Adaptive nonlinear continuous-discrete filtering

The mean square optimal adaptive filtering problem for wide class of the nonlinear continuous-discrete stochastic systems is solved. The state vector of a system is determined by the Ito stochastic differential equation and the observation described by stochastic difference equations depend on unknown vector parameters. Equations for conditional densities, optimal estimates of state vector and covariance matrices are given. In particular case of linear continuous-discrete systems with unknown parameters the optimal adaptive filtering equations are derived. The examples are considered. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.