Title :
Spectral analysis of the DC kernel for regularized system identification
Author :
Tianshi Chen;Gianluigi Pillonetto;Alessandro Chiuso;Lennart Ljung
Author_Institution :
Division of Automatic Control, the Department of Electrical Engineering, Linkö
Abstract :
System identification with regularization methods has attracted increasing attention recently and is a complement to the current standard maximum likelihood/prediction error method. In this paper, we focus on the kernel-based regularization method and give a spectral analysis of the so-called diagonal correlated (DC) kernel, one family of kernel structures that has been proven useful for linear time-invariant system identification. In particular, using the theory of Bessel functions, we derive the eigenvalues and corresponding eigenfunctions of the DC kernel. Accordingly, we derive the Karhunen-Loève expansion of the stochastic process whose covariance function is the DC kernel.
Keywords :
"Kernel","Eigenvalues and eigenfunctions","Spectral analysis","Linear systems","Hilbert space","Integral equations","Yttrium"
Conference_Titel :
Decision and Control (CDC), 2015 IEEE 54th Annual Conference on
DOI :
10.1109/CDC.2015.7402844