Identification of Linear Dynamic Systems using Dynamic Iterative Principal Component Analysis

Abstract

The paper is concerned with identifying models from data that have errors in both outputs and inputs, popularly known as the errors-in-variables (EIV) problem. The total least squares formulation of the problem is known to offer a few well-known solutions. In this work, we present a novel and systematic approach to the identification of linear dynamic models for the EIV case in the principal component analysis (PCA) framework. A methodology for the systematic recovery of the process model, including the determination of order and delay, using what we term as dynamic, iterative PCA is presented. The core step consists of determining the structure of the constraint matrix by a systematic exploitation of the stacking and PCA order, input-output partitioning of the constraint matrix and an appropriate rotation. Optimal estimates of the (input-output) noise covariance matrices are also obtained. The proposed method can be applied to a broad class of linear processes including the case of unequal and unknown error variances. Simulation results are presented to demonstrate the effectiveness and consistency of the proposed method.