基于SVD和Cholesky求逆方法的精密单点定位研究

Research on precise point positioning based on SVD and Cholesky inversion method

针对精密单点定位(Precise Point Positioning,PPP)数据处理过程中矩阵求逆方法对PPP算法的定位效果进行研究。介绍矩阵广义逆在线性方程解中的作用,对奇异值分解(Singular Value Decomposition,SVD)求逆法和Cholesky分解求逆法进行论述,进一步描述PPP算法原理、观测方程建立和参数估计过程。采用国际全球导航卫星系统(Global Navigation Satellite System,GNSS)监测评估系统(International GNSS Monitoring and Assessment System,iGMAS)观测站北斗数据,验证SVD分解法和Cholesky分解法应用于动态PPP参数估计的效果。实验结果表明,基于SVD分解法的动态PPP每个历元数据处理所需时间均值为291 ms,北方向、东方向、垂向三维方向定位误差分别为5.95 cm、8.04 cm、20.31 cm。使用Cholesky分解法的动态PPP每个历元数据处理所需时间为189 ms,三维方向定位误差分别为2.65 cm、4.05 cm、8.04 cm。相比于SVD分解法,Cholesky分解法更适用于PPP参数估计中的法方程求逆。

In the process of precise point positioning(PPP),the accuracy and efficiency of matrix inversion method is carried out a study on the positioning effect of the PPP algorithm.Firstly,the properties of matrix generalized inversion and focuses on two different matrix decomposition inversion methods are introduced,including SVD decomposition and Cholesky decomposition.Then,the principle of PPP method is described in detail,with emphasis on the process of establishing observation equation and parameter estimation.The International GNSS Monitoring and Assessment System(iGMAS)observation station is used to evaluate the performances of SVD decomposition method and Cholesky decomposition method.The experimental results show that the average time required for data processing of each epoch of kinematic PPP based on SVD decomposition method is 291ms,and the three-dimensional positioning errors of north,east and up directions are 5.95 cm,8.04cm and 20.31 cm,respectively.The data processing time of kinematic PPP using Cholesky decomposition method is 189 ms,and the three-dimensional positioning errors are 2.65 cm,4.05 cm and 8.04 cm respectively.Compared with SVD decomposition method,Cholesky decomposition method is more suitable for the inversion of normal equation in PPP parameter estimation.