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Stochastic differential equations for the electromagnetic field scattered by the sea surface : applications to remote sensing

Abstract : Radar remote sensing in a maritime context is often hindered by radar waves reflected by the sea, termed sea clutter due to its noise-like character. A thorough understanding of it is required for detection and imaging applications. Statistical models have long been used for the sea clutter (K distribution, Weibull distribution etc) but they are static in nature. We propose to use a dynamic model developed by T. R. Field, which represents the sea clutter as a stochastic process solving stochastic differential equations. We introduce Field's model for the sea surface radar cross section (RCS) and speckle. The complex reflectivity of the sea surface then depends on three parameters: A, B and α. We compute the transition probabilities of the RCS and speckle by analytical resolution of Fokker-Planck equations, and propose to use them as a tool for synchronizing observations taken at differents positions and times, as in Synthetic Aperture Radar. We derive maximum likelihood (ML) estimators for A and B, and show numerically that the exact transition probabilities from the Fokker-Planck equations can be approximated in a satisfactory manner by Gaussians using Euler-Maruyama's scheme. α, for its part, is estimated by ergodicity (moment). We adapt Field's model to account for the presence of a simple target and show that it is possible to estimate the target constant by ML using Gaussian approximations for the transition probabilities. In the last part, we address the nonobservability of the RCS by estimating it from the complex reflectivity (observable). We obtain a sequence of estimators applicable to real data. Finally, bayesian estimation of the clutter parameters, and target detection, are introduced and discussed as potential future directions for research.
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Clément J. Roussel. Stochastic differential equations for the electromagnetic field scattered by the sea surface : applications to remote sensing. Signal and Image Processing. ENSTA Bretagne - École nationale supérieure de techniques avancées Bretagne, 2019. English. ⟨NNT : 2019ENTA0007⟩. ⟨tel-02569917⟩

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