Research On Parameter Estimation Theory And Numerical Realization Problem And Its Application In GNSS PPP Algorithm

The Global Navigation Satellite System(GNSS)is a high-availability,high-precision,all-weather positioning method.In addition to meeting the positioning needs of geodesy,automatic driving and other,it is also of great significance for meteorological monitoring and earth remote sensing.Since GNSS was originally designed as a positioning system for distance resection,many different GNSS application implementations rely on parameter estimation based on GNSS observation equations.Therefore,strict and reliable GNSS parameter estimation methods are the cornerstone of GNSS applications.In recent years,the development of multi-system GNSS and real-time positioning has put forward new requirements for the reliability,strictness and numerical efficiency of GNSS algorithms.For example,the positioning of offshore buoys requires higher algorithm stability,real-time performance,and numerical efficiency than traditional ground stations.In this paper,with GNSS Precise Point Positioning(PPP)as the background,the equivalence and ill-conditioning problem of the linear equations parameter estimation method are discussed from the theoretical and implementation aspects.Specifically,the work of this article includes:(1)Derivation and discussion of the equivalence of the three parameter estimators of indirect adjustment,Kalman filtering and information filtering,and derivation and discussion of the equivalent conditions of the block-wise least squares and the parameter elimination based on observation combination;(2)Taking the three PPP models of ionospheric free(IF)model,UofC model and uncombined(UC)model as examples,the equivalence/inequality between them is discussed from the theoretical and practical perspectives.The results show that UofC model and UC model are equivalent.Although the IF model is not equivalent to them,the specific performance difference is negligible;(3)The cause of matrix ill-conditioning and its relationship with eigenvalue decomposition are discussed theoretically.The ill-conditioning problem of Kalman filter when handling missing predicted value and the information filter when handling conditional constraint are discussed.Conditional information filtering is also proposed for these ill-conditioning problems;(4)Taking the receiver clock jump problem as an example,the specific phenomena of Kalman filter and information filter affected by ill-conditioning are discussed through practical analysis.The results show that Kalman filter is difficult to solve parameters stably due to ill-conditioning,and information filter can handle such problems stably;(5)Based on the aforementioned achievements,a real-time PPP positioning terminal is designed.The value of its real-time high-precision positioning capability to marine buoys and other application scenarios are demonstrated through pseudo-dynamic positioning.