Abstract
In this paper, the filtering problem is solved for a general class of nonlinear distributed parameter systems with a Gaussian white noise disturbance under noisy observations.
The mathematical models for the system and the observation mechanism are respectively described by a stochastic nonlinear partial differential equation and by an integral equation.
The principal line of attack is to introduce Girsanov's theorem of the transformation of absolutely continuous measures to the filtering theory. Using the differential generator extended to the case of stochastic partial differential equations, a version of conditional expectation is derived in a form of integro-differential equations for which the optimal filter dynamics is easily determined.
The remainder of this paper is devoted to the method of physical realization of nonlinear filters. By using the Taylor series expansion, an approximated filter dynamics is derived. Sample path behaviors of the approximated filter are also examined by digital simulation experiments.
