On Higher Order Approximated Optimal Filter Derived by Invariant Imbedding Techniques

Abstract

The problem considered in this paper is the sequential estimation of a state in noisy nonlinear dynamic systems based on noisy nonlinear observations of a state. The class of systems considered is those in which the dynamical behavior is described by an ordinary differential equation with high nonlinearities, and the observations are obtained by the measurement devices with high nonlinearities. No statistical assumptions are required concerning both the natures of the input noises to the system and the measurement noises on the output. For the estimation purposes a least squares criterion is used.
An algorithm for estimating the state of noisy nonlinear dynamic systems is derived using invariant imbedding techniques. The new feature of the algorithm derived is that a sequential least squares estimator with higher order weighting functions is obtained for the class of problems considered. The sequential estimator equations obtained will be called the equations of the higher order approximated optimal filter.
A number of digital simulations are performed in order to compare the higher order approximated optimal filter obtained in this paper with the filter without a second weighting function proposed by D.M. Detchmendy & R. Sridhar. Simulated results from examples indicate that the proposed estimation algorithm is effective for the estimation problem of noisy dynamic systems with high nonlinearities.