significant subfields in “Synthetic Aperture Radar (SAR)” research is considered to be target detection. Numerous studies have been conducted on target identification, with the majority of them favoring filter-oriented methods. The fundamental goal of radar systems is to “detect moving targets on the ground.” Decomposing a complex matrix into a structured sparse matrix and a low-rank matrix is a fundamental mathematics issue. Surveillance and reconnaissance rely heavily on “Ground Moving Target Indication (GMTI),” but it's not a simple task. The SAR ATI was first developed for calculating the radial velocity of ground-moving objects. Yet, overlapping stationary clutter can corrupt the recorded differential phase, resulting in mistakes in position and velocity calculations. The main concept of this paper is to propose a novel “Adaptive Simplified Fractional Fourier Transform (A-SFrFT)” using the intelligent meta-heuristic improvement. This adaptive SFrFT efficiently estimates the “Doppler parameters of the moving targets.” The improved “Harris Hawks Optimization (HHO)” termed Trio Updating HHO (TU-HHO) is used as the meta-heuristic algorithm that enhances the performance of the SFrFT-based target estimation. The mathematical analysis and simulation findings show that the suggested methods recommended strategy is successful.