A new kernel-based approach to system identification with quantized output data
This addresses system identification challenges for control or signal processing applications where output data is quantized, representing an incremental improvement over existing kernel-based methods.
The paper tackles linear system identification with quantized output data by proposing a novel kernel-based Bayesian method using stable spline kernels and MCMC techniques, showing effectiveness compared to state-of-the-art kernel-based methods in simulations.
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.