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Continuous-Time DC Kernel-A Stable Generalized First-Order Spline Kernel
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Chinese Univ Hong Kong, Peoples R China.ORCID iD: 0000-0001-8655-2655
2018 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 12, p. 4442-4447Article in journal (Refereed) Published
Abstract [en]

The stable spline (SS) kernel and the diagonal correlated (DC) kernel are two kernels that have been applied and studied extensively for kernel-based regularized LTI system identification. In this note, we show that similar to the derivation of the SS kernel, the continuous-time DC kernel can be derived by applying the same "stable" coordinate change to a "generalized" first-order spline kernel, and thus, can be interpreted as a stable generalized first-order spline kernel. This interpretation provides new facets to understand the properties of the DC kernel. In particular, we derive a new orthonormal basis expansion of the DC kernel and the explicit expression of the norm of the reproducing kernel Hilbert space associated with the DC kernel. Moreover, for the nonuniformly sampled DC kernel, we derive its maximum entropy property and show that its kernel matrix has tridiagonal inverse.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 63, no 12, p. 4442-4447
Keywords [en]
Kernal; MaxEnt; orthonormal basis expansion; regularization methods; system identification; tridiagonal inverse
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-153695DOI: 10.1109/TAC.2018.2825365ISI: 000451997000040OAI: oai:DiVA.org:liu-153695DiVA, id: diva2:1276206
Note

Funding Agencies|Thousand Youth Talents Plan - central government of China; National Natural Science Foundation of China [61773329]; Shenzhen Research Projects - Shenzhen Science and Technology Innovation Council [Ji-20170189, Ji-20160207]; Chinese University of Hong Kong, Shenzhen [2014.0003.23]; Swedish Research Council [2014-5894]; [PF. 01.000249]

Available from: 2019-01-07 Created: 2019-01-07 Last updated: 2019-01-07

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
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  • vancouver
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  • Other style
More styles
Language
  • de-DE
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  • sv-SE
  • Other locale
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Output format
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