Optimizations For Equivalent Weight Function In Robust Estimation And Evaluation Of Its Robustness

In this paper,based on the spatial unconstrained adjustment of the GNSS network,some researches on the theory and application of the related variance estimation based on the variance expansion model are carried out.The main contents of the research are summarized as follows:1.The theory of unconstrained adjustment of the spatial GNSS network.adj-ustment and program implementation.The role of unconstrained adjustment is d-escribed.The mathematical model of unconstrained adjustment of the spatial G-NSS network and the accuracy evaluation of adjustment results are introduced.The programming model of the adjustment model is programmed using C++ programming language.The program realizes the reading and storage of the baseline file,the automatic writing of the unconstrained adjustment error equation of the GNSS network,and the adjustment and output of the adjustment.2.The model of the influence of the observation error on the adjustment correction is deduced.The theory of M-estimation and the principle of equivalence weight are expounded for the independent observation measurement.On this basis,the theory of robust M-estimation is introduced.Finally,the commonly used estimation of the tolerance is enumerated.The equivalence weight function model is used to compare and analyze the robustness of various equivalence weight models through an example.The experimental results show that the IGG scheme has better detection and resistance to gross errors than other robust schemes.3.This paper introduces the equivalence weighted correlation robust estimation model,and selective analysis and points out its shortcomings in the relevant observing process robustness estimation process.This paper expounds the model of relative robustness estimation based on variance expansion model.Aiming at the deficiencies in the equivalent weighted model based on equivalence weights,a new dependent observable-measurement robustness estimation model is constructed based on the variance expansion model.The solution is based on the problem of weight matrix asymmetry and other problems in the model of the equivalent weight estimation of the equivalent weight,and uses the robustness of the median to calculate the error of the unit weight in the iterative calculation,making the standardized residual calculation more robustly.4.Correlation Observed Robust Estimation Model Program Implementation.The C + + programming language is used to embed the robust estimation model of the relevant observables into the unconstrained adjustment program of the GNSS network.5.Through a measured GNSS network,by artificially adding two sets of gross errors of different signs and sizes,the model constructed in this paper and the least squares and RECO schemes are compared in four aspects that include the posterior unit weight variance,the difference of corrections between obser-vation with gross errors and correction of no gross errors,the error of adjustment value of coordinate and deviations of coordinate.The experimental results show that the model established in this paper can get more consistent adjustment results with the least-squares adjustment when the gross errors are not significant;when the gross errors are significant(with gross errors),the least squares are more affected by the gross errors.The adjustment result is seriously distorted.Both the RECO program and the models constructed in this paper can better identify and resist gross errors.