On the structure of the multi-mode filters for passive wavefront curvature ranging in a distributed array system

This work presents some new results on the structures of, and our interpretation on, the multi-rank filters used for passive wavefront curvature (WFC) ranging. Such a WFC ranging systems uses a large-scale distributed arrays with many spatially separated modular arrays, operating under environments subject to a spatial coherence loss. Working on the modular array level beamformed data, the multi-rank filters along with the weighting coefficients provide further spatial filtering capability to rake in spatial coherence existing in the distorted wavefronts impinging on different modular arrays. Such multi-rank filters can improve ranging performance through different combining schemes, beyond what achieved by the bearing-only based triangulation. For a real-valued inter-module spatial coherence matrix, the derived multi-rank filters follow a nicely balanced structure comprised of in-phase and quadrature (I/Q) modes with varying spatial directions. The results provide a simple solution for us to discovering levels of coherence existing in different modes for multi-mode combining.