Separation approach for numerical solution of the Fokker-Planck equation in estimation problem
|Authors:||Simandl Miroslav, University of West Bohemia in Pilsen, Czech Republic|
Svacha Jaroslav, University of West Bohemia in Pilsen, Czech Republic
|Topic:||1.4 Stochastic Systems|
|Session:||Control, Estimation and Analysis of Stochastic Systems|
|Keywords: ||stochastic systems, state estimation, nonlinear filters, Fokker-Planck equation, numerical solutions, finite volume method,finite difference method|
The paper deals with a filter design for nonlinear continuous stochastic systems with discrete-time measurements. The general recursive solution is given by the Fokker-Planck equation (FPE) and by the Bayesian rule. The stress is laid on computation of the predictive conditional probability density function from FPE. A new usable numerical scheme is designed. In the scheme, the separation technique based on an upwind volume method and a finite difference method for hyperbolic and parabolic part FPE is used. The approach is illustrated in some numerical examples.