Perspectives of orthonormal basis functions based kernels in Bayesian system identification

M.A.H. Darwish, G. Pillonetto, Roland Toth

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

5 Citations (Scopus)


Kernel-based regularization approaches for lin- ear time-invariant system identification have been introduced recently. This class of methods corresponds to a particu- lar 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.
Original languageEnglish
Title of host publication54th IEEE Conference on Decision and Control (CDC 2015), 15-18 December 2015, Osaka, Japan
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)978-1-4799-7885-4
ISBN (Print)978-1-4799-7884-7
Publication statusPublished - 2015
Event54th IEEE Conference on Decision and Control (CDC 2015) - "Osaka International Convention Center", Osaka, Japan
Duration: 15 Dec 201518 Dec 2015
Conference number: 54


Conference54th IEEE Conference on Decision and Control (CDC 2015)
Abbreviated titleCDC 2015
Internet address


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