A New Method for Synthesis of Nonlinear Parameter and State Estimators for Noisely Disturbed Processes

Abstract

In the framework of Markov processes z~T - (zT, y T),described by ITOs differential or corresponding difference equations, a new method is shown which uses Lyapunov function V for synthesis of an estimator ẑ(t)=F(y(t')/O ≤t' ≤ t). In order to solve this nonlinear estimation problem we consider any auxiliary processes R (t) and a Lyapunov function which depends on R (t) and the estimation error z-ẑ. The estimator and the auxiliary processes are determined by optimization of the increase of V. In contrast to the theory of asymptotic stochastic stability we don't need the condition that z is exact estimable with probability one. The discussed method connects the theory of optimal estimation after Kushner and stratonovich and of the stochastic stability which was missed in the past. The presented examples and simulation results demonstrate the effectivity and simplicity of our method.