Preprint Article Version 1 This version is not peer-reviewed

Set-Membership Quaternion Normalized LMS Algorithm

Version 1 : Received: 3 December 2018 / Approved: 5 December 2018 / Online: 5 December 2018 (04:21:21 CET)

How to cite: Moradi, H.R.; Zardadi, A. Set-Membership Quaternion Normalized LMS Algorithm. Preprints 2018, 2018120061 (doi: 10.20944/preprints201812.0061.v1). Moradi, H.R.; Zardadi, A. Set-Membership Quaternion Normalized LMS Algorithm. Preprints 2018, 2018120061 (doi: 10.20944/preprints201812.0061.v1).

Abstract

In this paper, we propose the set-membership quaternion normalized least-mean-square (SM-QNLMS) algorithm. For this purpose, first, we review the quaternion least-mean-square (QLMS) algorithm, then go into the quaternion normalized least-mean-square (QNLMS) algorithm. By having the QNLMS algorithm, we propose the SM-QNLMS algorithm in order to reduce the update rate of the QNLMS algorithm and avoid updating the system parameters when there is not enough innovation in upcoming data. Moreover, the SM-QNLMS algorithm, thanks to the time-varying step-size, has higher convergence rate as compared to the QNLMS algorithm. Finally, the proposed algorithm is utilized in wind profile prediction and quaternionic adaptive beamforming. The simulation results demonstrate that the SM-QNLMS algorithm outperforms the QNLMS algorithm and it has higher convergence speed and lower update rate.

Subject Areas

adaptive filtering; set-membership filtering; quaternion; SM-QNLMS; wind profile prediction; quaternionic adaptive beamforming

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