Research On Bootstrap Resampling For Nonlinear Adjustment Precision Estimation

In the field of modern geodetic data processing,the precision estimation methods of nonlinear adjustment mainly include that approximate function method and approximate the nonlinear function probability density distribution method.The approximate function method obtains the variance matrix of parameter estimated values based on the Taylor series expansion principle,so that it needs to undergo the complex partial derivative operation.The approximate nonlinear function probability density distribution method replaces the derivative calculation via resampling the original observation data,but there are still some problems.How to develop and improve the precision estimation theory of nonlinear adjustment by using the derived-free method is a subject worthy of study.Based on the Bootstrap resampling theory,this thesis researches various resampling strategies under the Bootstrap framework,which aims to obtain more accurate parameter estimated values and more reliable precision information.The detail researches are as follows:1)The Bootstrap precision estimation method based on independent identically distributed(IID)framework is researched.In order to make the parameter estimated values and the precision information more accurate,this thesis first introduces the IID-Bootstrap resampling method into the linear model,and verified the feasibility and effectiveness of the Bootstrap method through experiments.Meanwhile,this paper researches the influences of correlation of Bootstrap samples on the precision estimation results.Next,the IID-Bootstrap resampling method is extended to the theory of nonlinear adjustment precision estimation.By resampling the original observation sample or the residuals vector of the dependent variable to obtain Bootstrap samples and construct the sampling distribution,the Bootstrap method based on resampling observations and the Bootstrap method based on resampling residuals are researched.And further,the taking value of the Bootstrap resampling times is also researched.Finally,the two resampling methods are applied to the nonlinear regression model.The results show that the IID-Bootstrap resampling method can obtain more accurate statistical inference results than the existing methods,which verifies the reliability and advantages of the methods proposed in this paper.2)The weighted resampling improved IID-Bootstrap method for nonlinear adjustment precision estimation is researched.In order to make full use of the prior information and data properties of the population contained in the sample,so as to further improve the quality of parameter estimated values and precision information.Aiming at the resampling process of the IID-Bootstrap method is equal probability resampling of model stochastic variable.By normalizing the weights prior information of the observation sample and obtaining the empirical distribution function of random variables,the equal probability resampling of the IID-Bootstrap method is transformed into a weighted resampling strategy.And according to the new resampling strategy,the weighted resampling modified Bootstrap method based on sampling observations and the weighted resampling modified Bootstrap method based on sampling residuals are presented.In addition,the complete algorithms for solving the problem of nonlinear adjustment precision estimation are given,respectively.The weighted resampling improved IID-Bootstrap method is applied to adjustment model of triangulation network and the volcanic deformation Mogi model.The results of experiments show that the weighted sampling improved IID-Bootstrap method based on the resampling observations and the weighted sampling improved IID-Bootstrap method based on resampling residuals can obtain more accurate precision information than implementing the IID-Bootstrap resampling directly.The more reasonable results verify the effectiveness and reliability of the improved method in this paper,which provide a new sampling insight for further research on the nonlinear adjustment precision estimation.3)The Sieve-Block Bootstrap sampling method for precision estimation of the time series AR(Auto-Regressive)model considering random errors of design matrix is researched.Since the traditional least square method cannot take into account the random errors of design matrix when solving the time series AR model.In addition,it is difficult for the existing iterative method of AR model to use the propagation of variance and covariance to give the accurate precision estimation formula.In response to the above problems,this thesis introduces the Block Bootstrap resampling method into the precision estimation research of the AR model,and on the basis of it,the principle of the Sieve Bootstrap is introduced.This paper defines the Sieve-Block Bootstrap sampling method for precision estimation of the AR model considering random errors of design matrix.According to the different blocking criteria and sampling strategies,this paper gives four complete resampling procedures.The simulation experiment and the BDS(BeiDou Navigation Satellite System)precise satellite clock bias real experiment research and analysis show that,the Sieve-Block Bootstrap resampling method can obtain more reliable autoregressive coefficient estimated values and standard deviations than the least square method and the classical AR model iterative method,and it has stronger applicability.The method proposed in this thesis has certain reference significance for research how to improve the quality of autoregressive coefficients and how to improve the predictive ability of time series AR models.4)The Bootstrap method for inversion and precision estimation of earthquake source parameters is researched.There is a complex and multi-dimensional nonlinear relationship between the surface deformations and the earthquake source parameters in the theories of source parameters inversion.The traditional precision estimation methods based on the Taylor series expansion may inapplicable in the earthquake source parameters case.This paper introduces the Bootstrap resampling method into the nonlinear inversion and precision estimation of earthquake source parameters.The Bootstrap samples are obtained by resampling the GPS(Global Positioning System)surface deformation measurement data,and the Genetic Algorithm(GA)is applied to search the optimal source parameters.The calculation procedures of the Bootstrap method for precision estimation of the source parameters are designed.Applying the algorithm proposed in this paper in six simulated earthquakes,the Amatrice earthquake and the Visso earthquake experiments,and comparing with the Jackknife method and the Monte Carlo method via inversing the earthquake source parameters,obtaining the confidence intervals,and calculating the standard error.The experimental results show that,the precision estimation method proposed in this paper can obtain more reliable confidence intervals and more accurate precision information of earthquake source parameters than the Jackknife method.Those which verified the reliability and effectiveness of the Bootstrap method for evaluating the precision of source parameters.