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Analysis of Distributed Adaptive Filters Based on Diffusion Strategies Over Sensor Networks

机译：基于传感器网络扩散策略的分布式自适应滤波器分析

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摘要

In this paper, we will analyze a basic class of diffusion adaptive filters based on least mean squares algorithms. Both stability and performance analyses will be carried out under a general cooperative information condition, without such stringent conditions as statistical independence and stationarity that have been used in almost all the existing literature and, thus, makes our theory applicable to stochastic systems with feedback. In comparison with the existing work, a key theoretical difficulty that needs to be overcome in this paper is to analyze the product of asymmetric correlated nonstationary random matrices, which is inherent in the structure of the diffusion-type filtering algorithms. We will further demonstrate that the distributed adaptive filters can estimate a dynamic process of interest from noisy measurements by a set of sensors working in a cooperative way, in the natural scenario where none of the sensors can fulfill the estimation task individually due to insufficient information. Finally, the necessity of our cooperative information condition will also be discussed in this paper.
机译：在本文中，我们将基于最小均方算法分析一类基本的扩散自适应滤波器。稳定性和性能分析都将在一般的协作信息条件下进行，而没有几乎所有现有文献中都使用过的诸如统计独立性和平稳性这样严格的条件，因此，使我们的理论适用于带有反馈的随机系统。与现有工作相比，本文需要克服的一个关键理论困难是分析不对称相关非平稳随机矩阵的乘积，这是扩散型滤波算法的结构所固有的。我们将进一步证明，在自然情况下，由于信息不足，没有一个传感器可以单独完成估计任务，因此分布式自适应滤波器可以通过一组以协作方式工作的传感器，从嘈杂的测量结果中估计感兴趣的动态过程。最后，本文还将讨论我们合作信息条件的必要性。

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