Abstract
In this paper, an exponentially weighted Finite Impulse Response (FIR) filter is proposed for discrete-time linear time-varying systems. The weighting method of measurements was first introduced for the FIR structured estimators, then an optimal design of the exponentially weighted FIR filter was developed with respect to a minimum variance criterion for discrete-time linear time-varying systems. The proposed filter is designed to be unbiased and independent of initial state information. Due to the inclusion of the weighting factor, it is expected to be less prone to model uncertainty and numerical errors than the conventional optimal FIR filter. Moreover, the proposed FIR filter is reduced to the optimal time-varying FIR filter with an equal weight, and can thereby provide a more general solution than the conventional optimal FIR filter. Through a numerical study, the performance of the proposed FIR filter was shown by comparing it with the exponentially weighted Kalman filter and the conventional optimal FIR filter when the modeling uncertainties exist.
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