Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints  

作　　者：Leyang Wang Tao Chen 

机构地区：[1]Faculty of Geomatics,East China University of Technology,330013,Nanchang,China

出　　处：《Geodesy and Geodynamics》2021年第5期336-346,共11页大地测量与地球动力学（英文版）

基　　金：supported by the National Natural Science Foundation of China,Grant Nos.42174011,41874001 and 41664001;Innovation Found Designated for Graduate Students of ECUT,Grant No.DHYC-202020。

摘　　要：The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

关 键 词：Ill-posed problem Mixed additive and multiplicative random error model Equality constraints Weighted least squares Ridge estimation method U-curve method 

分 类 号：P207[天文地球—测绘科学与技术]