Suboptimum Maximum Likelihood Identification of ARMAX Processes

Abstract

A Suboptimum Maximum Likelihood (SML) method for ARMAX process identification from input-output observations is proposed. The proposed method is based on a quadratic approximation of the asymptotic negative log-likelihood function about an estimated point in the Moving Average parameter subspace, as well as an asymptotic ARX representation and fundamental properties of linear stochastic systems. The proposed method is shown to overcome the main drawbacks of the standard Maximum Likelihood and other alternative approaches by offering a low computational load and effectively circumventing the local extrema/wrong convergence problems and the need for initial guess parameter values. In addition, the consistency of the method is established, its extension to the multiple-input case presented, and, in contrast to most alternative approaches, its stability is mathematically guaranteed. The effectiveness of the proposed method is finally demonstrated through numerical simulations and comparisons with the Maximum Likelihood approach.