Weighted least squares regularization iteration solution and precision estimation for ill-posed multiplicative error model

Abstract

Aiming at the ill-posed problem of multiplicative error model, this paper introduces the Tikhonov regularization method to derive the weighted least squares regularization solution. Considering the complex nonlinear relationship between parameter estimations and the observations when using weighted least squares regularization method to solve the ill-posed multiplicative error model, the scaled unscented transformation (SUT) method is used to calculate the mean value and mean square error matrix of the nonlinear function by weighted without derivation for precision estimation of ill-posed multiplicative error model. The simulated and actual examples results show that the weighted least squares regularization iterative solution proposed in this paper can effectively weaken the ill-posed model, and the precision estimation method based on SUT method can obtain more reasonable precision information than the existing methods, and has strong applicability