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

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.Comment: 10 pages, 4 figure

Identification of sparse FIR systems using a general quantisation scheme

This paper presents an identification scheme for sparse FIR systems with quantised data. We consider a general quantisation scheme, which includes the commonly deployed static quantiser as a special case. To tackle the sparsity issue, we utilise a Bayesian approach, where an ℓ₁ a priori distribution for the parameters is used as a mechanism to promote sparsity. The general framework used to solve the problem is maximum likelihood (ML). The ML problem is solved by using a generalised expectation maximisation algorithm