An Optimal FIR Filter With Fading Memory

In this letter, we propose an optimal finite impulse response (FIR) filter with fading memory for a class of continuous-time state space models. The proposed optimal FIR filter with fading memory is linear with respect to outputs on the recent finite time horizon and it has a kernel function that is obtained from the classical least squares approach with weighting parameters by using the result on the linear quadratic tracking control. For the fast tracking ability, the less weight is put on to the older data. If the same weight is assigned to all data involved, the proposed FIR filter is shown to be reduced to the existing minimum variance unbiased FIR (MVUF) filter for a stochastic system. A numerical example is presented to illustrate the performance of the proposed optimal FIR filter with fading memory by comparing with the conventional Kalman infinite impulse response (IIR) filters and the MVUF filter.