Numerical simulation of nonlinear filtering problem

Abstract

In the paper, we give the numerical simulation of nonlinear filtering problem. We introduce the basic filtering problem and review the reduction from robust Duncan-Mortensen-Zakai equation to Kolmogorov equation firstly. Then the difference scheme of the Kolmogorov equation is given to calculate the nonlinear filtering equation. We derive the result that the solution of the difference scheme convergences pointwise to the solution of the initial-value problem of the Kolmogorov equation. Numerical experiments show that the numerical method can give the exact result. © 2011 Springer-Verlag.