A Configuration Optimization Method Based on Decoupled Recursive Strategy for Distributed UAV SAR 3D Imaging System

Compared with conventional synthetic aperture radar (SAR) three-dimensional (3D) imaging systems, distributed unmanned aerial vehicle (UAV) SAR systems offer enhanced flexibility and single-pass capability, enabling rapid 3D imaging. Their performance, however, critically depends on the spatial arrangement of UAVs. Improper configurations result in grating lobes and increase the sidelobe level, thereby degrading elevation reconstruction. Additionally, the coordinated operation of distributed UAVs imposes spatial constraints such as safety separation. To address these challenges, this paper formulates the configuration design as a multi-constraint, multi-objective optimization problem that simultaneously considers both imaging performance and operational feasibility. Based on compressive sensing (CS) theory, the influence of configuration on sparse imaging is analyzed, and practical constraints are integrated, including 3D span limits, safety separation, and mainlobe avoidance. A joint optimization model is established to minimize the cumulative coherence of the sensing matrix while maximizing system spatial compactness. To efficiently solve this high-dimensional problem, a decoupled recursive strategy is proposed. In the first stage, a hybrid algorithm combining particle swarm optimization (PSO) and covariance matrix adaptation evolution strategy (CMA-ES) performs global optimization in the baseline domain. In the second stage, a compact configuration is constructed within the feasible region via analytical spatial recursion. Experimental results demonstrate that the proposed approach effectively reduces sensing matrix coherence and improves 3D reconstruction quality.