Forward and backward probabilistic inference of the sea clutter
Résumé
The fast dynamics of the sea surface result in highly volatile time series of the sea clutter. Measures made by a moving sensor which observes the sea from different points of view cannot be compared directly if the clutter has significantly evolved during the sampling interval. The issue of transporting measures to a common time reference is addressed using a model in which the sea clutter and associated observables are homogeneous Markov processes described by stochastic differential equations. We solve the Fokker–Planck equations of the speckle and radar cross-section (RCS) to obtain their present to future transition probabilities, from which we derive those of the intensity and the real and imaginary parts of the reflectivity. Using Bayes’s formula and the independence property of the speckle and RCS, we show that the formula remain valid for the present to past transition probabilities. Numerical distributions are systematically computed and match the analytical distributions. The resulting two-way prediction capability can be used to probabilistically balance the dynamics of the sea clutter. A series of deterministic measures from different positions and times is transformed into a series of probabilistic measures from different positions at the same time.