Jiao Weili

Nested Regression Based Optimal Selection (NRBOS) of Rational Polynomial Coefficients

Although the rational function model (RFM) is widely applied in photogrammetry, the application of terrain-dependent RFM is limited because of the requirement for numerous ground control points (GCPs) and the strong correlation between the coefficients. A new method, NRBOS, based on nested regression was proposed to select the optimal RPCs automatically and to gain stable solutions of terrain-dependent RFM using a small amount of GCPs. Different types of images, including QuickBird, SPOT5, Landsat-5, and ALOS, were involved in the tests. NRBOS method performed better than conventional methods in estimating RPCs, and even provided a reliable solution when less than 39 GCPs were used. Additionally, the test results showed that the simplified RPCs are almost as accurate as the vendor-provided RPCs. Consequently, in favorable situations such as when the orientation parameters of the satellite are not available or are not suffi ciently accurate, the proposed method has the potential to take the place of the regular terrain-independent RFM.

Diagnosis of the Ill-condition of the RFM Based on Condition Index and Variance Decomposition Proportion (CIVDP)

The Rational Function Model (RFM) is a new generalized sensor model. It does not need the physical parameters of sensors to achieve a high accuracy that is compatible to the rigorous sensor models. At present, the main method to solve RPCs is the Least Squares Estimation. But when coefficients has a large number or the distribution of the control points is not even, the classical least square method loses its superiority due to the ill-conditioning problem of design matrix. Condition Index and Variance Decomposition Proportion (CIVDP) is a reliable method for diagnosing the multicollinearity among the design matrix. It can not only detect the multicollinearity, but also can locate the parameters and show the corresponding columns in the design matrix. In this paper, the CIVDP method is used to diagnose the ill-condition problem of the RFM and to find the multicollinearity in the normal matrix.