Filtering of linear partially observe stochastic systems: The fuzzy logic approach

In this paper we consider the filtering problem for a class of partially observed systems governed by linear stochastic differential equations. Using Takagi-Sugeno linear fuzzy model and assuming membership functions of Gaussian type, we have proposed minimum unbiased linear fuzzy filter, driven by the observed process, with the help of which the system states can be estimated from the observed data. Further, using calculus of variation, we have developed a set of necessary conditions of optimality on the basis of which filter parameters can be determined. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed filter.