Zhao, S., Shmaliy, Y. S., Liu, F., Ibarra-Manzano, O. & Khan, S. (2015). Effect of embedded unbiasedness on discrete-time optimal FIR filtering estimates. EURASIP Journal on Advances in Signal Processing, 2015(83), doi: 10.1186/s13634-015-0268-0
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Unbiased estimation is an efficient alternative to optimal estimation when the noise statistics are not fully known and/or the model undergoes temporary uncertainties. In this paper, we investigate the effect of embedded unbiasedness (EU) on optimal finite impulse response (OFIR) filtering estimates of linear discrete time-invariant state-space models. A new OFIR-EU filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint. We show that the OFIR-UE filter is equivalent to the minimum variance unbiased FIR (UFIR) filter. Unlike 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. Contrary to the UFIR filter which MSE is minimized by the optimal horizon of N opt points, the MSEs in the OFIR-EU and OFIR filters diminish with N and these filters are thus full-horizon. Based upon several examples, 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.
|Uncontrolled Keywords:||State estimation; Unbiased FIR filter; Optimal FIR filter; Kalman filter|
|Subjects:||T Technology > TK Electrical engineering. Electronics Nuclear engineering|
|Divisions:||School of Engineering & Mathematical Sciences > Engineering|
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