Parameter estimation for autoregressive Gaussian-mixture processes: the EMAX algorithm

• Main Authors: Verbout, S.M., Ooi, J.M., Ludwig, J.T., Oppenheim, A.V.
• Format: Conference Proceeding
• Language: English
• Subjects: Applied sciences; Contracts; Detection, estimation, filtering, equalization, prediction; Equations; Exact sciences and technology; Gaussian distribution; Gaussian noise; Gaussian processes; Higher order statistics; Information, signal and communications theory; Iterative algorithms; Maximum likelihood estimation; Parameter estimation; Probability density function; Signal and communications theory; Signal, noise; Telecommunications and information theory
• ISSN: 1520-6149; 2379-190X
• DOI: 10.1109/ICASSP.1997.604632

The problem of estimating parameters of discrete-time non-Gaussian autoregressive (AR) processes is addressed. The subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a Gaussian-mixture probability density function (PDF). Because the likelihood function for this problem is typically unbounded in the vicinity of undesirable, degenerate parameter estimates, a global maximum likelihood approach is not appropriate. Hence, an alternative approach is taken whereby a finite local maximum of the likelihood surface is sought. This approach, which is termed the quasi-maximum likelihood (QML) approach, is used to obtain estimates of the AR parameters as well as the means, variances, and weighting coefficients that define the Gaussian-mixture PDF. A technique for generating solutions to the QML problem is derived using a generalized version of the expectation-maximization principle.