Bayesian kernel-based system identification with quantized output data

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 (MCMC) methods to provide an estimate of the system. In particular, we show how to 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 when employed in identification of systems with quantized data.

On the Coordinate Change to the First-Order Spline Kernel for Regularized Impulse Response Estimation

“…For comparison, we also show the result with the TC kernel and the Empirical Bayes. Recall that the TC kernel is defined as (10). Fig.…”

“…While various kernels have been proposed (e.g., [5,6,7]), three most widely used kernels are the so-called Stable Spline kernel (SS) [2], the Tuned-Correlated kernel (sometimes also called the firstorder stable spline kernel) [8], and the Diagonal-Correlated (DC) kernel [8]. These three kernels have simple structures and favorable properties, and their effectiveness are shown in various works, e.g., [8,9,10,11].…”

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

“…Using the Expectation-Maximization (EM) method [14], we design an iterative scheme for marginal likelihood maximization, where the E-step characterizing the EM method makes use of the Gibbs sampler (see also [7]), and the M-step results in a sequence of straightforward optimization problems. Interestingly, the resulting estimation scheme can be seen as a generalization of the method proposed in [19] to the Bayesian nonparametric framework and, differently from [5] and [12], it allows tuning all the kernel hyperparameters.…”

Hammerstein system identification with quantised inputs and quantised output observations

“…Related research begins with the linear systems [1, 9–12]. Wang et al [1] employed the empirical measure to design asymptotically efficient algorithms to identify the finite impulse response (FIR) systems with quantised observations and discussed the time complexity and space complexity.…”

“…Wang and Zhang [11] introduced a quadratic programming‐based method for identification of FIR dynamic systems from binary/quantised data. Bottegal et al [12] studied the Bayesian kernel‐based linear system identification with quantised output data and employed Markov chain Monte Carlo methods to provide an estimate of the system.…”