Unified Analysis of Harris Hawks and Hybrid Black Widow–Elephant Herding Optimization in SFFrFT-Based GMTI

Ground moving target indication (GMTI) in synthetic aperture radar (SAR) remains difficult when weak or slowly moving targets are embedded in stationary clutter. The two reference studies address this problem through simplified fractional Fourier transform variants whose fractional power is tuned by meta-heuristic optimization. The first study develops adaptive SFrFT (A-SFrFT) using trio updating Harris Hawks optimization (TU-HHO), while the second develops improved SFrFT (ISFrFT) using hybrid black widow-elephant herding optimization (HBWEHO). This paper provides a unified analysis of both strategies, focusing on their shared signal model, fractional-domain target estimation, optimization objectives, convergence behavior, localization evidence, and computational implications. The synthesis shows that both approaches recast Doppler parameter estimation as an error-minimization problem in which the fractional transform order is selected to concentrate moving-target energy while dispersing clutter. TU-HHO is positioned as an exploitation-oriented adaptive search mechanism, whereas HBWEHO is positioned as a diversity-preserving hybrid search mechanism. Together, the studies indicate that optimized SFrFT processing can improve target localization and reduce computational cost compared with baseline SFrFT and several single meta-heuristic variants. The paper also identifies limitations in comparability, statistical reporting, and real-data validation, and proposes a consistent evaluation framework for future GMTI research. Keywords: ground moving target indication; synthetic aperture radar; simplified fractional Fourier transform; Harris Hawks optimization; black widow optimization; elephant herding optimization; Doppler parameter estimation.