Solution for ill-posed EIV model regularization attending to its decreasing regularization characteristic

Abstract

Abstract The errors-in-variables (EIV) model is used for data processing in the field of geodesy. However, the EIV model may be ill-posed. By analyzing the decreasing regularization (D-regularization) characteristic of solutions for EIV models, algorithms using traditional methods such as singular value decomposition or the Tikhonov function can directly determine the irrationality of a model. When an EIV model is ill-posed, solutions in which the observation errors in the coefficient matrix are simulated by variables make the ill-posed nature of the model more serious. This is because the simulated observation errors are subtracted from the coefficient matrix in subsequent computations, which reduces the singular value of the normal matrix. This point is verified using an example. To account for the D-regularization of solutions in EIV models, a modified algorithm is derived by classifying the models into two categories, and the regularization parameters are iteratively revised based on the mean squared error. Finally, some conclusions are drawn from two separate examples.