In this paper, we consider the problem of distributed estimation over adaptive networks in the presence of noisy input, output and communication links. First, a diffusion average-estimate bias-compensated LMS (D-ABC-LMS) algorithm is devised for processing these noisy measurements. Different from the existing diffusion schemes, it consists of three steps: (i) bias-compensated weight update, (ii) average estimation and (iii) weight combination, where the second step utilizes a moving average technique to process imprecise exchange weights caused by communication link noise. Then, we analyze the stability and convergence of the D-ABC-LMS algorithm, and derive closed-form expressions to predict its steady-state mean-square deviation (MSD) and network MSD (NMSD). In addition, by introducing one more step via the adaptive mixture of the noisy exchange weight vectors and their denoised estimates, we propose a diffusion mixed average-estimate bias-compensated LMS (D-MABC-LMS) method for increasing the convergence rate of the D-ABC-LMS scheme. Finally, computer simulation results show the superiority of the proposed algorithms over previously reported techniques using noisy measurements over adaptive networks.

中文翻译：

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使用噪声测量的自适应网络上的扩散平均估计偏差补偿 LMS 算法

在本文中，我们考虑在存在噪声输入、输出和通信链路的情况下在自适应网络上进行分布式估计的问题。首先，设计了一种扩散平均估计偏置补偿 LMS (D-ABC-LMS) 算法来处理这些噪声测量。与现有的扩散方案不同，它包括三个步骤：（i）偏差补偿权重更新，（ii）平均估计和（iii）权重组合，其中第二步利用移动平均技术处理由通信链路噪声。然后，我们分析了 D-ABC-LMS 算法的稳定性和收敛性，并推导出闭式表达式来预测其稳态均方偏差 (MSD) 和网络 MSD (NMSD)。此外，通过噪声交换权重向量及其去噪估计的自适应混合再引入一步，我们提出了一种扩散混合平均估计偏置补偿 LMS (D-MABC-LMS) 方法，用于提高 D-ABC 的收敛速度-LMS 计划。最后，计算机模拟结果显示了所提出的算法优于先前报告的使用自适应网络上的噪声测量的技术。