 Video Synthetic Aperture Radar, SAR, is a cutting-edge research direction in the field of radar imaging. It has the ability to provide high-resolution and persistent imaging at any time and under any weather conditions. The persistent frequency agile, PFA, algorithm is commonly used due to its applicability to the spotlight mode and relative computational efficiency. However, it suffers from low efficiency and limited scene size. To address these issues, we propose a generalized persistent polar format algorithm, GP PFA, which is applicable to the persistent imaging requirements of airborne video SAR under multitasking conditions. Firstly, the wave number domain resampling characteristics of video SAR PFA are analyzed, and a generalized resampling method is proposed to achieve higher efficiency. Secondly, for the problem of scene size limitation caused by wavefront curvature error, an efficient compensation method applicable to different scene sizes is proposed. GP PFA is capable of video SAR imaging at different wavebands, different slant ranges, and arbitrary scene sizes. Point target and extended target experiments verify the effectiveness and efficiency of the proposed method. This article was authored by Jiawei Jiang, Yin Weili, Yinghao Yuan, and others. We are article.tv, links in the description below.