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⊤, 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.
Related
- Approximate maximum likelihood estimation for partially observed fractional diffusions from discrete observations
- Krylov geometry and optimal recovery under uncertain coherent noise
- Observability properties of the singular Grushin equation
- Cutoff for non-negatively curved diffusions
- A law of large numbers for kinetic interacting diffusions
BibTeX
@misc{coatanhay2026geometry,
title = {{Geometry and observability of latent texture-coherence diffusions in coherent sea-clutter radar observations}},
author = {Arnaud Coatanhay and Angélique Drémeau},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27587},
eprint = {2609.27587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27587},
}
RIS
TY - UNPB
TI - Geometry and observability of latent texture-coherence diffusions in coherent sea-clutter radar observations
AU - Arnaud Coatanhay
AU - Angélique Drémeau
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27587
UR - https://arxiv.org/abs/2609.27587
AB - 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^⊤, 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.
ER -