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A trend in the development of spaceborne Synthetic Aperture Radar (SAR) technology is the shift from a single-satellite repeated observation mode to a multi-satellite collaborative observation mode. However, current multi-satellite collaborative geolocation algorithms face challenges, such as geometric model mismatch and poor baseline estimation accuracy, arising from highly dynamic changes among multi-satellites. This paper introduces a high-precision and efficient geolocation algorithm for a spaceborne bistatic interferometric SAR (BiInSAR) system based on an improved range–Doppler (IRD) model. The proposed algorithm encompasses three key contributions. Firstly, a comprehensive description of the spatial baseline geometric model unique to the bistatic configuration is provided, with a specific focus on deriving the perpendicular baseline expression. Secondly, IRD geolocation functions are established to meet the specific requirements of the bistatic configuration. Then, a novel BiInSAR geolocation algorithm based on the IRD's functions is proposed, which can significantly improve the target geolocation accuracy by modifying the range–Doppler equation to suit the bistatic configuration. Meanwhile, a low-coupling parallel calculation method is proposed, which can improve the calculation speed by two to three times. Finally, the accuracy and efficiency of the algorithm are demonstrated using experimental data acquired by the TH-2 satellite, which is China's first spaceborne BiInSAR system. The experimental results prove that the IRD algorithm exhibits geolocation accuracy with an average error of less than 1 m and a standard deviation of less than 2.5 m while maintaining computational efficiency at a calculation speed of 1,429,678 pixels per second. [ABSTRACT FROM AUTHOR]