A new kernel-based approach to system identification with quantized output data

TL;DR

This paper proposes a Bayesian kernel-based method for linear system identification using quantized output data, employing MCMC techniques to estimate system parameters and hyperparameters effectively.

Contribution

It introduces a novel Gaussian process model with a stable spline kernel and develops MCMC algorithms for system identification with quantized data, enhancing existing kernel methods.

Findings

Outperforms state-of-the-art kernel-based methods in simulations

Effectively estimates system impulse response from quantized data

Provides accurate hyperparameter estimation via EM algorithm

Abstract

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response 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. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.