Perspectives of orthonormal basis functions based kernels in Bayesian system identification?

Kernel-based regularization approaches for linear time-invariant system identification have been introduced recently. This class of methods corresponds to a particular regularized least-squares methodology that may achieve a favorable bias/variance trade-off compared with classical Prediction Error Minimization (PEM) methods. However, to fully exploit this property, the kernel function itself needs to be appropriately designed for the identification problem at hand to be able to successfully capture all relevant aspects of the data-generating system. Hence, there is a need for a methodology that can accomplish this design step without affecting the simplicity of these approaches. In this paper, we propose a systematic kernel construction mechanism to capture dynamic system behavior via the use of orthonormal basis functions (OBFs). Two special cases are investigated as an illustration of the construction mechanism, namely Laguerre and Kautz based kernel structures. Monte-Carlo simulations show that OBFs-based kernels with Laguerre basis perform well compared with stable spline/TC kernels, especially for slow systems with dominant poles close to the unit circle. Moreover, the capability of Kautz basis to model resonant systems is also shown.