Abstract
Recently, many researchers attempted to consider the optimal estimation problems for a stochastic system with noisy observation from the viewpoint of the information theory. But their studies were mainly limited to the investigation on linear systems.
In this paper, we determine the optimal filter for a non-linear system from the information-theoretical viewpoint by considering the influence of non-linear elements.
As a result, it is derived that the optimal filter for the non-linear system coincides with the well-known Kushner filter.
Moreover, we treat the two-dimensional dynamical system as a numerical example, and show that it is possible to effectively evaluate the accuracy of estimation by using the entropy of the estimation error studied here.
