Regularization of the ill-conditioned matrix arising in orientation of optical spaceborne images

Coordinate transformation between image and object space is termed as sensor orientation or image georeferencing, varying sensor dependent or independent. Thus, the orientation parameters/coefficients could be estimated for the purpose of transformation between image and object coordinates. An ill-posed problem could be arised because of the ill-conditioned desing (Jacobian) matrix used for the estimation of parameters/coefficients, and this problem might cause undesired georeferencing accuracy. This thesis carried out the existence of ill-conditioned matrix and some regularization methods in the orientation of spaceborne images. The implementation was held using a couple of stereo SPOT 5 panchromatic images using its special sensor orientation model and a mono SPOT 6 panchromatic image using sensor independent RFM. Adjustment with condition equations and with observation equations were used for SPOT 5 and 6, respectively. Design (Jacobian) matrix was established with regard to the EOPs (Exterior Orientation Parameters) for SPOT 5 and 1st, 2nd, and 3rd degree RFM (Rational Functional Model) for SPOT 6, and was analysed with respect to ill-conditioning. Various methods such as Tikhonov regularization, matrix inversing and elimination approach were implemented for both SPOT 5 and 6. Additionaly, normalization into ±1 was used for SPOT 6 when the findings were reviewed, the Tikhonov regularization using eigenvalues and Moore-Penrose (pseudo) inversing method, an approach based on eigenvalues, reached the desised georeferencing accuracy for SPOT 5. Nevertheless, all remaining methods were not succeed as much as these eigenvalue based approaches. All methods were not succeed if the normalization into ±1 is not used for SPOT 6.