Solution to the rational function model based on the Levenberg-Marquardt algorithm

Conventional method of solving Rational Function Coefficients is based on the Least Squares Estimation. When there are large number of coefficients or the control points are not well-distributed, the normal equation will become ill-conditioned and the Least Squares Estimation cannot get reliable solution. A new method for solving the Rational Polynomial Coefficients (RPCs) is proposed, which substitutes the Least Squares Estimation with the Levenberg-Marquardt (LM) algorithm. The LM algorithm is a standard technique for nonlinear least-squares problems and can be thought of as a combination of steepest descent and the Gauss-Newton method. It can overcome the ill-condition of the normal equation and is very efficient in calculation. In this paper, we implement the LM algorithm with SPOT5 imagery registration and compare it with the Ridge Estimation method which is widely used to improve the condition number of the normal equation and the Rigorous Physical model. The empirical results have verified that LM algorithm is reliable and valid for solving the RPCs.