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With the wider availability of more and more images acquired from various satellites, the integration of different orientation models for different sensors has become an important task in order to maintain geometrical consistency. This study combines two heterogeneous geometric correction models, namely, direct georeferencing and the rational function model for multisatellite image positioning. Two types of adjustment models, collocation-based block adjustment (CBBA) and collocation-aided block adjustment (CABA), are proposed to reach the goal. The former is based on the concept that the adjustment is first performed on individual images, and then, all images are integrated. Discrepancies are compensated for by least squares collocation (LSC). The latter method entails simultaneous adjustment of the two heterogeneous models followed by LSC. Experimental results indicate that the proposed method can significantly improve the geometric accuracy as well as reduce geometric discrepancies between images. We also demonstrate that CABA is slightly better than CBBA.