Research On The Sterling Interpolation For Nonlinear Adjustment Precision Estimation And Its Applications

In the field of geodetic data processing,the precision estimation methods of nonlinear model mainly include method that approximate expression of function and method that approximate the probability density distribution of function.The approximate expression of function method requires complex derivative operations.The approximate the probability density distribution of function method is derived-free and has less research.How to use the derived-free precision estimation method to develop a non-linear adjustment precision estimation theory is a subject worthy of study.The derived-free Sterling interpolation method is introduced in this paper to conduct theoretical research on precision estimation of nonlinear adjustment.And the method is used to obtain precision information parameter with higher accuracy and reliability.The detail researches are as follows:The accuracy of the Sterling interpolation for nonlinear model error propagation is researched.The mean of any nonlinear function calculated by the Sterling interpolation method that can be achieved second-order precision is proposed by formula deduction.The optimal value of step factor h is(?),which is researched from the perspective of formula deduction when using the Sterling interpolation method to calculate the variance or covariance matrix of nonlinear functions.The Sterling interpolation method is applied in a 2D polynomial calculation,a forward intersection and a positive computation of Gaussian projection coordinates.The case studies in this paper indicate the Sterling interpolation method can obtain the accuracy information consistent with the existing methods,while the Sterling interpolation method has simpler operation and higher computing efficiency.The advantages of the Sterling interpolation method for precision estimation of complex nonlinear adjustment model are verified.A new method for parameter estimation in inequality constrained PEIV(Partial errors in variables)model and its Sterling interpolation method for precision estimation are researched.A new method to determine the parameter in inequality constrained PEIV model is proposed.Under the TLS(Total least square)rule,the inequality constrained PEIV model is converted to standard optimization problems.The SQP(Sequential quadratic programming)with Quasi-Newton correction is used to solve the problem.Considering that the PEIV model with inequality constraints is a class of nonlinear models,the Sterling interpolation method is used to evaluate the precision of parameter estimation.Simulation results show that this method can reduce iterations and increase convergence rate,and the parameter estimates calculated by the Sterling interpolation method are more accurate than the TLS method.The Sterling interpolation method for precision estimation of multiplicative error model is studied.The parameter estimates solved by WLS(Weighted least squares)are nonlinear function of observations,and the weights of observations are nonlinear function of the parameter estimates.The iterative process makes the parameters and the corrections of each step are random,and the relationship between parameter estimates and observations in iterative process of WLS are regarded as a nonlinear nested functions.The Sterling interpolation method is used to calculate the mean of parameter estimates and the mean of the corrections.Simulation experiments shows that compared with the existing methods,the method in this paper can obtain parameter estimates with smaller second norms and higher accuracy.The Sterling interpolation method is applied to the precision estimation of nonlinear inversion about seismic source geometric parameters.The MPSO(multiple-peaks particle swarm optimization)algorithm is used to invert the source geometry parameters.The complex nonlinear inversion process is regarded as a nonlinear function,and the Sterling interpolation method is introduced to estimate the accuracy of nonlinear functions.By constructing the statistics of the hypothesis test,the rationality of the used Okada model and the obtained geometric parameters is judged.A simulation experiment shows that the accuracy estimation method designed in this paper can obtain the square roots of the variance of the source geometry parameters.The results illustrate that changing the number of GPS observations does not affect the square roots of the variance of the seven source geometry parameters.When the number of GPS observations is constant,the square roots of the variance of the source geometry parameters increase with an increase in the level of noise in the GPS observations.Finally,the proposed accuracy estimation method is applied to the Lushan earthquake and the L'Aquila earthquake,and the applicability and feasibility of the proposed method are been verified.This novel method provides a new approach for the estimating the accuracy of the nonlinear inversion of earthquake source geometry parameters.