GPS精密单点定位算法研究与软件实现
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摘要
GPS精密单点定位是利用IGS提供的精密卫星星历和钟差产品,以单台双频GPS接收机的伪距和载波相位观测值来进行精密绝对定位的方法。其定位精度可达到静态厘米级和动态分米级的水平。除位置外,还可同时得到接收机钟差、对流层天顶延迟等产品,使得该技术在坐标框架的维持、高精度导航定位、大气延迟提取及精密授时等领域均具有广阔的应用前景。
本文系统研究了精密单点定位理论,着重分析了相关的技术难点,对部分关键问题,如参数估计、误差随机模型确定、实时质量控制等进行了详细论述。主要研究内容包括以下几方面:
1、精密单点定位观测方程及其误差源
在GPS原始观测方程的基础上,推导了无电离层组合和非组合两种精密单点定位方法的观测方程;详细阐述了精密单点定位过程中影响显著的误差源及相应的处理方案。
2、两种精密单点定位方法:参数估计策略及结果分析
介绍了两种精密单点定位方法的数学模型、未知参数的估计方案和随机模型,并比较了两种精密单点定位方法的优缺点,分别利用随机游走过程模拟对流层残差随机变化和白噪声过程描述钟差随机变化。分别对静态,仿动态,以及船载低动态数据和机载高动态数据进行处理,表明作者研发的PPP软件能达到较高的精度,在静动态条件下分别能达到厘米级和分米级的定位精度,滤波收敛后定位结果的稳定性可分别达到1～3厘米和6～10厘米。该精度与国内外同类的研究结果相当。
首次实验分析了两种PPP算法,比较了各自的特点以及在定位中的应用,实验结果表明,非组合PPP不仅能够有效减少各坐标分量解得滤波收敛时间,且滤波收敛解的稳定性也得到改善。
3、精密单点定位的实时质量控制
提出GPS精密单点定位的实时质量控制,并将基于预报残差的DIA质量控制过程引入到PPP定位中,通过实例证明:实施DIA质量控制后能加快滤波收敛速度,并提高精密单点定位解的稳定性和精度,实施DIA质量控制策略以后,各坐标分量经过约35分钟即可收敛到1分米以内,且收敛后X、Y、Z三分量的外符合精度可分别达到2、2、4厘米。
4、GPS精密单点定位的其他应用
利用静态精密单点定位技术,估计得到单站对流层天顶延迟和接收机钟差,通过与IGS发布的最终产品进行比较,分析了其精度。利用IGS跟踪站进行试验,试验结果表明,利用精密单点定位方法,基于单站24小时的双频观测数据,可估计得到无明显系统偏差、精度达毫米级的绝对天顶对流层延迟和实现0.1～0.3ns的时间传递精度,进而拓展了精密单点定位技术的应用范围。
Precise Point Positioning (PPP) is a positioning technique using dual-frequency pseudorange and carrier phase observations from a stand-alone GNSS receiver along with the precise orbit and clock solutions published by IGS, one can determine the position of anywhere in the global area with a high precision, decimeter even centimeter. Besides the position, the receive clock corrections, Zenith Troposphere Delays (ZTDs) and float ambiguity estimates could also be obtained with this technique, which broaden applications of PPP techniches in the field of high-precision navigation and positioning, atmosphere delays’determination, precise time and frequency transfer etc.
PPP technique and some key problems are discussed in this paper, including parameter estimations, stochastic model determinations, quality control, etc. The main contents and conclusions of this paper are as follows:
1. The observation equations of PPP technique and its systematic errors
Based on original dual-frequency GPS code and phase observations, the observation equations of ionosphere-free combination and uncombined PPP techniques are deduced. Several corrections to the systematic errors existing in the measurements, such as relativistic effects, phase wind-up etc, are also presented.
2. Two PPP techniques, including parameter estimation strategy and result analysis
Two PPP techniques are introduced, including their math models, unknown parameter estimation strategy and stochastic models. The advantages and disadvantages of each PPP technique are also discussed. Under different conditions such as static, simulated kinematic, low-dynamic offshore and high-dynamic airborne data, the overall performances of PPP techniques are investigated and analyzed. The results show that for both static and kinematic positioning, a position accuracy of 1～3 cm and 6～10 cm could be achieved with the author’s PPP software.
The positioning performances of two PPP techniques are compared for the first time. The results show that the convergence behavior and repeatability of filtered solutions can be well improved by comparing the uncombined PPP technique with the traditional one.
3. Real time quality control of PPP technique
Real time quality control of GPS PPP technique is proposed, the recursive DIA-procedure is adopted as quality control strategy to guarantee the reliability of the estimators from PPP technique. The results show that convergence behavior and repeatability of filtered solutions can be well improved after DIA-procedure.
4. Some other applications of GPS PPP technique
The receive clock corrections and ZTDs can also be obtained with PPP technique, their accuracy are analyzed by comparing with corresponding IGS products. The results show that, based on dual-frequency observations of single station, one can realize millimeter accuracy without systematic bias in ZTDs’determination and 0.1～0.3ns accuracy in time transfer, which demonstrate the wide applications of PPP implementation.
本文系统研究了精密单点定位理论,着重分析了相关的技术难点,对部分关键问题,如参数估计、误差随机模型确定、实时质量控制等进行了详细论述。主要研究内容包括以下几方面:
1、精密单点定位观测方程及其误差源
在GPS原始观测方程的基础上,推导了无电离层组合和非组合两种精密单点定位方法的观测方程;详细阐述了精密单点定位过程中影响显著的误差源及相应的处理方案。
2、两种精密单点定位方法:参数估计策略及结果分析
介绍了两种精密单点定位方法的数学模型、未知参数的估计方案和随机模型,并比较了两种精密单点定位方法的优缺点,分别利用随机游走过程模拟对流层残差随机变化和白噪声过程描述钟差随机变化。分别对静态,仿动态,以及船载低动态数据和机载高动态数据进行处理,表明作者研发的PPP软件能达到较高的精度,在静动态条件下分别能达到厘米级和分米级的定位精度,滤波收敛后定位结果的稳定性可分别达到1～3厘米和6～10厘米。该精度与国内外同类的研究结果相当。
首次实验分析了两种PPP算法,比较了各自的特点以及在定位中的应用,实验结果表明,非组合PPP不仅能够有效减少各坐标分量解得滤波收敛时间,且滤波收敛解的稳定性也得到改善。
3、精密单点定位的实时质量控制
提出GPS精密单点定位的实时质量控制,并将基于预报残差的DIA质量控制过程引入到PPP定位中,通过实例证明:实施DIA质量控制后能加快滤波收敛速度,并提高精密单点定位解的稳定性和精度,实施DIA质量控制策略以后,各坐标分量经过约35分钟即可收敛到1分米以内,且收敛后X、Y、Z三分量的外符合精度可分别达到2、2、4厘米。
4、GPS精密单点定位的其他应用
利用静态精密单点定位技术,估计得到单站对流层天顶延迟和接收机钟差,通过与IGS发布的最终产品进行比较,分析了其精度。利用IGS跟踪站进行试验,试验结果表明,利用精密单点定位方法,基于单站24小时的双频观测数据,可估计得到无明显系统偏差、精度达毫米级的绝对天顶对流层延迟和实现0.1～0.3ns的时间传递精度,进而拓展了精密单点定位技术的应用范围。
Precise Point Positioning (PPP) is a positioning technique using dual-frequency pseudorange and carrier phase observations from a stand-alone GNSS receiver along with the precise orbit and clock solutions published by IGS, one can determine the position of anywhere in the global area with a high precision, decimeter even centimeter. Besides the position, the receive clock corrections, Zenith Troposphere Delays (ZTDs) and float ambiguity estimates could also be obtained with this technique, which broaden applications of PPP techniches in the field of high-precision navigation and positioning, atmosphere delays’determination, precise time and frequency transfer etc.
PPP technique and some key problems are discussed in this paper, including parameter estimations, stochastic model determinations, quality control, etc. The main contents and conclusions of this paper are as follows:
1. The observation equations of PPP technique and its systematic errors
Based on original dual-frequency GPS code and phase observations, the observation equations of ionosphere-free combination and uncombined PPP techniques are deduced. Several corrections to the systematic errors existing in the measurements, such as relativistic effects, phase wind-up etc, are also presented.
2. Two PPP techniques, including parameter estimation strategy and result analysis
Two PPP techniques are introduced, including their math models, unknown parameter estimation strategy and stochastic models. The advantages and disadvantages of each PPP technique are also discussed. Under different conditions such as static, simulated kinematic, low-dynamic offshore and high-dynamic airborne data, the overall performances of PPP techniques are investigated and analyzed. The results show that for both static and kinematic positioning, a position accuracy of 1～3 cm and 6～10 cm could be achieved with the author’s PPP software.
The positioning performances of two PPP techniques are compared for the first time. The results show that the convergence behavior and repeatability of filtered solutions can be well improved by comparing the uncombined PPP technique with the traditional one.
3. Real time quality control of PPP technique
Real time quality control of GPS PPP technique is proposed, the recursive DIA-procedure is adopted as quality control strategy to guarantee the reliability of the estimators from PPP technique. The results show that convergence behavior and repeatability of filtered solutions can be well improved after DIA-procedure.
4. Some other applications of GPS PPP technique
The receive clock corrections and ZTDs can also be obtained with PPP technique, their accuracy are analyzed by comparing with corresponding IGS products. The results show that, based on dual-frequency observations of single station, one can realize millimeter accuracy without systematic bias in ZTDs’determination and 0.1～0.3ns accuracy in time transfer, which demonstrate the wide applications of PPP implementation.
引文
[1] http://www.igs.org/components/
[2] IGS Central Bureau.2009 Annual Report, 2010.
[3] Zumberge J, Heflin M, Jefferson D, Watkins M and Webb F. Precise point positioning for the efficient and rpbust analysis of GPS data from large networks [J]. Journal of Geophysical Research, 1997,102(B3): 5005-5017.
[4] Kouba J, Héroux H. Precise point positioning using IGS orbit and clock products [J]. GPS Solutions, 2001, 5(2): 12-28.
[5] Gao Y, Shen X.Improving Ambbiguity Convergence in Carrier Phase-Based Precise Point Positioning[M] . Proceedings of ION National Technical Meeting, 2001.
[6] Gao Y, Shen X. A New Method Of Carrier Phase Based Precise Point Positioning[J]. Journal of the institute of navigation,2002, Vol. 49,No.2.
[7] Gao Y, Chen K, Shen X. Real-Time Kinematic Positioning Based on Un-Differenced Carrier Phase Data Processing [M]. Proceedings of ION National Technical Meeting, Anaheim, California, 2003.
[8] Abdel-salam M. Precise Point Positioning Using Un-Differenced Code and Carrier Phase Observations [D]. Canada: University of Calgary, 2005.
[9] Han S C, Kwon J H, Jekeli C. Accurate Absolute GPS Positioning Through Satellite Clock Error Estimation[J]. Journal of Geodesy, 2001, 77: 33-43.
[10] Keshin M O, Le A Q, Marel H. Single and Dual-frequency Precise Point Positioning: Approaches and Performance [M]. Proceedings of the 3rd ESA Workshop on Satellite Navigation User Equipment Technologies, NAVITEC 2006, Noordwijk, The Netherlands, 11-13 December 2006, 8 pages.
[11] Leandro R F. Precise Point Positioning with GPS: A New Approach for Positioning, Atmospheric Studies, and Signal Analysis [D]. Canada: University of New Brunswick, 2009.
[12] Muellerschoen R J, Bertiger W I, Lough M F. Results of an Internet-based Dual-frequency Global Differential GPS System [C]. IAIN World Congress, San Diego, 2000.
[13]叶世榕. GPS非差相位精密单点定位理论与实现[D].武汉:武汉大学,2002.
[14]刘经南,叶世榕. GPS非差相位精密单点定位技术探讨[J] .武汉大学学报.信息科学版,2002,27(3):234-240.
[15] Zhang X H, Anderson O B. Surface ice f low velocity and tide retrieval of the Amery ice shelf using precise point positioning [M]. Journal of Geodesy, 2006, 80(4): 171-176.
[16] Zhang X H, Forsberg R. Assessment of long-range kinematic GPS positioning errors by comparison with airborne laser altimetry and satellite altimetry [M]. Journal of Geodesy,2007, 81(3):201-211.
[17] CHEN W, HU C W et al. Absolute Ionospheric Delay Estimation Based on GPS PPP and GPS Active Network[A], The 2004 International Symposium on GNSS/GPS[C], Sydney, Australia,6–8 December 2004.
[18] Zhang B C. Determination of Un-differenced Atmospheric Delays for Network-based RTK. In: Proceedings of Institute of Navigation GNSS 2009,Savannah, USA, 2009. 2727 ~ 2738.
[19]张宝成,欧吉坤,袁运斌等.基于GPS双频原始观测值的精密单点定位算法及应用.测绘学报,已接收.
[20]党亚民,秘金钟,成英燕.全球导航卫星系统原理与应用[M] .北京:测绘出版社, 2007.
[21]程鹏飞,蔡艳辉,文汉江等.全球卫星导航系统:GPS, GLONASS, Galileo及其他系统[M].北京:测绘出版社,2009.
[22]李征航,黄劲松. GPS原理与应用[M] .武汉:武汉大学出版社2005.
[23] ftp://igscb.jpl.nasa.gov/igscb/station/general/
[24]葛茂荣,刘经南.GPS定位中对流层折射估计研究[J].测绘学报,1996,25(4):285~29.
[25]魏子卿,葛茂荣.GPS相对定位的数学模型.北京:测绘出版社,1998.
[26]宋文尧,张牙.卡尔曼滤波.北京:科学出版社,1991.1.
[27]杨元喜.自适应动态导航定位[M].北京:测绘出版社,2006.
[28] Baarda W. A Testing Proeedure for Use in Geodetic Networks [M]. Delft:Comm. New Service,1968.
[29] Mertikas S P, Rizos C. On-line Detection of Abrupt Changes in the Carrier-Phase Measurements of GPS [J]. Journal of Geodesy ,1997(53):469~482.
[30]陈小明.高精度GPS动态定位的理论与实践[D].硕士论文,武汉:武汉测绘科技大学,1997.
[31]刘大杰,陶本藻.实用测量数据处理方法[M].北京:测绘出版社,2000.
[32]陶本藻.卡尔曼滤波模型误差的识别[J].地壳变形与地震, 199911(4):15-18.
[33] SALZMANN M. Least Squares Filtering and Testing for Geodetic Navigation Applications [D], 1993, Ph.D. thesis. Department of Geodetic Engineering, Delft University of Technology.
[34] TEUNISSEN P.J.G, The GPS Phase-Adjusted Pseudorande[A],1992, K. Linkwitz, U. Hangleiter: High precision navigation 92, Ferd[C]. Dummlers Verlag, Bonn. 115-125.
[35] TEUNISSEN P.J.G. Minimal Detectable Biases of GPS Data[J]. Journal of Geodesy, 1998,72:236-244.
[36] Bar-Sever YE, Kroger PM, Borjesson JA. Estimating Horizontal Gradients of Tropospheric Path Delay with a Single GPS Receiver, Journal of Geophysical Research, 1998, 103(B3):5019-5035.
[37] Abdel-salam M, Gao Y. Precise GPS Atmosphere Sensing Based on Un-Differenced Observations, Proceedings of ION National Technical Meeting, Long Beach, California,2004.
[38] Leandro R. F, Santos M. C and Langley R. B. PPP-based Ionospheric Activity Monitoring, Proceedings of ION National Technical Meeting, Fort Worth, Texas,2007.
[39] Diego Orgiazzi, Patrizia Tavella. Experimental Assessment of the Time Transfer Capability of Precise Point Positioning (PPP) [J]. GPS World, 2006.
[40] Jim Ray, K.S. Geodetic techniques for time and frequency comparisons using GPS phase and code measurements [J]. Metrologia, 2005(42): 215-232.
[41] Orgiazzi D, Tavella P and Lahaye F. Experimental Assessment of the Time Transfer Capability of Precise Point Positioning(PPP), Frequency Control Symposium and Exposition, 2005. Proceedings of the 2005 IEEE International: 337-345.
[42] Defraigne P, Bruyninx C and Guyennon N. PPP and Phase-only GPS Time and Frequency transfer, Frequency Control Symposium, 2007 Joint with the21st European Frequency and Time Forum. IEEE International, May 29 -June 1 2007: 904-908.
[43] http://acc.igs.org/
[44] Ge M R, Gendent G, Rothacher M, et al. Resolution of GPS carrier-phase ambiguities in Precise Point Positioning(PPP) with daily observations, 2008, 82(7):389-399.
[45] Cheng P F,Ivestigations on the Establishment of DGPS Services in China,PhDThesis,Graz,,July 1998
[46]秘金钟,赵春梅,李玮.GALILEO中国区域完备性监测指标SISMA研究,武汉大学学报,2009(10):1172~1175
[2] IGS Central Bureau.2009 Annual Report, 2010.
[3] Zumberge J, Heflin M, Jefferson D, Watkins M and Webb F. Precise point positioning for the efficient and rpbust analysis of GPS data from large networks [J]. Journal of Geophysical Research, 1997,102(B3): 5005-5017.
[4] Kouba J, Héroux H. Precise point positioning using IGS orbit and clock products [J]. GPS Solutions, 2001, 5(2): 12-28.
[5] Gao Y, Shen X.Improving Ambbiguity Convergence in Carrier Phase-Based Precise Point Positioning[M] . Proceedings of ION National Technical Meeting, 2001.
[6] Gao Y, Shen X. A New Method Of Carrier Phase Based Precise Point Positioning[J]. Journal of the institute of navigation,2002, Vol. 49,No.2.
[7] Gao Y, Chen K, Shen X. Real-Time Kinematic Positioning Based on Un-Differenced Carrier Phase Data Processing [M]. Proceedings of ION National Technical Meeting, Anaheim, California, 2003.
[8] Abdel-salam M. Precise Point Positioning Using Un-Differenced Code and Carrier Phase Observations [D]. Canada: University of Calgary, 2005.
[9] Han S C, Kwon J H, Jekeli C. Accurate Absolute GPS Positioning Through Satellite Clock Error Estimation[J]. Journal of Geodesy, 2001, 77: 33-43.
[10] Keshin M O, Le A Q, Marel H. Single and Dual-frequency Precise Point Positioning: Approaches and Performance [M]. Proceedings of the 3rd ESA Workshop on Satellite Navigation User Equipment Technologies, NAVITEC 2006, Noordwijk, The Netherlands, 11-13 December 2006, 8 pages.
[11] Leandro R F. Precise Point Positioning with GPS: A New Approach for Positioning, Atmospheric Studies, and Signal Analysis [D]. Canada: University of New Brunswick, 2009.
[12] Muellerschoen R J, Bertiger W I, Lough M F. Results of an Internet-based Dual-frequency Global Differential GPS System [C]. IAIN World Congress, San Diego, 2000.
[13]叶世榕. GPS非差相位精密单点定位理论与实现[D].武汉:武汉大学,2002.
[14]刘经南,叶世榕. GPS非差相位精密单点定位技术探讨[J] .武汉大学学报.信息科学版,2002,27(3):234-240.
[15] Zhang X H, Anderson O B. Surface ice f low velocity and tide retrieval of the Amery ice shelf using precise point positioning [M]. Journal of Geodesy, 2006, 80(4): 171-176.
[16] Zhang X H, Forsberg R. Assessment of long-range kinematic GPS positioning errors by comparison with airborne laser altimetry and satellite altimetry [M]. Journal of Geodesy,2007, 81(3):201-211.
[17] CHEN W, HU C W et al. Absolute Ionospheric Delay Estimation Based on GPS PPP and GPS Active Network[A], The 2004 International Symposium on GNSS/GPS[C], Sydney, Australia,6–8 December 2004.
[18] Zhang B C. Determination of Un-differenced Atmospheric Delays for Network-based RTK. In: Proceedings of Institute of Navigation GNSS 2009,Savannah, USA, 2009. 2727 ~ 2738.
[19]张宝成,欧吉坤,袁运斌等.基于GPS双频原始观测值的精密单点定位算法及应用.测绘学报,已接收.
[20]党亚民,秘金钟,成英燕.全球导航卫星系统原理与应用[M] .北京:测绘出版社, 2007.
[21]程鹏飞,蔡艳辉,文汉江等.全球卫星导航系统:GPS, GLONASS, Galileo及其他系统[M].北京:测绘出版社,2009.
[22]李征航,黄劲松. GPS原理与应用[M] .武汉:武汉大学出版社2005.
[23] ftp://igscb.jpl.nasa.gov/igscb/station/general/
[24]葛茂荣,刘经南.GPS定位中对流层折射估计研究[J].测绘学报,1996,25(4):285~29.
[25]魏子卿,葛茂荣.GPS相对定位的数学模型.北京:测绘出版社,1998.
[26]宋文尧,张牙.卡尔曼滤波.北京:科学出版社,1991.1.
[27]杨元喜.自适应动态导航定位[M].北京:测绘出版社,2006.
[28] Baarda W. A Testing Proeedure for Use in Geodetic Networks [M]. Delft:Comm. New Service,1968.
[29] Mertikas S P, Rizos C. On-line Detection of Abrupt Changes in the Carrier-Phase Measurements of GPS [J]. Journal of Geodesy ,1997(53):469~482.
[30]陈小明.高精度GPS动态定位的理论与实践[D].硕士论文,武汉:武汉测绘科技大学,1997.
[31]刘大杰,陶本藻.实用测量数据处理方法[M].北京:测绘出版社,2000.
[32]陶本藻.卡尔曼滤波模型误差的识别[J].地壳变形与地震, 199911(4):15-18.
[33] SALZMANN M. Least Squares Filtering and Testing for Geodetic Navigation Applications [D], 1993, Ph.D. thesis. Department of Geodetic Engineering, Delft University of Technology.
[34] TEUNISSEN P.J.G, The GPS Phase-Adjusted Pseudorande[A],1992, K. Linkwitz, U. Hangleiter: High precision navigation 92, Ferd[C]. Dummlers Verlag, Bonn. 115-125.
[35] TEUNISSEN P.J.G. Minimal Detectable Biases of GPS Data[J]. Journal of Geodesy, 1998,72:236-244.
[36] Bar-Sever YE, Kroger PM, Borjesson JA. Estimating Horizontal Gradients of Tropospheric Path Delay with a Single GPS Receiver, Journal of Geophysical Research, 1998, 103(B3):5019-5035.
[37] Abdel-salam M, Gao Y. Precise GPS Atmosphere Sensing Based on Un-Differenced Observations, Proceedings of ION National Technical Meeting, Long Beach, California,2004.
[38] Leandro R. F, Santos M. C and Langley R. B. PPP-based Ionospheric Activity Monitoring, Proceedings of ION National Technical Meeting, Fort Worth, Texas,2007.
[39] Diego Orgiazzi, Patrizia Tavella. Experimental Assessment of the Time Transfer Capability of Precise Point Positioning (PPP) [J]. GPS World, 2006.
[40] Jim Ray, K.S. Geodetic techniques for time and frequency comparisons using GPS phase and code measurements [J]. Metrologia, 2005(42): 215-232.
[41] Orgiazzi D, Tavella P and Lahaye F. Experimental Assessment of the Time Transfer Capability of Precise Point Positioning(PPP), Frequency Control Symposium and Exposition, 2005. Proceedings of the 2005 IEEE International: 337-345.
[42] Defraigne P, Bruyninx C and Guyennon N. PPP and Phase-only GPS Time and Frequency transfer, Frequency Control Symposium, 2007 Joint with the21st European Frequency and Time Forum. IEEE International, May 29 -June 1 2007: 904-908.
[43] http://acc.igs.org/
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