maximum of likelihood
Y.I. Kolchugin, U.G. Skorobogatov
Nonlinear filtering is a new and powerful methodology for signal processing, conditioned by the progress in the algorithm theory area and the growing computer capacity. In this article, we present a review of stochastic ﬁltering technology, most widely used in the signal processing problems. Among them the stochastic differential equations (SDE) parameter estimator, maximum likelihood estimates, tool of Bayesian statistics, the Kalman ﬁlter having Bayesian interpretation, and relatively new a class of particle filters have been founded on sequential Monte Carlo routines.
We turn out that despite the analyticity of original equations the observing of precise estimates scarcely ever possible by the deterministic methods that do not recognize the stochastic nature of the problem.
On the other hand, statistical techniques rarely reflect analytical nature the functions used in optimization process. Diffusion coefficient and nonlinear drift of SDE, for example. But in spite of that and complexity of the specific calculations, for dimensions greater than two and strong nonlinearity the stochastic technique has superiority in a precise, optimality and lead to rapid producing required estimates.