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.
To analyze the size and location of the calibration field and the stabilization of systematic error parameters, calibration
field designing for airborne Position and Orientation System (POS) using actual photogrammetric data is discussed in
this paper. The empirical results have verified that a region of 4 strips with 7 images in each strip is appropriate for use as
a calibration field, whose location should be within 1° in longitude from the center of the project. If the equipment is
changed, the POS must be recalibrated. Otherwise, the flight interval of the calibration field should not exceed 30 days.