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

• Published in: Signal processing Vol. 87; no. 5; pp. 1014 - 1030
• Main Authors: So, H.C., Chan, Y.T., Ho, K.C., Chan, Frankie K.W.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2007; Elsevier Science
• Subjects: Applied sciences; Detection, estimation, filtering, equalization, prediction; Equation-error approach; Exact sciences and technology; Infinite impulse response filtering; Information, signal and communications theory; Monic constraint; Signal and communications theory; Signal, noise; Telecommunications and information theory; Unit-norm constraint; Weighted least squares; Unit-norm constraint; Infinite impulse response filtering; Monic constraint; Weighted least squares; Equation-error approach; Performance evaluation; Infinite impulse response filter; Filtering; Computer simulation; Algorithm; Relaxation; Weighting; Gaussian noise; Least squares method; System identification; Maximum likelihood; Signal to noise ratio
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2006.09.010

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.