On-board processing is increasingly prevalent due to its efficient utilization of satellite resources. Among these resources, geometric rectification can significantly enhance positioning accuracy for subsequent tasks, such as object detection. This approach mitigates the heavy burden on downlink bandwidth and minimizes time delays by transmitting targeted patches rather than raw data. However, existing rectification methods are often unsuitable due to the limitations and conditions imposed on satellites. Factors like hardware quality, heat dissipation, storage space, and geographic positioning are frequently constrained and prone to inaccuracies. This paper proposes a novel on-board rectification method. The method introduces a two-step matching framework to address substantial positioning errors and incorporates a feature-compression strategy to reduce the storage space of reference patches. Quantitative and practical experiments demonstrate the method’s efficacy in terms of storage space, time efficiency, and geometric rectification accuracy.