Deterministic regression methods for unbiased estimation of time-varying autoregressive parameters from noisy observations

• Published in: Signal processing 2012-04, Vol.92 (4), p.857-871
• Main Authors: Ijima, Hiroshi, Grivel, Eric
• Format: Article
• Language: English
• Subjects: Additives; Applied sciences; Computer Science; Detection, estimation, filtering, equalization, prediction; Eigenvalues; Engineering Sciences; Errors-in-variables; Exact sciences and technology; Gaussian; Generalized eigenvalue decomposition; Information, signal and communications theory; Least squares; Least squares method; Noise; Parameter estimation; Parameter tracking; Regression; Signal and communications theory; Signal and Image Processing; Signal, noise; Telecommunications and information theory; Time-varying autoregressive (TVAR) model; Tracking
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2011.09.020

A great deal of interest has been paid to autoregressive parameter estimation in the noise-free case or when the observation data are disturbed by random noise. Tracking time-varying autoregressive (TVAR) parameters has been also discussed, but few papers deal with this issue when there is an additive zero-mean white Gaussian measurement noise. In this paper, one considers deterministic regression methods (or evolutive methods) where the TVAR parameters are assumed to be weighted combinations of basis functions. However, the additive white measurement noise leads to a weight-estimation bias when standard least squares methods are used. Therefore, we propose two alternative blind off-line methods that allow both the variance of the additive noise and the weights to be estimated. The first one is based on the errors-in-variable issue whereas the second consists in viewing the estimation issue as a generalized eigenvalue problem. A comparative study with other existing methods confirms the effectiveness of the proposed methods. ► We propose two methods for estimating time-varying autoregressive (TVAR) parameters. ► Observation data are disturbed by random noise. ► TVAR parameters are assumed to be weighted combinations of basis functions. ► A comparative study with other existing methods confirms the effectiveness of the proposed methods.