Geometry and observability of latent texture-coherence diffusions in coherent sea-clutter radar observations

Abstract

A coherent radar observes sea clutter through a non-injective multiplicative combination of latent texture and coherence variables. We study a class of partially observed slow--fast diffusions for which the projected quadratic covariance has the form \(Q=S+qyy^\top\), using Field's sea-clutter diffusion as a solvable benchmark. For fixed-shape fast covariance, we derive an exact generalized spectral-gap criterion for recovery of the latent slow coordinate and a stability bound. When the fast covariance changes shape, we obtain an invariant scale--shape decomposition and exact conditions for reinforcement or cancellation of the latent quadratic signature. We then quantify the loss of resolvability caused by finite sampling and receiver noise. Controlled CIR--OU simulations verify the analytic identities and exhibit regimes in which structural observability does not yield stable reconstruction.