Sparse Bayesian ARX models with flexible noise distributions

TL;DR

This paper introduces a Bayesian approach for estimating linear dynamic system models with nonstandard, potentially multi-modal noise distributions, outperforming traditional methods especially in the presence of outliers or sensor anomalies.

Contribution

The paper develops a flexible Bayesian estimation method for ARX models that effectively handles complex, nonstandard noise distributions, including multi-modal and outlier-prone data.

Findings

Bayesian method performs well in standard noise scenarios

Significantly better in nonstandard, multi-modal noise conditions

Outperforms traditional methods with outlier-prone data

Abstract

This paper considers the problem of estimating linear dynamic system models when the observations are corrupted by random disturbances with nonstandard distributions. The paper is particularly motivated by applications where sensor imperfections involve significant contribution of outliers or wrap-around issues resulting in multi-modal distributions such as commonly encountered in robotics applications. As will be illustrated, these nonstandard measurement errors can dramatically compromise the effectiveness of standard estimation methods, while a computational Bayesian approach developed here is demonstrated to be equally effective as standard methods in standard measurement noise scenarios, but dramatically more effective in nonstandard measurement noise distribution scenarios.