Minimum variance unbiased FIR filter for discrete time-variant systems

This paper is concerned with the minimum variance unbiased (MVU) finite impulse response (FIR) filtering problem for linear system described by discrete time-variant state-space models. An MVU FIR filter is derived by minimizing the variance from the unbiased FIR (UFIR) filter. The relationship between the filter gains of MVU FIR, UFIR and optimal FIR (OFIR) filters is derived analytically, and the mean square errors (MSEs) of different FIR filters are compared to provide an insight into the estimation performance. Simulations provided verify that errors in the MVU FIR filter are in between the UFIR and OFIR filters. It is also shown that the MVU FIR filter can offer optimal estimates without a prior knowledge of the initial state, and exhibits better robustness against temporary modeling uncertainties than the Kalman filter.