Research On GNSS-PPP Stochastic Model Considering Unmodeled Error Characteristics

With the rapid development of GNSS,the application of high-precision and highreliability satellite positioning technology has been more and more widely,and the construction of a reasonable stochastic model is helpful to improve the accuracy and reliability of satellite positioning.At present,most of the commonly used stochastic models are empirical models,and the unmodeled error characteristics are not well understood,which leads to the unreasonable stochastic models.To solve this problem,this paper firstly presents an inversion method of unmodeled errors based on precise point positioning,and analyzes its characteristics in depth.Then,a stochastic model based on equation residuals was constructed by mapping between unmodeled errors and equation residuals,which improved the positioning accuracy of PPP.Finally,the stochastic model is modified based on Kalman filter to ensure the reliability of PPP positioning.The main work and conclusions of this paper are as follows:(1)The positioning principle of GNSS-PPP is briefly introduced,as well as the model establishment and positioning solution method.This paper introduces the development overview of GNSS and the positioning principle,summarizes the error source and correction strategy in PPP positioning process,and gave the mathematical model and random model establishment method as well as the PPP positioning solution method.(2)The unmodeled error inversion method is presented,and the rationality of the height Angle stochastic model is analyzed based on the unmodeled error characteristics.Based on precise point positioning,a high precision unmodeled error inversion method is presented,and the variation of unmodeled error with altitude Angle of different satellites under the same epoch is analyzed.The experimental results showa result:For different satellites under the same epoch,it is not that the larger the satellite altitude Angle is,the smaller the unmodeled error will be,but that the height Angle weighting method may make the satellite observation value with large unmodeled error obtain a larger weight in the positioning calculation,which is inconsistent with the actual situation.Finally,we attempt based on the high Angle by epoch projections for unmodeled errors,experiments show that: with unmodeled error size change rule by troposphere model,latitude station and the ionosphere processing strategy,and the influence of such factors as different situations of unmodeled errors with the tendency of the altitude Angle is different also,based on the high Angle carries on the forecast.(3)Based on the mapping relationship between unmodeled errors and equation residuals,a stochastic model building method based on residuals is presented.In this paper,the mapping relationship between the unmodeled error and the residual error is given according to the residual theory,and the residual random model is constructed based on the satellite residual,and its positioning accuracy is analyzed in PPP.The experimental results show that compared with the height angle random model,the positioning accuracy of the residual model in the three-dimensional direction can be improved by more than 13.3%,indicating that the residual model can better reflect the weight of different satellites in positioning,and has strong adaptability and stability.(4)Taking into account the degree of freedom,a modified method of PPP stochastic model based on Kalman filter is given to ensure the reliability of positioning results.When the freedom is too low in the measurement,the confidence probability with the median error as the measurement index is difficult to reach the theoretical value.In this paper,the correction formula of the median error under the condition of low freedom is given and applied to the solution of satellite positioning,to modify the random model of Kalman filter.The experimental results show that the revised stochastic model not only ensures the accuracy of satellite positioning,but also increases the reliability of satellite positioning,which further improves the PPP positioning theory.