Estimation of the parameters of stochastic differential equations for sea clutter

Abstract

When the sea surface is illuminated by a radar sufficiently far away and in the absence of a coherent target, the scattered electromagnetic signal, called ‘sea clutter’ is unpredictable and can be represented by a stochastic process. A model based on stochastic differential equations and consistent with previous statistical models (K distribution) has been proposed. It depends on three parameters: ${\cal A}$ A , ${\cal B}$ B , and $\alpha $ α . To estimate them, maximum likelihood estimators for ${\cal A}$ A and ${\cal B}$ B , and an estimator based on the hypothesis of ergodicity for $\alpha $ α are proposed in this study. The authors compare three expressions for the transition probabilities: the exact one, Euler's approximation, and Nowman's approximation. By regenerating the trajectories from the same Brownian increments, they can quantify the typical error made on the sea clutter from the typical error made on the estimated parameters. Though the exact transition probabilities minimise the error on the sea clutter, they show that an approximation such as Euler's is sufficient.