Unbiased equation-error based algorithms for efficient system identification using noisy measurements

Authors:
H. C. So;Y. T. Chan;K. C. Ho;Frankie K. W. Chan
Affiliations:
Department of Electronic Engineering, City University of Hong Kong Tat Chee Avenue, Kowloon, Hong Kong;Department of Electrical and Computer Engineering, Royal Military College of Canada Kingston, Ont., Canada K7K 7B4;Department of Electrical and Computer Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA;Department of Electronic Engineering, City University of Hong Kong Tat Chee Avenue, Kowloon, Hong Kong
Venue:
Signal Processing
Year:
2007

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Abstract

Based on the equation-error approach, two constrained weighted least squares algorithms are developed for unbiased infinite impulse response system identification. Both white input and output noise are present, and the ratio of the noise powers is known. Through a weighting matrix, the first algorithm uses a generalized unit-norm constraint which is a generalization of the Koopmans-Levin method. The second method employs a monic constraint which in fact is a relaxation algorithm for maximum likelihood estimation in Gaussian noise. Algorithm modifications for the input-noise-only or output-noise-only cases are also given. Via computer simulations, the effectiveness of the proposed estimators is demonstrated by contrasting with conventional benchmarks in different signal-to-noise ratio and data length conditions.