Discrete-Time State Estimation Using Unbiased FIR Filters with Minimized Variance

Optimal or unbiased estimators are widely used for state estimation and tracking. 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 denoising 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. Key–Words: State estimation, minimum variance, unbiased filter, FIR filter.