顾及历元间坐标差信息的GPS模糊度快速固定改进方法
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摘要
单频全球定位系统模糊度在航解算过程中存在法方程病态的问题,利用历元间坐标差信息可以在一定程度上削弱法方程的病态性,提高模糊度浮点解的精度和模糊度收敛速度。为进一步提高历元间坐标差法固定模糊度的效率,提出了一种改进的历元间坐标差方法,该方法对历元间坐标差虚拟观测误差方程进行了重构,并给出了新的虚拟观测值方差阵。实验结果表明,新方法较之以往的历元间坐标差方法具有更优的稳定性和效率。
Single-frequency GPS ambiguity resolution on-the-fly has the problem that normal equation is ill-posed. Using epoch-differenced coordinate information between neighboring epochs can mitigate the ill-condition problem to some extent, as a result, the accuracy of the float ambiguity solution will be improved and the convergence time of ambiguity will be shortened. In order to further improve the ambiguity fixing effciency of epoch-differenced method, the epoch-differenced coordinate pseudo-observation error equation and its new variance matrix is reconstructed. The experimental results show that, compared with the previous algorithm with epoch-differenced coordinate information, the new method has higher stability and efficiency.
Single-frequency GPS ambiguity resolution on-the-fly has the problem that normal equation is ill-posed. Using epoch-differenced coordinate information between neighboring epochs can mitigate the ill-condition problem to some extent, as a result, the accuracy of the float ambiguity solution will be improved and the convergence time of ambiguity will be shortened. In order to further improve the ambiguity fixing effciency of epoch-differenced method, the epoch-differenced coordinate pseudo-observation error equation and its new variance matrix is reconstructed. The experimental results show that, compared with the previous algorithm with epoch-differenced coordinate information, the new method has higher stability and efficiency.
引文
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[5] Cui Jianyong, Chen Mingjian. The Virtual Observation Equation in GPS Dynamic Positioning[J]. Engineering of Surveying and Mapping,2013,22(4):9-12(崔建勇,陈明剑. GPS动态定位中的虚拟观测方程研究[J]. 测绘工程,2013,22(4):9-12)
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[7] Chen Yuanjun,Yi Zhonghai,Kuang Cuilin,et al. Fast GPS Ambiguity Resolution with Variance Component Estimation Based on Virtual Observation[J]. Joural of Geodesy and Geodynamics, 2016,36(2):158-161 (陈源军,易重海,匡翠林,等. 基于虚拟观测值后验方差估计的整周模糊度快速固定方法[J]. 大地测量与地球动力学, 2016,36(2):158-161)
[8] Xu Guochang. GPS Theory, Algorithms and Applications [M]. 2nd ed. Beijing: Tsinghua University Press, 2011: 123-126 (许国昌. GPS理论、算法与应用[M]. 2版.北京:清华大学出版社,2011:123-126)
[9] Yuan Hong, Wan Weixing, Ning Baiqi,et al. A New Cycle Slip Detection and Correction Method Using Triple Differences Solution[J]. Acta Geodaetica et Cartographica Sinica, 1998, 27(3):189-194(袁洪,万卫星,宁百齐,等. 基于三差解检测与修复GPS载波相位周跳新方法[J]. 测绘学报,1998, 27(3):189-194)
[10] Chen Yuanjun,Yi Zhonghai. A New Method to Detect and Repair Cycle-Slip Based on a Double-Diffe- renced Model for Receivers and Epochs[J]. Geomatics and Information Science of Wuhan University, 2017,42(6):845-850 (陈源军,易重海. 基于站际历元二次差模型探测与修复周跳的新方法[J]. 武汉大学学报·信息科学版,2017,42(6):845-850)
[11] Dai Wujiao,Feng Guangcai,Zhu Jianjun. A Method for Selecting Ridge Parameter Based on Helmert Variance Components Estimation[J]. Journal of Geodesy and Geodynamics, 2006,26(4):30-33(戴吾蛟,冯光财,朱建军. 一种基于Helmert方差分量估计的岭参数确定方法[J]. 大地测量与地球动力学,2006,26(4):30-33)
[12] Teunissen P J G. The Least-Square Ambiguity Decorrelation Adjustment: A Method for Fast GPS Ambiguity Estimation[J]. Journal of Geodesy, 1995,70(1): 65-82
[13] Verhagen S, Teunissen P J G. The Ratio Test for Future GNSS Ambiguity Resolution[J]. GPS Solutions, 2013, 17(4): 535-548
[14] He Haibo.Precise Kinematic GPS Surveying and Quality Control[D].Zhengzhou:Information Engineering University,2002 (何海波. 高精度GPS动态测量及质量控制[D].郑州:信息工程大学,2002)
[15] Liu Jingnan, Deng Chenlong, Tang Weiming. Review of GNSS Ambiguity Validation Theory[J]. Geomatics and Information Science of Wuhan University,2014, 39(9):1 009-1 016 (刘经南, 邓辰龙, 唐卫明. GNSS 整周模糊度确认理论方法研究进展[J]. 武汉大学学报·信息科学版, 2014,39(9):1 009-1 016)
[2] Liu Genyou,Ou Jikun. Kinematic Positioning Algorithm with Coordinate Function Constraint[J]. Geomatics and Information Science of Wuhan University, 2004,29(5):389-393 (刘根友,欧吉坤. 具有坐标函数约束的动态定位算法[J]. 武汉大学学报·信息科学版, 2004,29(5):389-393)
[3] Luo Xiaowen, Ou Jikun. A New Approach for Fast Integer Ambiguity Resolution Suitable for Medium-long Baseline in GPS Network RTK[J]. Geomatics and Information Science of Wuhan University,2007,32(2):156-159( 罗孝文,欧吉坤. 中长基线GPS网络RTK模糊度快速解算的一种新方法[J]. 武汉大学学报·信息科学版,2007, 32(2):156-159)
[4] Ma Yang, Ou Jikun,Yuan Yunbin,et al. Solving Equality Constraint Inversion with Ill-Posed Constraint Matrix Using United Method[J]. Geomatics and Information Science of Wuhan University, 2011,36(7):816-819 (马洋,欧吉坤,袁运斌,等. 采用联合平差法处理附有病态等式约束的反演问题[J]. 武汉大学学报·信息科学版,2011,36(7):816-819)
[5] Cui Jianyong, Chen Mingjian. The Virtual Observation Equation in GPS Dynamic Positioning[J]. Engineering of Surveying and Mapping,2013,22(4):9-12(崔建勇,陈明剑. GPS动态定位中的虚拟观测方程研究[J]. 测绘工程,2013,22(4):9-12)
[6] Chen Yuanjun,Yi Zhonghai,Kuang Cuilin,et al. Accelerating Ambiguity Fixing in Kinematic Positioning Using Epoch-Differenced Coordinate Information[J].Geomatics and Information Science of Wuhan University, 2016,41(7):989-994 (陈源军,易重海,匡翠林,等. 利用历元间坐标差信息加快动态定位中模糊度固定[J]. 武汉大学学报·信息科学版,2016,41(7):989-994)
[7] Chen Yuanjun,Yi Zhonghai,Kuang Cuilin,et al. Fast GPS Ambiguity Resolution with Variance Component Estimation Based on Virtual Observation[J]. Joural of Geodesy and Geodynamics, 2016,36(2):158-161 (陈源军,易重海,匡翠林,等. 基于虚拟观测值后验方差估计的整周模糊度快速固定方法[J]. 大地测量与地球动力学, 2016,36(2):158-161)
[8] Xu Guochang. GPS Theory, Algorithms and Applications [M]. 2nd ed. Beijing: Tsinghua University Press, 2011: 123-126 (许国昌. GPS理论、算法与应用[M]. 2版.北京:清华大学出版社,2011:123-126)
[9] Yuan Hong, Wan Weixing, Ning Baiqi,et al. A New Cycle Slip Detection and Correction Method Using Triple Differences Solution[J]. Acta Geodaetica et Cartographica Sinica, 1998, 27(3):189-194(袁洪,万卫星,宁百齐,等. 基于三差解检测与修复GPS载波相位周跳新方法[J]. 测绘学报,1998, 27(3):189-194)
[10] Chen Yuanjun,Yi Zhonghai. A New Method to Detect and Repair Cycle-Slip Based on a Double-Diffe- renced Model for Receivers and Epochs[J]. Geomatics and Information Science of Wuhan University, 2017,42(6):845-850 (陈源军,易重海. 基于站际历元二次差模型探测与修复周跳的新方法[J]. 武汉大学学报·信息科学版,2017,42(6):845-850)
[11] Dai Wujiao,Feng Guangcai,Zhu Jianjun. A Method for Selecting Ridge Parameter Based on Helmert Variance Components Estimation[J]. Journal of Geodesy and Geodynamics, 2006,26(4):30-33(戴吾蛟,冯光财,朱建军. 一种基于Helmert方差分量估计的岭参数确定方法[J]. 大地测量与地球动力学,2006,26(4):30-33)
[12] Teunissen P J G. The Least-Square Ambiguity Decorrelation Adjustment: A Method for Fast GPS Ambiguity Estimation[J]. Journal of Geodesy, 1995,70(1): 65-82
[13] Verhagen S, Teunissen P J G. The Ratio Test for Future GNSS Ambiguity Resolution[J]. GPS Solutions, 2013, 17(4): 535-548
[14] He Haibo.Precise Kinematic GPS Surveying and Quality Control[D].Zhengzhou:Information Engineering University,2002 (何海波. 高精度GPS动态测量及质量控制[D].郑州:信息工程大学,2002)
[15] Liu Jingnan, Deng Chenlong, Tang Weiming. Review of GNSS Ambiguity Validation Theory[J]. Geomatics and Information Science of Wuhan University,2014, 39(9):1 009-1 016 (刘经南, 邓辰龙, 唐卫明. GNSS 整周模糊度确认理论方法研究进展[J]. 武汉大学学报·信息科学版, 2014,39(9):1 009-1 016)