Identification of Errors-in-Variables ARX Models Using Modified Dynamic Iterative PCA

TL;DR

This paper introduces a novel algorithm for identifying errors-in-variables ARX models in SISO systems with colored noise, jointly estimating error variances, model order, delay, and parameters using a modified DIPCA approach.

Contribution

It extends DIPCA to handle colored noise and jointly estimates all key parameters without prior knowledge of noise variances or system orders.

Findings

Effective in identifying EIV-ARX models with colored noise

Joint estimation improves accuracy over existing methods

Simulation results validate the proposed algorithm's efficacy

Abstract

Identification of autoregressive models with exogenous input (ARX) is a classical problem in system identification. This article considers the errors-in-variables (EIV) ARX model identification problem, where input measurements are also corrupted with noise. The recently proposed DIPCA technique solves the EIV identification problem but is only applicable to white measurement errors. We propose a novel identification algorithm based on a modified Dynamic Iterative Principal Components Analysis (DIPCA) approach for identifying the EIV-ARX model for single-input, single-output (SISO) systems where the output measurements are corrupted with coloured noise consistent with the ARX model. Most of the existing methods assume important parameters like input-output orders, delay, or noise-variances to be known. This work's novelty lies in the joint estimation of error variances, process order, delay, and model parameters. The central idea used to obtain all these parameters in a theoretically rigorous manner is based on transforming the lagged measurements using the appropriate error covariance matrix, which is obtained using estimated error variances and model parameters. Simulation studies on two systems are presented to demonstrate the efficacy of the proposed algorithm.