Online Identification of Time-Varying Systems: a Bayesian approach

TL;DR

This paper presents a Bayesian online system identification method for time-varying systems, enabling real-time estimation by updating hyper-parameters efficiently and tracking system changes effectively.

Contribution

It introduces a novel Bayesian approach with hyper-parameter estimation and forgetting factors for real-time tracking of time-varying systems.

Findings

Efficient hyper-parameter updates via a single gradient step.

Closed-form impulse response estimates under Gaussian assumptions.

Two methods for system tracking using a forgetting factor.

Abstract

We extend the recently introduced regularization/Bayesian System Identification procedures to the estimation of time-varying systems. Specifically, we consider an online setting, in which new data become available at given time steps. The real-time estimation requirements imposed by this setting are met by estimating the hyper-parameters through just one gradient step in the marginal likelihood maximization and by exploiting the closed-form availability of the impulse response estimate (when Gaussian prior and Gaussian measurement noise are postulated). By relying on the use of a forgetting factor, we propose two methods to tackle the tracking of time-varying systems. In one of them, the forgetting factor is estimated by treating it as a hyper-parameter of the Bayesian inference procedure.