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On-orbit geometric calibration is a key technology to guarantee the geometric quality of high-resolution optical satellite imagery. In this paper, we present an approach for the on-orbit geometric calibration of high-resolution optical satellite imagery, focusing on two core problems: constructing an on-orbit geometric calibration model and proposing a robust calculation method. First, a rigorous geometric imaging model is constructed based on the analysis of the major error sources. Second, we construct an on-orbit geometric calibration model through performing reasonable optimizing and parameter selection of the rigorous geometric imaging model. On this basis, the calibration parameters are partially calculated with a stepwise iterative method by dividing them into two groups: external and internal calibration parameters. Furthermore, to verify the effectiveness of the proposed calibration model and methodology, on-orbit geometric calibration experiments for ZY1-02C panchromatic camera and ZY-3 three-line array camera are conducted using the reference data of the Songshan calibration test site located in the Henan Province, China. The experimental results demonstrate a certain deviation of the on-orbit calibration result from the initial design values of the calibration parameters. Therefore, on-orbit geometric calibration is necessary for optical satellite imagery. On the other hand, by choosing multiple images, which cover different areas and are acquired at different points in time to verify their geometric accuracy before and after calibration, we find that after on-orbit geometric calibration, the geometric accuracy of these images without ground control points is significantly improved. Additionally, due to the effective elimination of the internal distortion of the camera, greater geometric accuracy was achieved with less ground control points than before calibration. [ABSTRACT FROM AUTHOR]