Research On Unscented Transformation For Nonlinear Adjustment Accuracy Evaluation

With the rapid development of geodetic observation technology,the nonlinear adjustment model is becoming more complex and the data source is becoming more abundant,which puts forward higher requirements for the nonlinear adjustment method and accuracy.The existing researches focus on the improvement of parameter estimation methods and neglect the analysis of the accuracy of parameter estimation.In recent years,some researches have pointed out that compared with the traditional linearization and Taylor expansion methods to approximate nonlinear functions,the study of nonlinear functions by approximate nonlinear function probability density can effectively avoid complex derivation operation and obtain high precision results,but there are still some problems need to be further developed.Based on Unscented Transformation(UT),this paper studies the selection of parameters and the approximation ability of various sampling strategies under UT framework,and further applies the UT to various practical geodetic problems,aiming at obtaining more accurate parameter estimation and accuracy information,and complements the accuracy evaluation theory of nonlinear adjustment.The specific research of this thesis is as follows:1)The selection of parameters of various sampling strategies in the framework of UT is researched.In this thesis the particle swarm optimization(PSO)algorithm is introduced into the UT,and the selection of parameters of several commonly used sampling strategies is analyzed from a numerical perspective,and a method for determining the sampling parameters is given.The higher-order term information ignored by the recommend parameters of the UT is further considered,and the approximation ability of the UT is tapped and improved by selecting proper parameters.For the first time,the Minimal Skew Simplex(MSS)Sampling and the Scaled Minimal Skew Simplex(SMSS)Sampling were applied to nonlinear accuracy evaluation.Considering the influence of non-normally distributed data on non-linear error propagation in geodetic survey,this paper analyzes and discusses the parameters of unscented transformation through the multivariate equations and the actual geodetic problem respectively for normal and non-normally distributed data.The ability of selection and approximation is verified.Experiments show that the method in this thesis can effectively determine the UT parameters,improve the approximation ability of the unscented transformation.2)The influence of deviation correction on the estimation of nonlinear adjustment parameters is studied In this thesis,the SUT(the scaled Unscented Transformation)method is applied to the data processing of biased estimation,Partial errors-in-variables(Partial EIV)model,in geodesy.Taking the total least square method as an example,the relationship between observation value error and deviation of parameter estimation in line fitting and coordinate transformation is studied,and the influence of unequal precision of observation components on parameter estimates deviation of conventional TLS method is considered.3)The SUT method for variance component estimation of Partial EIV model is studied.SUT sampling method is applied to the minimum norm quadratic unbiased estimation of Partial EIV model in this thesis.Using the variance component estimation modified stochastic model then use it as a priori information to obtain the weighted mean and second order precision information by SUT sampling method.Considering the deviation of the nonlinear model,the deviation correction is carried out,and the second order precision information is calculated by SUT method.Experiments shows that combing SUT method and variance component estimation to deal with Partial EIV model can effectively avoid complicated derivation operation and get a more accurate parameter value and reasonable second-order accuracy information.The accuracy evaluation theory of variance component estimation of Partial EIV model is improved.4)The SUT method for nonlinear fault parameter inversion and its accuracy evaluation is studied.Considering that the sampling method of Monte Carlo method has certain randomness and the inversion results of nonlinear optimization algorithm are not completely stable each time,which may affect the precision of parameters.The Scaled Unscented Transformation(SUT)method based on deterministic sampling strategy is introduced to estimate the precision of fault parameters.Firstly,the SUT method is used to estimate the precision of the curve fitting parameters obtained by Particle Swarm Optimization algorithm and compared with the results of least squares method and Monte Carlo method to verify the effectiveness of the proposed method.Considering the inevitable error in the observed data,we preprocess the simulated GPS data to obtain the approximate mean of observations,then contrast and analyze the inversion results and precision information obtained by SUT method and Monte Carlo method based on hybrid PSO/Simplex algorithm(MPSO).The influence of the “adjusted” observations,positions of the observation points and the level of noise added to deformation observations are considered besides.Finally,the methods of this paper are applied to the Lushan(China)earthquake.The experimental results show that both SUT method and Monte Carlo method can obtain better parameter estimates with “adjusted”observations;SUT method can obtain accurate precision information of fault parameters;Monte Carlo method can only judge mean square errors of parameters from the order of magnitude and the correlations between parameters are not accurate;When the threedimensional deformation data can effectively constrain the surface deformation field,the influence of the positions of the observation points on the fault parameters estimates is small;When the noise added to the observations increases,the fitting effect of the fault parameters estimates become worse and the accuracy of fault parameters estimates decreases.