Regularized Sparse Modeling Method And Its Geodetic Application

The inversion of geodynamic parameters and the establishment of spatio-temporal distribution models using the spatio-temporal observation data obtained by geodetic technology have always been a hot topic in the field of geodetic survey.As the most effective means of data analysis,statistical modeling plays an important role in model construction and parameter calculation.The difficulties include the form selection of the function model and the determination of the number of independent variables.How to accurately select the model variables and stably solve the unknown parameters is of great significance.In view of this,this paper focuses on the existing regularization sparse modeling theory and methods,integrates the commonly used geodetic modeling methods,and expands the application of sparse modeling in the prediction of earth rotation parameters and the velocity field of crustal movement.The main contents include the following points :(1)The proposal and development of regularized sparse modeling theory are studied.The regularization theory is derived from the least squares criterion,and the development process of L1 norm regularization sparse modeling theory and the definition and properties of various improved methods are summarized.The parameter solving formulas of the mainstream regularization sparse modeling estimation criteria are derived.The principles of various algorithms are analyzed and the detailed calculation steps are given.The formal unification and characteristics of the model estimation criteria are summarized,and CVIC index is proposed for the shortcomings of CV verification index.The advantages,disadvantages and applicability of various methods are analyzed by simulation examples.(2)The common modeling methods of geodesy are integrated.It mainly includes time series analysis models such as ARMA model,deterministic analysis model and ARIMA model,spatial interpolation fitting methods such as polyhedral function fitting,spherical harmonic function,Kriging interpolation and inverse distance weighting,and widely applicable extreme learning machine model.Based on the above method,the model construction and parameter solution process of earth rotation parameters(ERP)and velocity field are given in this paper,and the sparse modeling method is introduced into the model criterion function solution.(3)The application of sparse modeling for ERP prediction is studied.This paper expounds the development of ERP measurement method and data source,analyzes the composition of ERP cycle items and preprocesses the original data.Aiming at the shortcomings of AR model order criterion,the sparse modeling method is introduced into AR model construction,and the three component parameters of ERP are predicted and analyzed.The results show that the sparse modeling method has better model parameter selection effect than the order criterion,and the constructed model has higher prediction performance.(4)Application research on sparse modeling of velocity field.The modeling method of station time series is analyzed,and the velocity data source of land network station is extracted.The Euler vector method is used to establish the regional velocity field model in China,and the results are compared with the existing literature.Based on the sparse modeling method,the problem of node selection of multi-faceted function fitting method and order item selection of spherical harmonic function model is solved.The experimental results show that the sparse modeling method reduces the model redundancy and enhances the generalization ability of the model,and has better velocity field modeling effect.The velocity field model is established by using extreme learning machine,and the relationship between parameter setting and model accuracy is analyzed.This paper has 48 figures,23 tables,104 references.