A Refocusing Algorithm for Ships with 3D Complex Oscillatory Motions Based on the Inversion of the Space-Variant Modulated Phase History

The signals of ship targets with complex oscillatory motion exhibit three-dimension (3D) space-variant attributes. This phenomenon deteriorates the performance of the imaging algorithms based on 2D space-variant signal model. This manuscript proposes a novel imaging algorithm to achieve well-focused ISAR images of ships exhibiting complex oscillatory motion. This algorithm employs a scatterer-specific focusing strategy that effectively compensates for the 3D space-variant phase errors, thereby achieving high-precision focusing. Firstly, we establish the signal model of complex oscillatory motion based on quaternion, based on which the space-variant characteristics of imaging parameters are analyzed. According to the analysis, the range cell migration (RCM) is corrected uniformly by phase difference (PD), Lv's distribution (LVD) algorithm and Keystone transform (KT). After range migration correction, the Viterbi dynamic programming algorithm is employed to extract the instantaneous frequency (IF) of the scatterer in the time-frequency image. Then, we design specific focusing procedures based on the completeness of the IF. If the IF is complete, RCM has been fully corrected and a 1D phase function is formed to focus this scatterer. For a slightly missing IF, residual RCM correction is performed by joint compensation in the range frequency/azimuth time domain until the completeness of IF increases to an acceptable level. The information is insufficient for a largely missing IF, which serves as the condition for the termination of the focusing program. The effectiveness of the proposed algorithm is validated through both simulated data and measured data experiments.