Open AccessUnbiased, optimal, and in‐betweens: the trade‐off in discrete finite impulse response filtering
Author(s) -
Zhao Shunyi,
Shmaliy Yuriy S.,
Liu Fei,
Khan Sanowar H.
Publication year - 2016
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2015.0360
Subject(s) - finite impulse response , kalman filter , mathematics , robustness (evolution) , mean squared error , gaussian , algorithm , control theory (sociology) , statistics , computer science , artificial intelligence , biochemistry , chemistry , physics , control (management) , quantum mechanics , gene
In this survey, the authors examine the trade‐off between the unbiased, optimal, and in‐between solutions in finite impulse response (FIR) filtering. Specifically, they refer to linear discrete real‐time invariant state‐space models with zero mean noise sources having arbitrary covariances (not obligatorily delta shaped) and distributions (not obligatorily Gaussian). They systematically analyse the following batch filtering algorithms: unbiased FIR (UFIR) subject to the unbiasedness condition, optimal FIR (OFIR) which minimises the mean square error (MSE), OFIR with embedded unbiasedness (EU) which minimises the MSE subject to the unbiasedness constraint, and optimal UFIR (OUFIR) which minimises the MSE in the UFIR estimate. Based on extensive investigations of the polynomial and harmonic models, the authors show that the OFIR‐EU and OUFIR filters have higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters.