Abstract: Resolution and swath width are two important and direct image performance metrics for evaluating the imaging reconnaissance capability of Synthetic Aperture Radar (SAR). Improving resolution enables the acquisition of more detailed target features, while expanding swath width provides broader scene information. Staggered Pulse Repetition Interval (PRI) signals are an important signal form of SAR, allowing simultaneous realization of high resolution in the azimuth direction and wide swath width during SAR imaging. Therefore, accurately extracting staggered PRI signals from mixed radar signals is of great significance for anti-SAR reconnaissance. This paper proposes an improved staggered PRI signal de-Interleaving algorithm based on Ramanujan subspace projection theory. The detection threshold has been redesigned, and the period identification criteria have been optimized to improve the success rate of PRI estimation. Additionally, a sequence-correlation-based pulse sequence extraction algorithm is introduced, which not only adapts to pulse loss but also significantly simplifies the staggered signal extraction process. Simulation results demonstrate that the improved algorithm can effectively de-Interleave multiple staggered PRI signals arriving simultaneously, with good adaptability to pulse loss, and outperforms existing algorithms.