Recursive Filtering in Discrete Nonlinear Systems with Unknown Parameters

Optimal filtering for a wide class of discrete stochastic systems defined by nonlinear difference equations with unknown parameters is studied. Equations describing the conditional probability densities for the case in which the unknown parameter vector is continuous and discrete are derived. Recursive equations for the mean-square optimal filter are derived. Nonlinear systems with additive perturbations are studied in detail. For discrete nonlinear systems with unknown parameters, the optimal filter is shown to be described by the Lainiotis exact filtering equations. Using the Lainiotis separation theorem, new families of parallel recursive estimation algorithms are designed. The application of the results to pattern recognition, signal detection, and system identification is examined.