In signals of opportunity (SOPs)-based positioning utilizing low Earth orbit (LEO) satellites, ephemeris data derived from two-line element files can introduce increasing error over time. To handle the erroneous measurement, an additional base receiver with a known position is often used to compensate for the effect of ephemeris error when positioning the user terminal (UT). However, this approach is insufficient for the long baseline (the distance between the base receiver and UT) as it fails to adequately correct Doppler shift measurement errors caused by ephemeris inaccuracies, resulting in degraded positioning performance. Moreover, the lack of clock synchronization between the base receiver and UT exacerbates erroneous Doppler shift measurements. To address these challenges, we put forth a robust double-difference Doppler shift-based positioning framework, coined 3DPose, to handle the clock synchronization issue between the base receiver and UT, and positioning degradation due to the long baseline. The proposed 3DPose framework leverages double-difference Doppler shift measurements to eliminate the clock synchronization issue and incorporates a novel ephemeris error correction algorithm to enhance UT positioning accuracy in case of the long baseline. The algorithm specifically characterizes and corrects the Doppler shift measurement errors arising from erroneous ephemeris data, focusing on satellite position errors in the tangential direction. To validate the effectiveness of the proposed framework, we conduct comparative analyses across three different scenarios, contrasting its performance with the existing differential Doppler positioning method. The results demonstrate that the proposed 3DPose framework achieves an average reduction of 90% in 3-dimensional positioning errors compared to the existing differential Doppler approach.