Nonlinear filter design using Fokker-Planck-Kolmogorov probability densityevolutions

The Fokker-Planck-Kolmogorov equation (FPKE) in conjunction with Bayes' con ditional density update formula provides optimal estimates for a general co ntinuous-discrete nonlinear filtering problem. It is well known that the an alytical solution of FPKE and Bayes' formula are extremely difficult to obt ain except in a few special cases. Hence, we address this problem using num erical approaches. The efficient numerical solution of FPKE presented relie s on the key issue of adaptively calculating the domain over which the stat e probability density function (pdf) is to be evaluated, which is done usin g Chebyshev's inequality. Application to a passive tracking example shows t hat this approach can provide consistent estimators when measurement nonlin earities and noise levels are high.