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    This summary is machine-generated.

    This study introduces Bayesian-learning-based diffusion least mean square (BL-DLMS) algorithms to enhance learning performance. These algorithms offer improved tracking and steady-state performance, especially in nonstationary environments with noisy inputs.

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    Area of Science:

    • Signal Processing
    • Machine Learning
    • Adaptive Filters

    Background:

    • Conventional diffusion least mean square (DLMS) algorithms face limitations in learning performance.
    • Adaptive filtering is crucial for various signal processing applications.

    Purpose of the Study:

    • To propose novel Bayesian-learning-based DLMS (BL-DLMS) algorithms for improved learning performance.
    • To enhance tracking and steady-state performance in dynamic environments.

    Main Methods:

    • Bayesian inference within a Gaussian state-space model framework.
    • Development of variable step-size and uncertainty estimation mechanisms.
    • Design of a control method for sudden change scenarios and derivation of a lower bound for steady-state performance.

    Main Results:

    • The proposed BL-DLMS algorithms achieve superior learning performance.
    • Variable step-size and uncertainty estimation enhance adaptability.
    • Improved tracking and steady-state performance demonstrated in simulations.

    Conclusions:

    • BL-DLMS algorithms offer significant improvements over conventional DLMS.
    • The methods are effective in nonstationary scenarios and with noisy inputs.
    • Theoretical and simulation results confirm the algorithms' efficacy.