ON THE PARTIAL DIFFERENTIAL EQUATION FOR THE CONDITIONAL PROBABILITY DISTRIBUTION FOR NONLINEAR DYNAMIC SYSTEMS WITH NOISY MEASUREMENTS

摘要

The partial integro-differential equation has been derived for the conditional probability density distribution of the output of a nonlinear system excited by nonadditive white Gaussian noise, with nonlinear mea¬surements corrupted by white Gaussian noise. This equation reduces to the well-known Kolmogoroff forward equation when there are no measurements. The usefulness of the differential equation is demonstrated by deriving from it, for linear systems, the Wiener-Kalman filter.