Improvement of the Stability Solving Rational Polynomial Coefficients

The rational function model (RFM) utilized for high resolution satellite imagery (HRSI) provides a transformation from image to object space coordinates in a geographic reference system. Compared with the rigorous model based on the collinearity condition equation or the affine model, the RFM with 80 coefficients would be over parameterized. That would result in an ill-conditioned normal equation. Tikhonov regularization is often used to resolve this problem, and many applications have verified its serviceability. This paper will detail the method for regularization parameter selection. However, Tikhonov regularization makes the two sides of equation unequal, resulting in a biased solution. An unbiased method The Iteration by Correcting Characteristic Value (ICCV) was introduced, and a strategy to resolve the ill-conditioned problem for solving rational polynomial coefficients (RPCs) was discussed in this paper. The tests with SPOT-5 and QuickBird imagery were accomplished. The empirical results have shown that our methodology can effectively improve the condition of the normal equations.