Quaternion kernel recursive least-squares algorithm

Various kernel-based algorithms have been successfully applied to nonlinear problems in adaptive filters over the last two decades. In this paper, we study a kernel recursive least squares (KRLS) algorithm in the quaternion domain. By the generalized Hamilton-real calculus method, we can apply the k...

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Veröffentlicht in:Signal processing Jg. 178; S. 107810
Hauptverfasser: Wang, Gang, Qiao, Jingci, Xue, Rui, Peng, Bei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.01.2021
Schlagworte:
Kernel recursive least square
Quaternion involutions
Quaternion kernel adaptive filter
Recursive least squares
Quaternion involutions
Quaternion kernel adaptive filter
Kernel recursive least square
Recursive least squares
ISSN:0165-1684, 1872-7557
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Zusammenfassung:Various kernel-based algorithms have been successfully applied to nonlinear problems in adaptive filters over the last two decades. In this paper, we study a kernel recursive least squares (KRLS) algorithm in the quaternion domain. By the generalized Hamilton-real calculus method, we can apply the kernel trick to calculate the quaternion KRLS filter. In order to show the feasibility of the proposed algorithm, firstly we investigate the quaternion recursive least squares (QRLS) algorithm, and simulations show that the proposed QRLS algorithm has the same steady error as that of the closed-form solution; Secondly, we generalize the QRLS algorithm to the quaternion KRLS algorithm, theoretical analysis show the convergence, and simulations are described demonstrating the performance of the proposed algorithm.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2020.107810