Fuzzy Kalman filtering

The classical Kalman filtering (KF) algorithm has recently been extended to interval linear systems with interval parameters under the same statistical assumptions on noise, where the new algorithm is called Interval Kalman Filtering (IKF) scheme. The IKF algorithm has the same structure, and preserves the same optimality, as the classical KF scheme but provides interval-valued estimates. If the interval system has confidence description about the distribution of its interval values, we can further incorporate the IKF scheme with fuzzy logic inference, so as to develop a new filtering algorithm, called Fuzzy Kalman Filtering (FKF) algorithm. This algorithm preserves the same recursive mechanism of the KF and IKF, but produces a scalar-valued (rather than an interval-valued) estimate at each iteration of the filtering process. To compare the FKF to the IKF, computer simulation is included, which shows that the FKF is also robust against system parameter variations.