In this paper, the optimal finite impulse response (OFIR) with embedded unbiasedness (EU) filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint for discrete time-invariant state-space models. Un like the OFIR filter, the OFIR-EU filter does not require the initial conditions. In terms of accuracy, the OFIR-EU filter occupies an intermediate place between the UFIR and OFIR filters. With a two-state harmonic model, we show that the OFIR-UE filter has higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters.
['Shunyi Zhao', 'Yuriy S. Shmaliy', 'Sanowar H. Khan', 'd Fei Liu']
Improving state estimates over finite data using optimal FIR filtering with embedded unbiasedness