An Optimized Method for Selecting Rational Polynomial Coefficients Based on Multicollinearity Analysis

In the geometric processing of high-resolution satellite imagery,the general rational function model(RFM) consists of 78 rational polynomial coefficients(RPCs),and the correlation between these coefficients will result in difficulties and accuracy degradation in solving the RPC.The rigorous error equations for solving the RPCs are derived,and an optimized method of selecting the RPCs by analyzing the multicollinearity between column vectors of the design matrix is proposed.A SPOT-5 HRG image in level 1A is selected and used.The empirical results have shown that selecting 20 to 30 RPCs could effectively eliminate the correlation between the coefficients,remove the oscillation in approximating the terrain by using the RFM,and obviously raise the solution accuracy of the RPCs and geometric processing accuracy based on the RFM with less ground control points(GCPs) available.When the GCPs are sufficient,the selected RPCs could acquire a consistent geometric accuracy in approximating the terrain with the 78 RPCs solved by the traditional least-squares method.