A New Regularized Solution to Ill-Posed Problem in Coordinate Transformation

Abstract

Coordinates transformation is generally required in GPS applications. If the transformation parameters are solved with the known coordinates in a small area using the Bursa model, the precision of transformed coordinates is generally very poor. Since the translation parameters and rotation parameters are highly correlated in this case, a very large condition number of the coefficient matrix A exists in the linear system of equations x b  A . Regularization is required to reduce the effects caused by the intrinsic ill-conditioning of the problem and noises in the data, and to stabilize the solution. Based on advanced regularized methods, we propose a new regularized solution to the ill-posed coordinate transforma-tion problem. Simulation numerical experiments of coordinate transformation are given to shed light on the relationship among different regularization approaches. The results indicate that the proposed new method can obtain a more rea-sonable resolution with higher precision and/or robustness.