New Trinion and Quaternion Set-Membership Affine Projection Algorithms

摘要

This brief introduces new data-selective adaptive filtering algorithms for trinion and quaternion spaces mathbb{T} and mathbb{H}. The work advances the set-membership trinion- and quaternion-valued normalized least mean square (SMTNLMS and SMQNLMS) and the set-membership trinion- and quaternion-valued affine projection (SMTAP and SMQAP) algorithms. We derive set-membership trinion algorithms and then, as special cases, obtain trinion algorithms not employing the set-membership strategy. Prediction simulations based on recorded wind data are provided, showing the improved performance of the proposed algorithms in terms of reduced computational complexity. Then, the quaternion-based SMQAP and SMQNLMS algorithms are derived, and their improved performances are verified in an adaptive beamforming problem.