不确定性数学理论在GNSS精确定位中的研究
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摘要
卫星导航定位技术的发展,在各应用领域产生了巨大的经济与社会效益。通过捕获伪码计算伪距的传统定位模式,如今已经不能满足高精度定位的需求。载波相位定位技术的发展,一定程度上解决了这个问题,但双差定位模型需要实时获得基准站的差分信息,极大限制了载波相位定位技术的应用范围。
本文以载波相位绝对定位模型为基础,探讨了整周模糊度解算与周跳检测修复的问题,将不确定性数学理论融入其中,进行了开创性的研究。
本文首先介绍了传统伪距定位模型,并通过简化矩阵的特性,利用QR分解,提出了新的递推解算算法。然后研究了载波相位测量与定位的原理,并建立了静态与动态的绝对定位模型。分析出载波相位精确定位的难点,集中在整周模糊度求解和周跳检测与修复方面。
在整周模糊度的解算中,首先总结传统解算算法,分析传统方法的不足,由于解算矩阵的病态性严重,导致模糊度搜索集合的区域极大。本文结合不确定性数学中的粗糙集理论,提出粗糙规整映射,设计了变粒度搜索算法,简化了搜索区域的结构,可实现整周模糊度解组合的快速搜索,并结合RATIO检验,快速得到正确解。仿真结果表明,该算法较传统方法可有效提高整周模糊度的解算效率。
周跳检测与修复,作为载波相位定位所用原始数据的预处理步骤,是完好性检测的重要部分。本文首先分析了通过研究载波观测值序列的数学特性,利用时间序列分析的方法,结合数据之间的相关性信息,提出基于模糊数学理论的数据相关度概念,通过对所建AR ( p )模型的分析,得出当3≤p≤5时是折中性选择,利用数据相关度对三组模型进行了加权组合,仿真结果表明,该算法较传统方法更能有效的检测与修复周跳。
With the development of GNSS, huge benefit has been produced. The traditional orientation pattern is unable to satisfy the requirement of the high precision orientation. Carrier phase measurement solves the problem in a certain extent. This paper makes researches on ambiguity estimation and circle slips detection based on the carrier phase measurement model using the uncertainty mathematics theory to solve those problems.
At first, the traditional orientation model using pseudorange is introduced. With the characteristics of the predigesting matrix and QR analysis, a new algorithm has been found, so we create the static and dynamic models for the absolute orientation. The conclusion indicates that the difficulties are ambiguity estimation and circle slips.
In the study of ambiguity estimation, we firstly make a summary of the traditional algorithms and analyze those deficiencies. The oversize condition-number of the matrix brings on the oversize searching area for the ambiguity. With the rough sets theory in uncertainty mathematics, the original theory named Rough Integer Mapping is brought forward to solve those problems. Searching algorithm with granularity changing is designed and predigests the topology of the ambiguity searching area. With RATIO test, the right ambiguity combinations could be confirmed quickly. The simulation indicates that the new algorithm could enhance the efficiency of ambiguity estimation obviously.
As the pretreatment of the original data for the carrier phase orientation, the detection and adjustment of the circle slips, is important department of the RAIM. The mathematic characteristics of the carrier phase observation serials are analyzed firstly. Using Time Serial Analysis method and the pertinency information between the neighbor data, we get the conception of data correlation based on Fuzzy mathematics theory. Through analyzing the AR ( p )model, we get the range:3≤p≤5, and combine the three models using the data correlation theory. The simulation indicates that this new algorithm can get an effective result for detection and adjustment of cycle slips.
本文以载波相位绝对定位模型为基础,探讨了整周模糊度解算与周跳检测修复的问题,将不确定性数学理论融入其中,进行了开创性的研究。
本文首先介绍了传统伪距定位模型,并通过简化矩阵的特性,利用QR分解,提出了新的递推解算算法。然后研究了载波相位测量与定位的原理,并建立了静态与动态的绝对定位模型。分析出载波相位精确定位的难点,集中在整周模糊度求解和周跳检测与修复方面。
在整周模糊度的解算中,首先总结传统解算算法,分析传统方法的不足,由于解算矩阵的病态性严重,导致模糊度搜索集合的区域极大。本文结合不确定性数学中的粗糙集理论,提出粗糙规整映射,设计了变粒度搜索算法,简化了搜索区域的结构,可实现整周模糊度解组合的快速搜索,并结合RATIO检验,快速得到正确解。仿真结果表明,该算法较传统方法可有效提高整周模糊度的解算效率。
周跳检测与修复,作为载波相位定位所用原始数据的预处理步骤,是完好性检测的重要部分。本文首先分析了通过研究载波观测值序列的数学特性,利用时间序列分析的方法,结合数据之间的相关性信息,提出基于模糊数学理论的数据相关度概念,通过对所建AR ( p )模型的分析,得出当3≤p≤5时是折中性选择,利用数据相关度对三组模型进行了加权组合,仿真结果表明,该算法较传统方法更能有效的检测与修复周跳。
With the development of GNSS, huge benefit has been produced. The traditional orientation pattern is unable to satisfy the requirement of the high precision orientation. Carrier phase measurement solves the problem in a certain extent. This paper makes researches on ambiguity estimation and circle slips detection based on the carrier phase measurement model using the uncertainty mathematics theory to solve those problems.
At first, the traditional orientation model using pseudorange is introduced. With the characteristics of the predigesting matrix and QR analysis, a new algorithm has been found, so we create the static and dynamic models for the absolute orientation. The conclusion indicates that the difficulties are ambiguity estimation and circle slips.
In the study of ambiguity estimation, we firstly make a summary of the traditional algorithms and analyze those deficiencies. The oversize condition-number of the matrix brings on the oversize searching area for the ambiguity. With the rough sets theory in uncertainty mathematics, the original theory named Rough Integer Mapping is brought forward to solve those problems. Searching algorithm with granularity changing is designed and predigests the topology of the ambiguity searching area. With RATIO test, the right ambiguity combinations could be confirmed quickly. The simulation indicates that the new algorithm could enhance the efficiency of ambiguity estimation obviously.
As the pretreatment of the original data for the carrier phase orientation, the detection and adjustment of the circle slips, is important department of the RAIM. The mathematic characteristics of the carrier phase observation serials are analyzed firstly. Using Time Serial Analysis method and the pertinency information between the neighbor data, we get the conception of data correlation based on Fuzzy mathematics theory. Through analyzing the AR ( p )model, we get the range:3≤p≤5, and combine the three models using the data correlation theory. The simulation indicates that this new algorithm can get an effective result for detection and adjustment of cycle slips.
引文
[1] Elliott D.Kaplan, Christopher J.Hegarty. Understanding GPS Principles and Applications. Beijing: Publishing House of Electronics Industry, 2005
[2]刘基余. GPS卫星导航定位原理与方法.北京:科学出版社, 2003
[3]秦永元,张洪钺,汪叔华.卡尔曼滤波与组合导航原理.西安:西北工业大学出版社, 1998
[4]彭祖赠,孙韫玉.模糊(Fuzzy)数学及其应用.武汉:武汉大学出版社, 2007
[5]张文修,吴伟志等.粗糙集理论与方法.第一版.北京:科学出版社, 2001
[6]张守信. GPS卫星测量定位理论与应用.长沙:国防科技大学出版社, 1996
[7]金凯德.数值分析.北京:机械工业出版社, 2005
[8]霍家道,郝燕玲.导航信号卡尔曼滤波定位解算方法研究.中国航海, 2004, 3(1): 44-48
[9] Eunwoo Choi, David A. Cicci. Analysis of GPS static positioning problems. Applied Mathematics and Computation 2003, 4(3): 37-51
[10]张云鹏,缪栋,杨小冈. GPS伪距导航定位解算新算法研究.电子科技, 2004, 12(01): 47-50
[11] Abel.J.S, Chaffee.J.W. Existence and Uniqueness of GPS Solutions. IEEE Transactions on Aerospace and Electronic System 1991, (11): 952-956
[12] Joho B, Lundberg. Alternative algorithms for the GPS static positioning solution. IEEE USA Applied Mathematics and Computation 2001, (10): 21-34
[13]陈小明,刘基余. GPS动态载波相位测量的波数在航解算.导航, 1996, 32(4): 30-38
[14]刘立龙.动态对动态GPS高精度定位理论及其应用研究: [博士学位论文].武汉:武汉大学, 2005
[15] Eunwoo Choi, etc. Analysis of GPS static positioning problems. Applied Mathematics and Computation, 2003,140(1): 37-25
[16]贾沛璋,吴连大.单频GPS周跳检测与估计算法.天文学报, 2001, 192-197
[17]刘立龙,刘基余,李广成.一种适合单频GPS动态求解模糊度的方法,飞行器测控学报, 2005, 12(1): 6-10
[18]刘根友.单频GPS接收机动态定位的相位与伪距联合算法及周跳检测.地壳形变与地震, 2001, 8(1): 120-122
[19]何海波.高精度GPS动态测量及质量控制: [博士学位论文].郑州:解放军信息工程大学, 2002
[20]王仁谦. GPS动态定位理论研究: [博士学位论文].长沙:中南大学, 2004
[21] P.J.G. Teunissen. The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation .Journal of Geodesy, 1995, (70): 65-82
[22] P.J.G.Teunissen. A New Method for Fast Carrier Phase Ambiguity Estimation. Proc. IEEE Position Location&Navigation Symp. Las Vegas, 1994, (4): 562-573
[23] P.J.G.Teunissen.一个新的GNSS模糊度估计类.武汉大学学报信息科学版, 2004, 29(9): 757-762
[24]刘立龙,刘基余等.一种GPS快速定位技术研究.宇航学报, 2005, 13(1): 39-42
[25] Bani, Allberta. Kinematic Systems in Geodesy and Surveying and Remote Sensing. International Association of Geodesy Symposia, 2005, 13(9): 299-308
[26] Joho B, Lundberg. Alternative algorithms for the GPS static positioning solution. IEEE USA Applied Mathematics and Computation, 2001, 41(3): 112-118
[27]王永生.一种消除GPS模糊度相关性的新算法.航空学报, 2002, 9(5): 32-36.
[28]赵健康,王银华.基于GPS相位法对舰船等大型载体定姿中的模糊数求解方法.宇航学报, 2001, 12(1): 43-47
[29] Han, S. and C. Rios. Improving the computational efficiency of the ambiguity function algorithm. Journal of Geodesy, 1996, 70(6): 330-341
[30]姬生月,欧吉坤等.一种适合于单频接收机快速模糊数求解的新方法.武汉测绘科技大学学报, 2000, 25(2): 102-104
[31]康荣雷,舒兰等.粗糙归整映射与整周模糊度解算.现代电子技术, 2008, 31(9): 138-140
[32]唐卫明. GPS载波相位平滑伪距精度分析与应用探讨.测绘信息与工程, 2005, 30(3): 37-39
[33] Mohamd A H, Schwarz K P. A simple and economical algorithm for GPS ambiguity resolution on the fly using whitening filters. Navigation, 1998, 45(3): 221-231
[34]常青,高晖,柳重堪. GPS定位算法研究.遥测遥控, 1998, 9(5): 6-11
[35]蔡艳辉,程鹏飞,李夕银.用卡尔曼滤波进行GPS动态定位,测绘通报, 2006, 18(3): 47-50
[36]黄丁发,熊永良等.全球定位系统(GPS)—理论与实践.成都:西南交通大学出版社, 2006
[37] Christian Tiberius. 0.99999999 confidence ambiguity resolution with GPS and Galileo. GPS Solutions, 2002, 6(5): 96-99
[38] Deng Qiang, Huang Shunji. Research on GPS Code Pseudorange Smoothing Technique by Carrier Observables. Journal of UESTC of China, 1996, 25(5): 112-118
[39]腾云龙,陈小平,唐应辉.提高GPS定位精度的改进卡尔曼滤波算法研究.现代电子技术, 2008, 31(3): 4-6
[40] Yu Guorong, Sheng Renjun. Cycle slip detection approach based on time-relative positioning theory. Journal of Southeast University (English Edition), 2005, 21(3): 363-368
[41] Liu Jiyu. A Real-time Solution for GPS Measured Distances without Cycle Slips, Survey Review(UK), 1993, 32(7): 31-38
[42] Eunwoo Choi, David A. Cicci. Analysis of GPS static positioning problems. Applied Mathematics and Computation, 2003, 22(5): 112-118
[43] Arnaud M, Flori A. Bias and precision of different sampling methods for GPS positions. Photogram metric Engineering and Remote Sensing, 1998, 64(6): 597-600
[44]张树京,齐立新.时间序列分析简明教程.北京:清华大学出版社, 2003
[45]范胜林,秦岭等. GPS姿态系统中周跳的检测及修复方法.数据采集与处理, 2002, 13(7): 22-23
[46] Gao Y, Li z. Cycle slip detection and ambiguity resolution algorithm for dual-frequency GPS data processing. Marine Geodesy, 1999, 22(4): 169-181
[47] Michaud S, Santeree R. Time-relative positioning with a single civil GPS receiver. GPS Solutions, 2001, 5(2): 71-77
[48] Collin F, Warnat R. Application of the wavelet transform for GPS cycle slip correction and comparison with Kalman filter. Manuscripta Geodetica, 1995, 20(3): 161-172
[49]王永超,黄智刚.时钟改进模型辅助RAIM算法研究.电子学报, 2001, 35(6): 1084-1088
[50] Kihara M. Study of a GPS satellite selection policy to improve positioning accuracy.Position Location and Navigation Symposium, IEEE April 1994, 10(8): 267-273
[51] M.E.Cannon, K.P.Schwarz, M.wei, D.Delikaraoglou. A consistency test of airborne GPS using multiple monitor stations. Bulletin Geodesique, 1992, 66(8): 2-11
[52] Umar I.Bhatti, Washington Y.Ochieng, Shaojunfeng. Integrity of an integrated GPS/INS system in the presence of slowly growing errors. Part I: A critical review GPS Solutions, 2007, 11(8): 183-192
[53] Grejner Brzezinska. GPS error modeling and OTF ambiguity resolution for high-accuracy GPS/INS integrated system. Journal of Geodesy, 1998, 72(9): 626-638
[2]刘基余. GPS卫星导航定位原理与方法.北京:科学出版社, 2003
[3]秦永元,张洪钺,汪叔华.卡尔曼滤波与组合导航原理.西安:西北工业大学出版社, 1998
[4]彭祖赠,孙韫玉.模糊(Fuzzy)数学及其应用.武汉:武汉大学出版社, 2007
[5]张文修,吴伟志等.粗糙集理论与方法.第一版.北京:科学出版社, 2001
[6]张守信. GPS卫星测量定位理论与应用.长沙:国防科技大学出版社, 1996
[7]金凯德.数值分析.北京:机械工业出版社, 2005
[8]霍家道,郝燕玲.导航信号卡尔曼滤波定位解算方法研究.中国航海, 2004, 3(1): 44-48
[9] Eunwoo Choi, David A. Cicci. Analysis of GPS static positioning problems. Applied Mathematics and Computation 2003, 4(3): 37-51
[10]张云鹏,缪栋,杨小冈. GPS伪距导航定位解算新算法研究.电子科技, 2004, 12(01): 47-50
[11] Abel.J.S, Chaffee.J.W. Existence and Uniqueness of GPS Solutions. IEEE Transactions on Aerospace and Electronic System 1991, (11): 952-956
[12] Joho B, Lundberg. Alternative algorithms for the GPS static positioning solution. IEEE USA Applied Mathematics and Computation 2001, (10): 21-34
[13]陈小明,刘基余. GPS动态载波相位测量的波数在航解算.导航, 1996, 32(4): 30-38
[14]刘立龙.动态对动态GPS高精度定位理论及其应用研究: [博士学位论文].武汉:武汉大学, 2005
[15] Eunwoo Choi, etc. Analysis of GPS static positioning problems. Applied Mathematics and Computation, 2003,140(1): 37-25
[16]贾沛璋,吴连大.单频GPS周跳检测与估计算法.天文学报, 2001, 192-197
[17]刘立龙,刘基余,李广成.一种适合单频GPS动态求解模糊度的方法,飞行器测控学报, 2005, 12(1): 6-10
[18]刘根友.单频GPS接收机动态定位的相位与伪距联合算法及周跳检测.地壳形变与地震, 2001, 8(1): 120-122
[19]何海波.高精度GPS动态测量及质量控制: [博士学位论文].郑州:解放军信息工程大学, 2002
[20]王仁谦. GPS动态定位理论研究: [博士学位论文].长沙:中南大学, 2004
[21] P.J.G. Teunissen. The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation .Journal of Geodesy, 1995, (70): 65-82
[22] P.J.G.Teunissen. A New Method for Fast Carrier Phase Ambiguity Estimation. Proc. IEEE Position Location&Navigation Symp. Las Vegas, 1994, (4): 562-573
[23] P.J.G.Teunissen.一个新的GNSS模糊度估计类.武汉大学学报信息科学版, 2004, 29(9): 757-762
[24]刘立龙,刘基余等.一种GPS快速定位技术研究.宇航学报, 2005, 13(1): 39-42
[25] Bani, Allberta. Kinematic Systems in Geodesy and Surveying and Remote Sensing. International Association of Geodesy Symposia, 2005, 13(9): 299-308
[26] Joho B, Lundberg. Alternative algorithms for the GPS static positioning solution. IEEE USA Applied Mathematics and Computation, 2001, 41(3): 112-118
[27]王永生.一种消除GPS模糊度相关性的新算法.航空学报, 2002, 9(5): 32-36.
[28]赵健康,王银华.基于GPS相位法对舰船等大型载体定姿中的模糊数求解方法.宇航学报, 2001, 12(1): 43-47
[29] Han, S. and C. Rios. Improving the computational efficiency of the ambiguity function algorithm. Journal of Geodesy, 1996, 70(6): 330-341
[30]姬生月,欧吉坤等.一种适合于单频接收机快速模糊数求解的新方法.武汉测绘科技大学学报, 2000, 25(2): 102-104
[31]康荣雷,舒兰等.粗糙归整映射与整周模糊度解算.现代电子技术, 2008, 31(9): 138-140
[32]唐卫明. GPS载波相位平滑伪距精度分析与应用探讨.测绘信息与工程, 2005, 30(3): 37-39
[33] Mohamd A H, Schwarz K P. A simple and economical algorithm for GPS ambiguity resolution on the fly using whitening filters. Navigation, 1998, 45(3): 221-231
[34]常青,高晖,柳重堪. GPS定位算法研究.遥测遥控, 1998, 9(5): 6-11
[35]蔡艳辉,程鹏飞,李夕银.用卡尔曼滤波进行GPS动态定位,测绘通报, 2006, 18(3): 47-50
[36]黄丁发,熊永良等.全球定位系统(GPS)—理论与实践.成都:西南交通大学出版社, 2006
[37] Christian Tiberius. 0.99999999 confidence ambiguity resolution with GPS and Galileo. GPS Solutions, 2002, 6(5): 96-99
[38] Deng Qiang, Huang Shunji. Research on GPS Code Pseudorange Smoothing Technique by Carrier Observables. Journal of UESTC of China, 1996, 25(5): 112-118
[39]腾云龙,陈小平,唐应辉.提高GPS定位精度的改进卡尔曼滤波算法研究.现代电子技术, 2008, 31(3): 4-6
[40] Yu Guorong, Sheng Renjun. Cycle slip detection approach based on time-relative positioning theory. Journal of Southeast University (English Edition), 2005, 21(3): 363-368
[41] Liu Jiyu. A Real-time Solution for GPS Measured Distances without Cycle Slips, Survey Review(UK), 1993, 32(7): 31-38
[42] Eunwoo Choi, David A. Cicci. Analysis of GPS static positioning problems. Applied Mathematics and Computation, 2003, 22(5): 112-118
[43] Arnaud M, Flori A. Bias and precision of different sampling methods for GPS positions. Photogram metric Engineering and Remote Sensing, 1998, 64(6): 597-600
[44]张树京,齐立新.时间序列分析简明教程.北京:清华大学出版社, 2003
[45]范胜林,秦岭等. GPS姿态系统中周跳的检测及修复方法.数据采集与处理, 2002, 13(7): 22-23
[46] Gao Y, Li z. Cycle slip detection and ambiguity resolution algorithm for dual-frequency GPS data processing. Marine Geodesy, 1999, 22(4): 169-181
[47] Michaud S, Santeree R. Time-relative positioning with a single civil GPS receiver. GPS Solutions, 2001, 5(2): 71-77
[48] Collin F, Warnat R. Application of the wavelet transform for GPS cycle slip correction and comparison with Kalman filter. Manuscripta Geodetica, 1995, 20(3): 161-172
[49]王永超,黄智刚.时钟改进模型辅助RAIM算法研究.电子学报, 2001, 35(6): 1084-1088
[50] Kihara M. Study of a GPS satellite selection policy to improve positioning accuracy.Position Location and Navigation Symposium, IEEE April 1994, 10(8): 267-273
[51] M.E.Cannon, K.P.Schwarz, M.wei, D.Delikaraoglou. A consistency test of airborne GPS using multiple monitor stations. Bulletin Geodesique, 1992, 66(8): 2-11
[52] Umar I.Bhatti, Washington Y.Ochieng, Shaojunfeng. Integrity of an integrated GPS/INS system in the presence of slowly growing errors. Part I: A critical review GPS Solutions, 2007, 11(8): 183-192
[53] Grejner Brzezinska. GPS error modeling and OTF ambiguity resolution for high-accuracy GPS/INS integrated system. Journal of Geodesy, 1998, 72(9): 626-638