GPS非差相位精密单点定位研究
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摘要
本文全面展示了作者关于GPS非差相位精密单点定位所做的研究,内容涵盖了数学模型,误差改正模型,数据预处理方法和参数估计方法以及相关的实验、分析与应用。
文中简要介绍了精密单点定位的数学模型、误差改正模型和数据预处理方法。重点研究了精密单点定位参数估计方法。针对传统Kalman滤波的缺陷,提出了适合动态精密单点定位事后处理的二次Kalman滤波方法。详细推导了平方根信息滤波与平滑算法的公式并给出了参数分类的方法。推导了通用的递归最小二乘公式,新公式基于正交变换解法,是递归最小二乘和平方根信息滤波与平滑的统一表示。
为了进一步开展研究,作者开发了具有静态和动态事后处理功能的精密单点定位软件。软件综合考虑了各种误差改正,同时实现了二次Kalman滤波,平方根信息滤波与平滑和递归最小二乘三个参数估计模块。三个模块都采用了灵活的参数消去和恢复技术。静态和动态实测数据解算实验表明,软件可以实现2-3厘米的静态定位精度和10-20厘米的动态定位精度,其中动态数据来源包括陆地、空中和海上的运动载体。
基于这个软件平台,作者进行了相关的实验和分析,得出了以下结论。
1.二次Kalman滤波能有效克服传统Kalman滤波的缺陷,取得了较好的动态定位精度。
2.三个参数估计模块的定位结果非常接近;Kalman虑波用于静态定位效率最高,平方根信息滤波与平滑用于动态定位耗时最少。
3.不同轨道和钟差产品的静态定位精度相当,采用30秒钟差产品的动态定位精度要比5分钟钟差产品的定位精度提高约50%。
4.忽略DCB会引起精密单点定位结果系统性误差并且主要体现在接收机钟差上。DCB对静态定位的影响可以忽略;对动态定位的影响较大,应该认真加以考虑。
最后,作者有机会获得了汶川地震时中国天津地区12个GPS连续运行站的1秒采样观测数据,采用精密单点定位技术进行了地震期间地表运动分析实验。实验结果令人鼓舞,能够分辨出地震期间测站在东西和南北方向的周期性运动。
This thesis exhibits a comprehensive investigation on GPS Precise Point Positioning (PPP)with un-differenced carrier phase which includes mathematical models, error mitigations, datapreprocessing and parameter estimation as well as TcorrelativeT experiments, analysis andapplication.
A brief introduction of mathematical models, error mitigations and data preprocessingtechniques was presented. Research was emphasized on methods of parameter estimation. A newapproach named“Tow-Way”Kalman Filter was proposed to conquer the disadvantage oftraditional Kalman Filter for kinematic PPP post processing. TA detailed deduction of Square RootInformation Filtering & Smoothing (SRIF&SRIS) and the method to categorise the unknownparameters were presented. A set of more universal Tformulas of Recursive Least Square (RLS)was derived by the author. The new formula using orthogonal transformation algorithm unifiestraditional RLS and SRIF&SRIS.
To further our research, a piece of softwareT named“GPS-PPP”with the function for staticand kenamatic precise point positioning post processing was developed by the author. In thisTsoftwareT, varied error mitigations were implemented along with three modules for parameterestimation which include Tow-Way Kalman Filter, SRIF&SRIS and RLS. TFlexible Ttechniquesfor parameter elimination and restoration were employedT Tin all the three estimation modules.Test with plenty of both static and dynamic data demonstrated that an accuracy of 2-3 cmprecision and 10-20 cm precision has been achieved for static and kinematic positioningrespectively. The dynamic data used for test came from land, marine and airborne vehicles.
Supported by the software package GPS-PPP, a series of correlative experiments andanalysis were carried out and conclusions were as follows: Firstly, Tow-Way Kalman Filter hassucceeded in overcoming the shortcoming of traditional Kalman Filter, and the result ofkinematic PPP with Tow-Way Kalman Filter is close to that with the other parameter estimationmethods presented by many references. Secondly, PPP results with different estimation moduleswere consistent to each other, and Kalman Filter has the highest calculating efficiency for staticpositioning while SRIF&SRIS enjoys the least time cost for kinematic positioning. Thirdly,Experiments demonstrated that static PPP results using different Orbit & Clock products sharenearly the same precision while using products with 30 sec sample rate Clocks would improvekinematic PPP result by 50% than that using products with 5min Clock. Fourthly, it has beenconcluded that ignoring DCB correction will result in systemic errors for PPP result whichmainly influence receiver clock estimation and the influence of DCB on static positioning is small enough to be ignored, but for kinematic PPP it has to be considered seriously.
Last but no least, it occurs to the author to receive a set of data with 1 Hz sample rate from 12 continuous operation stations in Tianjin China on the date of Wenchuan Earthquake 12 May, 2008. Experiment of using PPP for far-field ground motion analysis of Wenchuan Earthquake was carried out and the result was really encouraging that the periodic motion in both east-west and south-north directions of the stations could be distinguished.
文中简要介绍了精密单点定位的数学模型、误差改正模型和数据预处理方法。重点研究了精密单点定位参数估计方法。针对传统Kalman滤波的缺陷,提出了适合动态精密单点定位事后处理的二次Kalman滤波方法。详细推导了平方根信息滤波与平滑算法的公式并给出了参数分类的方法。推导了通用的递归最小二乘公式,新公式基于正交变换解法,是递归最小二乘和平方根信息滤波与平滑的统一表示。
为了进一步开展研究,作者开发了具有静态和动态事后处理功能的精密单点定位软件。软件综合考虑了各种误差改正,同时实现了二次Kalman滤波,平方根信息滤波与平滑和递归最小二乘三个参数估计模块。三个模块都采用了灵活的参数消去和恢复技术。静态和动态实测数据解算实验表明,软件可以实现2-3厘米的静态定位精度和10-20厘米的动态定位精度,其中动态数据来源包括陆地、空中和海上的运动载体。
基于这个软件平台,作者进行了相关的实验和分析,得出了以下结论。
1.二次Kalman滤波能有效克服传统Kalman滤波的缺陷,取得了较好的动态定位精度。
2.三个参数估计模块的定位结果非常接近;Kalman虑波用于静态定位效率最高,平方根信息滤波与平滑用于动态定位耗时最少。
3.不同轨道和钟差产品的静态定位精度相当,采用30秒钟差产品的动态定位精度要比5分钟钟差产品的定位精度提高约50%。
4.忽略DCB会引起精密单点定位结果系统性误差并且主要体现在接收机钟差上。DCB对静态定位的影响可以忽略;对动态定位的影响较大,应该认真加以考虑。
最后,作者有机会获得了汶川地震时中国天津地区12个GPS连续运行站的1秒采样观测数据,采用精密单点定位技术进行了地震期间地表运动分析实验。实验结果令人鼓舞,能够分辨出地震期间测站在东西和南北方向的周期性运动。
This thesis exhibits a comprehensive investigation on GPS Precise Point Positioning (PPP)with un-differenced carrier phase which includes mathematical models, error mitigations, datapreprocessing and parameter estimation as well as TcorrelativeT experiments, analysis andapplication.
A brief introduction of mathematical models, error mitigations and data preprocessingtechniques was presented. Research was emphasized on methods of parameter estimation. A newapproach named“Tow-Way”Kalman Filter was proposed to conquer the disadvantage oftraditional Kalman Filter for kinematic PPP post processing. TA detailed deduction of Square RootInformation Filtering & Smoothing (SRIF&SRIS) and the method to categorise the unknownparameters were presented. A set of more universal Tformulas of Recursive Least Square (RLS)was derived by the author. The new formula using orthogonal transformation algorithm unifiestraditional RLS and SRIF&SRIS.
To further our research, a piece of softwareT named“GPS-PPP”with the function for staticand kenamatic precise point positioning post processing was developed by the author. In thisTsoftwareT, varied error mitigations were implemented along with three modules for parameterestimation which include Tow-Way Kalman Filter, SRIF&SRIS and RLS. TFlexible Ttechniquesfor parameter elimination and restoration were employedT Tin all the three estimation modules.Test with plenty of both static and dynamic data demonstrated that an accuracy of 2-3 cmprecision and 10-20 cm precision has been achieved for static and kinematic positioningrespectively. The dynamic data used for test came from land, marine and airborne vehicles.
Supported by the software package GPS-PPP, a series of correlative experiments andanalysis were carried out and conclusions were as follows: Firstly, Tow-Way Kalman Filter hassucceeded in overcoming the shortcoming of traditional Kalman Filter, and the result ofkinematic PPP with Tow-Way Kalman Filter is close to that with the other parameter estimationmethods presented by many references. Secondly, PPP results with different estimation moduleswere consistent to each other, and Kalman Filter has the highest calculating efficiency for staticpositioning while SRIF&SRIS enjoys the least time cost for kinematic positioning. Thirdly,Experiments demonstrated that static PPP results using different Orbit & Clock products sharenearly the same precision while using products with 30 sec sample rate Clocks would improvekinematic PPP result by 50% than that using products with 5min Clock. Fourthly, it has beenconcluded that ignoring DCB correction will result in systemic errors for PPP result whichmainly influence receiver clock estimation and the influence of DCB on static positioning is small enough to be ignored, but for kinematic PPP it has to be considered seriously.
Last but no least, it occurs to the author to receive a set of data with 1 Hz sample rate from 12 continuous operation stations in Tianjin China on the date of Wenchuan Earthquake 12 May, 2008. Experiment of using PPP for far-field ground motion analysis of Wenchuan Earthquake was carried out and the result was really encouraging that the periodic motion in both east-west and south-north directions of the stations could be distinguished.
引文
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[2]李征航,黄劲松. GPS测量与数据处理[M].武汉:武汉大学出版社, 2005: 197.
[3] Abdel-salam, M. A. t. Precise Point Positioning Using Un-Differenced Code and Carrier Phase Observations [D]. Calgary: Uinversity of Calgary, 2005: 206.
[4] Kleusberg, A. and P. J. G. Teunissen. GPS for Geodesy [Ed]. Berlin,Germany: Springer-Verlag, 1996: 407.
[5]刘基余. GPS卫星导航原理与定位方法[M]. (2版).北京:测绘出版社, 2008.
[6]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: 115.
[7] Colombo, O. L. and A. W. Sutter. Evaluation of Precise, Kinematic GPS Point Positioning [C]. Proceedings of the Institute Of Navigation (ION) GNSS-2004 Meeting, Long Beach, California, 2004.
[8] Gao, Y. and K. Chen. Performance Analysis of Precise Point Positioning Using Real-Time Orbit and Clock Products [J]. Journal of Global Positioning Systems, 2004,3(1-2): 95-100.
[9] Kouba, J. A GUIDE TO USING INTERNATIONAL GPS SERVICE(IGS) PRODUCTS [OL]. ftp://igscb.jpl.nasa.gov/igscb/resource/pubs/GuidetoUsingIGSProducts.pdf. 2003: 31.
[10] Kouba, J. and P. Heroux. Precise Point Positioning Using IGS Orbit and Clock Products [J]. GPS Solutions, 2001,5(2): 12-28.
[11] Zhang, X. Precise Point Positioning Evaluation and Airborne Lidar Calibration [R]: Danish National Space Center, 2005.
[12] Heroux, P. and J. Kouba. GPS Precise Point Positioning Using IGS Orbit Products [J]. Phys Chem Earth, 2001,26(6-8): 573-378.
[13] Bisnath, S. Precise Orbit Determination of Low Earth Orbiters with a Single GPS Receiver-Based, Geometric Strategy [R]. Fredericton, New Brunswick, Canada: Department of Geodesy and Geomatics Engineering, University of New Brunswick, 2004: 143.
[14] HU, C., W. CHEN, S. GAO, et al. Data Processing for GPS Precise Point Positioning [J]. Transaction of Najing University of Aeronautics & Astronautics, 2005,22(2): 124-131.
[15] Shen, X. Improving Ambiguity Convergence in Carrier Phase-Based Precise Point Positioning [D]. Calgary: University of Calgary, 2002: 195.
[16] Witchayangkoon, B. ELEMENTS OF GPS PRECISE POINT POSITIONING [D]. Maine: The University of Maine, 2000: 286.
[17] Le, A. Q. and C. Tiberius. Single-frequency precise point positioning with optimal filtering [J]. GPS Solutions, 2006,11: 61-69.
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