Identification of Switched Autoregressive Systems from Large Noisy Data Sets

TL;DR

This paper presents a new method for identifying switched autoregressive models from large, noisy datasets, effectively estimating system parameters even with limited noise distribution information.

Contribution

The paper introduces a novel approach that leverages expected values and the law of large numbers for system identification under high noise conditions.

Findings

Effective with large datasets and high noise levels

Outperforms polynomial and mixed-integer optimization methods in computational efficiency

Demonstrated success through academic examples

Abstract

The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is assumed that only partial information on the probability distribution of the noise is available. Given input-output data, we aim at identifying switched system coefficients and parameters of the distribution of the noise which are compatible with the collected data. System dynamics are estimated through expected values computation and by exploiting the strong law of large numbers. We demonstrate the efficiency of the proposed approach with several academic examples. The method is shown to be extremely effective in the situations where a large number of measurements is available; cases in which previous approaches based on polynomial or mixed-integer optimization cannot be applied due to very large computational burden.