RM-GMSD and FRM-GMSD: Subspace-Based Detection of High-Speed Range-Spread Targets in Cluttered Environments

This article addresses high-speed range-spread (RS) target detection in cluttered environments, considering both range migration (RM) and RS effects, as well as the disturbance of clutter. The target is modeled as multiple scatters with identical velocities. We first propose the generalized matched subspace detector for RM (RM-GMSD) targets, which projects pulse-compressed echo data onto a joint subspace of multiple hypothesized scatter echoes. However, RM-GMSD lacks compatibility with conventional extended target detection frameworks, preventing direct application of effective scatter selection algorithms, which are crucial for mitigating collapse loss caused by weak or ineffective scatters. To overcome this, we analyze RM-GMSD’s geometric projection properties and propose the flexible RM-GMSD (FRM-GMSD). Unlike RM-GMSD, FRM-GMSD exploits the orthogonality of subspaces associated with different hypothesized scatters across range cells. It follows a two-stage process: first, projecting echo data onto multiple 1-D subspaces and then performing noncoherent integration. This reformulation aligns FRM-GMSD with the conventional RS target detection framework, enabling effective scatter selection. Notably, incorporating effective scatter information allows FRM-GMSD to achieve optimal detection performance. Finally, numerical simulations and real-world data validate the effectiveness of the proposed approach.