Identification of Errors-in-Variables ARX Models Using Modified Dynamic Iterative PCA
This work provides an incremental improvement for system identification researchers working on ARX models with noisy input and colored output noise, by jointly estimating parameters usually assumed known.
This paper addresses the identification of Errors-in-Variables (EIV) ARX models, where both input and output measurements are corrupted by noise, specifically colored noise in the output. The proposed algorithm, a modification of Dynamic Iterative Principal Components Analysis (DIPCA), jointly estimates error variances, process order, delay, and model parameters, which are typically assumed known in existing methods. Simulation studies on two systems demonstrate its efficacy.
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.