Multichannel Quaternion Least Mean Square Algorithm

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Quaternion least-mean-quare (QLMS) algorithm has been thoroughly investigated in the past for the adaptive filtering of 3D and 4D signals. However, QLMS is restricted to one-channel processing of such 3D and 4D processes. To address this shortcoming, we proposed the multichannel QLMS so that we can exploit the additional information from the multitude of 3D-4D vector sensors. For rigour, we provide the stability bound of the multichannel QLMS and demonstrate its robustness against noise. Simulations on real world 4D signals support the analysis.
Original languageEnglish
Title of host publicationInternational Conference on Acoustics, Speech, and Signal Processing
Subtitle of host publicationICASSP
Place of PublicationBrighton UK
Number of pages4
ISBN (Electronic)978-1-4799-8131-1
Publication statusE-pub ahead of print - 17 Apr 2019


  • Signal Processing
  • adaptive filters
  • quaternion
  • machine learning

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