Diffusion-Probabilistic Least Mean Square Algorithm

Sihai Guan, Chun Meng, Bharat Biswal

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, a novel diffusion estimation algorithm is proposed from a probabilistic perspective by combining the diffusion strategy and the probabilistic least mean square (LMS) at all distributed network nodes. The proposed method, namely diffusion-probabilistic LMS (DPLMS), is more robust to the input signal and impulsive noise than previous algorithms like the diffusion sign-error LMS (DSE-LMS), diffusion robust variable step-size LMS (DRVSSLMS), and diffusion least logarithmic absolute difference (DLLAD) algorithms. Instead of minimizing the estimation error, the DPLMS algorithm is based on approximating the posterior distribution with an isotropic Gaussian distribution. In this paper, the stability of the mean estimation error and the computational complexity of the DPLMS algorithm are analyzed theoretically. Simulation experiments are conducted to explore the mean estimation error for the DPLMS algorithm with varied conditions for input signals and impulsive interferences, compared to the DSE-LMS, DRVSSLMS, and DLLAD algorithms. Both results from the theoretical analysis and simulation suggest that the DPLMS algorithm has superior performance than the DSE-LMS, DRVSSLMS, and DLLAD algorithms when estimating the unknown linear system under the changeable impulsive noise environments.

Original languageEnglish (US)
Pages (from-to)1295-1313
Number of pages19
JournalCircuits, Systems, and Signal Processing
Issue number3
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Applied Mathematics


  • Distributed network
  • Impulsive noise
  • Input signals
  • Probabilistic


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