv
List of Figures ...... xvii
List of Abbreviations ...... xxiii
Chapter 1: Introduction ...... 1
1.1 Background ...... 1
1.2 Motivation ...... 5
1.3 Overview ...... 5
Chapter 2: Satellite Navigation Systems ...... 7
2.1 Global Positioning System (GPS) ...... 7
viii
2.1.1 GPS Signal Structure ...... 10
2.1.2 GPS Modernization ...... 11
2.2 GLONASS ...... 13
2.3 GALILEO...... 16
2.4 BEIDOU ...... 17
2.5 QZSS ...... 18
2.6 IRNSS...... 20
Chapter 3: GNSS Measurements, Error Sources, and Error Mitigation ...... 22
3.1 GNSS Measurements ...... 23
3.1.1 Pseudorange (Code Phase) Measurements ...... 23
3.1.2 Carrier Phase Measurements ...... 25
3.2 GNSS Error Sources and Error Mitigation ...... 27
3.2.1 Satellite Related Errors ...... 29
3.2.1.1 Satellite Ephemeris and Clock Errors ...... 29
3.2.1.1.1 International GNSS Service (IGS) ...... 31
3.2.1.2 Relativistic Effects ...... 34
3.2.1.3 Satellite Phase Center Offset and Variation ...... 35
3.2.1.4 Phase Wind-up Effect ...... 37
3.2.2 Signal Propagation Related Errors ...... 38
ix
3.2.2.1 Ionospheric Delay ...... 38
3.2.2.2 Tropospheric Delay ...... 41
3.2.2.3 Multipath Effect ...... 44
3.2.3 Receiver Related Errors ...... 46
3.2.3.1 Receiver Antenna Phase Center Offset and Variation ...... 46
3.2.3.2 Receiver Clock Error ...... 47
3.2.3.3 Sagnac Effect ...... 47
3.2.3.4 Receiver Noise and Inter-channel Bias ...... 49
3.2.4 Receiver Station Related Errors ...... 49
3.2.4.1 The Solid Earth Tides ...... 49
3.2.4.2 Polar Motion (Polar Tides) ...... 51
3.2.4.3 Ocean Tide Loading ...... 51
3.2.4.4 Atmospheric Loading...... 52
Chapter 4: PPP Mathematical Models ...... 54
4.1 GPS PPP Mathematical Model ...... 54
4.1.1 Adjustment Model ...... 58
4.2 GPS/GLONASS PPP Mathematical Model ...... 59
Chapter 5: Analysis of PPP in Post-processed Static Mode ...... 68
5.1 Study Area ...... 68
x
5.2 Data Preparation ...... 70
5.2.1 The Multi-Purpose Toolkit for GPS/GLONASS Data (TEQC) Software ...... 72
5.3 Data Processing ...... 73
5.3.1 Canadian Spatial Reference System (CSRS) Precise Point Positioning (PPP) 74
5.4 Evaluation Procedure ...... 78
5.5 Accuracy and Repeatability Investigation...... 81
5.5.1 Accuracy Investigation for East Component ...... 83
5.5.2 Accuracy Investigation for North Component ...... 86
5.5.3 Accuracy Investigation for Up Component ...... 88
5.5.4 Repeatability Investigation ...... 96
5.6 Data Simulation for Static PPP ...... 99
5.6.1 Data Simulation at Station KIRU ...... 106
5.6.2 Data Simulation at Station HLFX ...... 109
5.6.2.1 Half Sky Study at Station HLFX ...... 112
5.6.3 Data Simulation at Station NKLG ...... 115
5.7 Convergence Investigation ...... 121
Chapter 6: Analysis of PPP in Post-processed Kinematic Mode ...... 126
6.1 Data Acquisition ...... 126
6.2 Data Processing ...... 128
xi
6.2.1 Differential Kinematic Solution ...... 128
6.2.1.1 Online Positioning User Service (OPUS) ...... 128
6.2.1.2 Real Time Kinematic Library (RTKLIB) ...... 130
6.2.2 PPP Solution ...... 131
6.3 Evaluation Procedure ...... 131
6.4 Experiments and Results ...... 133
6.4.1 Experiment 1...... 133
6.4.1.1 CSRS-PPP Solution for First Dataset ...... 136
6.4.1.2 RTKLIB Solution for First Dataset...... 141
6.4.2 Experiment 2...... 145
6.4.2.1 CSRS-PPP Solution for Second Dataset ...... 148
6.4.2.2 RTKLIB Solution for Second Dataset ...... 150
6.4.3 Experiment 3...... 152
6.4.3.1 CSRS-PPP Solution for Third Dataset ...... 155
6.4.3.2 RTKLIB Solution for Third Dataset ...... 157
Chapter 7: Conclusions and Recommendations for Future Study ...... 159
7.1 Conclusions ...... 159
7.2 Recommendations for Future Study ...... 163
References ...... 164
xii
Appendix A: TEQC Software Processing Commands ...... 168
A.1: TEQC Command for Removing Satellite Data ...... 168
A.2: TEQC Command for Extracting Data from Observation File ...... 168
A.3: TEQC Command for Quality Check of Observation File ...... 169
Appendix B: Statistical Analysis for Coordinate Differences at Each IGS Station ...... 170
xiii
List of Tables
Table 2.1: Comparison of GPS and GLONASS systems...... 16
Table 2.2: Overview of the Global Navigation Satellite Systems...... 18
Table 3.1: Precise GPS satellite orbits and clock corrections provided by the IGS
[http://www.igs.org/products]...... 33
Table 3.2: IGS RTS product description (IGS-RTS, 2016)...... 34
Table 5.1: Properties of selected IGS stations...... 70
Table 5.2: Geodetic coordinates of the IGS stations in WGS84 frame...... 70
Table 5.3: Obtained RINEX observation files for each day by TEQC software...... 72
Table 5.4: Specifications of CSRS-PPP online service...... 77
Table 5.5: RMSE3D in centimeters for GPS observations...... 92
Table 5.6: RMSE3D in centimeters for GLONASS observations...... 92
Table 5.7: RMSE3D in centimeters for GPS+GLONASS observations...... 92
Table 5.8: The number of GPS PPP solutions with elevation angle of 40 degrees obtained from 2, 4, and 8-hour observations at each station...... 100
Table 5.9: The average number of visible satellites with each elevation cut-off angle at station KIRU...... 107
Table 5.10: The average number of visible satellites with each elevation cut-off angle at station HLFX...... 110 xiv
Table 5.11: Positioning errors obtained from CSRS-PPP for each case in half sky study.
...... 114
Table 5.12: Positioning errors obtained from RTKLIB for each case in half sky study. 115
Table 5.13: The average number of visible satellites with each elevation cut-off angle at station NKLG...... 117
Table 6.1: Observation details for first dataset...... 134
Table 6.2: RMSE values obtained from GPS-only kinematic PPP solutions of CSRS-PPP.
...... 137
Table 6.3: RMSE values obtained from combined GPS/GLONASS kinematic PPP solutions of CSRS-PPP...... 138
Table 6.4: RMSE values obtained from GPS-only kinematic PPP solutions of RTKLIB.
...... 142
Table 6.5: RMSE values obtained from GPS/GLONASS kinematic PPP solutions of
RTKLIB...... 143
Table 6.6: Observation details for second dataset...... 145
Table 6.7: RMSE values for CSRS-PPP kinematic PPP solutions of second dataset. ... 150
Table 6.8: RMSE values for RTKLIB kinematic PPP solutions of second dataset...... 150
Table 6.9: Observation details for third dataset...... 152
Table 6.10: RMSE values for CSRS-PPP kinematic PPP solutions of the third dataset. 156
Table 6.11: RMSE values for RTKLIB kinematic PPP solutions of third dataset...... 157
Table 7.1: The percentage of improvement in 3D RMSE when GPS/GLONASS observations are used instead of GPS-only observations at each station ( indicates
xv
combined GPS/GLONASS observations provide better positioning accuracy than GPS- only observations for that observation duration) ...... 160
Table B.1: Statistical Analysis for coordinate differences at station KIRU ...... 171
Table B.2: Statistical Analysis for coordinate differences at station HLFX...... 171
Table B.3: Statistical Analysis for coordinate differences at station NKLG ...... 172
xvi
List of Figures
Figure 2.1: GPS nominal constellation...... 9
Figure 2.2: GPS signal structures (Hegarty & Chatre, 2008)...... 13
Figure 2.3: GLONASS nominal constellation...... 14
Figure 2.4: QZSS constellation ground track (Tsujino, 2005)...... 19
Figure 2.5: Signal spectrum of all GNSS systems...... 21
Figure 3.1: GNSS positioning [http://www.polarislandsurvey.com/survey/gps.php]...... 23
Figure 3.2: Satellite ephemeris error (Kaplan & Hegarty, 2006)...... 30
Figure 3.3: IGS organizational diagram [http://kb.igs.org/hc/en-us/articles/202014583-
Organizational-Diagram]...... 32
Figure 3.4: IGS tracking network [https://igscb.jpl.nasa.gov/network/netindex.html]. ... 32
Figure 3.5: Satellite antenna phase center offset (Kouba, 2015)...... 36
Figure 3.6: Multipath error (El-Rabbany, 2002)...... 45
Figure 3.7: Choke ring antenna...... 46
Figure 3.8: Sagnac effect correction (Ashby, 2006)...... 48
Figure 5.1: Layout of the IGS stations used for the study...... 69
Figure 5.2: Sample quality check plot...... 73
Figure 5.3: Processing flow...... 74
Figure 5.4: Processing procedure of CSRS-PPP online service...... 75 xvii
Figure 5.5: CSRS-PPP online service...... 76
Figure 5.6: Left handed local geodetic coordinate system, (r,s,t) (Jekeli, 2012)...... 79
Figure 5.7: Number of satellites tracked at high latitude station KIRU...... 82
Figure 5.8: Number of satellites tracked at mid latitude station HLFX...... 82
Figure 5.9: Number of satellites tracked at low latitude station NKLG...... 83
Figure 5.10: RMSE values at each station for the east component...... 84
Figure 5.11: RMSE values at each station for the north component...... 87
Figure 5.12: RMSE values at each station for the up component...... 89
Figure 5.13: RMSE3D values of GLONASS, GPS, and GPS/GLONASS PPP solutions . 93
Figure 5.14: RMSE3D values of RTKLIB GLONASS, GPS, and GPS/GLONASS PPP solutions ...... 95
Figure 5.15: Standard Deviations of the observations at the station KIRU...... 96
Figure 5.16: Standard Deviations of the observations at the station HLFX...... 97
Figure 5.17: Standard Deviations of the observations at station NKLG...... 97
Figure 5.18: 3D repeatability for each station...... 98
Figure 5.19: GPS (left image) and combined GPS/GLONASS (right image) sky plot at
KIRU station with 10o cut-off angle for day of 213 of year 2014...... 101
Figure 5.20: GPS (left image) and combined GPS/GLONASS (right image) sky plot at
HLFX station with 10o cut-off angle for day of 213 of year 2014...... 101
Figure 5.21: GPS (left image) and combined GPS/GLONASS (right image) sky plot at
NKLG station with 10o cut-off angle for day of 213 of year 2014...... 102
xviii
Figure 5.22: Number of satellites and PDOP values at station KIRU with 10o cut-off angle on day of 213...... 103
Figure 5.23: Number of satellites and PDOP values at station HLFX with 10o cut-off angle on day of 213...... 104
Figure 5.24: Number of satellites and PDOP values at station NKLG with 10o cut-off angle on day of 213...... 105
Figure 5.25: RMSE2D values for different cut-off angles at station KIRU...... 106
Figure 5.26: RMSE values of height component for different cut-off angles at station
KIRU...... 108
Figure 5.27: RMSE2D values for different cut-off angles at station HLFX...... 109
Figure 5.28: RMSE values of height component for different cut-off angles at station
HLFX...... 111
Figure 5.29: First case in half sky study...... 112
Figure 5.30: Second case in half sky study...... 113
Figure 5.31: Third case in half sky study...... 113
Figure 5.32: RMSE2D values for different cut-off angles at station NKLG...... 116
Figure 5.33: RMSE values of height component for different cut-off angles at station
NKLG...... 118
Figure 5.34: RMSE2D values for 24 hour measurement session for one week...... 120
Figure 5.35: RMSE values of height component for 24 hour measurement session for one week...... 121
xix
Figure 5.36: The average convergence time with GPS and combined GPS/GLONASS observations, 2-hour solutions ...... 122
Figure 5.37: Distribution of the convergence time of GPS static PPP solutions...... 124
Figure 5.38: Distribution of the convergence time of combined GPS/GLONASS static
PPP solutions...... 124
Figure 6.1: Measurement van (GPSVan)...... 127
Figure 6.2: OPUS online service (http://www.ngs.noaa.gov/OPUS/)...... 129
Figure 6.3: a) RTKLIB main window, b) RTKLIB options dialog...... 130
Figure 6.4: Trajectory of first kinematic dataset...... 134
Figure 6.5: TEQC quality check plot for first kinematic data...... 135
Figure 6.6: RMSE values obtained from GPS-only kinematic PPP solutions of
CSRS-PPP...... 137
Figure 6.7: RMSE values obtained from combined GPS/GLONASS kinematic PPP solutions of CSRS-PPP...... 138
Figure 6.8: Local coordinate errors of CSRS-PPP GPS-only kinematic PPP solution with
60-m initialization...... 140
Figure 6.9: Local coordinate errors of CSRS-PPP GPS+GLONASS kinematic PPP solution with 60-m initialization...... 140
Figure 6.10: RMSE values obtained from GPS-only kinematic PPP solutions of RTKLIB.
...... 142
Figure 6.11: RMSE values obtained from combined GPS/GLONASS kinematic PPP solutions of RTKLIB...... 143
xx
Figure 6.12: Local coordinate errors of RTKLIB GPS-only kinematic PPP solution with
60-m initialization...... 144
Figure 6.13: Local coordinate errors of RTKLIB GPS+GLONASS kinematic PPP solution with 60-m initialization...... 144
Figure 6.14: Trajectory of second kinematic data set...... 146
Figure 6.15: TEQC quality check plot for second dataset...... 147
Figure 6.16 Local coordinate errors of CSRS-PPP GPS-only kinematic PPP solution for second dataset...... 149
Figure 6.17: Local coordinate errors of CSRS-PPP GPS+GLONASS kinematic PPP solution for second dataset...... 149
Figure 6.18: Local coordinate errors of RTKLIB GPS-only kinematic PPP solution for second dataset...... 151
Figure 6.19: Local coordinate errors of RTKLIB GPS+GLONASS kinematic PPP solution for second dataset...... 151
Figure 6.20: Trajectory of third data set...... 153
Figure 6.21: TEQC quality check plot for third dataset...... 154
Figure 6.22: Local coordinate errors of CSRS-PPP GPS-only kinematic PPP solution for third dataset...... 155
Figure 6.23: Local coordinate errors of CSRS-PPP GPS+GLONASS kinematic PPP solution for third dataset...... 156
Figure 6.24: Local coordinate errors of RTKLIB GPS-only kinematic PPP solution for third dataset...... 158
xxi
Figure 6.25: Local coordinate errors of RTKLIB GPS+GLONASS kinematic PPP solution for third dataset...... 158
xxii
List of Abbreviations
C/A……………………………………………………………………. Coarse/Acquisition
CDMA...…………………………………..………………Code Division Multiple Access
CODE...………………………………………...Center for Orbit Determination in Europe
CORS...…………………………………………Continually Operating Reference System
CSRS-PPP...………….The Canadian Spatial Reference System Precise Point Positioning
DGPS…………………………………………….Differential Global Positioning Systems
ECEF...………………………………………………………...Earth Centered Earth Fixed
FDMA……………………………………………….Frequency Division Multiple Access
FOC……………………………………………………………Full Operational Capability
GLONASS…………………………………...Russian Global Navigation Satellite System
GNSS………………………………………………...Global Navigation Satellite Systems
GPS…………………………………………………………….Global Positioning System
IGS……………………………………………………………International GNSS Service
IGS-RTS…………………………………………………………IGS – Real Time Service
IRNSS………………………………………Indian Regional Navigation Satellite System
ITRF……………………………………………International Terrestrial Reference Frame
JPL………………………………………………………………Jet Propulsion Laboratory
LOS…………………………………………………………………………...Line of Sight xxiii
NAD83…………………………………………………….North American Datum (1983)
NOAA………………………………..National Oceanic and Atmospheric Administration
NRCAN………………………………………………………...Natural Resources Canada
P-code………………………………………………………………………Precision Code
PCV………………………………………………………………...Phase Center Variation
PNT…………………………………………………Positioning, Navigation, and Timing
PPP……………………………………………………………….Precise Point Positioning
PZ-90………………………………………………………...GLONASS Reference Frame
QZSS………………………………………………………..Quasi-Zenith Satellite System
RINEX……………………………………………Receiver Independent Exchange Format
RMSE…………………………………………………………….Root Mean Square Error
SBAS………………………………………………Satellite-Based Augmentation System
TEC…………………………………………………………………Total Electron Content
UTC…………………………………………………………..Coordinated Universal Time
WGS-84……………………………………………………World Geodetic System (1984)
xxiv
Chapter 1: Introduction
1.1 Background
The position information could be obtained by either absolute or relative positioning methods based on GNSS measurements. While the relative positioning method requires simultaneous measurement data from two or more GNSS receivers, the absolute positioning method is performed with utilizing measurement data obtained from a single GNSS receiver. The relative positioning method has been extensively used to provide high accuracy position information for geodetic and geoscience applications.
With the emergence of precise satellite orbit and clock corrections produced primarily by the International GNSS Service (IGS), Jet Propulsion Laboratory (JPL), and the Center for Orbit Determination in Europe (CODE), high-accuracy position determination with a single GNSS receiver became possible. Thus, the Precise Point
Positioning (PPP) method which requires no reference stations with known coordinates unlike the relative positioning method, has been developed. The first theoretical aspects of PPP which performs the absolute positioning was provided by Zumberge et al. (1997).
The studies conducted on PPP over the last few years have showed that PPP could almost reach the level of accuracy provided by the relative positioning method.
It has been shown that PPP can be effectively used for scientific and civil applications, such as surveying and mapping (Abd-Elazeem et al., 2011), monitoring 1
crustal movement (Calais et al., 2006), detection of seismic ground motion (Avallone et al., 2011), observing high frequency sea level variations (Kuo et al., 2012), and determining the precise location of the objects at land, sea, and air (Gao et al., 2005).
PPP is an absolute positioning method which utilizes the precise orbit and clock corrections that could be downloaded from IGS or acquired in real time from a few service suppliers to provide high-accuracy position information in a global reference frame. Since it employs a single GNSS receiver, and requires no measurements of reference station whose coordinates are known, it is a cost-effective positioning method.
Therefore, it is a very useful tool in remote areas with no accessible GNSS reference network. By using dual frequency GNSS receivers, decimeter-to-centimeter-level or better accuracy could be obtained via PPP method (Bisnath & Gao, 2009). However, in practice, there are a number of difficulties in using PPP to achieve this level of accuracy.
The method requires good satellite geometry and reception of satellite signals with as few interruptions as possible. In addition, some specific error sources, such as satellite antenna phase center offset, satellite phase wind-up effect, the solid Earth tides, the ocean loading effect and so forth, should be taken into account when processing the observation data.
The positioning accuracy of PPP mainly depends on the satellite geometry, and it degrades at places with weak satellite geometry for user receiver, such as mountainous areas, forested areas, urban areas including tall buildings, and open pit mines. Even if
PPP is implemented under open sky condition, its positioning accuracy might get worse
2
due to poor satellite geometry. Therefore, the addition of a second global satellite system could be crucial to improve the positioning accuracy and performance of PPP.
For many years, the Precise Point Positioning method was carried out with only
GPS observations. In recent years, with the revival of GLONASS and the advent of precise GLONASS orbit and clock corrections, combined use of GPS and GLONASS measurements for PPP has become increasingly popular. A lot of studies analyzing the positioning performance of combined GPS/GLONASS PPP were conducted by researchers. The main results obtained from these studies are briefly summarized below.
Cai and Gao (2007) carried out a test to evaluate the performance of the PPP method by using the GPS and GLONASS observations when there were a total of 12 operational GLONASS satellites. Despite the limited number of GLONASS satellites, the results of the study showed that the convergence time to the desired positioning accuracy level was associated with the improvements in the satellite geometry. Moreover, the results illustrated that the integration of GPS and GLONASS observations could improve the positioning accuracy.
Piriz et al. (2009) examined the 24-hour observation data collected by 19 globally distributed IGS control stations with using MagicGNSS online service, which was developed to provide PPP solutions for GNSS users. The RMSE values of differences between positions obtained by GPS-only and GLONASS-only observations were found to be about 5 mm and 12 mm in horizontal and vertical components, respectively. In addition, according to processed one hour data, the solutions obtained by combined
3
GPS/GLONASS observations have been reported to be significantly (about 50 %) more accurate than the solutions obtained by only GPS observations.
Azab et al. (2011) evaluated the efficiency of dual frequency GPS/GLONASS
PPP in post processed static mode. In the study, Bernese 5.0 software package, a high precision scientific software for post-processing of multi-GNSS data, was utilized to process the datasets collected by five IGS stations distributed across North America. The results showed that the satellite visibility and geometry improved significantly with the addition of GLONASS constellation by about 60% and 30%, respectively. It has also been reported that the performance of dual frequency GPS/GLONASS PPP was better than the performance of dual frequency GPS PPP in terms of accuracy, convergence, and repeatability.
Cai and Gao (2013) analyzed the combined GPS/GLONASS PPP method consisting of functional and stochastic models. In that study, the performance of static and kinematic GPS/GLONASS PPP was evaluated. According to the results, if there were a sufficient number of GPS satellites with good geometry, adding GLONASS observations to GPS observations would not significantly improve the accuracy of the solutions (only about 2 mm improvement observed).
Alkan et al. (2015) investigated the accuracy performance of GPS and combined
GPS/GLONASS static PPP in urban area by using two different online PPP services:
Canadian Spatial Reference System PPP service (CSRS-PPP) and MagicGNSS operated by Spanish GMV Aerospace and Defense Co. It has been shown that better than 1 dm accuracy could be obtained by employing combined GPS/GLONASS PPP while
4
accuracy of about 1-2 dm could be reached with GPS PPP after one hour dual frequency observation. In addition, the superiority of CSRS-PPP over MagicGNSS in terms of reachable positioning accuracy level was demonstrated in the study.
1.2 Motivation
The PPP method is gaining greater acceptance in the daily practice, so it is important to evaluate the achievable performance of PPP in terms of accuracy, repeatability, and convergence time. In this study, it was aimed to assess the current strengths and limitations of the combined GPS/GLONASS PPP method in post-processed static and kinematic positioning modes. For this purpose, accuracy, repeatability, and convergence analyses were conducted by using code and carrier phase pseudorange observations collected over one week at three IGS stations selected in different latitude regions for static PPP processing. Regarding kinematic PPP, dual frequency data collected via a measurement van was utilized to obtain PPP-derived coordinates, which then were compared to those of the differential method solutions for accuracy and initialization analyses.
1.3 Overview
This thesis consists of seven chapters. Chapter 1 gives an overview of the Precise
Point Positioning method and previous related studies. In addition, the motivation of the study is presented in this chapter. Chapter 2 introduces the current and planned status of the global and regional navigation satellite systems. Chapter 3 discusses the principle of
5
satellite based positioning, basic GNSS observables, error sources affecting the measurements, and error mitigation techniques. Chapter 4 deals with the functional mathematical model of GPS PPP and combined GPS/GLONASS PPP methods. Chapters
5 and 6 present the results and analysis of static and kinematic PPP studies, respectively.
Finally, Chapter 7 provides the conclusions with respect to benefits and challenges of combined GPS/GLONASS PPP, and gives recommendations for future research.
6
Chapter 2: Satellite Navigation Systems
A satellite navigation system is a space-based radio positioning system which provides three dimensional position, velocity, and time information for positioning, navigation, and timing purposes (Kaplan & Hegarty, 2006). A satellite navigation system serving on a global scale is also called as Global Navigation Satellite System (GNSS).
Today, the GPS and GLONASS systems are the only globally operational GNSS systems in the world. In addition, the European Union and China are currently developing their own GNSS systems which are expected to be operational by 2020. There are also regional satellite navigation systems: the Japanese QZSS and the Indian IRNSS. In this chapter, the information on all these global and regional navigation systems will be provided in detail.
2.1 Global Positioning System (GPS)
The Global Positioning System (GPS) is a satellite-based positioning, navigation, and time transfer system, which is financed, operated, and developed by the U.S.
Department of Defense (DoD) (Defense Science Board Washington D.C., 2005). GPS is a passive one way ranging system, designed to continuously provide position and time information to users anywhere in the world, and under any weather condition (El-
Rabbany, 2002). Despite the fact that in the early 1970s, DoD’s primary purpose in 7
generating GPS was to fulfill the requirements of U.S. military for positioning and timing, today, GPS is constantly utilized by the unlimited number of users around the world (Misra & Enge, 2002).
GPS consists of three segments: the space segment, the control segment, and the user segment. The space segment is composed of a constellation of satellites which are orbiting the Earth with an orbital period of about 11 hours and 58 minutes at an approximate altitude of 20,200 km above the Earth’s surface (El-Rabbany, 2002). The main responsibility of the space segment is to continuously broadcast radio navigation signals. The control segment, whose responsibility is to properly operate the GPS system, consists of a network of ground facilities, a master control station, an alternate master control station, 4 ground antennas sending commands and navigation data to the constellation, and 16 monitoring stations tracking the GPS satellites to monitor the health and accuracy of the satellite constellation. The user segment comprises both DoD authorized (military) and civilian GPS users, and their GPS receivers which are capable to determine three dimensional position in the GPS reference system (World Geodetic
System-WGS84) and time information by using the received signals from satellites.
Whilst DoD is in charge of managing both space and control system, market forces are responsible for the progress of civil GPS receivers in the user segment (Misra & Enge,
2002).
GPS system employs a constellation of 24 satellites located in six equally spaced orbital planes with approximate 55o inclination angle to the equator by definition, see
Figure 2.1. This layout is known as a baseline constellation. With the baseline
8
constellation, four satellites are placed in each of nearly circular orbital plane, so between four and eight satellites would be visible for almost all users over the world (Misra &
Enge, 2002). While the availability of at least 24 operational satellites is guaranteed by the U.S., 95% of the time, 31 operational GPS satellites have been available for the past several of years (GPS.gov, 2016).
Figure 2.1: GPS nominal constellation.
In order to test the practicability of GPS, ten experimental satellites, called Block
I (1st generation) satellites, was sent into orbit between 1978 and 1985, and so the development of GPS satellite constellation got started. These satellites were followed by
Block II (2nd generation) satellites launched between 1989 and 1990, Block IIA (A for advanced) satellites launched between 1990 and 1997, Block IIR (R for replenishment) satellites launched between 1997 and 2004, Block IIR-M (M for modernized) satellites launched between 2005 and 2009, and Block IIF (F for follow-on) satellites launched
9
between 2010 and 2016, respectively. Each successive generation of GPS satellites was produced with better features, such as improved design lifespan with radiation-hardened electronics, increasing performance, and reduced price (Misra & Enge, 2002).
GPS satellite constellation as of March 2016, consists of 12 Block IIR, 7 Block
IIR-M, and 12 Block IIF operational satellites. The new generation of GPS satellites called GPS III (3rd generation) is on the way, and the first GPS III satellite is expected to be launched in a few years.
2.1.1 GPS Signal Structure
Originally, GPS satellites were designed to continuously broadcast utilizing two different radio frequencies in the L band which are called L1 (1575.42 MHz) and L2
(1227.60 MHz) (Misra & Enge, 2002). The L1 and L2 carrier frequencies are derived from the fundamental frequency of 10.23 MHz, which is produced by the atomic clocks aboard the satellites. A multiplication of fundamental frequency with 154 and 120 results in the center frequencies of L1 and L2 carriers whose wavelengths are about 19 and 24 cm, respectively (Hofmann-Wellenhof, Lichtenegger, & Collins, 2001). Both carriers are modulated by pseudo-random noise (PRN) code for timing and the navigation data messages which includes ephemeris and time parameters for positioning. Both coarse/acquisition (C/A) and encrypted precision [P(Y)] codes are transmitted on L1 carrier, whereas L2 carrier is used to broadcast only the P(Y) code to enable DoD authorized users to remove the first order effects of ionosphere. The P(Y) code refers to
10
precise code for DoD-authorized users, and the C/A code is a less accurate code for civil users.
The PRN codes are generated as a unique sequence of zeros and ones by a mathematical formula, so the same carrier frequency can be used to transmit by all satellites without any interference (Misra & Enge, 2002). The C/A code is unique sequence of chips (1023 bits) with a chip width of about 300m, repeated every millisecond. The P(Y) code is made up of an extremely long sequence of chips (~1014 chips). Its chip width is approximate 30m and it is repeated every week (Hofmann-
Wellenhof, Lichtenegger, & Collins, 2001).
2.1.2 GPS Modernization
To improve the accuracy and availability of the GPS system for all users, and to keep its superiority among other global navigation systems, such as GLONASS and
GALILEO, the U.S. initiated a comprehensive modernization program comprising the upgrade of GPS space and control segments.
Under modernization program, the U.S firstly terminated the Selective
Availability (SA) in May 2000, which was used to deliberately degrade the civilian GPS accuracy, and started to launch new modernized satellites called Block IIR-M in 2005.
These satellites were equipped with the new civil signal (L2C) on the L2 carrier and new military code (M-code) signals on both L1 and L2 carriers, which offer better jamming resistance than P(Y) code signal. One of the reasons for the addition of L2C signal was to
11
allow dual frequency civil GPS receivers to correct for the first-order ionospheric signal group delay in order to boost the accuracy.
The IIR-M generation of GPS satellites was followed by Block IIF constellation satellites which are capable to transmit third civil signal on new radio frequency L5
(1176.45 MHz), is also called L5. This signal was designed to meet the requirements for transportation safety-of-life applications (GPS.gov, 2016).
Lastly, the U.S. plans to take next step in modernization process of the GPS space segment by launching a new generation of GPS satellites (GPS III) in the near future.
Besides all legacy signals, GPS III constellation satellites are going to transmit fourth civil signal on L1 carrier (i.e. L1C) to make GPS interoperable with other international
(regional or global) navigation satellite systems (Leick, Rapoport, & Tatarnikov, 2015).
The evolution of GPS signals is shown in Figure 2.2.
As for the upgrade of the GPS control segment, the number of monitoring stations were increased from 6 to 16 under the Legacy Improvement Initiative (L-AII), which was completed in 2008. Therefore, the accuracy of the transmitted message from GPS satellites was improved by about 15% (GPS.gov, 2016).
In 2007, Architecture Evaluation Plan (AEP) was initiated to substitute the master control station for the new one based on latest IT technologies. Furthermore, in 2008,
Next Generation Operational Control System (OCX) was planned to be established in order to provide the control segment with superior properties, such as completely controlling the new civil signals (GPS.gov, 2016).
12
C/A-code : Coarse acquisition code L1C : Civil signal on L1 (1575.42 MHz) frequency P(Y)-code : Encrypted precise code L2C : Civil signal on L2 (1227.6 MHz) frequency M-code : Military code L5 : Civil signal on L5 (1176.45 MHz) frequency Figure 2.2: GPS signal structures (Hegarty & Chatre, 2008).
2.2 GLONASS
GLONASS (Globalnaya Navigatsionnaya Sputnikovaya Sistema) is a global navigation system developed by Russia, which reached the fully operational status in
1995 for the first time. In the late 1990s, the big decline in the number of GLONASS satellites occurred due to several reasons, such as short lifespan of GLONASS satellites and decreased government funding. However, after the Russian government decided to
13
provide more funding to the GLONASS system in 2001, it reached global coverage with full constellation of 24 satellites (21 satellites + 3 active spares) in 2011. Today,
GLONASS is the only alternative fully operational global navigation system to GPS.
Similar to GPS, GLONASS also consists of space, control, and user segments. The space segment of GLONASS was designed to be made of at least 24 operational satellites positioned in 3 orbital plane which are separated by 120o from each other. Each orbital plane has inclination of 64.8o with respect to the equator, and includes equally spaced satellites at an altitude of approximate 19100 km. The orbital period of GLONASS satellites which are operated in nearly circular orbits is about 11 hour and 15 minutes
(Leick, Rapoport, & Tatarnikov, 2015).
Figure 2.3: GLONASS nominal constellation.
Different from GPS satellites, each GLONASS satellite transmits at different L1 and L2 frequencies except when the satellites are placed in antipodal slots of the same orbit (Frequency Division Multiple Access - FDMA). Presently, the L1 carrier frequency 14
varies between 1598.0625 and 1605.375MHz, and the L2 carrier frequency contains the range from 1242.9375 to 1248.625 MHz. The frequencies of both L1 and L2 carriers are derived from 5.0 MHz, which is a common onboard frequency standard. Like GPS satellites, originally, GLONASS satellites were designed to transmit civil C/A code on L1 carrier and precise P code on both L1 and L2 carriers.
Under the modernization program, the new generation GLONASS satellites called GLONASS-M were furnished with a new civil signal (also called L2C) on L2 carrier. Moreover, with GLONASS-K1 satellites, the third civil signal at L3 band (~1201
MHz), obtained by code division multiple access (CDMA) technique, became available to allow interoperability between GLONASS and other international navigation systems.
The next generation satellites called GLONASS-K2 are planned to supply additional
CDMA signals together with legacy FDMA signals on all carriers (Leick, Rapoport, &
Tatarnikov, 2015).
Beside the upgrade of the space segment, GLONASS modernization program also includes the enhancement of both control and user segments. In order to achieve the global coverage and the more accurate and reliable satellite signals, new monitoring stations were established inside and outside the Russian territory. As for the user segment, the Russian government implemented new regulations to increase the usage of
GLONASS receivers instead of advanced GPS receivers in Russia.
15
GPS GLONASS
Nominal number of 24 24 satellites Operational satellites in 30 23 Feb 16, 2016 Orbital Planes 6 (separated with 60o) 3 (separated with 120o) Orbital Radius 26.560 km 25.510 km Nominal eccentricity ~0 ~0 Orbital height ~20.200 km ~19.100 km Orbital plane inclination 55o 64.8o Orbital period ~11h 58m ~11h 15m Ground track repeatability Every sidereal day Every 8 sidereal days Code Division Multiple Frequency Division Multiple access technique Access Multiple Access (CDMA) (FDMA*) L1 carrier 1575.42 MHz 1598.0625 – 1605.375 MHz L2 carrier 1227.60 MHz 1242.9375 – 1248.625 MHz C/A code on L1 1.023 MHz 0.511 MHz P code on L1 and L2 10.23 MHz 5.11 MHz Reference system WGS-84 PZ-90 Time reference UTC (USNO) UTC (SU) * changing to CDMA in the future Table 2.1: Comparison of GPS and GLONASS systems.
2.3 GALILEO
GALILEO is a global navigation satellite system which is being developed and funded by the European Union. Different from GPS and GLONASS, it will be a global positioning and navigation service under civilian authority. GALILEO is planned to have
16
a constellation consisting of 27 operational and 3 spare satellites, positioned in 3 orbital planes with an inclination angle of 56 degrees. Similar to the other global navigation systems, GALILEO satellites will revolve the Earth in nearly circular orbit at the altitude of about 23.222 km (Leick, Rapoport, & Tatarnikov, 2015). The system is expected to be operational with full constellation by 2020. The GALILEO satellite constellation as of
October 2015, is made up of only 3 space vehicles.
Like GPS signals, GALILEO signals (E1, E5a, E5b, and E6) employ a CDMA spread spectrum technique to allow all satellites to transmit at the same frequencies without interference. The carrier frequencies of GALILEO E1 and GALIEO E5A signals are chosen to be the same as GPS L1 (1575.42 MHz) and GPS L5 (1176.45 MHz) signals so as to enable interoperability between GPS and GALIEO. Similar to GPS, GALILEO also utilizes the same algorithm to generate the ephemeris structure (Leick, Rapoport, &
Tatarnikov, 2015).
2.4 BEIDOU
BEIDOU, also known as Compass Navigation Satellite System (CNSS), is a satellite positioning and navigation system which is being developed by China. The system is planned to be in service on a global basis by 2020. When completed, it will have 5 geostationary earth orbit (GEO) satellites at an altitude of 35.786 km, 27 medium- earth orbit (MEO) satellites at an altitude of 21.528 km, and 3 inclined geosynchronous satellite orbit (IGSO) satellites at an altitude of 35.786 km. The inclination angle of the
17
orbital planes of MEO and IGSO satellites towards to the equator is 55 degrees. The GEO satellites are placed from longitude 58.75 E to 160E.
The BEIDOU satellites broadcast in B1 (1561.098 MHz), B2 (1207.14 MHz), and
B3 (1268.52 MHz) frequency bands, and BEIDOU signals utilize CDMA spread spectrum technique like GPS, GALILEO, and modern GLONASS signals (Leick,
Rapoport, & Tatarnikov, 2015).
GPS GLONASS GALILEO BEIDOU
Country USA Russian Europe Union China Federation No. of Orbital 6 3 3 3 (MEO*) planes Orbital height 20.200 km 19.100 km 23.222 km 21.528 km (MEO) Orbital period ~11h 58m ~11h 15m ~14h 7m ~12h 50m (MEO) Nominal 24 24 30 35 number of satellites Coverage Global Global Under Regional status as of construction
2016 Global by 2020 Global by 2020 * Medium Earth Orbit Table 2.2: Overview of the Global Navigation Satellite Systems.
2.5 QZSS
The Japanese Quasi-Zenith Satellite System (QZSS) is a regional navigation satellite system which is arranged to provide at least one satellite for more than 12 hours a day at or near to zenith over Japan. Currently, although the system has only one
18
satellite, it is arranged to have a constellation consisting of 4 satellites by the end of 2018.
However, the final constellation is expected to consist of 7 satellites. The three QZSS satellites are planned to be located in highly elliptical orbit (HEO) at an altitude varying between 32.000 and 40.000 km, and all of the satellites will seem to draw the figure-8 when they orbit.
Figure 2.4: QZSS constellation ground track (Tsujino, 2005).
In order to improve the performance of QZSS through combining it with other navigation systems, its signals L1-C/A, L1C, L2C, and L5 are generated as being suitable for current GNSS receivers (Leick, Rapoport, & Tatarnikov, 2015).
19
2.6 IRNSS
The Indian Regional Navigation Satellite System (IRNS) is a developing positioning and navigation service whose full constellation will consist of 3 GEO satellites and 4 IGSO satellites. The IRNSS satellites are planned to transmit signals in
L5 (1176.45 MHz) and S band (2492.08 MHz). Better than 10m absolute positioning accuracy over India and better than 20m absolute positioning accuracy in the Indian
Ocean and regions encompassing the India up to 1500 km are anticipated with the completion of the system (Leick, Rapoport, & Tatarnikov, 2015).
20
BPSK : Binary Phase-Shift Keying TMBOC : Time-Multiplexed BOC BOC : Binary Offset Carrier AltBOC : Alternative BOC CBOC : Composite BOC Figure 2.5: Signal spectrum of all GNSS systems.
21
Chapter 3: GNSS Measurements, Error Sources, and Error Mitigation
The position of a receiver can be determined by measuring the distances from a receiver to a set of GNSS satellites whose positions and clock offsets are known. The positioning process can be thought as locating the intersection of the fictitious spheres around the satellites, whose radii are the measured ranges between the visible satellites and the receiver. The intersection of two spheres obtained by two range measurements is a circle, along which the receiver could lie anywhere. By adding the third measurement, the position of the receiver is narrowed down to the two points where the third sphere intersects with that circle. Since one of the resulting points generally is quite far from the
Earth or having an absurd velocity, the receiver can dismiss that point autonomously, and thus, the position of the receiver can be determined without requiring any further measurement. However, in practice, additional fourth measurement is required in order to correct the receiver’s clock bias which causes the three spheres not to intersect at an exact point. With the four or more observations, a unique XYZ position of the receiver-antenna phase center at a particular epoch can be determined (Grejner-Brzezinska, 2015), see
Figure 3.1.
22
Figure 3.1: GNSS positioning [http://www.polarislandsurvey.com/survey/gps.php].
3.1 GNSS Measurements
The fundamental GNSS observables (measurements) utilized for positioning and timing are pseudoranges and carrier phases. While pseudoranges are derived from measured signal propagation time, charier phases are acquired from phase differences between the received carrier signal and a reference carrier signal generated by the receiver’s internal oscillator (Leick, Rapoport, & Tatarnikov, 2015).
3.1.1 Pseudorange (Code Phase) Measurements
A pseudorange is an apparent distance between the satellite and the receiver. It is determined by multiplying the speed of light in vacuum with the signal propagation time which is the difference between the signal emission time generated by the atomic clock on the satellite and the signal reception time generated by receiver clock. Because of the
23
fact that there is no synchronization between the atomic clock on the satellite and the receiver clock, this measured distance contains a bias, and thus, it is not a geometric distance between the satellite and the receiver antenna. Therefore, the computed distance is called as a pseudorange (Hofmann-Wellenhof, Lichtenegger, & Collins, 2001).
In order to obtain the pseudorange, the signal propagation time is determined by the receiver based on the comparison of the received code and receiver-generated code.
In other words, the length of time needed to align the received code with the receiver- generated code is measured by the receiver. Traditionally, the precision of the pseudoranges is approximately %1 of the chip length (Misra & Enge, 2002).
By means of disregarding all kinds of errors affecting the measurement, the pseudorange determined by the apparent signal travel time can be written as:
푠 푃(푡) = 푐[푡푟(푡) − 푡 (푡 − 휏)] (3.1)
where:
푃(푡) is the measured apparent range (i.e. pseudorange) at system time 푡
푡푟(푡) is the arrival time measured by the receiver clock
푡푠(푡 − 휏) is the signal emission time marked on the navigation message; 휏 is the signal travel time
푐 is the speed of light in vacuum (=299 792 458 m / s).
24
With considering clock biases and other errors, Equation (3.1) can be shown as:
푠 푃(푡) = 푐[푡 + 훿푡푟(푡) − (푡 − 휏 + 훿푡 (푡 − 휏))] + 휀푃(푡) (3.2)
푠 = 푐휏 + 푐[ 훿푡푟(푡) − 훿푡 (푡 − 휏)]+푇 + 퐼푃 + 푀 + 휀푃(푡) where:
푐휏 is the geometric (vacuum) distance
훿푡푟(푡) is the receiver clock bias
훿푡푠(푡 − 휏) is the satellite clock bias
푇 and 퐼푃 are the tropospheric and ionospheric delays, respectively
푀 is the multipath effect on measured pseudorange 푃(푡)
휀푃(푡) is the modelling errors, unmodeled effects, and measurement noise.
3.1.2 Carrier Phase Measurements
The carrier phase measurement is the phase difference between the carrier signal received from the satellite and the replica carrier signal generated in the receiver at the measurement epoch. Ideally, the range between the receiver and the satellite is the sum of the measured fractional cycle and the total number of full carrier cycles. However, the receiver cannot determine the number of the full cycles, also known as integer ambiguity, at the initial signal acquisition. Therefore, the receiver measures the initial fractional phase difference, and then it keeps track of the changes in that measurement and counting the number of full cycles. In this case, the initial integer ambiguity will not change as long as the tracking of satellite signal is not interrupted. On the other hand, any break in
25
observing of the signal due to the buildings, trees, etc. causes a new integer ambiguity value to be resolved.
With the determination of the integer ambiguity, the range between a satellite and a receiver can be obtained more precisely and accurately relative to the pseudoranges determined based on the PRN codes. While the positioning acquired with real-valued ambiguity parameters is called a float solution, the positioning based on the ambiguities that are fixed at integer values is referred to as a fixed solution. The ambiguity fixed positioning is more accurate than the ambiguity float positioning. Typically, the noise of the carrier phase measurements is in the order of a few millimeters (Misra & Enge,
2002).
By neglecting the clock errors and other error sources, one can write the carrier phase measurement in unit of cycles as follows:
푠 훷(푡) = 훷푟 (푡) − 훷 (푡 − 휏) + 푁 (3.3) where:
훷푟 (푡) is the phase of the replica signal generated by the receiver at measurement epoch 푡
훷푠(푡 − 휏) is the phase of the received signal at time 푡, or the phase of the signal at the satellite at time (푡 − 휏); 휏 is the signal propagation time
푁 is the integer ambiguity.
Equation (3.3) can also be written in view of that the phase is the product of time and frequency as follows:
26
𝜌(푡, 푡 − 휏) (3.4) 훷(푡) = 푓휏 + 푁 = + 푁 λ
where:
푓 and λ are the carrier frequency and wavelength, respectively
𝜌(푡, 푡 − 휏) is the geometric range between the receiver and the satellite at measurement epoch 푡.
Considering both satellite and receiver clock offsets, initial phase offsets, and some other errors in Equation (3.4), we get the following equation:
푐 휀 훷(푡) = 휆−1[𝜌(푡, 푡 − 휏) + 푇 + 퐼 ] + (훿푡 − 훿푡푠) + 푁 + (휑푠 − 휑 ) + 훷 (3.5) 훷 휆 푟 푟 휆 where:
푇 and 퐼훷 are the tropospheric and ionospheric delays, respectively
푠 훿푡푟 and 훿푡 are the receiver and satellite clock offsets from GNSS system time, respectively
푠 휑 and 휑푟 are the initial fractional phases at the transmitter and the receiver, respectively
휀훷 denotes the remaining errors.
3.2 GNSS Error Sources and Error Mitigation
The errors in the measured ranges are called as either bias or noise which cause the deterioration in the positioning accuracy when they are not accounted for. Whilst noise is a random error with a mean of zero over a short period of time, a bias is systematic error inclined to remain constant over a prolonged period of time. There are 27
several error sources, including satellite and receiver clock offsets, satellite position errors, atmospheric uncertainties which alter the signal travel time, and the multipath errors caused by reflection of the signal due to the surfaces around the antenna, and receiver noise (Misra & Enge, 2002). All of the error sources together generate the error budget which is responsible for the accuracy of the estimated position. In order to enhance the positioning accuracy, the effect of the errors should be completely removed or minimized as much as possible.
The error sources can be broadly grouped into four categories: satellite-related errors, signal propagation related errors, receiver-related errors, and receiver-station related errors. Since the data collected simultaneously at base and rover stations are processed by differencing respective observables from both stations in differential GNSS
(DGNSS), some of the satellite related errors, receiver related errors, receiver station related errors, and atmosphere induced errors which are spatially and temporarily correlated over short baselines could be eliminated completely or partially. Hence, millimeter level accuracy is achievable by applying DGNSS. On the other hand, as PPP method utilizes the observations from a single receiver, all possible error sources should be dealt with separately in order to obtain cm level or better accuracy with PPP.
The common error sources which should be taken into account in all kinds of
GNSS positioning methods are satellite ephemeris error, satellite and receiver clock errors, tropospheric and ionospheric delays, receiver antenna phase center variation, multipath error, and receiver measurement noise. Besides these common errors sources, some additional error sources which are satellite antenna phase center offset and
28
variation, phase wind-up effect, relativistic effect, the Earth tide, ocean tide loading, atmospheric loading, and Sagnac effect should be considered in precise positioning applications.
Most of the error sources above are handled by the help of the models except receiver clock error, tropospheric wet zenith delay, and ionospheric delay while implementing PPP. The effect of ionospheric delay on position accuracy is alleviated by the ionosphere free linear combination, whereas a receiver clock and tropospheric wet zenith delay are considered as extra unknowns needed to be estimated.
3.2.1 Satellite Related Errors
3.2.1.1 Satellite Ephemeris and Clock Errors
The difference between the estimated satellite trajectory and the true satellite trajectory is known as an ephemeris error (El-Rabbany, 2002). It is caused by the along- track, cross-track (perpendicular to along-track), and radial positional perturbations of the satellite, which occur due to the gravitational forces of the Earth, Sun, and Moon. The satellite orbit error in range measurements is mainly due to the satellite position error in radial direction since the projections of the satellite position errors in the along-track and across-track directions onto the line of sight are relatively small (Misra & Enge, 2002). A small error in the satellite orbits can cause a positioning error varying between 2 m and 5 m (El-Rabbany, 2002).
29
SV : Satellite vehicle ρ : Measured pseudorange dr : Satellite position error vector a : Unit vector on line of sight Figure 3.2: Satellite ephemeris error (Kaplan & Hegarty, 2006).
A satellite clock error can be defined as a bias due to the drift in the atomic clock on board the satellite with respect to the system time. Even though the amount of drift is not significant because of the long term stability of atomic clocks (about 1 sec in
3,000,000 years), it can cause a few meters error in range measurements (El-Rabbany,
2002).
Satellite clock and orbit errors could be corrected by using the broadcast ephemeris transmitted within the navigation message in real time or by using the precise ephemeris which contains the observed satellite orbits with some delay. The precise ephemerides are based on the observations at the globally distributed reference stations
30
whose coordinates were precisely determined. They could be obtained from the
International GNSS service (IGS).
3.2.1.1.1 International GNSS Service (IGS)
International GNSS service (IGS) is a civilian organization whose mission is to provide high quality GNSS observation data sets and products, such as precise ephemerides, satellites clock information, and Earth rotation parameters for Earth science research, and positioning, navigation, and timing applications. It is composed of a global network of over 400 GNSS ground stations, 28 data centers (4 global, 6 regional, 17 operational and 1 project data center), 12 data analysis centers where advanced algorithms are used in processing of the observation data sets obtained from ground stations to generate the high accuracy products, and 28 regional associate analysis centers, see Figures 3.3 and 3.4 (IGS, 2015).
31
Figure 3.3: IGS organizational diagram [http://kb.igs.org/hc/en-us/articles/202014583- Organizational-Diagram].
Figure 3.4: IGS tracking network [https://igscb.jpl.nasa.gov/network/netindex.html].
32
IGS provides the users with a number of products having different accuracies and latencies. The more accurate products are generated by IGS with a long latency. For instance, IGS’s precise GPS satellite ephemerides are categorized as ultra-rapid (igu), rapid (igr), and final (igs) ephemerides. While the accuracy is increased from ultra-rapid to final products, the timeliness is gradually getting worse. As for GLONASS, IGS only provides a final ephemeris with a precision of about 3 cm and with a latency varying between 12 and 18 days.
IGS’s ultra-rapid product was designed to meet the increasing need of near real- time GPS data processing. It consists of two parts called as ultra-rapid (observed half) and ultra-rapid (predicted half) ephemerides. While the first part is determined through
24-hour of past GPS observations, the second half is generated from 24-hour prediction of GPS satellite orbits and clocks. Table 3.3 provides the accuracy values for all precise
GPS satellite ephemerides provided by the IGS.
Sample Sat. Orbit and clock Accuracy Latency Updates Interval Ultra-Rapid orbit ~5 cm four times real time 15 min (predicted half) clock ~3 ns daily Ultra-Rapid orbit ~3 cm four times 3-9 hours 15 min (observed half) clock ~150 ps daily orbit ~2.5 cm 15 min IGS Rapid 17-41 hours daily clock ~75 ps 5 min orbit ~2.5 cm 15 min IGS Final 12-18 days weekly clock ~75 ps 30s Table 3.1: Precise GPS satellite orbits and clock corrections provided by the IGS [http://www.igs.org/products].
33
In order to render real-time data processing possible, the real-time service (RTS) was established by the IGS. IGS-RTS provides real-time access to its GNSS orbit and clock correction products for precise point positioning (PPP) and its relevant applications like disaster monitoring. IGS-RTS products are formatted with RTCM SSR standard and are transmitted via NTRIP protocol. IGS-RTS official products currently consist of GPS satellite orbit and clock corrections, see Table 3.2 for product description. There is also an experimental product including combined GPS and GLONASS corrections. Studies on the production of solutions for other GNSS systems are being continued (IGS-RTS,
2016).
Sample Sat. Orbit and clock Accuracy Latency Updates Interval Real-time service orbit ~5 cm 5-60s 25 seconds continuous (RTS) (estimated) clock ~0.5 ns 5s Table 3.2: IGS RTS product description (IGS-RTS, 2016).
3.2.1.2 Relativistic Effects
As the satellite and the receiver clocks move at different speeds, and they experience different gravitational forces, the measured signal propagation time contains the general and special relativistic effects. According to general relativity, the satellite clock appears to tick faster than the receiver clock because the gravitational force decreases with altitude. On the other hand, according to special relativity, since the satellite clock moves much faster than the receiver clock, it appears to run slowly. Since the extent of the general and special relativistic effects on a satellite clock are different,
34
they cannot cancel each other (Ashby, 2006). Therefore, total relativistic effect (i.e. both general and special relativistic effects) should be taken into account in precise applications.
The total relativistic effect in terms of frequency drift for GPS satellite clocks is about 4.5*10-10 s/s. This amount is made of a constant offset (about 4.46*10-10 s/s) and periodic variations up to 10-11 s/s (Gerard & Luzum, 2010). While the correction for a constant offset is made before the launch of the satellite by reducing the frequency of atomic clock on board, the corrections for periodic variations may be taken care of by using IGS precise clock products (Min, Yunzhi & Xiayoun, 2011).
The periodical relativistic correction for GPS satellite can be computed by the following equation (Gerard & Luzum, 2010):
2 (3.6) ∆ = − √푎 ∙ 퐺푀 ∙ (푒 ∙ sin 퐸) 푟푒푙 푐2 where:
∆푟푒푙 is periodical relativistic correction (ns)
푐 is the speed of light in vacuum
퐺푀 is the earth gravitational constant
푎, 푒, and 퐸 are the GPS orbit semi-major axis, eccentricity, and eccentricity anomaly angle, respectively.
3.2.1.3 Satellite Phase Center Offset and Variation
Because of the fact that precise satellite orbit and clock products are generated with respect to satellite’s mass center, the offset between satellite’s mass center and the 35
satellite’s antenna phase center, which code and phase measurements refer to, must be taken into account in precise applications, such as PPP. The satellite phase center offsets are generally in body z direction towards to the Earth for many satellites, but for some satellites, they are also in body x direction towards to the Sun (Kouba, 2015).
The relative GPS antenna phase center offsets with zero phase center variation are adopted by IGS until November 4, 2006. Since that time, absolute antenna phase center offsets (PCO) with non-zero phase center variations (PCV) are utilized to relate the antenna mass center to antenna phase center. Satellite antenna phase center corrections
(PCO and PCVs) are distributed in the igsXX.atx file (XX is currently 2008) by IGS
(Kouba, 2015).
- Z direction towards to Earth - Y axis completes the right handed system Figure 3.5: Satellite antenna phase center offset (Kouba, 2015).
The antenna phase center offset corrections are generally provided in the satellite- fixed coordinate system whose origin is at the satellite’s center of mass. The corrections could be obtained with the following equation (Leick, Rapoport, & Tatarnikov, 2015):
36
′ 푋푠푎 = 푋푠푐 + [푖 푗 푘] 푋 (3.7)
where:
푋푠푎 is the position of the satellite antenna phase center in Earth Centered Earth Fixed
(ECEF) coordinate system
푋푠푐 is the position of the satellite’s center of mass in ECEF coordinate system
푋′ is the antenna phase center offset in satellite fixed coordinate system
푖, 푗, and 푘 are the unit vectors along the x, y, and z axis of satellite fixed coordinate systems in ECEF , respectively.
3.2.1.4 Phase Wind-up Effect
Since right circularly polarized (RCP) radio signals are emitted by GPS and
GLONASS satellites, the carrier phase measurements are affected by the mutual orientation of the satellite and receiver antenna. A change of one cycle in the carrier phase measurement could be detectable due to the rotation of the satellite antenna or receiver antenna around its vertical axis. This error in the carrier phase measurements is named as phase wind-up effect. Generally, the receiver antenna is kept in a fixed orientation during the static positioning, whereas the satellite antenna slowly rotates because satellite solar panels are directed towards to the Sun. In addition, during the eclipses, the satellite antenna could have one full rotation within a time shorter than 30 minutes. While this effect is trivial for DGNSS unless baselines are longer than a couple
37
hundreds of meters, it should be taken into account in PPP. The phase wind up effect, which is completely absorbed into station clock solution during the kinematic positioning, can be corrected as follows (Kouba, 2015):
퐷′ = 푥′ − 푘(푘 ∙ 푥′) − 푘 × 푦′
퐷 = 푥 − 푘(푘 ∙ 푥) + 푘 × 푦 (3.8)
∆∅ = 푠푖푔푛(휁) 푐표푠−1(퐷′ ∙ 퐷 / |퐷′||퐷|) where:
휁 = 푘 ∙ (퐷′ × 퐷)
∆∅ is phase wind up correction in radians
푘 is the satellite to receiver unit vector
퐷′ and 퐷 are effective dipole vectors of satellite and the receiver, respectively
(푥, 푦, 푧) and (푥′, 푦′, 푧′) are local receiver and satellite body coordinate unit vectors, respectively.
3.2.2 Signal Propagation Related Errors
3.2.2.1 Ionospheric Delay
The ionosphere is the layer of the Earth’s atmosphere, which extends from 50 to
1000 km above the Earth’s surface. This layer includes free electrons and ions broken apart from the neutral gas molecules due to the effect of the Sun’s ultraviolet radiation.
The number of free electrons in ionosphere causes a change in the velocity (speed and
38
direction) of the radio signal passing through it. Because of that phenomenon known as a refraction, the signal travel time gets changed. Consequently, the range measurement corrupted by the ionospheric effect is obtained. The error in the range measurement due to the ionosphere called as ionospheric delay, which is the dominant error source in
GNSS whose contribution to position error could be tens of meters (Hofmann-Wellenhof,
Lichtenegger, & Collins, 2001). Therefore, its effects on measurements should be handled carefully.
The ionosphere behaves as dispersive medium for radio signals, and its refractive index depends upon the frequency of the radio signal (Misra & Enge, 2002). The first order approximation of the phase refractive index, a measure of how much the speed of phase of the wave changed inside the medium, and the group refractive index, a measure of how much the speed of wave packet (information) changed inside the medium, can be expressed respectively as follows:
40.3 ∙ 푛 (3.9) 푛 = 1 − 푒 푝 푓2
40.3 ∙ 푛 (3.10) 푛 = 1 + 푒 푔 푓2 where:
푛푝 and 푛푔 are the phase refractive index and the group refractive index, respectively
푓 is the frequency of the radio wave (Hz)
3 푛푒 is the electron density (el/m ).
39
With the refractive indexes, the phase delay and the group delay can be obtained in meters, respectively by the following formulas (Misra & Enge, 2002):
40.3 40.3 (3.11) 퐼 = ∫(푛 (푙) − 1)푑푙 = − ∫ 푛 (푙)푑푙 = − ∙ 푇퐸퐶 훷 푝 푓2 푒 푓2
40.3 40.3 (3.12) 퐼 = ∫(푛 (푙) − 1)푑푙 = + ∫ 푛 (푙)푑푙 = + ∙ 푇퐸퐶 푃 푔 푓2 푒 푓2 where:
퐼훷 and 퐼푃 are the phase delay and the group delay, respectively
푇퐸퐶 (Total electron content) is the total number of free electrons along the signal path.
From the equations above, it can be concluded that while the pseudorange measurements are longer than the geometric range between satellite and the receiver, the phase measurements are smaller than the geometric range. In other words, as ionosphere slows down the propagation of the codes, it speeds up the propagation of the carrier phases.
The effect of the ionospheric errors in the observations obtained from single frequency GPS receiver can be mitigated up to about 50% by using the Klobuchar ionosphere model which is broadcasted within the navigation message. Regarding the ionospheric errors in the observations of dual frequency GNSS receiver, the first order ionospheric error can be fully removed by applying the ionosphere free linear combination of the measurements on L1 and L2 carrier frequencies. This method is also widely used in precise point positioning in order to lessen the effect of ionospheric error.
40
The ionosphere free combinations for pseudoranges and carrier phase measurements respectively can be expressed as follows (Misra & Enge, 2002):
2 2 푓퐿1 푓퐿2 (3.13) 푃푖표푛표−푓푟푒푒 = 2 2 푃퐿1 − 2 2 푃퐿2 (푓퐿1 − 푓퐿2) (푓퐿1 − 푓퐿2)
2 2 푓퐿1 푓퐿2 (3.14) 훷푖표푛표−푓푟푒푒 = 2 2 훷퐿1 − 2 2 훷퐿2 (푓퐿1 − 푓퐿2) (푓퐿1 − 푓퐿2)
where:
푃푖표푛표−푓푟푒푒 and 훷푖표푛표−푓푟푒푒 are the iono-free pseudorange and charier phase measurements, respectively
푃퐿1 and 푃퐿2 are the pseudorange measurements on L1 and L2, respectively
훷퐿1 and 훷퐿2 are the carrier phase measurements on L1 and L2, respectively
푓퐿1 and 푓퐿2 are the frequencies of L1 and L2, respectively.
3.2.2.2 Tropospheric Delay
The troposphere is the lowest part of the atmosphere, which extends from Earth’s surface up to about 50 km (El-Rabbany, 2002). It is made up of the dry gases (including mostly N2 and O2) and water vapor (Misra & Enge, 2002). Since troposphere acts as non- dispersive medium for the radio frequencies below 15 GHz, both code and carrier phase measurements contain the same amount of delay error. Therefore, tropospheric delay in the measurements, resulted from tropospheric effects cannot be mitigated by applying 41
ionosphere free linear combinations of the measurements on the satellite radio signals of different frequencies (El-Rabbany, 2002).
The errors caused by troposphere can be compensated by the help of the models based on certain parameters, such as altitude, temperature, humidity, and pressures of dry gases, and water vapor (Misra & Enge, 2002).
The tropospheric delay consists of two parts: the dry and wet parts. Although the dry part caused by the dry gases in the troposphere contributes about 90% of total tropospheric delay, it can be easily handled by modelling. On the other hand, because of the irregular variation of the water vapor, the modeling of the wet part is the main problem when dealing with the tropospheric delay. Typically, the dry and wet tropospheric delays are estimated at zenith direction, and by the help of mapping functions based on the elevation angle, they are projected onto the satellite-to-receiver line of sight (LOS) direction, as shown in the following equation (Misra & Enge, 2002):
푇 = 푇푧,푑 ∙ 푚푑(퐸) + 푇푧,푤 ∙ 푚푤(퐸) (3.15) where:
푇 is the total tropospheric delay at LOS
퐸 is the satellite elevation angle
푇푧,푑 is the estimated zenith dry delay
푇푧,푤 is the estimated zenith wet delay
푚푑(퐸) and 푚푤(퐸) are the mapping functions for dry and wet components, respectively.
42
The Saastamoinen and Hopfield models are the most widely used simple models to deal with the tropospheric delay (Misra & Enge, 2002). The Saastamoinen model uses the variations in pressure, temperature, and humidity with respect to the receiver latitude, whereas the Hopfield model exploits the fact that dry and wet refractivities are correlated with the atmospheric conditions at the receiver’s height above the ellipsoid. The zenith dry and wet delay can be estimated with for example, Saastamoinen model
(Saastamoinen, 1972) as follows:
푇푧,푑 = 0.002277 ∙ (1 + 0.0026 ∙ cos(2휑) + 0.00028 ∙ 퐻) ∙ 푃0 (3.16)
1255 (3.17) 푇푧,푤 = 0.002277 ∙ ( + 0.05) ∙ 푒0 푇0 where:
푃0 is the total pressure (millibars)
푒0 is the partial water vapor pressure (millibars)
푇0 is the temperature (Kelvin)
휑 is the latitude (degree) and 퐻 is the orthometric height (meter).
The temperature and the pressures to be used in this model are obtained either by measurements at the receiver location or by using models of the atmosphere.
There are also a number of mapping functions that have been introduced. The simplest form of the dry and wet mapping functions is 1/sin(E), which is not useful when
43
the satellite elevation angle is lower than 15 degrees. More advanced mapping function can be expressed as (Misra & Enge, 2002):
푎 1 + 푖 (3.18) 푏 1 + 푖 1 + 푐푖 푚푖(퐸) = 푎 푠푖푛(퐸) + 푖 푏 푠푖푛(퐸) + 푖 푠푖푛(퐸) + 푐푖 where:
푖 refers to dry or wet
푎푖 , 푏푖 and 푐푖 are the empirical coefficients determined with respect to model parameters including height, latitude, temperature, pressure, and the day of the year
퐸 is the satellite elevation angle.
In PPP, while the dry tropospheric delay in zenith direction is generally handled with the models, the wet tropospheric delay in zenith direction is taken into account as additional unknown parameter, and it is estimated together with the receiver coordinates, receiver clock bias, and ambiguities.
3.2.2.3 Multipath Effect
The reflected signals from the objects near to the GNSS receiver antenna results in a multipath error which deteriorates the accuracy of the code and phase measurements.
The multipath error can be up to about one quarter of the carrier wavelength for phase measurements, whereas it can reach several meters for the code measurements (El-
Rabbany, 2002).
44
Figure 3.6: Multipath error (El-Rabbany, 2002).
The effect of the multipath error could be mitigated by using specially designed antennas called choke-ring antennas, see Figure 3.7. In addition, setting up the GNSS receiver in a proper site far beyond the reflective objects and choosing higher elevation mask angles to not observe the low elevation satellites whose signals are highly vulnerable to multipath could diminish the extent of the possible multipath error.
45
Figure 3.7: Choke ring antenna.
3.2.3 Receiver Related Errors
3.2.3.1 Receiver Antenna Phase Center Offset and Variation
The receiver antenna phase center offset and phase center variation which could be defined as the deviation of the electrical phase center of the antenna from the geometrical center of the antenna should also be considered to obtain cm level or better accuracy in precise applications such as PPP. The receiver antenna phase center offset
(PCO) which refers to a constant vector between the antenna phase center (APC) and the antenna reference point (ARP) may be obtained from the manufacturer or it is determined along with antenna phase center variation (PCV) by calibration process (El-Rabbany,
2002). The calibration values for the frequency dependent PCO and the PCV which varies with the satellite elevation, azimuth angle, and the signal frequency are provided by the IGS. 46
3.2.3.2 Receiver Clock Error
Each GNSS receiver is equipped with a clock to measure the signal propagation time of received signal. In order to produce cost effective receivers, quartz crystal oscillators are used in the receiver clock rather than atomic frequency oscillators which are preferred in satellite clocks. However, the long term stability of the quartz crystal oscillators are not as good as atomic frequency oscillators (El-Rabbany, 2002). Therefore, the receiver clock offset resulted from the poor long term stability of the quartz crystal oscillators must be taken into account while the position of the user is determined. In
PPP, the receiver clock offset is considered as one of the unknowns, and must be estimated.
3.2.3.3 Sagnac Effect
Sagnac effect arises due to the rotation of the Earth as the signal travels from satellite to the receiver. The rotation of the Earth causes synchronization problem between the satellite and the receiver clocks. This issue, known as Sagnac effect, can result in hundreds of nanoseconds time error. Therefore, GNSS receiver should apply
Sagnac effect correction which could be obtained as follows (Ashby, 2006):
47
푣 ∙ 푅 (3.19) ∆푡 = 푠푎푔푛푎푐 푐2 where:
∆푡푠푎푔푛푎푐 is Sagnac effect correction (ns)
푐 is the speed of light
푣 is the receiver velocity in inertial reference frame
푅 is the vector of path between satellite and receiver.
t : Transmitter time T t : Receiver time R ω : Earth’s angular velocity Figure 3.8: Sagnac effect correction (Ashby, 2006).
48
3.2.3.4 Receiver Noise and Inter-channel Bias
The random error in the measurements resulted from the antenna, amplifiers, cables, and the receiver oscillator is called receiver measurement noise, which is at millimeter level for phase observations and can reach meter level for code measurements.
By using high quality receiver equipment, it can be smoothed (Misra & Enge, 2002).
The GNSS signal arrives to the receiver electronics by passing through two paths.
The first path is between the satellite and the receiver antenna, and it is unique to each satellite. On the other hand, the second path takes place between the receiver antenna and the receiver electronics, and it is common for all satellites. Since the signal travel time through the second path changes with respect to the frequency of signal, the receiver suffers from this phenomenon called as inter-channel bias (Yudanov et al., 2011). With the modern receiver’s microprocessor, this bias can be efficiently calibrated. As for any remaining bias, differencing method could be utilized (Allred, Daniels, & Ehsani, 2008).
3.2.4 Receiver Station Related Errors
3.2.4.1 The Solid Earth Tides
The gravitational attraction of the Sun and the Moon on the Earth’s surface produces the Earth tides which causes permanent and periodical site displacements. The periodic horizontal and vertical displacements can be expressed with spherical harmonics of degree and order (n,m) represented by Love number and Shida number. The tidal displacement can be up to 5 cm in horizontal direction, as it can reach approximately 30
49
cm in radial direction. With the long term static positioning (over 24 hours), the periodic component of the Earth tide effect could be largely removed; nevertheless, the permanent component, that could be up to 12 cm in radial direction in middle latitude region, could not be cleared away. Therefore, this effect should be taking into account in precise positioning. The correction which provides 5 mm-level of precision by only accounting for the second degree tides and height correction term can be shown as (Kouba, 2015):
3 4 퐺푀푗 푟 ℎ 2 ℎ ∆푟⃗ = ∑ {[3푙 (푅̂ ∙ 푟̂)] 푅̂ + [3 ( 2 − 푙 ) (푅̂ ∙ 푟̂) − 2]푟̂} + 퐺푀 푅3 2 푗 푗 2 2 푗 2 푗=2 푗 (3.20)
[−0.025푚 ∙ sin ∅ ∙ cos ∅ ∙ sin(휃푔 + λ)] ∙ 푟̂
where:
∆푟⃗ is the site displacement vector in ECEF Cartesian coordinate system
퐺푀and 퐺푀푗 are the gravitational parameters of the Earth, the Moon (j=2) and the Sun
(j=3)
푟 and 푅푗 are the geocentric state vectors of the station, the Moon and the Sun
푟̂ and 푅̂푗 are the geocentric unit state vectors of the station, the Moon and the Sun
푙2 and ℎ2 are the nominal second degree Love and Shida dimensionless numbers, respectively
∅ and λ are the latitude and the longitude of the site, respectively
휃푔 is the Greenwich Mean Sidereal Time.
50
3.2.4.2 Polar Motion (Polar Tides)
Due to the motion of the Earth’s rotation axis with respect to the Earth’s crust, periodical displacements in the position of the station occur. The effects of the polar tides dominated by the Chandler (~430 days) and seasonal periods can cause a positioning error of about 25 mm in vertical and 7 mm in the horizontal directions. The corrections at mm level for latitude, longitude and height components can be obtained as follows
(Kouba, 2015):
∆∅ = −9 cos 2∅[(푋푝 − 푋̅푝) cos λ − (푌푝 − 푌̅푝) sin λ ];
(3.21) ∆λ = 9 sin 2∅[(푋푝 − 푋̅푝) sin λ + (푌푝 − 푌̅푝) cos λ ];
∆ℎ = −33 cos 2∅[(푋푝 − 푋̅푝) cos λ − (푌푝 − 푌̅푝) sin λ ]; where:
∆∅, ∆λ, and ∆ℎ are corrections for latitude, longitude and height components, respectively
∅ and λ are the latitude and the longitude of the station, respectively
(푋푝 − 푋̅푝) and (푌푝 − 푌̅푝) are the pole coordinate discrepancies from the mean pole
(푋̅푝, 푌̅푝).
3.2.4.3 Ocean Tide Loading
The ocean tide loading is an applied force to the underlying layer due to the ocean mass redistribution resulted from gravitational forces. It is made up of diurnal and semi
51
diurnal periodic components, which cause comparatively smaller site displacement than the Earth tides. The effect of ocean tide loading is significant in the areas near to ocean coast lines. It can reach up to 2 cm and 5 cm in horizontal and vertical directions, respectively. Hence, ocean tide loading effect should be considered unless the station is far (>1000 km) away from the ocean coast in order to reach cm level precise positioning.
The correction for ocean tide loading effect can be obtained as follows (Kouba, 2015):
(3.22) ∆푐 = ∑ 푓푗퐴푐푗 cos(푤푗푡 + χ푗 + 푢푗 − ∅푐푗) 푗 where:
∆푐 is ocean tide correction
푓푗 and 푢푗 are dependent on the longitude of the lunar node j symbolizes the 11 tidal waves denoted as M2, S2, N2, K2, K1, O1, P1, Q1, Mf, Mm, and Ssa
푤푗 and χ 푗 are the angular velocity and the astronomical arguments at t=0h for corresponding wave j, respectively
퐴푐푗 and ∅푐푗 are the station specific amplitude and the phase.
3.2.4.4 Atmospheric Loading
Because of the redistribution of the atmospheric mass, there is an atmospheric pressure loading on the Earth surface, which causes vertical site displacement up to 20 mm and horizontal site displacement up to 3 mm. The magnitudes of displacements, which vary with respect to the geographical location of the station, become larger in mid-
52
latitude areas. A basic approach used to estimate the vertical displacement (mm) is
(Petrov, 2004):
∆푟 = −0.35푝 − 0.55푝′ (3.23) where:
∆푟 is vertical displacement due to atmospheric loading
푝 is the difference between local instantaneous pressure at the site and the standard pressure (101.3 kPa)
푝′ is the mean pressure anomaly in the region within 2000 km from the site.
53
Chapter 4: PPP Mathematical Models
The accuracy performance of the PPP method is highly dependent on the number and the geometry of tracked satellites. Therefore, GPS-only observations could remain insufficient in some environments which are subject to poor satellite visibility, such as urban canyons, mountainous regions, forested areas, and open-pit mines. In fact, although there is an adequate number of GPS satellites in open areas, the obtained accuracy of the
PPP method might decrease due to the poor satellite geometry. After GLONASSS once again reached its full constellation, combined GPS and GLONASS observations started to be used in the PPP method in order to improve the number and the geometry of tracked satellites. In this section, the mathematical models of GPS and combined
GPS/GLONASS PPP, which describe the relation between the observation and unknowns, will be discussed comprehensively.
4.1 GPS PPP Mathematical Model
Traditionally, both code and phase measurements collected by dual frequency
GPS receivers are utilized in the PPP method. Ionosphere free linear combinations of the code and phase measurements on L1 and L2 carrier signals are implemented in order to remove the first order ionospheric effects. The code and phase measurements between a receiver and a satellite can be written simply as follows (Cai & Gao, 2007): 54
푃푖 = 𝜌 + 푐(푑푡 − 푑푇) + 푑표푟푏 + 푇 + 퐼푖 + 푀푖 + 푒푖 (4.1)
훷푖 = 𝜌 + 푐(푑푡 − 푑푇) + 푑표푟푏 + 푇 − 퐼푖 + 휆푖푁푖 + 푚푖 + 휀푖 (4.2)
where:
푖 denotes the carrier signal (i.e. 퐿1 and 퐿2)
푃푖 is the measured pseudorange on 퐿푖 carrier signal (m)
Φi is the measured carrier phase on 퐿푖 carrier signal (m)
𝜌 is the true geometric range between receiver and satellite (m), it can be computed as a function of satellite (푋푧, 푌푠, 푍푠) and receiver (푋푟, 푌푟, 푍푟) position:
2 2 2 (4.3) 𝜌 = √(푋푠 − 푋푟) + (푌푠 − 푌푟) + (푍푠 − 푍푟)
푐 is the speed of light in vacuum (m/s)
푑푡 is the receiver clock offset (s)
푑푇 is the satellite clock offset (s)
푑표푟푏 is the satellite ephemeris error (m)
푇 is the tropospheric delay (m)
퐼푖 is the ionospheric delay on 퐿푖 carrier signal (m)
λ푖 is the wavelength of 퐿푖 carrier signal (m/cycle)
55
푁푖 is the phase ambiguity term associated with 퐿푖 carrier signal (cycle), which includes the initial fractional phase biases at the receiver and the satellite
푀푖is the multipath effect on measured pseudorange 푃푖 (m)
푚푖 is the multipath effect on measured carrier phase Φ푖 (m)
푒푖 is the measurement noise for pseudoranges on 퐿푖 carrier signal (m)
휀푖 is the measurement noise for carrier phases on 퐿푖 carrier signal (m).
By applying the Ionosphere-free linear combinations of code and phase measurements on L1 and L2 frequencies, Equations (4.4) and (4.5) could be obtained as follows:
2 2 푓1 푃1 − 푓2 푃2 (4.4) 푃1,2 = 2 2 푓1 − 푓2
= 𝜌 + 푐(푑푡 − 푑푇) + 푑표푟푏 + 푇 + 푀1,2 + 푒1,2
2 2 푓1 훷1 − 푓2 훷2 (4.5) 훷1,2 = 2 2 푓1 − 푓2
푐(푓1푁1−푓2푁2) = 𝜌 + 푐(푑푡 − 푑푇) + 푑표푟푏 + 푇 + 2 2 + 푚1,2 + 휀1,2 푓1 −푓2
where:
푃1,2 and 훷1,2 are iono-free code and phase measurements, respectively
푀1,2 and 푚1,2 show the iono-free linear combination of 푀1/푀2 and 푚1/푚2, respectively 56
푓1 and 푓2are the frequencies of 퐿1 and 퐿2 carrier signals (Hz), respectively.
Using precise ephemeris and clock corrections, ionosphere-free linear combinations of code and phase measurements can be rewritten as:
(4.6) 푃1,2 = 𝜌 + 푐푑푡 + 푇 + 푀1,2 + 푒1,2
(4.7) 훷1,2 = 𝜌 + 푐푑푡 + 푇 + 푁1,2휆1,2 + 푚1,2 + 휀1,2
where:
푁1,2 is the non-integer carrier phase ambiguity term of the ionosphere-free linear phase combination
휆1,2 is the carrier combination wavelength.
As seen in Equations (4.6) and (4.7) above, the unknowns which are determined with the estimation process are Cartesian coordinates of the station, the receiver clock offset, the tropospheric delay, and combined ambiguity terms for each satellite. Instead of estimating total tropospheric delay, the dry tropospheric delay could be handled with modeling, and the wet tropospheric delay could only be estimated as an additional parameter.
Although the linear combination can remove the first order ionospheric effect completely, it has some disadvantages for users. Since the combined ambiguity term loses its integer property with linear combination, it can only be estimated as a float
57
value. In addition, because of the linear combination, the measurement noises contaminate the measurements about three times worse than the original ones.
In order to determine the unknowns, either least-squares adjustment method or extended Kalman filtering may be utilized.
4.1.1 Adjustment Model
By linearizing the observation Equations (4.6) and (4.7) with the a priori parameters and observations (푋0, 푙), the following matrix equation could be obtained
(Kouba and Heroux, 2001):
퐴훿 + 푊 − 푉 = 0 (4.8) where:
퐴 is the design matrix
훿 is the vector of corrections
푊 = 푓(푋0, 푙) is the misclosure vector
푉 is the residuals vector.
The design matrix A is made up of four types of parameters obtained by taking the partial derivatives of the observation equation with respect to unknown vector 푋, see
Equation (4.10). These parameters are the position of the receiver (푋푟, 푌푟, 푍푟), the receiver clock offset (푑푡), the zenith wet tropospheric delay (푇푧,푤), and combined carrier phase ambiguities (푁1,2) associated with each satellite.
58
휕푓(푋, 푙푃푖 ) (4.9) 휕푓(푋, 푙푃 ) 휕푓(푋, 푙푃 ) 휕푓(푋, 푙푃 ) 휕푓(푋, 푙 ) 휕푓(푋, 푙푃푖) 푖 푖 푖 푃푖 푗 휕푋 휕푌 휕푍 휕푇 휕푁1,2 (푗=1,푛푠푎푡) 퐴 = 푟 푟 푟 휕푑푡 푧,푤 휕푓(푋, 푙Φ푖) 휕푓(푋, 푙Φ푖) 휕푓(푋, 푙Φ푖) 휕푓(푋, 푙Φ푖) 휕푓(푋, 푙Φ푖) 휕푓(푋, 푙Φ푖) 휕푋 휕푌 휕푍 휕푑푡 휕푇 푗 [ 푟 푟 푟 푧,푤 휕푁1,2 (푗=1,푛푠푎푡)]
푇 푗 (4.10) 푋 = [푋푟 푌푟 푍푟 푑푡 푇푧,푤 푁1,2 (푗=1,푛푠푎푡)]
By using the a priori weighted constraints (푃푥0), the least squares solution can be
obtained as:
푇 −1 푇 훿 = −(푃푥0 + 퐴 푃푙퐴) 퐴 푃푙푊 (4.11)
where 푃푙 is observation weight matrix
Then the estimated parameters are:
푋̂ = 푋0 + 훿 (4.12)
and the covariance matrix is computed as:
−1 푇 −1 퐶푥̂ = 푃푥̂ = (푃푥0 + 퐴 푃푙퐴) (4.13)
4.2 GPS/GLONASS PPP Mathematical Model
The code and phase measurements on L1 and L2 frequencies for a GLONASS
satellite R could be written as follows (Cai & Gao, 2013):
푅 푅 ( 푅 푅) 푅 푅 푅 푅 푅 푅 (4.14) 푃푖 = 𝜌 + 푐 푑푡 − 푑푇 + 푑표푟푏 + 푇 + 퐼푖 + 푏푃푖 + 푀푃푖 + 푒푃푖
훷푅 = 𝜌푅 + 푐(푑푡푅 − 푑푇푅) + 푑푅 + 푇푅 − 퐼푅 + 휆푅푁푅 + 푏푅 + 푚푅 + 휀푅 (4.15) 푖 표푟푏 푖 푖 푖 훷푖 훷푖 훷푖
59
where i=1,2 and
The superscript 푅 indicates the GLONASSS system
푅 푃푖 is the measured pseudorange on Li frequency (m)
R Φi is the measured carrier phase on Li frequency (m)
𝜌푅 is the geometric range between a receiver and a satellite (m)
푑푡푅 is the receiver clock offset (s)
푑푇푅 is the satellite clock offset (s)
푅 푑표푟푏 is the satellite ephemeris error (m)
푇푅 is tropospheric delay (m)
푅 퐼푖 is ionospheric delay on Li frequency (m)
푅 휆푖 is the carrier wavelength on Li frequency (m)
푅 푁푖 is the phase ambiguity term associated with Li frequency (cycle),
푀푅 and 푚푅 are the multipath error in pseudorange and carrier phase measurements (m), 푃푖 Φ푖 respectively
푒푅 and 휀푅 are the receiver noise in pseudorange and carrier phase measurements (m), 푃푖 Φ푖 respectively
푏푅 and 푏푅 is the hardware delay biases in pseudorange and carrier phase measurements 푃푖 Φ푖
(m), respectively.
Since the satellite hardware delay biases could be removed by using precise satellite clock corrections, the receiver hardware delay biases should only be taken into account in the equations above. The hardware delay biases consist of an average term and
60
satellite dependent bias term which is also known as inter channel bias (Cai & Gao,
2013):
푅 푅 푅 (4.10) 푏푃푖 = 푏푃푖,푎푣푔 + 훿푏푃푖
푏푅 = 푏푅 + 훿푏푅 = 푏푅 + (푏푅 − 푏푅 + 훿푏푅 ) (4.11) Φ푖 Φ푖,푎푣푔 Φ푖 푃푖,푎푣푔 Φ푖,푎푣푔 푃푖,푎푣푔 Φ푖 where:
푏푅 and 푏푅 are receiver code and carrier phase hardware delays 푃푖 Φ푖
푏푅 and 푏푅 are receiver code and carrier phase average hardware delays 푃푖,푎푣푔 Φ푖,푎푣푔
훿푏푅 and 훿푏푅 are receiver code and carrier phase inter channel biases, respectively. 푃푖 Φ푖
Since the satellite dependent bias is smaller than the measurement noise in pseudorange measurements, it can be safely neglected in the equation. However, the satellite dependent term bias is bigger than the measurement noise in carrier phase measurements, so it is kept in the respective equation. Moreover, the average term cannot be separated from the receiver clock error. By considering these facts, the equations of pseudorange and carrier phase measurements can be rewritten as follows (Cai & Gao,
2013):
푅 푅 푅 푅 푅 푅 푅 푅 푅 푅 (4.12) 푃푖 = 𝜌 + (푐푑푡 + 푏푃푖,푎푣푔) − 푐푑푇 + 푑표푟푏 + 푇 + 퐼푖 + 푀푃푖 + 푒푃푖
훷푅 = 𝜌푅 + (푐푑푡푅 + 푏푅 ) − 푐푑푇푅 + 푑푅 + 푇푅 − 퐼푅 + 휆푅푁푅 + 훿푏̃푅 + 푚푅 + 휀푅 푖 푃푖,푎푣푔 표푟푏 푖 푖 푖 훷푖 훷푖 훷푖
(4.13) where 훿푏̃푅 = (푏푅 − 푏푅 + 훿푏푅 ) 푖,Φ푖 Φ푖,푎푣푔 푃푖,푎푣푔 Φ푖
61
Similar to Equations (4.12) and (4.13) written for a GLONASS satellite, the following equations can be formed for a GPS satellite:
퐺 퐺 퐺 퐺 퐺 퐺 퐺 퐺 퐺 퐺 (4.14) 푃푖 = 𝜌 + (푐푑푡 + 푏푃푖,푎푣푔) − 푐푑푇 + 푑표푟푏 + 푇 + 퐼푖 + 푀푃푖 + 푒푃푖
훷퐺 = 𝜌퐺 + (푐푑푡퐺 + 푏퐺 ) − 푐푑푇퐺 + 푑퐺 + 푇퐺 − 퐼퐺 + 휆퐺푁퐺 + 훿푏̃퐺 + 푚퐺 + 휀퐺 푖 푃푖,푎푣푔 표푟푏 푖 푖 푖 훷푖 훷푖 훷푖
(4.15)
By applying the precise GPS and GLONASS ephemeris and clock corrections, and iono–free linear combination of code and phase measurements, Equations (4.12),
(4.13), (4.14) and (4.15) can be rewritten as:
2 푅 2 푅 (4.16) 푅 푓1,푅푃1 − 푓2,푅푃2 푃1,2 = 2 2 푓1,푅 − 푓2,푅
푅 푅 푅 푅 푅 푅 = 𝜌 + (푐푑푡 + 푏푃(1,2),푎푣푔) + 푇 + 푀푃1,2 + 푒푃1,2
2 푅 2 푅 (4.17) 푅 푓1,푅훷1 − 푓2,푅훷2 훷1,2 = 2 2 푓1,푅 − 푓2,푅
푅 𝜌푅 + (푐푑푡푅 + 푏푅 ) + 푇푅 훿푏̃푅 푚푅 휀푅 = 푃(1,2),푎푣푔 + (푁1,2 + Φ1,2) + Φ1,2 + Φ1,2
62
2 퐺 2 퐺 (4.18) 퐺 푓1,퐺푃1 − 푓2,퐺푃2 푃1,2 = 2 2 푓1,퐺 − 푓2,퐺
퐺 퐺 퐺 퐺 퐺 퐺 = 𝜌 + (푐푑푡 + 푏푃(1,2),푎푣푔) + 푇 + 푀푃1,2 + 푒푃1,2
2 퐺 2 퐺 (4.19) 퐺 푓1,퐺훷1 − 푓2,퐺훷2 훷1,2 = 2 2 푓1,퐺 − 푓2,퐺
퐺 𝜌퐺 + (푐푑푡퐺 + 푏퐺 ) + 푇퐺 훿푏̃퐺 푚퐺 휀퐺 = 푃(1,2),푎푣푔 + (푁1,2 + Φ1,2) + Φ1,2 + Φ1,2
where:
The superscripts 푅 and 퐺 describe the GLONASS and GPS systems, respectively
푅 퐺 푃1,2 and 푃1,2 are ionosphere-free code measurements (m)
푅 퐺 훷1,2 and 훷1,2 are ionosphere-free carrier phase measurements (m)
푓1,푅 and 푓2,푅 are the carrier phase frequencies on GLONASS L1 and L2 (Hz), respectively
푓1,퐺 and 푓2,퐺 are the carrier phase frequencies on GPS L1 and L2 (Hz), respectively
푅 퐺 푁1,2 and 푁1,2 are the ionosphere free combined ambiguity terms (m)
푅 퐺 푏푃(1,2),푎푣푔 and 푏푃(1,2),푎푣푔 are ionosphere free combined average hardware delays (m)
훿푏̃푅 and 훿푏̃퐺 are ionosphere free satellite dependent hardware bias (m) Φ1,2 Φ1,2
푀푅 and 푚푅 are the multipath effect in GLONAS code and phase measurements (m), 푃1,2 Φ1,2 respectively
63
푀퐺 and 푚퐺 are the multipath effect in GPS code and phase measurements (m), 푃1,2 Φ1,2 respectively
푒푅 and 휀푅 are the receiver noise in GLONASS code and phase measurements (m), 푃1,2 Φ1,2 respectively
푒퐺 and 휀퐺 are the receiver noise in GPS code and phase measurements (m), 푃1,2 Φ1,2 respectively
Due to the fact that the satellite dependent hardware bias cannot be split from ionosphere free combined ambiguity term, and the receiver clock offset merges with the average hardware bias term in data processing, the equations above can be simplified as follows (Cai & Gao, 2013):
푅 푅 ̅푅 푅 푅 푅 (4.20) 푃1,2 = 𝜌 + 푐푑푡 + 푇 + 푀푃1,2 + 푒푃1,2
푅 푅 ̅푅 푅 ̅푅 푅 푅 (4.21) 훷1,2 = 𝜌 + 푐푑푡 + 푇 + 푁1,2 + 푚훷1,2 + 휀훷1,2
퐺 퐺 ̅퐺 퐺 퐺 퐺 (4.22) 푃1,2 = 𝜌 + 푐푑푡 + 푇 + 푀푃1,2 + 푒푃1,2
퐺 퐺 ̅퐺 퐺 ̅퐺 퐺 퐺 (4.23) 훷1,2 = 𝜌 + 푐푑푡 + 푇 + 푁1,2 + 푚훷1,2 + 휀훷1,2
64
where:
The superscripts R and G describe the GLONASS and GPS systems, respectively
푐푑푡 ̅ is the sum of receiver clock offset and combined average hardware bias (= 푐푑푡 +
푏푃(1,2),푎푣푔)
푁̅1,2 is the sum of combined ambiguity and combined satellite based hardware bias
(= 훿푏̃ ) 푁1,2 + Φ1,2
A receiver clock offset could be written as the difference between reception time determined with receiver clock and reception time with respect to system (GPS or
GLONASS) time as:
푑푡 = 푡 − 푡푠푦푠푡푒푚 (4.24)
Rather than determining the GLONASS receiver clock offsets, the difference between the GPS and GLONASS system times is generally introduced as a system time difference parameter in the equations (Cai & Gao, 2013):
푅 푑푡 = 푡 − 푡퐺퐿푂푁퐴푆푆
= (푡 − 푡퐺푃푆) + (푡퐺푃푆 − 푡퐺퐿푂푁퐴푆푆) (4.24)
퐺 = 푑푡 + 푑푡푠푦푠푡푒푚
65
Through Equation (4.24), the GLONASS receiver clock offset 푐푑푡푅̅ can be obtained in terms of the GPS receiver clock offset and system time difference parameter as follows:
푅̅ 푅 푅 푐푑푡 = 푐푑푡 + 푏푃(1,2),푎푣푔
퐺 푅 = (푐푑푡 + 푐푑푡푠푦푠푡푒푚) + 푏푃(1,2),푎푣푔 (4.24) = (푐푑푡퐺 + 푏퐺 ) + (푐푑푡 + 푏푅 − 푏퐺 ) 푃(1,2),푎푣푔 푠푦푠푡푒푚 푃(1,2),푎푣푔 푃(1,2),푎푣푔
= 푐푑푡̅퐺 + ( 푐푑푡 + 푏푅 − 푏퐺 ) 푠푦푠푡푒푚 푃(1,2),푎푣푔 푃(1,2),푎푣푔
퐺 = 푐푑푡̅ + 푐푑푡푠푦푠푡푒푚̅ where:
푐푑푡푠푦푠푡푒푚̅ is the sum of the system time difference parameter and a bias parameter
(= 푐푑푡 + (푏푅 − 푏퐺 )). 푠푦푠푡푒푚 푃(1,2),푎푣푔 푃(1,2),푎푣푔
Lastly, by rewriting Equations (4.20), (4.21), (4.22), and (4.23) in view of
Equation (4.24), the following equations are generated:
푅 푅 ̅퐺 ̅ 푅 푅 푅 (4.25) 푃1,2 = 𝜌 + 푐푑푡 + 푐푑푡푠푦푠푡푒푚 + 푇 + 푀푃1,2 + 푒푃1,2
푅 푅 ̅퐺 ̅ 푅 ̅푅 푅 푅 (4.26) 훷1,2 = 𝜌 + 푐푑푡 + 푐푑푡푠푦푠푡푒푚 + 푇 + 푁1,2 + 푚훷1,2 + 휀훷1,2
66
퐺 퐺 ̅퐺 퐺 퐺 퐺 (4.27) 푃1,2 = 𝜌 + 푐푑푡 + 푇 + 푀푃1,2 + 푒푃1,2
퐺 퐺 ̅퐺 퐺 ̅퐺 퐺 퐺 (4.28) 훷1,2 = 𝜌 + 푐푑푡 + 푇 + 푁1,2 + 푚훷1,2 + 휀훷1,2
In combined GPS/GLONASS PPP, the unknown vector to be estimated consists
퐺 of three dimensional position of the receiver (푋푟, 푌푟, 푍푟), a receiver clock offset (푑푡̅ ), a system time difference parameter (푑푡푠푦푠푡푒푚̅ ), a zenith wet tropospheric delay (푇푧,푤), and
푅 퐺 real-value ambiguity parameters (푁̅1,2, 푁̅1,2) associated with each GPS and GLONASS satellite.
67
Chapter 5: Analysis of PPP in Post-processed Static Mode
This chapter discusses the preperation of data for analyis, the processing procedure to obtain PPP solutions, and statistical computations to evaluate the performance of GPS,
GLONASS, and combined GPS/GLONASS precise point positioning. The results of assessment are also interpreted in this chapter.
5.1 Study Area
In this study, in order to analyze the current performances of GPS and GLONASS
Precise Point Positioning, and the benefits of using combined GPS/GLONASS observations for post-processed static PPP in terms of accuracy, repeatability, and convergence time, 3 IGS stations (i.e. KIRU, HLFX and NKLG) with accurately known coordinates, located in differerent latitude regions (i.e. high, mid, and low latitude regions) are arbitrarily selected, see Figure 5.1.
68
Figure 5.1: Layout of the IGS stations used for the study.
The main reason for choosing the IGS stations at different latitudes is to investigate the PPP solutions obtained from different satellite constellations. Thus, the positioning accuracy level of GPS PPP, GLONASS PPP, and GPS/GLONASS PPP could be analyzed by employing different number of satellites and receiver-satellite geometries over different latitude regions. The properties of selected IGS stations can be found in
Table 5.1. In addition, the approximate coordinates of IGS stations are given in Table 5.2.
69
Site ID Country Constellation Receiver Antenna Type type KIRU Sweden GPS/GLONASS/Galileo SEPT SEPCHOKE_MC BeiDou/QZSS/SBAS POLARX4 + SPKE HLFX Canada GPS/GLONASS TPS NET- TPSCR.G3 + G3A NONE NKLG Gabon GPS/GLONASS/Galileo TRIMBLE TRM59800.00 + BeiDou/SBAS NETR9 SCIS
Table 5.1: Properties of selected IGS stations.
Site ID Latitude [dms] Longitude [dms] Ellips. height [m] KIRU +675126.28 +0205806.24 391.10
HLFX +444100.78 -0633640.60 3.10
NKLG +002114.067758 +0094019.654568 31.50
Table 5.2: Geodetic coordinates of the IGS stations in WGS84 frame.
5.2 Data Preparation
Daily GNSS data of three IGS stations at 30-second sampling rate for the week
01-07 August 2014 is obtained from the Scripps Orbit and Permanent Array Center
(SOPAC) which is serving as a Global Data Center and a Global Analyis Center. The reason for the selection of this date range is that all the RINEX observation files delivered by each of the three IGS stations is about 100% complete during this period of time. The main goal here is to statistically compare the positioning accuracy of the datasets under similar conditions.
70
First of all, since the downloaded data is in the Hatanaka-compressed format, it is converted to Receiver Independent Exchange Format (RINEX) by using the RNXCMP software provided by SOPAC. By using the Multi-Purpose Toolkit for GPS/GLONASS data (TEQC) (Estey & Wier, 2014), daily GNSS RINEX files containing both GPS and
GLONASS observations are grouped into 3 categories according to the observation type:
GPS RINEX files, GLONASS RINEX files, and mixed GPS/GLONASS RINEX files. In addition, daily RINEX files are divided up to different sessions (i.e. 2, 4, 8, and 24-hour) to investigate the effect of observation duration on positioning accuracy and precision, thus 22 RINEX observation files are generated for each station and each type of RINEX file per a day, see Table 5.3. The resulting files consist of twelve 2-hour, six 4-hour, three 8-hour, and one 24-hour observation sessions. Totally, 1386 observation files are obtained for the entire week.
In addition, the quality of RINEX observation files is checked using the TEQC software. Because of the fact that IGS stations located on the areas far away from reflective objects and providing unobstructed line of sight between the receiver and satellites, cycle slips due to ionosphere and/or multipath are rarely detected throughout the quality check.
71
Data span OBSERVATION SESSIONS (GPS time) 24 h 0-24
8h 0-8 8-16 16-24
4h 0-4 4-8 8-12 12-16 16-20 20-24
2h 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24
Table 5.3: Obtained RINEX observation files for each day by TEQC software.
5.2.1 The Multi-Purpose Toolkit for GPS/GLONASS Data (TEQC) Software
TEQC is an efficient GNSS toolkit that can run on Windows and Linux operating
systems. It was developed by UNAVCO (University NAVSTAR Consortium) to enable
the users to deal with the pre-processing issues, such as data translation, data editing, and
data quality check. It can provide the plots showing signal problems, including loss of
lock (cycle slips) and multipath. Furthermore, it can be employed to extract data from
RINEX observation files, see Appendix A for used TEQC commands. TEQC software
can be downloaded from the Internet for free (https://www.unavco.org/software/data-
processing/teqc/teqc.html).
The Figure 5.2 displays the sample quality check plot for GNSS observation data.
In the plot, the quality of the signals is indicated as a function of time for each satellite
vehicle (SV). The “I” symbol represents one or more ionospheric phase slips, “e” symbol
means the acqusition of L2C code with the legacy signals during the observation, and
“o” symbol points out the high-accuracy dual frequency GPS phase and code
pseudorange observations. The “c” symbol indicates that one or more times only L1 and
72
C/A observables are available in that time interval at certain times. Further information on TEQC quality check can be obtained directly from TEQC tutorial
(https://www.unavco.org/software/data- processing/teqc/doc/UNAVCO_Teqc_Tutorial.pdf).
SV : Satellite vehicle o : High accuracy dual frequency code and phase observation I : Ionospheric phase slip c : One or more times only L1 and C/A observables are available e : Acquisition of L2C signal Figure 5.2: Sample quality check plot.
5.3 Data Processing
After preparing the RINEX observation files for each IGS station, data processing is implemented to obtain PPP solutions by using the Canadian Spatial Reference System-
Precise Point Positioning (CSRS-PPP) online service (Mireault et al., 2008). Figure 5.3 shows all of the subsequent steps in the analysis of the data.
73
Figure 5.3: Processing flow.
5.3.1 Canadian Spatial Reference System (CSRS) Precise Point Positioning (PPP)
CSRS-PPP is an online post-processing service providing a PPP solution for GPS- only, GLONASS-only, and combined GPS/GLONASS observation data, see Figure 5.5.
This service, which is offered by Natural Resources Canada (NRCan), can process either static or kinematic data obtained from single or dual frequency receivers. After uploading the observation data to the service, estimated precise positions in either North American
Datum of 1983 (NAD83) or International Terrestrial Frame (ITRF) (depending on the
74
user choice) are sent to the users via email. Figure 5.4 illustrates the processing procedure of CSRS-PPP online service.
Figure 5.4: Processing procedure of CSRS-PPP online service.
CSRS-PPP online service utilizes the ionosphere free linear combinations of measurements on L1 and L2 carriers in order to get rid of the first order ionospheric effects when observation data obtained from dual frequency receiver is uploaded to the system. On the other hand, if observation data obtained from single frequency receiver is used, CSRS-PPP employs only IGS Total Electron Content (TEC) maps produced at 2- hour interval in Ionosphere Map Exchange (IONEX) format to deal with the ionospheric effects.
75
Figure 5.5: CSRS-PPP online service.
CSRS-PPP uses the pressure and temperature data obtained from Global Pressure and Temperature Model (GPT) in order to estimate the zenith hydrostatic and wet tropospheric delays. It implements Davis et al. Model (Davis et al., 1985) for zenith dry delay and the Hopfield Model (Hopfield, 1969b) for zenith wet delay. Furthermore, it utilizes the Global Mapping Function (GMF) (Marini, 1972) to compute the total tropospheric delay in the line-of-sight direction.
Regarding the precise ephemerides, CSRS-PPP applies the best available ephemeris (i.e. ultra-rapid, rapid or final) while it processes the observation data. As for the satellite and receiver antenna phase center corrections, it uses the IGS ANTEX files.
76
Table 5.4 provides the specifications for CSRS-PPP online service. More information on
CSRS-PPP could be found on NRCan website (http://www.nrcan.gc.ca/home).
CSRS-PPP online service
GNSS system GPS / GLONASS
Observation data Single / Dual frequency
Minimal cut-off angle 10o
Reference frame of the output ITRF2008 / NAD83 coordinates Format of the output coordinates LLH / XYZ / UTM
Precise satellite orbit and clock IGS (Final, Rapid or Ultra-rapid) products Satellite and receiver antenna phase IGS ANTEX center offsets Dry tropospheric delay model Davis et al.(GPT)
Wet tropospheric delay model Hopfield (GPT)
Mapping function GMF
Ionospheric delay model Iono-free linear combination (dual freq.data) Tec maps (single freq. data) Data transfer E-mail
Table 5.4: Specifications of CSRS-PPP online service.
77
5.4 Evaluation Procedure
The Cartesian (ECEF) coordinates obtained from CSRS-PPP online service are compared with the accepted true ITRF2008 Cartesian coordinates of the IGS points at the time of observation, which are computed using ITRF web site (http://itrf.ensg.ign.fr/).
The discrepancies between the estimated and true coordinates are converted to the north, east, and up components in a local geodetic system, referenced to the WGS-84 ellipsoid, by using the geodetic latitudes and longitudes of IGS stations as shown in Equation (5.1), see the Appendix B for statistical analysis of coordinate differences.
푒푡 − sin λ0 cos λ0 0 푋푡 − 푋0 (5.1) [푛푡] = [− sin 휑0 cos λ0 − sin 휑0 sin λ0 cos 휑0] [ 푌푡 − 푌0 ] 푢푡 cos 휑0 cos λ0 cos 휑0 sin λ0 sin 휑0 푍푡 − 푍0
where:
푋0, 푌0, and 푍0 are the accepted true Cartesian coordinates of the IGS station at the epoch of the observation
λ0 and 휑0 are the accepted true geodetic longitude and latitude of the IGS station with respect to WGS-84 ellipsoid, respectively
푡 is the epoch of observation
푋푡, 푌푡, and 푍푡 are the Cartesian coordinates of the IGS point, obtained by static PPP
푒푡, 푛푡, and 푢푡 are the east, north, and up components in local geodetic system, respectively, see Figure 5.6.
78
Figure 5.6: Left handed local geodetic coordinate system, (r,s,t) (Jekeli, 2012).
Root Mean Square Error (RMSE), which indicates the accuracy of the measurements with respect to true (reference) value, is calculated for each component of the local geodetic coordinate system by using Equation (5.2):
푛 2 (5.2) ∑ 휖푖,푗 푅푀푆퐸 = √ 푖=1 푖,푗 푛 where:
휖푖,푗 is the difference between observation (PPP result) and the true value (ITRF result) in the local geodetic system
푖 is the epoch of observation
푗 stands for north, east and up components
푛 is the total number of the epochs.
79
Standard deviation, which indicates the precision (repeatability) of the observation, is calculated for each component by using Equation (5.3):
푛 2 (5.3) ∑ (푦푖,푗 − 휇) 𝜎 = √ 푖=1 푖,푗 푛 − 1 where:
푖 is the epoch number
푗 stands for north, east and up components
푦푖,푗 is the measurement at the epoch of observation
휇 is the average of the measurements,
푛 is the total number of the epochs (measurements).
Lastly, 3D 푅푀푆퐸 is computed based on 푅푀푆퐸푒, 푅푀푆퐸푛 and 푅푀푆퐸푢 as follows:
2 2 2 (5.4) 푅푀푆퐸3퐷 = √푅푀푆퐸퐸 + 푅푀푆퐸푁 + 푅푀푆퐸푈 where:
푅푀푆퐸퐸 is the RMSE estimated for east component
푅푀푆퐸푁 is the RMSE estimated for north component
푅푀푆퐸푈 is the RMSE estimated for up component.
80
5.5 Accuracy and Repeatability Investigation
In this study, the PPP-derived coordinates of IGS stations are obtained by using
GPS-only observations, GLONASS-only observations, and combined GPS/GLONASS observations, respectively. Figures 5.7, 5.8, and 5.9 demonstrate the daily number of tracked GPS and GLONASS satellites at each IGS station. As can be seen from the figures, using GLONASS satellites along with GPS satellites increases the number of observable satellites.
At the KIRU station located in high latitude region, with addition of GLONASS satellites, the number of tracked satellites is increased by about 80%. For other two stations, the increase in the number of satellites is about 75%. The higher number of visible satellites at high-latitude IGS station could be caused by the relatively higher inclination angle (~65o) of GLONASS orbital planes. As a result of higher number of visible satellites, it could be expected that more reliable PPP solutions would be obtained at station KIRU.
81
Figure 5.7: Number of satellites tracked at high latitude station KIRU.
Figure 5.8: Number of satellites tracked at mid latitude station HLFX.
82
Figure 5.9: Number of satellites tracked at low latitude station NKLG.
5.5.1 Accuracy Investigation for East Component
As anticipated, the RMSE values of the east component gets smaller at each station as the observation duration increases, see Figure 5.10. While this improvement in
RMSE value is quite explicit at HLFX and NKLG stations for each consecutive observation duration regardless of the constellation type used, KIRU station gives the comparable RMSE values for 8-hour and 24-hour observation durations with each GNSS constellation type.
83
Figure 5.10: RMSE values at each station for the east component.
The positioning accuracy (i.e. estimated RMSE values) in east direction is about
1.6, 1.3, and 2 cm after 2-hour GPS observation at station KIRU, HLFX, and NKLG, respectively. With the addition of GLONASS observations, it is reduced to 1.3, 1, and 1.4 cm. As for the 4-hour observation session, similar improvement trend in positioning accuracy with addition of GLONASS observations could be observed. However, after 8- hour observation, the accuracy values obtained by GPS-only observations are slightly better than the ones obtained from combined observations for each station.
84
From the Figure 5.10, for KIRU station, it can also be concluded that GLONASS- only observations and GPS-only observations provide very close results (difference of at most 0.1 cm) with each observation session. On the other hand, for other stations, the accuracy of point positioning based on GPS-only observations is clearly better than the accuracy obtained by using GLONASS-only observations.
In summary, for all stations, using combined GPS/GLONASS observations leads to better positioning accuracy (i.e. small RMSE values) for short observation durations; however, the same contribution of combined GPS/GLONASS observations cannot be observed for long observation durations. This situation is probably because of the fact that the average number of visible GPS satellites and accumulating GPS satellite geometry for 24 hours observation is adequate to meet the required redundancy for least squares adjustment in order to obtain optimum result.
Moreover, since GLONASS precise orbit and clock products are not as precise as the products of GPS, and adding GLONASS observation means additional parameters
(i.e. charier phase ambiguities for each added GLONASS satellite, and system time difference) to be estimated for least square estimation, using GLONASS observations with GPS observations could also deteriorate positioning accuracy in east direction for
24-hour observation session.
85
5.5.2 Accuracy Investigation for North Component
According to the results, the north component is the most accurately estimated component among all other components. Overall, the RMSE values in north direction varies between 0.3 cm and 1.5 cm. This situation may result from the satellite constellation configuration since the separation between orbital planes leads to more sensitivity in terms of even distribution of satellites on north-south direction.
Moreover, the apparent movement of satellites is generally on north-south direction rather than on east-west direction. Because of this fact, the geometry between the receiver and satellites on north-south direction changes quickly, and thus carrier phase ambiguities can be estimated quickly. In this case, most of the time, positioning accuracy of the PPP method on north-south direction is better than that on east-west direction.
86
Figure 5.11: RMSE values at each station for the north component.
As can be seen in Figure 5.11, at KIRU station, GLONASS-only observations furnish better accuracy than GPS-only observations for each observation duration, which is a reasonable result since the GLONASS satellites enjoy orbital planes having slightly higher inclination relative to the equator than the GPS orbital planes. On the other hand, for the other stations, GPS-only observations yield better results compared to
GLONASS-only observations.
Similar to the situation in the east component, the positive effect of using combined GPS/GLONASS observations can only be seen for short observation durations. 87
However, for long observation durations, addition of GLONASS observations to GPS observations may not lead to more accurate results than GPS-only observations.
5.5.3 Accuracy Investigation for Up Component
As expected, the accuracy of the height component is 2 to 3 times worse than the accuracy of horizontal components because of the fact that receivers cannot see the satellites below the horizon. In this context, the KIRU station provides the worst accuracy values compared to the others for each type of constellation (GPS, GLONASS, and
GPS+GLONASS) for all observation durations. At this station, the obtained accuracy ranges from 1.7 to 3 cm while HLFX and NKLG stations provide an accuracy of 0.3-2 cm and 0.4-3.2 cm, respectively, for all scenarios. Furthermore, different from the situations in east and north directions, GPS-only observations gives better accuracy than
GLONASS-only observations for each observation duration in the up component at station KIRU.
88
Figure 5.12: RMSE values at each station for the up component.
As shown in Figure 5.12, at station KIRU, the positioning accuracy reached by
GPS-only observations is better than the accuracy provided by the combined
GPS/GLONASS observations for each observation duration. However, combined
GPS/GLONASS observations always give better result than GPS-only observations at the mid-latitude station HLFX.
Regarding the equatorial station NKLG, whilst GPS-only observations work better than combined GPS/GLONASS observations in terms of accuracy for 2, 4, and 8-
89
hour observation durations, for 24-hour observation duration, combined GPS/GLONASS observations produce slightly better result than GPS-only observations.
From the Figures 5.10, 5.11, and 5.12, it can be concluded that in mid-latitude region, the positioning accuracy in horizontal components, which is obtained from GPS- only observations, are usually better than the ones GLONASS-only observations provide, and one might take the advantage of combined GPS/GLONASS observations for short observation durations in terms of accuracy. However, for long observation durations, there is no significant benefit of using combined GPS/GLONASS observations on horizontal positioning accuracy. As for the height component, it can be seen that combined GPS/GLONASS observations always provide more accurate results than GPS- only observations for all observation sessions.
In the equatorial region, better accuracy values can always be obtained for each component with GPS-only observations relative to GLONASS-only observations. While combined GPS/GLONASS observations perform better than GPS-only observations for short observation durations in east and north directions, more accurate results can be reached with GPS-only observations for longer than 8-hour measurements. On the other hand, in the up direction, GPS-only observations serve better accuracy than combined observations except for the 24-hour observation.
In high latitude region, the relatively good performance of GLONASS with respect to positioning accuracy in east and north directions could be noticed. While
GLONASS delivers more accurate results than GPS in north direction for each observation duration, GLONASS and GPS provide very close results in east direction. In
90
these directions, the advantage of combined observations could be observed only for short observation durations. On the other hand, in this latitude region, GPS-only observations always give better accuracy values than GLONASS-only and combined
GPS/GLONASS observations with each observation duration for up component.
Tables 5.5, 5.6, and 5.7 show that the three-dimensional positioning accuracy of selected IGS stations, obtained from GPS-only observations, GLONASS-only observations, and combined GPS/GLONASS observations for each observation duration.
As can be seen, GPS-only observations provide better 3D positioning accuracy than
GLONASS-only observations at each IGS stations for each observation duration.
According to the tables, at station KIRU, while combined GPS/GLONASS observations give better results for 2-hour observation duration, GPS-only observations are better than combined GPS/GLONASS observations for 4, 8, and 24-hour observation durations.
Regarding the station NKLG, combined GPS/GLONASS observations perform better than GPS-only observations for 2 and 4-hour observation durations. On the other hand, at station HLFX, 3D positioning accuracy obtained by combined GPS/GLONASS observations is better than the ones provided by GPS-only observations for each observation duration.
91
Observation Duration Station 2-hour 4-hour 8-hour 24-hour
KIRU 3.2 2.2 1.9 1.9
HLFX 2.3 1.5 1.1 0.6
NKLG 2.3 1.7 0.8 0.6
Table 5.5: RMSE3D in centimeters for GPS observations.
Observation Duration Station 2-hour 4-hour 8-hour 24-hour
KIRU 3.5 2.9 2.4 2.3
HLFX 3.1 1.9 1.2 0.9
NKLG 4.6 2.8 2.0 1.3
Table 5.6: RMSE3D in centimeters for GLONASS observations.
Observation Duration Station 2-hour 4-hour 8-hour 24-hour
KIRU 3.0 2.4 2.1 2.1
HLFX 1.9 1.3 1.0 0.6
NKLG 2.0 1.6 1.0 0.6
Table 5.7: RMSE3D in centimeters for GPS+GLONASS observations.
92
In view of these results, it can be concluded that while one can always benefit from combined GPS/GLONASS observation concerning 3D positioning accuracy in mid- latitude region, using combined GPS/GLONASS observations would be useful in high latitude and equatorial regions only for short observation durations, see Figure 5.13.
Figure 5.13: RMSE3D values of GLONASS, GPS, and GPS/GLONASS PPP solutions
As for the comparison of GPS and GLONASS systems, it can be stated that GPS is always better than GLONASS with respect to vertical accuracy regardless of the type of latitude region where observations are acquired. However, GPS may not be always superior to GLONASS in terms of horizontal accuracy. GLONASS’s performance is 93
quite similar to GPS’s performance in east and north directions at station located in high latitude region.
In this study, in order to verify the investigation results obtained with CSRS-PPP online service, accuracy analysis is also carried out using an open source program package ‘RTKLIB’ for relatively small amount of data collected by selected IGS stations from August 01-02, 2014. As can be seen from the Figures 5.13 and 5.14, the results obtained from RTKLIB static PPP solutions are consistent with the results acquired from
CSRS-PPP static PPP solutions. While combined GPS/GLONASS PPP solutions provide improved positioning accuracy comparing with GPS-only PPP solutions for observations of short duration, GPS-only PPP solutions may furnish comparable and sometimes even slightly better accuracy as the observation duration increases.
94
Figure 5.14: RMSE3D values of RTKLIB GLONASS, GPS, and GPS/GLONASS PPP solutions
Regarding the accuracy performance of two systems, it can be clearly seen from
Figures 5.13 and 5.14 that relatively lower positioning accuracy can be achieved via
RTKLIB for each type of observation (i.e. GPS-only, GLONASS-only, and combined
GPS/GLONASS observations) and for each observation duration. RTKLIB yields slightly poorer performance than CSRS-PPP online service in terms of positioning accuracy for long observation sessions, as it may provide approximately two to three times worse accuracy for short observation sessions.
95
5.5.4 Repeatability Investigation
In this investigation, all 2, 4, 8, and 24-hour observations during the week 01-07
August 2014 are used to analyze the effect of combined observations on the position repeatability for each station. Figures 5.15, 5.16, and 5.17 below show that the repeatability of the estimated components gets improved with longer observation duration. A precision of up to 1 cm could be obtained with 24-hour dual frequency observation in each direction. From these figures, it is also apparent that there are no significant differences among the results obtained by GLONASS-only, GPS-only, and combined GPS/GLONASS observations.
Figure 5.15: Standard Deviations of the observations at the station KIRU.
96
Figure 5.16: Standard Deviations of the observations at the station HLFX.
Figure 5.17: Standard Deviations of the observations at station NKLG.
97
Similar to the case of the positioning accuracy investigation, the performance of the GLONASS-only observations is quite close to the performance of GPS-only observations in terms of precision for the station KIRU located in high latitude region.
Furthermore, sometimes GLONASS-only observations provide better results than GPS- only observations, see Figure 5.18.
Figure 5.18: 3D repeatability for each station.
Regarding the comparison of east, north, and up components at each station, the repeatability of the north component seems to be the best for each observation duration and constellation type, while the repeatability of the up component looks slightly worse than the repeatability of the east component.
98
Moreover, although the best precision can generally be obtained by combined
GPS/GLONASS observations for each observation duration and component, for the up component at station NKLG, GPS-only observations yield the better results with all observation durations, which may be resulted from the satellite configuration during the test.
5.6 Data Simulation for Static PPP
In order to see the effect of adding GLONASS observations to GPS observations for static PPP in the case of low satellite visibility, 3 different elevation cut-off angles are selected besides the default elevation cut-off angle in the CSRS-PPP online service, which is 10 degrees. Generally, in spite of the fact that 10 degree and 15 degree elevation cut-off angles are preferred for static positioning, in this study, bigger elevation cut-off angles (20,30, and 40 degrees) are chosen to assess the possible contribution of
GLONASS observations under the marginal conditions. As anticipated, with 40 degree elevation cut-off angle, most of the time the GPS PPP solution cannot be obtained because of the insufficient number of satellites for each station. Moreover, at station
NKLG, there are also three cases in which although adding GLONASS satellites increases the number of visible satellites, it cannot be adequate to produce the PPP solution with 2-hour observation. Therefore, accuracy evaluation of GPS PPP method with 40 degree elevation cut-off angle is carried out using relatively small number of PPP solutions, which are obtained from 2, 4, and 8-hour observations at each station, see
Table 5.8.
99
2-hour 4-hour 8-hour (# out of 12) (# out of 6) (# out of 3) KIRU 4 3 2
HLFX 5 3 2
NKLG 5 3 2
Table 5.8: The number of GPS PPP solutions with elevation angle of 40 degrees obtained from 2, 4, and 8-hour observations at each station.
For the analysis, data of one full day (01 August 2014) is arbitrarily selected, and similarly to the previous accuracy investigation, the RMSE values of components are calculated for different lengths of observation. However, in this analysis, the RMSE for horizontal components (i.e. 2D RMSE) is considered, which is computed by Equation
(5.5):
2 2 (5.5) 푅푀푆퐸2퐷 = √푅푀푆퐸퐸 + 푅푀푆퐸푁
where:
RMSEE is the RMSE value of east component in local geodetic system
RMSEN is the RMSE value of north component in local geodetic system.
Figures 5.19, 5.20, and 5.21 show the sky plots with an elevation cut-off angle of
10 degree for GPS and combined GPS/GLONASS observations at each station for the selected day. As can be seen in these figures, using GLONASS satellites improves both the total number of visible satellites and sky coverage. Therefore, it is reasonable to infer that using of combined GPS and GLONASS observations would provide better results for these stations than GPS-only observations on that day. 100
Figure 5.19: GPS (left image) and combined GPS/GLONASS (right image) sky plot at KIRU station with 10o cut-off angle for day of 213 of year 2014.
Figure 5.20: GPS (left image) and combined GPS/GLONASS (right image) sky plot at HLFX station with 10o cut-off angle for day of 213 of year 2014.
101
Figure 5.21: GPS (left image) and combined GPS/GLONASS (right image) sky plot at NKLG station with 10o cut-off angle for day of 213 of year 2014.
Figures 5.22, 5.23, and 5.24 depict the number of GPS and combined
GPS/GLONASS satellites, and corresponding Position Dilution of Precision (PDOP) values at 10 degrees cut-off angle during the day. As anticipated, the PDOP values decrease due to the increase in the number of tracked satellites. The average PDOP value decreases from 2 to 1.3, from 2 to 1.4 and from 1.8 to 1.3 at station KIRU, HLFX, and
NKLG, respectively. Therefore, it can be assumed that by using combined
GPS/GLONASS observations, the better accuracy can be obtained at 10 degrees cut-off angle for each station on that day.
102
Figure 5.22: Number of satellites and PDOP values at station KIRU with 10o cut-off angle on day of 213. 103
Figure 5.23: Number of satellites and PDOP values at station HLFX with 10o cut-off angle on day of 213. 104
Figure 5.24: Number of satellites and PDOP values at station NKLG with 10o cut-off angle on day of 213. 105
5.6.1 Data Simulation at Station KIRU
As can be seen in Figure 5.25, the accuracy of the results deteriorates as the cut- off angle increases since the bigger elevation angle leads to lower number of observable satellites and unfavorable receiver-satellite geometry. The average number of visible satellites with each elevation cut-off angle are given in Table 5.9.
Figure 5.25: RMSE2D values for different cut-off angles at station KIRU.
106
Elevation cut-off angle 10o 20o 30o 40o # of GPS sat. 10 7 5 4 # of GPS+GLO sat. 18 14 10 7 Table 5.9: The average number of visible satellites with each elevation cut-off angle at station KIRU.
In addition, at this station, for each observation duration and cut-off angle, combined GPS/GLONASS observations provide more accurate results than GPS-only observations, and the contribution of GLONASS observations to the obtained accuracy is explicitly demonstrated for shorter observation durations and the bigger cut-off angles.
For example, an about 2 cm improvement in the positioning accuracy is observed with the addition of GLONASS observations at 40 degrees cut-off angle with 2-hour observation.
On the other hand, for long observation durations (i.e. 24-hour observation), it can be seen from Figure 5.25 that there is no meaningful difference between the accuracy values obtained from GPS-only observations and combined GPS/GLONASS observations at each elevation cut-off angle. Both positioning accuracy values of GPS and combined GPS/GLONASS observations fluctuate between 0.4 and 1 cm with 24- hour observation.
107
Figure 5.26: RMSE values of height component for different cut-off angles at station KIRU.
For the height component at KIRU station, the positioning accuracy gets improved with the increase of observation length, see Figure 5.26. While positioning accuracy varies between 2 and 10 cm for 2-hour observation duration, it gets values between 1.5 and 3 cm for 24-hour observation duration.
Figure 5.26 also shows that for each observation duration, GPS-only observations usually tend to give better results at elevation cut-off angles of 10 and 20 degrees. On the other hand, combined GPS/GLONASS observations perform better as the elevation cut- off angle increases.
108
5.6.2 Data Simulation at Station HLFX
As shown in Figure 5.27, at mid-latitude station, the accuracy of the horizontal component does not get worse significantly with the increase of the cut-off angle different from the situation at station KIRU located in high latitude. In addition, there is not much improvement in the positioning accuracy with the increase of observation duration.
Figure 5.27: RMSE2D values for different cut-off angles at station HLFX.
109
It can also be seen that the results obtained by GPS-only observations are more accurate at each cut-off angle except for 2-hour observations. For this observation duration, using combined GPS/GLONASS observations always give better results at every cut-off angles. However, with increasing observation duration, GPS-only observations can be sufficient to provide optimum positioning accuracy at this station; adding GLONASS observations slightly degrades the positioning accuracy, although it increases the visible number of satellites, see Table 5.10.
Elevation cut-off angle 10o 20o 30o 40o # of GPS sat. 9 7 5 5 # of GPS+GLO sat. 15 12 9 7 Table 5.10: The average number of visible satellites with each elevation cut-off angle at station HLFX.
110
Figure 5.28: RMSE values of height component for different cut-off angles at station HLFX.
Figure 5.28 illustrates that most of the time, combined GPS/GLONASS observations are likely to give better accuracy for the height component. This tendency can be detected much more for high cut-off angles (i.e. 30 and 40 degrees) with 2 and 4- hour observations. With the increase of observation duration, the difference between the accuracy values obtained by GPS-only and combined GPS/GLONASS observations gets smaller at each cut-off angle.
111
5.6.2.1 Half Sky Study at Station HLFX
Different from the other data simulation studies, at station HLFX, half sky (i.e. partially blocked sky) study is also carried out by selecting three cases to assess the value of using GLONASS satellites with GPS satellites regarding static PPP, see Figures 5.29,
5.30, and 5.31. In the study, it is aimed to analyze the impacts of being on the one side of a building where everything on the opposite side is occluded on static PPP.
a) GPS-only (3 SV) b) GPS+GLONASS (6 SV, PDOP: 2.9)
Figure 5.29: First case in half sky study.
112
a) GPS-only (3 SV) b) GPS+GLONASS (6 SV, PDOP: 3.7)
Figure 5.30: Second case in half sky study.
a) GPS-only (3 SV) b) GPS+GLONASS (6 SV, PDOP: 5.5)
Figure 5.31: Third case in half sky study.
113
As shown in the figures above, the chosen cases provide an insufficient number of
GPS satellites to conduct PPP in that time interval. With the addition of required number of GLONASS satellites, PPP solutions can be obtained for each case. Positioning errors
(i.e. difference between true coordinates of the station and combined GPS/GLONASS
PPP-derived coordinates) in local coordinate system are given in Table 5.11. As can be seen, using combined GPS/GLONASS observations in static PPP method may provide dm to cm-level positioning when GPS-only observations cannot even produce a PPP solution.
휹e [cm] 휹n [cm] 휹u [cm] 휹3D [cm]
First case -16.3 8.1 17.8 25.5
Second case 6.6 1.6 9.2 11.4
Third case 5.4 0.7 8.0 9.7
Table 5.11: Positioning errors obtained from CSRS-PPP for each case in half sky study.
In this study, the positioning performance of RTKLIB software package is also compared with that of CSRS-PPP online service. Similar to the case of accuracy investigation, RTKLIB again provides lower positioning accuracy comparing with
CSRS-PPP online service for each cases, see Table 5.12. Interestingly, different from the other cases, RTKLIB furnishes approximately 4.5 times worse positioning accuracy for first case.
114
휹e [cm] 휹n [cm] 휹u [cm] 휹3D [cm]
First case -68.5 39.9 86.4 117.2
Second case -7.6 3.3 10.9 13.7
Third case 6.9 2.8 -7.1 10.3
Table 5.12: Positioning errors obtained from RTKLIB for each case in half sky study.
5.6.3 Data Simulation at Station NKLG
At station NKLG, GPS-only observations usually yield better accuracy at every cut-off angel for 4, 8, and 24 hour observation, see Figure 5.32. However, there is no big difference between the results of GPS-only observations and combined GPS/GLONASS observations.
115
Figure 5.32: RMSE2D values for different cut-off angles at station NKLG.
For 2-hour observation, combined GPS/GLONASS observations are better at all cut-off angels. It is probably caused by the low number of visible GPS satellites for 2 hour observation duration. With the addition of GLONASS satellites, there is sufficient redundancy for the least square adjustment to get better results than GPS-only observations provide, see Table 5.13.
116
Elevation cut-off angle 10o 20o 30o 40o # of GPS sat. 9 7 5 5 # of GPS+GLO sat. 16 12 8 6 Table 5.13: The average number of visible satellites with each elevation cut-off angle at station NKLG.
For the height component at station NKLG, with 10 degrees cut-off angle, GPS- only observations work better for each observation duration, while at 20, 30, and 40 degrees cut-off angles, combined GPS/GLONASS observations yield more accurate results, see Figure 5.33.
While the contribution of using GLONASS observations can be detected much more for short observation durations, it is negligible for long observation durations, especially for 24-hour observation duration.
117
Figure 5.33: RMSE values of height component for different cut-off angles at station NKLG.
In summary, for the horizontal component, it can be concluded from the above figures that at high latitude areas, the contribution of GLONASS observations to positioning accuracy can be detected for each cut-off angle and observation duration
(especially for short observation duration) since more satellites can be tracked there because of higher inclination angle of orbital planes of GLONASS satellites. On the other hand, this contribution is generally seen explicitly with high cut-off angle and short observation duration at the points located in mid and low latitude areas. At those points,
118
while the observation duration increases, the positive effect of using combined
GLONASS and GPS observations is occasionally observed even for high cut-off angle.
For the height component, while the accuracy improvement due to the combined
GPS/GLONASS observations can be usually seen for each cut-off angle and observation duration at station HLFX located in mid-latitude region, while for low latitude station,
NKLG, GPS-only observations sometimes provide better results (at 10 degree cut-off angle). Interestingly, at the station KIRU, GPS-only observation furnishes better results at low degree cut-off angles (10 and 20 degrees) with each observation duration. As the cut- off angle increases; however, using combined GPS/GLONASS observations gives better positioning accuracy for each station and observation duration.
To further analyze the contribution of using GLONASS observations along with
GPS observations to positioning accuracy for 24-hour observation duration, one week data is processed by using the different cut-off angles (10, 20, 30, and 40 degree) at each
IGS station as in the previous investigation.
As can be seen in Figure 5.34, for 24 hour observation duration, there is no significant differences between the RMSE2D values obtained from GPS-only and combined GPS/GLONASS observations for each station during the whole week. The results are quite comparable, so it can be said that there is no reason for using both GPS and GLONASS observations for 24-hour observation duration.
119
Figure 5.34: RMSE2D values for 24 hour measurement session for one week.
Similar to the horizontal component, the RMSE values for height component are also quite comparable, see Figure 5.35. Although combined GPS/GLONASS observations generally perform better at high cut-off angles, they do not make much difference in terms of positioning accuracy. According to Figure 5.34, GPS-only and combined GPS/GLONASS results have at most a difference of 1 cm.
120
Figure 5.35: RMSE values of height component for 24 hour measurement session for one week.
5.7 Convergence Investigation
In order to identify the impact of using combined GPS/GLONASS observations on the convergence time of post-processed static PPP, 2-hour observation sessions at each IGS station are analyzed for each day of the week on which daily observation files are obtained. Similar to the previous investigations, TEQC software is employed to divide the observation files into smaller parts. The resulting observation files are processed with CSRS-PPP online service and the convergence time of each static PPP solution is acquired by determining the time when the solution starts providing sub-
121
decimeter level 3D positioning accuracy. The average convergence time for each day is shown in Figure 5.36.
Figure 5.36: The average convergence time with GPS and combined GPS/GLONASS observations, 2-hour solutions
According to Figure 5.36, for both GPS-only and combined GPS/GLONASS observations, there are small variations in the values of the average convergence time from day to day. The average convergence time of GPS-only and combined
GPS/GLONASS static PPP solutions are quite consistent during the whole week. As the average convergence time of combined GPS/GLONASS static PPP solutions ranges between 15 and 20 minutes, the average convergence time of GPS static PPP solutions fluctuates between 25 and 32 minutes.
122
Figures 5.37 and 5.38 show the distribution of convergence time of both GPS and combined GPS/GLONASS static PPP solutions. While the convergence time of GPS- only static PPP solutions ranges from 10 to 55 minutes, for combined GPS/GLONASS static PPP solutions, the convergence time varies between 5 and 40 minutes during the whole week. Generally, the convergence time of GPS static PPP solutions takes place between 20 and 40 minutes, however, because of some reasons, such as low number of visible satellites and poor receiver-satellite geometry, it may exceed 40 minutes for some observation data.
As can also be seen in Figure 5.36, the average convergence time for each day improves significantly with the addition of GLONASS observations. For a whole week, the average convergence time of GPS-only observations is 27.9 minutes, whilst the average convergence time of combined GPS and GLONASS observations is 17.2 minutes. By using GLONASS observations with GPS observations, about 38.3 percent improvement in convergence time is obtained.
123
Figure 5.37: Distribution of the convergence time of GPS static PPP solutions.
Figure 5.38: Distribution of the convergence time of combined GPS/GLONASS static PPP solutions. 124
Since there is an increase in the number of visible satellites and an improvement in the receiver-satellite geometry for each 2-hour observation data with the addition of
GLONASS satellites, the convergence time of combined GPS/GLONASS static PPP solutions falls between 10 and 25 minutes most of the time. Nevertheless, there are a few long convergence times for some observation files due to the relatively poor satellite- receiver geometry.
125
Chapter 6: Analysis of PPP in Post-processed Kinematic Mode
In this study, the positioning accuracy of post-processed GPS and combined
GPS/GLONASS kinematic PPP is investigated by comparing kinematic PPP solutions to carrier phase-based differential kinematic GPS (DGPS) solution which is accepted as a ground truth. The purpose of the study is to determine the impact of using combined
GPS/GLONASS observations on the accuracy of kinematic PPP.
In addition, the effect of the initialization time on the positioning accuracy of
GPS and combined GPS/GLONASS kinematic PPP is investigated for one dataset by employing static observation sessions of different lengths with subsequent kinematic observation session. For this analysis, 1-hour static observation is carried out prior to starting the kinematic observation, and by using TEQC software, static data of various duration are extracted, including durations of 10, 20, 30, 40, and 50 minutes, respectively.
In this analysis, the kinematic observation data with various length static parts are processed, and 3D positioning accuracy of kinematic PPP is computed for each solution.
6.1 Data Acquisition
During the study, three different kinematic datasets with a sample rate of 0.2 seconds are collected by operating a Topcon receiver along with LEIAS10 NONE external GNSS geodetic antenna mounted on SPIN Lab measurement van, see Figure 6.1. 126
The first kinematic dataset is obtained at OSU West Campus parking lot which is a fairly open sky area with few reflective objects. The second and third kinematic datasets are acquired in suburban areas providing partial sky view for GNSS antennas due to a few scattered houses and trees along the road.
Figure 6.1: Measurement van (GPSVan).
Besides kinematic data collection, static data collection is conducted in order to estimate the differential kinematic coordinates of each point in the trajectory. For this purpose, a reference station is placed in the West Campus parking lot prior acquisition of kinematic data. In Figure 6.4, the approximate position of the reference station is shown as red ‘X’ character. 127
6.2 Data Processing
6.2.1 Differential Kinematic Solution
As stated previously, the differential kinematic solution is used as a ground truth
(i.e. actual location) for PPP solutions (i.e. estimated location). It is generated by processing static data collected by the reference station together with the kinematic data acquired during the test by the RTKLIB software. Before obtaining a kinematic solution, the collected static data during the field test is processed by using the Online Positioning
User Service (OPUS) offered by National Geodetic Service (NGS) to determine the coordinates of the reference station, which are regarded as fixed coordinates in the differential kinematic positioning process.
6.2.1.1 Online Positioning User Service (OPUS)
The Online Positioning User Service (OPUS) (NGS, 2016) is a web-based positioning tool utilized to process static dual frequency GPS data. The main motivation behind the development of OPUS by NGS is to enable the users to accurately connect to the National Spatial Reference System (NSRS) along with the latest International
Terrestrial Reference Frame (IGSxx/ITRFxx) in a short time, and to achieve highly accurate (about 1 to 2 cm) position information. With the latest version of OPUS, dual frequency (L1 and L2) static GPS data collected anywhere on Earth with a minimum of
20 minutes observation duration is processed, and corresponding position solution is sent to the user via email in ten minutes (NGS, 2016).
128
Based on the duration of observation data, either static or rapid-static positioning modes can be employed by OPUS. The PAGES software developed by NGS is used to process static data, and RSGPS software is used for rapid static data. In static positioning mode, the receiver’s coordinates are estimated by averaging three independent single baseline solutions. Each single baseline solution is obtained with double differenced carrier phase observations from one of the three nearby Continuously Operating
Reference Station (CORS) [NGS, 2016].
Figure 6.2: OPUS online service (http://www.ngs.noaa.gov/OPUS/).
129
6.2.1.2 Real Time Kinematic Library (RTKLIB)
RTKLIB is an open source portable program package which is written in C for standard and precise positioning with GPS, GLONASS, Galileo, QZSS, BeiDou, and
SBAS. Both real-time and post-processed Single, DGPS/DGNSS, Kinematic, Static,
Moving-Baseline, Fixed, PPP-Kinematic, PPP-Static, and PPP-Fixed positioning modes can be carried out with RTKLIB. In addition, it can provide the users with the capability to modify the data processing parameters such as elevation mask, data rate, type of satellite ephemeris, ionospheric and tropospheric correction models, integer ambiguity resolution method, and solution format, see Figure 6.3. Further information on RTKLIB software can be obtained directly from the RTKLIB manual
(http://www.rtklib.com/prog/manual_2.4.2.pdf).
a) b)
Figure 6.3: a) RTKLIB main window, b) RTKLIB options dialog.
130
6.2.2 PPP Solution
After extracting the dual frequency kinematic GPS data from collected dual frequency kinematic GPS/GLONASS data by TEQC software, both GPS and combined
GPS/GLONASS kinematic data is processed using CSRS-PPP online service to obtain
PPP-derived coordinates for each experiment. In addition, because of the fact that there is no perfect ground reference to test the performance of the PPP solution in kinematic case, an open source program package ‘RTKLIB’ is utilized apart from a professional grade
PPP online service ‘CSRS-PPP’ to get the PPP solution. However, all inferences are made based on CSRS-PPP results since RMSE values obtained from RTKLIB results are much higher than expected RMSE values (i.e.dm-level positioning accuracy) in kinematic PPP research. Therefore, RTKLIB results should be seen as a guide of how well an open source program can execute PPP in kinematic PPP.
In the first experiment, both GPS-only and combined GPS/GLONASS kinematic data along with generated static data in different lengths is also processed to investigate the possible contribution of the initialization time on the positioning accuracy.
6.3 Evaluation Procedure
In this section, the carrier phase based differential kinematic solution is accepted as a reference with the purpose of evaluating the positioning accuracy of GPS PPP and combined GPS/GLONASS PPP in kinematic mode. Figures 6.4, 6.10, and 6.14 show the trajectories derived from carrier phase based DGPS solution. As can be seen in these figures, quite consitent and smooth trajectories without any jumps are obtained using the
131
data collected during the test. Internal quality of the reference trajectories is estimated as
7 mm and 12 mm for horizontal and height components, respectively. Note here that the internal accuracy values could be optimistic.
Although the reference trajectories are obtained with high precision, it should also be taken into account that a part of the positioning errors of PPP (i.e. coordinate differences between the PPP solution and carrier phase based DGPS solution) results from the reference trajectories.
In order to assess the positioning accuracy of kinematic PPP solutions, the coordinate differences between the PPP and differential kinematic GPS solutions obtained from RTKLIB are converted to the north, east, and up components in the local geodetic system, and then RMSE values for each component are estimated by applying similar steps followed in the accuracy investigation of static PPP as shown below:
푛 2 (6.1) ∑ 휖푖,푗 푅푀푆퐸 = √ 푖=1 푖,푗 푛 where:
휖푖,푗 is the difference value between observation (PPP result) and the true value (DGPS result) in the local geodetic system defined with respect to WGS-84 ellipsoid
푖 is the epoch number
푗 stands for north, east, and up components
푛 is the total number of the epochs.
132
In addition, 3D RMSE is computed for each kinematic observation as follows:
2 2 2 (6.2) 푅푀푆퐸3퐷 = √푅푀푆퐸퐸 + 푅푀푆퐸푁 + 푅푀푆퐸푈 where:
푅푀푆퐸퐸 is the RMSE estimated for east component
푅푀푆퐸푁 is the RMSE estimated for north component
푅푀푆퐸푈 is the RMSE estimated for up component.
6.4 Experiments and Results
6.4.1 Experiment 1
The aim of this experiment is to assess the contribution of GLONASS observations to
GPS kinematic PPP in terms of accuracy and the effect of initialization time on the positioning accuracy of kinematic PPP. For this purpose, at the beginning, one hour static data is logged for initialization, and then about 24 minutes of kinematic data is obtained by driving loops at the OSU West Campus parking area. Figure 6.4 shows the observed trajectory of the measurement van during the test
133
Observation Receiver type Antenna Elevation Antenna duration Type mask height [m] [hh:mm:ss] [degree] Static Kinematic
TOPCON LEIAS10 10 00 01:00:00 00:24:13 NONE Table 6.1: Observation details for first dataset.
Figure 6.4: Trajectory of first kinematic dataset.
134
After data acquisition, to determine the quality of the collected data, TEQC software is employed. Figure 6.5 displays the quality check plot of the first kinematic observation data.
* : No A/S; L1 P1 L2 P2 SV : Satellite vehicle ^ : Large position change I : Ionospheric phase slip + : SV data, but below elev. mask R : GLONASS M : Multipath slip - : SV above elev. mask, but no data Figure 6.5: TEQC quality check plot for first kinematic data.
135
As can be seen in the figure above, there are a few cycle slips (‘I’ symbol) during data collection. Apart from the cycle slips, there are also observation gaps (‘+’ symbol) in the signals received from G15 and R04 satellites since they are below the elevation mask in that time bin. Overall, relatively high quality data is obtained through the experiment.
6.4.1.1 CSRS-PPP Solution for First Dataset
Figures 6.6 and 6.7 show the computed RMSE values for GPS and combined
GPS/GLONASS kinematic PPP results for each initialization time, respectively. As can be seen, the positioning accuracy of both GPS and combined GPS/GLONASS kinematic
PPP tends to improve as the initialization time increases. The best 3D RMSE is obtained with 60-minute initialization in both cases.
In GPS kinematic PPP solution, the improvement in 3D positioning accuracy shows up after 30-minute initialization. Initially, kinematic GPS PPP solution provides
3D RMSE of 0.24 m without static initialization. Because of the fact that CSRS-PPP online service also applies backward filtering in data processing, it could provide this high level of accuracy for kinematic PPP solution in such a short period of time.
With 60-minute initialization, after a decrease of about 41%, 3D positioning accuracy becomes 0.14 m. On the other hand, after 10-minute initialization, there is a significant decrease in the 3D RMSE value computed from the combined
GPS/GLONASS kinematic PPP solution. While 3D RMSE is 0.21 m without static initialization, it reaches 0.08 m with 60-minute initialization. In this case, about 62% improvement in 3D positioning accuracy is achieved.
136
Figure 6.6: RMSE values obtained from GPS-only kinematic PPP solutions of CSRS-PPP.
Initialization RMSEE [m] RMSEN [m] RMSEU [m] RMSE3D [m] time [min] 00 0.12 0.08 0.19 0.24 10 0.09 0.03 0.16 0.18 20 0.13 0.05 0.25 0.29 30 0.08 0.12 0.21 0.25 40 0.03 0.05 0.22 0.23 50 0.02 0.02 0.17 0.17 60 0.04 0.02 0.13 0.14 Table 6.2: RMSE values obtained from GPS-only kinematic PPP solutions of CSRS-PPP.
137
Figure 6.7: RMSE values obtained from combined GPS/GLONASS kinematic PPP solutions of CSRS-PPP.
Initialization RMSEE [m] RMSEN [m] RMSEU [m] RMSE3D [m] time [min] 00 0.04 0.04 0.21 0.21 10 0.10 0.03 0.20 0.22 20 0.07 0.02 0.14 0.16 30 0.05 0.02 0.08 0.10 40 0.02 0.02 0.08 0.09 50 0.02 0.02 0.08 0.09 60 0.02 0.02 0.08 0.08 Table 6.3: RMSE values obtained from combined GPS/GLONASS kinematic PPP solutions of CSRS-PPP.
138
Regarding the effect of using GLONASS observations along with GPS observations in terms of kinematic PPP positioning accuracy, it can be seen in both figures and tables above that combined GPS/GLONASS observations always provide better accuracy in all situations except for the situation employing 10-minute initialization, which could be just a random case here, and thus can be ignored. This can be caused by either the deterioration in the receiver-satellite geometry with the addition of GLONASS satellites or the acquisition of low quality GLONASS signals in that time bin.
The 3D positioning accuracy computed for non-initialization decreases from 0.24 m to 0.21 m, and then the 3D positioning accuracy computed with 60-minute initialization improves about 42%, and becomes 0.08 m when using GLONASS satellites together with GPS satellites. Figures 6.8 and 6.9 display the difference between local coordinates (i.e. north, east, and up) obtained from PPP solution and differential kinematic GPS solution for GPS-only and combined GPS/GLONASS kinematic observations with 60-minute initialization, respectively. As can be seen from these figures, differences in north, east, and up components fluctuate for the GPS kinematic
PPP solution, while they are relatively stable when GPS and GLONASS observations are used together.
139
Figure 6.8: Local coordinate errors of CSRS-PPP GPS-only kinematic PPP solution with 60-m initialization.
Figure 6.9: Local coordinate errors of CSRS-PPP GPS+GLONASS kinematic PPP solution with 60-m initialization.
140
6.4.1.2 RTKLIB Solution for First Dataset
Both GPS and combined GPS/GLONASS PPP solutions are also obtained using
RTKLIB open source program package for each initialization time. Figures 6.10 and 6.11 display corresponding RMSE values of GPS and combined GPS/GLONASS kinematic
PPP results. As can be seen from these figures, by employing RTKLIB solutions, quite high RMSE values are obtained compared to the ones computed from CSRS-PPP solutions.
According to the RTKLIB results, GPS-only observations produce better accuracy than combined GPS/GLONASS observations for first dataset in each case, see Tables 6.4 and 6.5. This situation is the opposite of that obtained from CSRS-PPP. It can be caused from the differences in the observation weighting procedure between RTKLIB and
CSRS-PPP.
As can be seen in Tables 6.4 and 6.5, without static initialization, 3D RMSE of
1.30 m is obtained from GPS-only observations, while 3D RMSE of 3.38 m is achieved using combined GPS/GLONASS observations. As the static initialization increases, both
GPS and combined GPS/GLONASS observations generally tend to provide relatively better accuracy. About 8% improvement in 3D RMSE is acquired for GPS-only observations, whereas about 20% improvement is obtained for combined observations with 60 minute static initialization. Figures 6.12 and 6.13 display the difference between local coordinates obtained from RTKLIB’s PPP solution and differential kinematic GPS solution for GPS-only and combined GPS/GLONASS kinematic observations with 60- minute initialization, respectively.
141
Figure 6.10: RMSE values obtained from GPS-only kinematic PPP solutions of RTKLIB.
Initialization RMSEE [m] RMSEN [m] RMSEU [m] RMSE3D [m] time [min] 00 0.39 0.78 0.97 1.30 10 0.41 0.78 0.96 1.30 20 0.42 0.77 0.99 1.33 30 0.38 0.60 1.04 1.26 40 0.40 0.66 0.91 1.19 50 0.37 0.66 0.88 1.17 60 0.36 0.72 0.88 1.19 Table 6.4: RMSE values obtained from GPS-only kinematic PPP solutions of RTKLIB.
142
Figure 6.11: RMSE values obtained from combined GPS/GLONASS kinematic PPP solutions of RTKLIB.
Initialization RMSEE [m] RMSEN [m] RMSEU [m] RMSE3D [m] time [min] 00 0.60 0.80 3.23 3.38 10 0.61 0.92 2.62 2.85 20 0.60 0.93 2.64 2.86 30 0.58 0.93 2.58 2.80 40 0.57 0.93 2.44 2.67 50 0.59 0.93 2.47 2.70 60 0.58 0.93 2.51 2.73 Table 6.5: RMSE values obtained from GPS/GLONASS kinematic PPP solutions of RTKLIB.
143
Figure 6.12: Local coordinate errors of RTKLIB GPS-only kinematic PPP solution with 60-m initialization.
Figure 6.13: Local coordinate errors of RTKLIB GPS+GLONASS kinematic PPP solution with 60-m initialization. 144
6.4.2 Experiment 2
In this experiment, a kinematic trajectory is obtained by driving a small loop
(approximate length of 14.3 miles) at low speed (less than about 35 miles per hour) on the Marion-Waldo Road located north from Columbus. As shown in Figure 6.14, the selected route in this rural area includes a few family houses and scattered trees that might cause cycle slips and multipath during the data acquisition. The reason for choosing this kind of route is to test the performance of kinematic PPP under somewhat worse sky view conditions. In addition, similar to the previous analysis of kinematic PPP, dual frequency GPS/GLONASS kinematic data is collected with a rover receiver, and then the benefit of using combined GPS/GLONASS observations on the accuracy of kinematic PPP is investigated.
Observation duration Receiver type Antenna Elevation Antenna [hh:mm:ss] Type mask height [m] Static Kinematic [degree] TOPCON LEIAS10 10 00 00:30:00 00:26:42 NONE Table 6.6: Observation details for second dataset.
145
Figure 6.14: Trajectory of second kinematic data set.
146
* : No A/S; L1 P1 L2 P2 SV : Satellite vehicle ^ : Large position change I : Ionospheric phase slip + : SV data, but below elev. mask R : GLONASS M : Multipath slip - : SV above elev. mask, but no data Figure 6.15: TEQC quality check plot for second dataset.
As can be seen in Figure 6.15, different from the first experiment, the low quality data, including signals with a lot of cycle slips is acquired during the experiment due to the high receiver dynamics. 147
6.4.2.1 CSRS-PPP Solution for Second Dataset
Figures 6.16 and 6.17 illustrate the north, east, and up errors of GPS-only and combined GPS/GLONASS kinematic PPP solutions as a function of time. As can be seen from these figures, the differences between the coordinates of PPP solution and DGPS solution are much larger than the ones acquired for the first kinematic dataset. This is probably caused by the relatively poor quality data and limited sky view condition.
According to Figure 6.15, cycle slips deteriorate the received signals most of the time during the observation.
Furthermore, Table 6.7 shows the computed RMSE values for GPS-only and combined GPS/GLONASS kinematic PPP solutions. As illustrated in the table, there is a slight improvement in both horizontal and vertical positioning accuracy after adding
GLONASS observations. By using GLONASS observations with GPS observations, 3D positioning accuracy becomes 0.61 m after a decrease of about 5%. This small improvement may be resulted from the relatively high number of poor quality GLONASS observations, see Figure 6.15.
148
Figure 6.16 Local coordinate errors of CSRS-PPP GPS-only kinematic PPP solution for second dataset.
Figure 6.17: Local coordinate errors of CSRS-PPP GPS+GLONASS kinematic PPP solution for second dataset.
149
GNSS Name RMSEE [m] RMSEN [m] RMSEU [m] RMSE3D [m]
GPS only 0.19 0.17 0.59 0.64
GPS+GLONASS 0.16 0.14 0.57 0.61
Table 6.7: RMSE values for CSRS-PPP kinematic PPP solutions of second dataset.
6.4.2.2 RTKLIB Solution for Second Dataset
As can be seen from Table 6.8, likewise the case with first experiment, 3D RMSE values achieved through RTKLIB solution are substantially worse than those obtained from CSRS-PPP solution. However, for this experiment, combined observations furnish better accuracy than GPS-only observations with RTKLIB. Using combined observations decreases 3D RMSE by about 23%. Figures 6.18 and 6.19 show the north, east, and up errors of GPS-only and combined GPS/GLONASS kinematic PPP solutions, respectively.
GNSS Name RMSEE [m] RMSEN [m] RMSEU [m] RMSE3D [m]
GPS only 0.31 0.20 3.50 3.52
GPS+GLONASS 0.77 0.61 2.53 2.71
Table 6.8: RMSE values for RTKLIB kinematic PPP solutions of second dataset.
150
Figure 6.18: Local coordinate errors of RTKLIB GPS-only kinematic PPP solution for second dataset.
Figure 6.19: Local coordinate errors of RTKLIB GPS+GLONASS kinematic PPP solution for second dataset. 151
6.4.3 Experiment 3
The third kinematic trajectory, see Figure 6.20, is acquired by driving at a speed of about 55 miles per hour on the Ohio State Route 4 having characteristics similar to those of the Marion-Waldo Road. There are no tall buildings, bridges, and dense forest along the route that may lead to signal loss and a significant decrease in the number of visible satellites. However, many cycle slips occur during the observation, and thus the low quality data is collected, see Figure 6.21.
Observation Elevation duration Receiver type Antenna mask Antenna [hh:mm:ss] Type [degree] height [m] Static Kinematic
TOPCON LEIAS10 10 00 00:00:00 00:33:15 NONE Table 6.9: Observation details for third dataset.
152
Figure 6.20: Trajectory of third data set.
153
* : No A/S; L1 P1 L2 P2 SV : Satellite vehicle ^ : Large position change I : Ionospheric phase slip + : SV data, but below elev. mask R : GLONASS M : Multipath slip - : SV above elev. mask, but no data Figure 6.21: TEQC quality check plot for third dataset.
154
6.4.3.1 CSRS-PPP Solution for Third Dataset
Different from the collection of the first and second datasets, static initialization is not carried out prior to kinematic observation in this data collection. Figures 6.22 and
6.23 display the north, east, and up errors obtained from GPS-only and combined
GPS/GLONASS kinematic PPP solutions. From these figures, the contribution of using combined GPS/GLONASS observations to positioning accuracy could be clearly seen.
Figure 6.22: Local coordinate errors of CSRS-PPP GPS-only kinematic PPP solution for third dataset.
155
Figure 6.23: Local coordinate errors of CSRS-PPP GPS+GLONASS kinematic PPP solution for third dataset.
GNSS Name RMSEE [m] RMSEN [m] RMSEU [m] RMSE3D [m]
GPS only 0.35 0.20 1.18 1.24
GPS+GLONASS 0.17 0.24 0.57 0.64
Table 6.10: RMSE values for CSRS-PPP kinematic PPP solutions of the third dataset.
Table 6.10 provides the computed RMSE values for GPS-only and combined
GPS/GLONASS kinematic PPP solutions. As can be seen in the table, except for the positioning accuracy of north component, the positioning accuracies of other components improve significantly by using GLONASS observations with GPS observations.
According to the results, while GPS-only kinematic PPP solution gives 3D positioning
156
accuracy of 1.24m, combined GPS/GLONASS kinematic PPP solution improves this value by about 48% and furnishes 3D positioning accuracy of 0.64 m.
6.4.3.2 RTKLIB Solution for Third Dataset
Similar to the case of first experiment, RTKLIB’s GPS-only solution provides better accuracy values than its combined GPS/GLONASS solution in kinematic PPP mode, see
Table 6.11. Although using GLONASS satellites together with GPS satellites improves the PDOP value by 33%, more accurate solution can be achieved using GPS-only observations via RTKLIB. The north, east, and up errors of GPS-only and combined
GPS/GLONASS kinematic PPP solutions are shown in Figures 6.24 and 6.25, respectively.
GNSS Name RMSEE [m] RMSEN [m] RMSEU [m] RMSE3D [m]
GPS only 1.1 0.67 2.88 3.15
GPS+GLONASS 2.59 2.89 3.09 4.96
Table 6.11: RMSE values for RTKLIB kinematic PPP solutions of third dataset.
157
Figure 6.24: Local coordinate errors of RTKLIB GPS-only kinematic PPP solution for third dataset.
Figure 6.25: Local coordinate errors of RTKLIB GPS+GLONASS kinematic PPP solution for third dataset. 158
Chapter 7: Conclusions and Recommendations for Future Study
7.1 Conclusions
With the full constellation of GLONASS satellites available, this study primarily set out to investigate the contribution of using GLONASS observations with GPS observations to static and kinematic PPP solutions in terms of positioning accuracy under varying conditions. The study also sought to determine how combined GPS/GLONASS observations affect the repeatability and convergence time of static PPP, and to assess the impact of initialization time on the positioning accuracy of kinematic PPP.
The efficiency of combined GPS/GLONASS observations for positioning accuracy and repeatability of static PPP was analyzed as a function of different latitude regions and observation duration (i.e. 2, 4, 8, and 24-hour). The benefit of combined
GPS/GLONASS observations with respect to GPS-only observations in static PPP concerning 3D positioning accuracy was evidenced for all observation sessions at the mid-latitude station. Approximately 4% improvement in 3D positioning accuracy was observed by adding GLONASS observations to GPS observations for 24-hour duration, and approximately 16% enhancement was acquired for 2-hour observation. As the observation duration increased, the contribution of the combined observations to 3D positioning accuracy gradually diminished. In contrast, at high latitude and equatorial stations, the benefit of combined observations on 3D positioning accuracy could only be 159
seen for short observation sessions, see Table 7.1. At high latitude station, approximately
6% improvement was detected for 2-hour observation. Regarding the equatorial station, about 10% and 7% improvement was obtained for 2 and 4-hour combined observations, respectively.
Properties of Stations Observation Durations Station Location Condition 2-hour 4-hour 8-hour 24-hour KIRU High lat. Open sky (6%) HLFX Mid lat. Open sky (16%) (13%) (9%) (4%) NKLG Low lat. Open sky (10%) (7%) Table 7.1: The percentage of improvement in 3D RMSE when GPS/GLONASS observations are used instead of GPS-only observations at each station ( indicates combined GPS/GLONASS observations provide better positioning accuracy than GPS- only observations for that observation duration)
In addition, another static test was conducted to identify the contribution of
GLONASS observations to static GPS PPP under limited sky view conditions. In this experiment, at each IGS station, combined observations always provided better horizontal positioning accuracy with each cut-off angle for 2-hour observation session. Generally, this improvement continued gradually as the sky view condition deteriorated. At the high latitude station, more than 50% improvement in horizontal positioning accuracy was obtained for 2-hour observation session by adding GLONASS observations under extremely limited sky view (i.e. elevation mask of 40 degrees). Under the same condition, about 23% improvement was observed at mid latitude and equatorial stations.
As for 24-hour observation, GPS-only and combined GPS/GLONASS observations
160
usually provided comparable horizontal positioning accuracy regardless of the sky view condition at each station. Regarding the vertical positioning accuracy, the advantage of combined observations could be explicitly detected at 30 and 40 degrees cut-off angles with 2 and 4-hour observation sessions in each latitude region. Likewise the case of horizontal accuracy, as observation duration increased, the effect of combined observations would be trivial for vertical positioning accuracy.
At station HLFX, half sky study was also conducted to detect the benefit of using combined GPS/GLONASS PPP when there is insufficient number of GPS satellites to carry out PPP. Three cases providing half open sky for GNSS antenna were investigated, and it was observed that dm to cm-level positioning could be achieved using combined
GPS/GLONASS observations.
As for the repeatability analysis of static PPP, using GLONASS observations with
GPS observations did not significantly enhance the precision of the coordinates for each observation session. Occasionally, even only GPS observations provided better results than combined observations. Similar to the case in the analysis of positioning accuracy, relatively big contribution of combined observations were detected for short observation durations (i.e. 2 and 4-hour sessions).
Regarding the effect of combined GPS/GLONASS observations on convergence time for static PPP, a significant decrease (about 38%) in time required to give cm level accuracy was observed after adding GLONASS observations to GPS observations during the study.
161
Based on the results of these analyses, it could be concluded that using combined
GPS/GLONASS observations in static PPP would be beneficial in terms of positioning accuracy for short observation sessions. In this case, addition of GLONASS data would enhance both the number of visible satellites and receiver-satellite geometry. Although
GLONASS’s positioning performance and the quality of its precise products are not as good as those of GPS, it could be still useful since it would provide enough redundancy together with GPS for least square adjustment. On the other hand, as observation duration increases, the combined observations may provide worse results even though observations are conducted under extremely limited sky view condition. The poor quality
GLONASS products and extra unknowns due to addition of GLONASS would contaminate the adjustment process for which GPS would already provide the required redundancy with long observation.
Three kinematic tests were also implemented to evaluate the performance of using
GLONASS observations with GPS observations by considering different sky view conditions. In these tests, a professional grade online PPP service ‘CSRS-PPP’ and an open source program ‘RTKLIB’ were employed to produce the PPP solution. However, since RTKLIB’s PPP performance was much worse than CSRS-PPP’s PPP performance,
CSRS-PPP solutions were only used in the evaluation stage. According to the results obtained from CSRS-PPP, after combining of GLONASS observations with GPS observations, about 12%, 5%, and 48% improvements in the positioning accuracy were obtained for the three kinematic datasets, respectively.
162
For the first kinematic dataset, the impact of initialization time on the positioning accuracy was also analyzed by using both GPS-only and combined GPS/GLONASS observations. After ten minutes initialization, the positioning accuracy of combined observations improved significantly, and this improvement continued to advance as initialization time increased. With 60-minute static initialization, about 61% improvement in 3D positioning accuracy was achieved relative to one obtained without initialization. Different from combined observations, GPS-only observations started to give enhanced positioning accuracy after 30 minutes initialization, and provided about
42% improvement in positioning accuracy with 60-minute initialization.
During the kinematic tests, since most of the time the quality of observations are degraded by cycle slips and the receiver-satellite geometry is generally less than optimal, combined GPS/GLONASS observations would usually provide better positioning accuracy than GPS-only observations. In fact, with at least 30-minute static initialization, the positioning accuracy of GPS/GLONASS kinematic PPP could improve significantly.
7.2 Recommendations for Future Study
The magnitude of the difference between accuracy values obtained from RTKLIB software package and CSRS-PPP online service for static observations of short duration and kinematic observations warrants further investigation with good quality data in a controlled environment. Additionally, the algorithms of both PPP software should be analyzed to determine their efficiency for post processing PPP.
163
References
Abd-Elazeem, M., Farah, A., & Farrag, F. (2011). Assessment study of using online (CSRS) GPS-PPP Service for mapping applications in Egypt. Journal of Geodetic Science, 1(3), 233-239.
Alkan, R. M., İlçi, V., Ozulu, I. M., & Saka, M. H. (2015). A comparative study for accuracy assessment of PPP technique using GPS and GLONASS in urban areas. Measurement, 69, 1-8.
Allred, B., Daniels, J. J., & Ehsani, M. R. (Eds.). (2008). Handbook of agricultural geophysics. CRC Press.
Ashby, N. (2004). The sagnac effect in the global positioning system. In Relativity in Rotating Frames (pp. 11-28). Springer Netherlands.
Ashby, N. (2006). Relativistic effects in the global positioning system. In Gravitation and Relativity: At the Turn of the Millenium. 15th International Conference on General Relativity and Gravitation (pp. 231-258).
Avallone, A., Marzario, M., Cirella, A., Piatanesi, A., Rovelli, A., Di Alessandro, C., ... & Mattone, M. (2011). Very high rate (10 Hz) GPS seismology for moderate‐ magnitude earthquakes: The case of the Mw 6.3 L'Aquila (central Italy) event. Journal of Geophysical Research: Solid Earth, 116(B2).
Azab, M., El-Rabbany, A., Shoukry, M. N., & Khalil, R. (2011). Precise point positioning using combined GPS/GLONASS measurements. Proc. FIG Working Week 2011.
Bisnath, S., & Gao, Y. (2009). Current state of precise point positioning and future prospects and limitations. In Observing our changing earth (pp. 615-623). Springer Berlin Heidelberg.
Cai, C., & Gao, Y. (2007). Precise point positioning using combined GPS and GLONASS observations. Positioning, 1(11).
164
Cai, C., & Gao, Y. (2013). Modeling and assessment of combined GPS/GLONASS precise point positioning. GPS solutions, 17(2), 223-236.
Calais, E., Han, J. Y., DeMets, C., & Nocquet, J. M. (2006). Deformation of the North American plate interior from a decade of continuous GPS measurements. Journal of Geophysical Research: Solid Earth, 111(B6).
Control Segment. (n.d.). Retrieved December 10, 2015, from http://www.gps.gov/systems/gps/control/
El-Rabbany, A. (2002). Introduction to GPS: The Global Positioning System. Boston, MA: Artech House.
Davis, J. L., Herring, T. A., Shapiro, I. I., Rogers, A. E. E., & Elgered, G. (1985). Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length. Radio science, 20(6), 1593-1607.
Estey, L., & Wier, S. (2014). Teqc Tutorial: Basics of Teqc Use and Teqc Products. UNAVCO.
Force, T. (2005). The Future of the Global Positioning System.
Gao, Y., Wojciechowski, A., & Chen, K. (2005). Airborne kinematic positioning using precise point positioning methodology. Geomatica, 59(1), 29-36.
The Global Positioning System. (n.d.). Retrieved December 01, 2015, from http://www.gps.gov/systems/gps/
Grejner-Brzezinska, D. A. (2015): "Introduction to GPS" CIVILEN 5441 Lecture Notes. The Ohio State University. December 2015.
Hegarty, C. J., & Chatre, E. (2008). Evolution of the global navigation satellite system (GNSS). Proceedings of the IEEE, 96(12), 1902-1917.
Hofmann-Wellenhof, B., Lichtenegger, H., & Collins, J. (2001). Global Positioning System (GPS): Theory and practice, 5th ed. Wien: Springer.
Hofmann-Wellenhof, B., Lichtenegger, H., & Wasle, E. (2008). GNSS–Global Navigation Satellite Systems–GPS, GLONASS, Galileo, and more. Springer, Vienna.
Hopfield, H. S. (1969). Two‐quartic tropospheric refractivity profile for correcting satellite data. Journal of Geophysical research, 74(18), 4487-4499.
IGS Overview (n.d.). Retrieved December 29, 2015, from https://igscb.jpl.nasa.gov/overview/viewindex.html 165
IGS Real-time Service (n.d.). Retrieved May 11, 2016, from http://www.igs.org/rts
Jekeli, C. (2012). Geometric Reference Systems in Geodesy. Report, Division of Geodetic Science, School of Earth Sciences, The Ohio State University.
Kaplan, E.D. and C.J. Hegarty (2006). Understanding GPS: Principles and Applications.2nd Edition. Artech House.
Kouba, J. (2015). A guide to using International GNSS Service (IGS) products.
Kouba, J., & Héroux, P. (2001). Precise point positioning using IGS orbit and clock products. GPS solutions, 5(2), 12-28.
Kuo, C. Y., Chiu, K. W., Chiang, K. W., Cheng, K. C., Lin, L. C., Tseng, H. Z., ... & Lin, H. T. (2012). High-Frequency Sea Level Variations Observed by GPS Buoys Using Precise Point Positioning Technique. Terrestrial, Atmospheric & Oceanic Sciences, 23(2).
Leick, A., Rapoport, L., & Tatarnikov, D. (2015). GPS satellite surveying. John Wiley & Sons.
Marini, J. W. (1972). Correction of satellite tracking data for an arbitrary tropospheric profile. Radio Science, 7(2), 223-231.
Min, Z. H. A. O., Yunzhi, W. A. N. G., & Xiaoyun, M. U. (2011). The Error Caused by Relativity in GPS Positioning System. Advances in Natural Science, 4(2), 18- 21.
Mireault, Y., Tétreault, P., Lahaye, F., Héroux, P., & Kouba, J. (2008). Online Precise Point Positioning. GPS World, Sep, 59-64.
Misra, P., & Enge, P. (2001). Global Positioning System: Signals, Measurements and Performance First Edition. Lincoln, MA: Ganga-Jamuna Press.
OPUS: Online Positioning User Service. The National Geodetic Survey. January 18, 2016. http://www.ngs.noaa.gov/OPUS/about.jsp
Petit, G., & Luzum, B. (2010). IERS conventions (2010) (No. IERS-TN-36). BUREAU INTERNATIONAL DES POIDS ET MESURES SEVRES (FRANCE).
Petrov, L. and J.P. Boy (2004). Study of the Atmospheric Pressure Loading Signal in VLBI Observations. Journal of Geophysical Research, Vol. 109, No. B03405,2004.
166
Píriz, R., Calle, D., Mozo, A., Navarro, P., Rodríguez, D., & Tobías, G. (2009, September). Orbits and clocks for GLONASS precise-point-positioning. InProc. ION GNSS (pp. 2415-2424).
Tsujino, T. (2005). Effectiveness of the Quasi-Zenith Satellite System in Ubiquitous Positioning.
Yudanov, S., Varyukhin, V., Shurygin, N., Stanislav, S. N., & Ashjaee, J. (2011). Inter- channel bias calibration for navigation satellite systems. U.S. Patent No. 8,022,868. Washington, DC: U.S. Patent and Trademark Office.
Zumberge, J. F., Heflin, M. B., Jefferson, D. C., Watkins, M. M., & Webb, F. H. (1997). Precise point positioning for the efficient and robust analysis of GPS data from large networks. Journal of Geophysical Research: Solid Earth, 102(B3), 5005- 5017.
167
Appendix A: TEQC Software Processing Commands
This appendix provides the commands used in TEQC for data extraction and quality check analysis of RINEX observation files.
A.1: TEQC Command for Removing Satellite Data
푡푒푞푐 − 퐺(푙푖푠푡) − 푅(푙푖푠푡) − 퐸(푙푖푠푡) 푖푛푝푢푡. 14표 > 표푢푡푝푢푡. 14표 where:
−퐺(푙푖푠푡) removes the GPS satellites listed in the parenthesis from observation file
−푅(푙푖푠푡) removes the GLONASS satellites listed in the parenthesis from observation file
−퐸(푙푖푠푡) removes the GALILEO satellites listed in the parenthesis from observation file
푖푛푝푢푡. 14표 is the name of RINEX observation file
표푢푡푝푢푡. 14표 is the name of RINEX observation file after removing satellite data.
A.2: TEQC Command for Extracting Data from Observation File
푡푒푞푐 − 푠푡 ℎℎ푚푚푠푠. 푠푠 − 푒 ℎℎ푚푚푠푠. 푠푠 푖푛푝푢푡. 14표 > 표푢푡푝푢푡. 14표 where:
−푠푡 ℎℎ푚푚푠푠. 푠푠 is the time of first observation (i.e. start time)
−푒 ℎℎ푚푚푠푠. 푠푠 is the time of last observation (i.e. end time)
푖푛푝푢푡. 14표 is the name of RINEX observation file 168
표푢푡푝푢푡. 14표 is the name of RINEX observation file after extracting data.
A.3: TEQC Command for Quality Check of Observation File
푡푒푞푐 + 푞푐 + +푐표푛푓푖푔 − 푂. 푖푛푡 푖푛푝푢푡. 14표 > 푙표푔. 푡푥푡 where:
+푞푐 is the quality check command
+ + 푐표푛푓푖푔 is the list of qc settings
−푂. 푖푛푡 refers to observation interval of collected data
푖푛푝푢푡. 14표 is the name of RINEX observation file
푙표푔. 푡푥푡 is the final quality check report.
169
Appendix B: Statistical Analysis for Coordinate Differences at Each IGS Station
This appendix gives the tables including the statistical details about the coordinate differences for each IGS station analyzed in this thesis.
2D 횫h
Const. Obs. Min.[m] Max.[m] Avg.[m] Min.[m] Max.[m] Avg.[m] type Duration
2h 0.001 0.052 0.015 0.000 0.067 0.026
4h 0.000 0.034 0.010 0.000 0.062 0.023 GLONASS 8h 0.002 0.014 0.008 0.008 0.034 0.021
24h 0.004 0.011 0.007 0.019 0.024 0.022
2h 0.002 0.076 0.015 0.001 0.097 0.021
4h 0.002 0.028 0.011 0.004 0.038 0.017 GPS 8h 0.001 0.018 0.009 0.010 0.023 0.016
24h 0.005 0.012 0.008 0.013 0.021 0.017
2h 0.001 0.049 0.013 0.001 0.085 0.022
4h 0.001 0.033 0.009 0.001 0.041 0.019 GPS+GLO. 8h 0.001 0.016 0.008 0.010 0.026 0.019
24h 0.004 0.012 0.007 0.016 0.022 0.019
Table B.1: Statistical Analysis for coordinate differences at station KIRU (X: 2251420.639 m, Y: 862817.324 m, Z: 5885476.828 m).
170
2D 횫h
Const. Obs. Min.[m] Max.[m] Avg.[m] Min.[m] Max.[m] Avg.[m] type Duration
2h 0.002 0.073 0.019 0.000 0.046 0.015
4h 0.002 0.038 0.011 0.000 0.028 0.011 GLONASS 8h 0.002 0.019 0.008 0.000 0.018 0.006
24h 0.003 0.011 0.006 0.000 0.009 0.005
2h 0.001 0.051 0.013 0.000 0.041 0.013
4h 0.001 0.023 0.008 0.000 0.027 0.009 GPS 8h 0.002 0.011 0.006 0.001 0.018 0.007
24h 0.002 0.006 0.004 0.000 0.009 0.003
2h 0.001 0.042 0.011 0.000 0.038 0.011
4h 0.002 0.027 0.008 0.000 0.021 0.008 GPS+GLO. 8h 0.002 0.016 0.006 0.000 0.017 0.005
24h 0.003 0.009 0.005 0.000 0.004 0.002
Table B.2: Statistical Analysis for coordinate differences at station HLFX (X: 2018905.619 m, Y: -4069070.509 m, Z: 4462415.473 m).
171
2D 횫h
Const. Obs. Min.[m] Max.[m] Avg.[m] Min.[m] Max.[m] Avg.[m] type Duration
2h 0.002 0.095 0.025 0.000 0.130 0.025
4h 0.003 0.045 0.014 0.000 0.059 0.018 GLONASS 8h 0.000 0.021 0.010 0.000 0.037 0.013
24h 0.003 0.010 0.005 0.002 0.021 0.010
2h 0.000 0.067 0.015 0.000 0.025 0.010
4h 0.001 0.065 0.009 0.000 0.018 0.008 GPS 8h 0.001 0.014 0.004 0.000 0.013 0.005
24h 0.001 0.005 0.003 0.000 0.008 0.004
2h 0.002 0.052 0.011 0.001 0.043 0.011
4h 0.001 0.042 0.009 0.001 0.023 0.008 GPS+GLO. 8h 0.000 0.018 0.006 0.001 0.021 0.006
24h 0.002 0.006 0.004 0.001 0.005 0.004
Table B.3: Statistical Analysis for coordinate differences at station NKLG (X: 6287385.738 m, Y: 1071574.741 m, Z: 39133.088 m).
172