Abstract
The purpose of this paper is to establish an approximate method of the state estimation for nonlinear dynamical systems under state-dependent noisy observations.
Guided by the state variable representation concept in control theory, the mathematical models of both the dynamical system and the observation mechanism are described by their respective nonlinear vector stochastic differential equations of Itô-type. The state-dependent observation noise is considered, which is proportional to the state variable.
First, by using the method of the stochastic linearization and following the concept of dynamic programming, the approximated filter dynamics is given in the Markovian framework. Secondly, the obtained dynamics is compared with another approximated filter dynamics obtained with a different approximation. The comparison includes the numerical results of digital simulation studies. Finally, the accuracy of the approximation presented is discussed in detail from the viewpoint of both qualitative and quantitative aspects.
