ARX Model Identification using Generalized Spectral Decomposition

TL;DR

This paper introduces a new automated method using generalized spectral decomposition for identifying ARX models, accurately estimating orders, delay, noise distribution, and parameters even in low SNR conditions.

Contribution

The paper presents a novel two-step framework that automatically estimates ARX model orders, delay, noise distribution, and parameters using generalized spectral decomposition.

Findings

Consistent parameter estimates at low SNR.

Effective order and delay estimation from generalized eigenvalues.

Robust performance demonstrated through simulation studies.

Abstract

This article is concerned with the identification of autoregressive with exogenous inputs (ARX) models. Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized for the estimation of ARX models but are known to deliver unbiased and consistent parameter estimates for a correctly supplied guess of input-output orders and delay. In this paper, we propose a novel automated framework which recovers orders, delay, output noise distribution along with parameter estimates. The primary tool utilized in the proposed framework is generalized spectral decomposition. The proposed algorithm systematically estimates all the parameters in two steps. The first step utilizes estimates of the order by examining the generalized eigenvalues, and the second step estimates the parameter from the generalized eigenvectors. Simulation studies are presented to demonstrate the efficacy of the proposed method and are observed to deliver consistent estimates even at low signal to noise ratio (SNR).