| Recently,with the complete construction and development of global navigation satellite systems,multi-frequencies,multi-types,and multi-systems combined GNSS data processing has become a research hotspot and trend.The increase in the number of observational satellites improves the positioning precision.But in the meanwhile,the difference in the observations among different systems and even same system has become a new challenge for multi-systems combined data processing.The stochastic model describes the random statistical characteristics of observations,and then provides the weight between the observations with different precision in the observation model.The stochastic model also has an effect on the integer ambiguity resolution,which is an important step in high-precision GNSS positioning.Therefore,the stochastic model is a good starting point for studying the combined multi-GNSS data processing.In addition,relative positioning has high research value in applications,because it can obtain high positioning precision only using broadcast ephemeris without many external products.However,most of the stochastic models for the relative positioning of multi-systems combination are based on the empirical stochastic model of GPS,which is relatively simple and cannot adapt to all realistic applications.Hence,this paper focuses on the above problems and the main contents and results are as follows:(1)The function model and the stochastic model of loosely combined and overlapping frequencies tightly combined relative positioning are derived from originally undifferenced observation,and the detailed construction process of corresponding Kalman filter model is given in detail.On this basis,the research on the stochastic model of the GEO satellite in BDS single-system is carried out.We set up different weight reduction strategies for the GEO satellite,which were 4,25 and 100 times the variances of observations,respectively.In the experiment,a group of zero-baseline data and medium-baseline data(about 42km)were processed respectively under different weight reduction strategies,and the relative positioning precision and the integer ambiguity resolution success rate of BDS under different weight reduction strategies were compared and analyzed.The results show that appropriately reducing the weight of GEO satellite observations can improve the accuracy of relative positioning.In the experiment,the weight factor setting of 4 times the error variance can take into account positioning.The accuracy and ambiguity of the fixed rate.In summary,the weight of GEO satellite observations can significantly affect the precision of the BDS relative positioning.Appropriately reducing the weight of GEO satellite observations can improve the precision of relative positioning.In the experiment,the positioning precision and the ambiguity success rate can be improved simultaneously by setting 4 times the weight reduction factor.(2)Based on the method of LS-VCE,this paper studies the stochastic model of GPS-BDSGalileo loosely combined relative positioning.A method of using LS-VCE to estimate the unknown parameters assumed in the stochastic model to improve the stochastic model of multisystems relative positioning loose combination is proposed.Three different refined stochastic models,called RSM1,RSM2 and RSM3,are constructed by estimating the variance components of different systems,the variance components of different types of observations,and the variance component of each satellite,respectively.Zero-baseline and short-baseline data were used to compare the proposed three refined stochastic model processing strategies with the empirical elevation-dependent model(EDM)at mask angles of 20°,30°,40°,and 50°,respectively.The effectiveness of the refined stochastic model for the loosely combined relative positioning of multi-systems is verified.The experimental results show that,comparing with EDM,the three refined stochastic models have a positive effect on the precision of the multisystems relative positioning,and the improvement of the ambiguity success rate is not obvious.Among them,the RSM3,fitted by estimating the precision of each satellite,performs the best.Comparing with EDM,precision at 20°,30°,40°,50° elevation mask angles can be improved4.6%,7.6%,13.2%,73.0% for L1-B1-E1 frequency,and 1.1%,4.8%,16.3%,64.5% for L2-B2-E5 a frequency,respectively.(3)In this paper,the GPS-Galileo short-baseline overlapped frequency band tightly combined relative positioning model and method are studied.The random walk method is used to estimate the DISB parameters of different frequency bands of tight combination in real time,and the time domain characteristics of the DISB parameters are analyzed in detail based on different types of baseline data.By comparing and analyzing the series of estimated DISB parameters of three baseline data set,namely,CUT0-CUT2,CUT0-CUT3 and CUT0-CUTA,in consecutive seven days.The results show that the DISB parameters of the carrier phase and the code observations are highly stable in the time domain.For the baseline data observed with identical receivers,the DISB in different types of baselines are basically at the same level.For baseline data observed with different receivers,the DISB parameters will converge gradually and are relatively stable.Therefore,the DISB parameters can be pre-corrected to improve the model strength of the multi-system tightly combined relative positioning.(4)In this paper,the stochastic model of GPS-Galileo tight combination system is studied,and an improved method of stochastic model is proposed based on the method of LS-VCE.Although this method increases the computation amount in the process of positioning solution to a certain extent,it can still ensure that the weight ratio of the observations of different systems can be estimated in real time,making the weight distribution between the observations of the combined system more reasonable and improving reliability of the solution results of the combined system.In the experiment,a total of six baseline data sets,two data sets of zerobaseline,ultrashort-baseline and short-baseline respectively,were used to analyze and verify the method.The experimental results show that,comparing with the empirical elevationdependent model,the refined stochastic model has a positive effect on the precision of the tightly combined relative positioning.The positioning precision on L1-E1 and L5-E5 a frequencies is improved by up to 10%.Meanwhile,the refined stochastic model can significantly improve the ratio,hypothesis test items in ambiguity resolution,and enhance the reliability of ambiguity resolution of the multi-system tightly combined relative positioning.This paper has 54 figures,26 tables and 122 references. |
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