Satellite image RPC parameters estimation method using the heteroscedastic errors-in-variables model

The positioning accuracy of a satellite image is mainly affected by the estimation accuracy of the rational polynomial coefficients (RPCs). Image point compensation or ground control point correction methods are usually used in the existing algorithms. Because the error characteristics of the design matrix elements are not considered, there are problems such as incomplete systematic error elimination and low parameter estimation accuracy. Considering the influence of the model systematic error, a heteroscedastic estimation method is proposed in this paper. First, the random model of matrix elements is established in the algorithm to describe the system characteristics more accurately. Taking into account the system deviations of the design matrix elements, the least square model is constructed using the Mahalanobis distance as the metric, and parameters are solved using the generalized eigenvalue method. The systematic error can be reduced theoretically. Experiment on different terrain images of TH-1 shows that the image correction accuracy of the proposed method is improved by more than 36 times compared with the traditional method, and the precision consistency is superior, which is of great significance to improving the accuracy of RPC parameters estimation and satellite imagery positioning.