Estimation of rational polynomial coefficients based on singular value decomposition

Jinshan Cao; Jianhong Fu

doi:10.1117/1.JRS.12.044003

9 November 2018 Estimation of rational polynomial coefficients based on singular value decomposition

Jinshan Cao, Jianhong Fu

Author Affiliations +

Journal of Applied Remote Sensing, Vol. 12, Issue 4, 044003 (November 2018). https://doi.org/10.1117/1.JRS.12.044003

Abstract

The rational function model (RFM) has been widely used in space-borne photogrammetry owing to its simplicity and generality. One of the key issues for using the RFM is to robustly estimate the rational polynomial coefficients (RPCs). However, owing to over-parameterization of the RFM, estimating the RPCs is an ill-posed problem. A feasible method for estimating the RPCs based on singular value decomposition is presented. The presented method can estimate the RPCs directly based on an observation vector and three matrices decomposed from the design matrix. Consequently, the numerical instability of computing the inverse matrix of the ill-conditioned normal matrix can be avoided. Experimental results of the SPOT-5, ZiYuan-3, and GaoFen-2 images show that the presented method can benefit the terrain-dependent and terrain-independent scenarios. Under the terrain-dependent scenario, the influence of the observation errors of actual ground control points (GCPs) can be eliminated effectively and the RPCs can be estimated robustly by selecting a proper regularization parameter and truncating some small singular values. Under the terrain-independent scenario, owing to a very important characteristic that the virtual GCPs do not have observation errors, the presented method can estimate the RPCs robustly even without the selection of the regularization parameter.

Citation Download Citation

Jinshan Cao and Jianhong Fu "Estimation of rational polynomial coefficients based on singular value decomposition," Journal of Applied Remote Sensing 12(4), 044003 (9 November 2018). https://doi.org/10.1117/1.JRS.12.044003

Received: 14 June 2018; Accepted: 2 October 2018; Published: 9 November 2018

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