Multi Quadric (MQ) interpolation function is used as a post-processing tool for the refinement of the object coordinates of the tie points obtained by the aerial triangulation (AT) technique. To apply the MQ function, initially a low order polynomial AT is applied to a photogrammetric block consisting of 4 strips and 77 photographs. The trend of the residual vector errors of the ground control points was then modeled by the MQ function. The calculated MQ coefficients were subsequently utilized to refine the ground coordinates for all tie points of the block.
The accuracy achieved by the MQ approach is compared with the standard polynomial, independent model and bundle adjustment AT techniques. The evaluated accuracy is based on the uniformly distributed checkpoints whose coordinates were determined by differential GPS receivers. The test results indicate that MQ function gives a marginal improvement of +-0.2; +-0.1 and +-0.2 meter RMSE for the X, Y and Z coordinates of the check points respectively as compared with the polynomial AT method. However, comparing the accuracy figures with the standard independent model and bundle adjustment, noticeable improvements were not observed.
Furthermore, the MQ potential for the elimination of the residual systematic errors for tie points due to imperfect interior orientation parameters was also investigated by introducing defective interior orientation parameters during tie data capture stage. The MQ function was then applied again as a post processor for removing the systematic trend. The results show an overall improvement of +- 0.80, +-1.08 and +-2.90 meter RMSE for the X, Y and Z coordinates of the tie points respectively. It could be concluded that the MQ interpolation function is an effective trend removal technique if camera interior orientation parameters are not known with the required accuracy. Test results also indicate that the MQ is superior to the polynomial interpolation functions as far as systematic trend removal in aerial triangulation is concerned.
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