Huang Fuyi, Zhang Sheng, Zheng Wei Xing
IEEE Trans Neural Netw Learn Syst. 2024 Oct;35(10):13217-13231. doi: 10.1109/TNNLS.2023.3266402. Epub 2024 Oct 7.
To improve the learning performance of the conventional diffusion least mean square (DLMS) algorithms, this article proposes Bayesian-learning-based DLMS (BL-DLMS) algorithms. First, the proposed BL-DLMS algorithms are inferred from a Gaussian state-space model-based Bayesian learning perspective. By performing Bayesian inference in the given Gaussian state-space model, a variable step-size and an estimation of the uncertainty of information of interest at each node are obtained for the proposed BL-DLMS algorithms. Next, a control method at each node is designed to improve the tracking performance of the proposed BL-DLMS algorithms in the sudden change scenario. Then, a lower bound on the variable step-size of each node of the proposed BL-DLMS algorithms is derived to maintain the optimal steady-state performance in the nonstationary scenario (unknown parameter vector of interest is time-varying). Afterward, the mean stability and the transient and steady-state mean square performance of the proposed BL-DLMS algorithms are analyzed in the nonstationary scenario. In addition, two Bayesian-learning-based diffusion bias-compensated LMS algorithms are proposed to handle the noisy inputs. Finally, the superior learning performance of the proposed learning algorithms is verified by numerical simulations, and the simulated results are in good agreement with the theoretical results.
为了提高传统扩散最小均方（DLMS）算法的学习性能，本文提出了基于贝叶斯学习的DLMS（BL-DLMS）算法。首先，从基于高斯状态空间模型的贝叶斯学习角度推导所提出的BL-DLMS算法。通过在给定的高斯状态空间模型中进行贝叶斯推理，为所提出的BL-DLMS算法获得了可变步长以及每个节点处感兴趣信息的不确定性估计。接下来，设计每个节点处的控制方法，以提高所提出的BL-DLMS算法在突变场景中的跟踪性能。然后，推导所提出的BL-DLMS算法每个节点可变步长的下限，以在非平稳场景（感兴趣的未知参数向量随时间变化）中保持最优稳态性能。之后，在非平稳场景中分析所提出的BL-DLMS算法的均值稳定性以及瞬态和稳态均方性能。此外，提出了两种基于贝叶斯学习的扩散偏差补偿LMS算法来处理有噪声的输入。最后，通过数值模拟验证了所提出学习算法的卓越学习性能，且模拟结果与理论结果吻合良好。
