Set-Membership Quaternion Normalized LMS Algorithm

In this paper, we propose the set-membership quaternion nor malized least-mean-square (SM-QNLMS) algorithm. For this purpose, first, we review the quaternion leas t-mean-square (QLMS) algorithm, then go into the quaternion normalized least-mean-square (QNLMS) algorit hm. By having the QNLMS algorithm, we propose the SM-QNLMS algorithm in order to reduce the update rate of the Q NLMS algorithm and avoid updating the system parameters when there is not enough innovation in upcoming d ata. 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 quatern io ic adaptive beamforming. The simulation results demonstrate that the SM-QNLMS algorithm outperforms the QN LMS algorithm and it has higher convergence speed and lower update rate.

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