Bayesian kernel-based system identification with quantized output data
This addresses system identification challenges in scenarios with quantized data, such as in digital control systems, but is incremental as it builds on existing kernel-based approaches.
The paper tackles the problem of linear system identification with quantized output data by introducing a Bayesian method using a stable spline kernel and MCMC, resulting in substantial accuracy improvements over state-of-the-art kernel-based methods in numerical 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 (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.