Fuzzy Kalman filter for non linear stochastic systems

In this paper, we present an approach for designing a non linear observer to estimate the states of a non linear stochastic discrete time T-S system. The non linear observer design involves representation of the non linear system as a family of local linear state space models. The state estimator for each linear local state space model uses standard Kalman filter theory and then, linear modeled filter is corrected by the fuzzy gain. Then a global state estimator is developed that combines the local state estimators. The global filter is shown to be unbiased minimum-variance estimator of state. Finally, the performances of the developed fuzzy Kalman filter (FKF) is illustrated through a comparison with the existing literature results.