Identification of MISO systems in Minimal Realization Form

TL;DR

This paper presents an automated method for identifying minimal realization MISO system transfer functions, including order, delay, and heteroskedastic noise variances, from corrupted input-output data within an error-in-variables framework.

Contribution

It introduces a novel automated approach for minimal realization MISO system identification, estimating order, delay, and heteroskedastic noise variances simultaneously.

Findings

Effective identification of transfer functions demonstrated in numerical case studies.

Accurate estimation of order, delay, and noise variances achieved.

Method outperforms traditional approaches under complex noise conditions.

Abstract

The paper is concerned with identifying transfer functions of individual input channels in minimal realization form of a Multi-Input Single Output (MISO) from the input-output data corrupted by the error in all the variables. Such a framework is commonly referred to as error-in-variables (EIV). A common approach in the existing methods for identification of MISO systems is to estimate a non-minimal order transfer function under a subset of simplistic assumptions like homoskedastic error variances, known order, and delay. In this work, we deal with the challenging problem of identifying order, delay in each input of minimal realization form separately while estimating the transfer functions. We also estimate the heteroskedastic noise variances in each of the multiple inputs and output variables. An automated approach for the identification of MISO systems of minimal realization form in the EIV framework is proposed. Numerical case studies are presented to illustrate the efficacy of the proposed algorithm in identifying the transfer function along with the order, delay, and noise variances.