Steady-State Performance Analysis of Quaternion-Valued Least Mean Square Adaptive Algorithm

  • Sen LiEmail author
  • Fengzhi Liu
  • Bin Lin
  • Rongxi He
  • Xiaomei Zhu
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 517)


The quaternion-valued least mean squares (QvLMS) adaptive algorithm has been proved valid for the adaptive filtering in quaternion domain. However, there have been few researches on its performance. This paper firstly deduces the energy conservation relation in quaternion domain and then analyzes the steady-state performance of QvLMS algorithm in stationary and non-stationary environment by using the quaternion energy conservation relation. The relevant expressions are deduced and then the step-size range which can guarantee the algorithm convergence is obtained. Simulation results demonstrate the rationality of the analysis.


Steady-state performance Quaternion adaptive filter Quaternion energy conservation relation 



This work was supported in part by the National Natural Science Foundation of China under Grants 61301228, 61501223 and the Fundamental Research Funds for the Central Universities under Grant 3132016331 and 3132016318.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Sen Li
    • 1
    Email author
  • Fengzhi Liu
    • 1
  • Bin Lin
    • 1
  • Rongxi He
    • 1
  • Xiaomei Zhu
    • 2
  1. 1.Department of Information Science and TechnologyDalian Maritime UniversityDalianChina
  2. 2.College of Computer Science and Technology, Nanjing Tech UniversityNanjingChina

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