A Fast Rational Model Approach to Parametric Spectral Estimation—Part I: The Algorithm

Abstract

A novel, fast rational model (ARMA) approach to parametric spectral estimation, based on correlation-type and guaranteed-stability versions of the Suboptimum Maximum Likelihood scheme that utilizes a quadratic approximation of the negative log-likelihood about an initial estimate in the MA parameter subspace, inverse function estimates, and fundamental ARMA process properties, is introduced. The proposed approach is exclusively based on linear operations, uses the autocovariance function as a “sufficient statistic,” and overcomes the main drawbacks/limitations of alternative approaches by offering high accuracy, minimal computational and memory storage requirements, no need for a priori information, mathematically guaranteed stability (and therefore the capability of estimating all types of spectra, including those characterized by sharp valleys), and complete elimination of the local extrema problem by yielding a unique estimate that is shown to asymptotically converge to the true spectrum. The paper is divided into two parts: The basic form of the proposed approach is derived in the first part, whereas in the second (Fassois, 1990), its consistency is proven, two guaranteed-stability versions developed, and its performance evaluated via numerical simulations and comparisons with standard techniques.