Minimum variance unbiased FIR state estimation of discrete time-variant models

State estimation and tracking often require optimal or unbiased estimators. In this paper, we propose a new minimum variance unbiased (MVU) finite impulse response (FIR) filter which minimizes the estimation error variance in the unbiased FIR (UFIR) filter. The relationship between the filter gains of the MVU FIR, UFIR and optimal FIR (OFIR) filters is found analytically. Simulations provided using a polynomial state-space model have shown that errors in the MVU FIR filter are intermediate between the UFIR and OFIR filters, and the MVU FIR filter exhibits better denoisng effect than the UFIR estimates. It is also shown that the performance of MVU FIR filter strongly depends on the averaging interval of N points: by small N, the MVU FIR filter approaches UFIR filter and, if N is large, it becomes optimal.