NDLI: Studies of discrete-time unbiased FIR filters of polynomial state-space models

Content Provider	IEEE Xplore Digital Library
Author	Shmaliy, Y.S. Ibarra-Manzano, O.
Copyright Year	2010
Description	Author affiliation: Electronics Department, Guanajuato University, Salamanca, 36885, Mexico (Shmaliy, Y.S.; Ibarra-Manzano, O.)
Abstract	We study an unbiased finite impulse response (FIR) filter in applications to discrete-time state space models with polynomial representation of the states. The unique l-degree polynomial FIR filter gain and the estimate variance are found for a general case. The noise power gain (NG) is derived for white Gaussian noises in the model and in the measurement. The filter does not involve any knowledge about noise in the algorithm. It is unstable at short horizons, 2 ≤ N ≤ l, and inefficient (NG exceeds unity) in the narrow range l ≪ N ≤ Nb, where Nb is ascertained by the cross-components in the measurement matrix C. With N ≫ Nb, the filter NG poorly depends on C and fits the asymptotic function $(l+1)^{2}/N.$ With very large N ⋙ 1, the estimate noise becomes negligible and the filter thus optimal in the sense of zero bias and zero noise. An example is given for a two-state system.
Starting Page	12
Ending Page	17
File Size	501962
Page Count	6
File Format	PDF
ISBN	9781424457939
e-ISBN	9781424457953
DOI	10.1109/MELCON.2010.5476347
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-04-26
Publisher Place	Malta
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Finite impulse response filter Polynomials State-space methods Gaussian noise Niobium IIR filters Noise measurement Global Positioning System Wireless communication Filtering
Content Type	Text
Resource Type	Article

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