Outlier robust system identification: a Bayesian kernel-based approach

TL;DR

This paper introduces a Bayesian kernel-based system identification method that is robust to outliers by modeling noise with Laplacian distributions and employing a novel MCMC scheme, improving estimation accuracy.

Contribution

It presents a new outlier-robust regularized kernel approach using Laplacian noise modeling and a Gibbs sampler for system identification, enhancing robustness and accuracy.

Findings

Significant improvement over existing methods in simulation accuracy.

Effective robustness to measurement outliers demonstrated.

Fast convergence of the proposed MCMC scheme.

Abstract

In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. To build robustness to outliers, we model the measurement noise as realizations of independent Laplacian random variables. The identification problem is cast in a Bayesian framework, and solved by a new Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the representation of the Laplacian random variables as scale mixtures of Gaussians, we design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods.