Estimation of Noise Variance from Noisy Measurements of AR and ARMA Systems: Application to Blind Identification of Linear Time-Invariant Systems

Takashi YAHAGI  Md.Kamrul HASAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.5   pp.847-855
Publication Date: 1994/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Processing and System Theory)
digital signal processing,  noise variance estimation,  parameter estimation,  AR system,  ARMA system,  

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In many applications involving the processing of noisy signals, it is desired to know the noise variance. This paper proposes a new method for estimating the noise variance from the signals of autoregressive (AR) and autoregressive moving-average (ARMA) systems corrupted by additive white noise. The method proposed here uses the low-order Yule-Walker (LOYW) equations and the lattice filter (LF) algorithm for the estimation of noise variance from the noisy output measurements of AR and ARMA systems, respectively. Two techniques are proposed here: iterative technique and recursive one. The accuracy of the methods depends on SNR levels, more specifically on the inherent accuracy of the Yule-Walker and lattice filter methods for signal plus noise system. The estimated noise variance is used for the blind indentification of AR and ARMA systems. Finally, to demonstrate the effectiveness of the method proposed here many numerical results are presented.