The Research On Algorithm Of Total Least Squares In Combined Point Positioning Of GNSS

In GNSS combined single-point positioning,classical LS is commonly used as a model for data adjustment;However,the positioning linearization equation coefficients include observation errors,and the influence of the matrix error of the classical LS coefficients on the final positioning results cannot be taken into account.Therefore,this thesis mainly focuses on the TLS and considers optimizing the GNSS combined single-point positioning mathematical model under the condition of taking into account the error of the coefficient matrix,aiming at improving the robustness and reliability of the combined orbit determination algorithm.The main research contents and conclusions of this thesis are as follows:1.Based on the TLS,based on matrix iterative decomposition,the GNSS combined single point positioning total least squares function model is studied and established;based on the detection of gross errors and abnormal observations in GNSS combined positioning,a comprehensive increase is proposed.The method of reconstructing observations using the minimum singular value decomposition of broad matrix and residual statistical analysis;at the same time,the main scheme of the combination of the time system and the coordinate system unified theory of GNSS multi-systems and the GNSS satellite coordinate calculation method was designed.2.In this thesis,the basic idea of TLS is theoretically analyzed using the principle of singular value decomposition.For the LS-TLS problem,the matrix QR decomposition principle and reduced decomposition method are used to derive the hybrid least squares solution method.This paper analyzes the difference between TLS and ordinary LS,and proves that classical LS is a special form of TLS.The TLS is an extension of classical LS.3.Finally,based on the theories and methods proposed in this thesis,the GNSS combined LS/TLS standard single-point positioning program based on VC++ is programmed and verified through a large number of experiments.Finally,this thesis compares the positioning accuracy of GPS and BDS in Hong Kong and Inner Mongolia,and the advantages and disadvantages of LS and TLS algorithms.Through experiments,this paper concludes that the TLS is better than the LS and multi-system positioning accuracy when the data outliers are high,and the stability is better than the single system;BDS is slightly better than Inner Mongolia in the current stage.