Reusable Adjoint-Octree MLFMA for Full-Wave Radar Signature Analysis of Multi-State UAV Formations

This study presents a reusable adjoint-octree multilevel fast multipole algorithm (MLFMA) for full-wave radar scattering analysis of multi-state unmanned aerial vehicle (UAV) formations. The method is motivated by remote-sensing applications in which dense angular sampling or long motion sequences are required for physically reliable signature generation. Instead of rebuilding a global octree for the full formation at every motion state, the proposed approach assigns each sub-target an independent target-attached local octree that translates and rotates with the rigid body. This preserves mesh–cell affiliation in the body-fixed frame and separates the system operator into a state-invariant intra-target near-field component and a state-dependent inter-target far-field component. Consequently, near-field matrices and sparse approximate inverse preconditioners are assembled once and reused throughout the state sequence, while only inter-target far-field coupling terms are updated. The method is evaluated for six representative UAV formations at 3.5 GHz using monostatic radar cross section (RCS) over a full azimuth sweep. Across all tested formations, the proposed solver reproduces the RCS behavior of conventional MLFMA while substantially reducing computational cost. For Formation A, the center-state total time decreases from 251.4 s to 66.06 s; for Formation C, it decreases from 470.95 s to 76.06 s. Over 100-state sequences, the resulting acceleration reaches approximately 11.8-fold and 15.2-fold, respectively. Jitter-envelope analysis further shows that orientation perturbation produces stronger signature uncertainty than planar displacement. The proposed framework therefore provides an efficient and physically consistent forward solver for radar remote-sensing studies of cooperative UAV formations.