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Algorithms for Improving Accuracy of Distributed Estimation over Adaptive Networks

Algorithms for Improving Accuracy of Distributed Estimation over Adaptive Networks
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In this dissertation, we study the problem of distributed estimation over adaptive networks, in which a set of nodes cooperates to estimate a parameter of interest from noisy measurements. Among several algorithms, we focus on the diffusion algorithms which have various benefits such as their wide stability range and enhanced performance. To improve their estimation performance, many variants have been proposed. In most of the previous work, the range of data usage of each node was fixed to only its neighborhood. In such situations, an aim of the study is to use broader information from expanded set of nodes to improve the estimation accuracy. For this purpose, we propose diffusion least-mean-square (LMS) algorithms that use multi-combination step. We allow each node in the network to use information from multi-hop neighbors to approximate a global cost function accurately. By minimizing this cost and dividing multi-hop range summation into 1-hop range combination steps, we derive new diffusion LMS algorithms. The resulting distributed algorithms consist of adaptation and multi-combination step. Multi combination allows each node to use information from non-adjacent nodes at each time instant, thereby reducing steady-state error. We analyze the output to derive stability conditions and to quantify the transient and steady-state behaviors. Theoretical and experimental results indicate that the proposed algorithms have lower steady-state error compared to the conventional diffusion LMS algorithms. We also propose a new combination rule for the multi-combination step which can further improve the estimation performance of the proposed algorithms. Another concern in this dissertation is multitask scenario, in which different clusters of a network estimate different optimum vectors. Specifically, we focus on the clustering problem when the nodes have no prior knowledge of cluster information. We propose a new adaptive clustering algorithm that is robust to various multitask environments. Positional relationships among optimal vectors and the reference signal are determined by using the mean-square deviation relation derived from one-step LMS update. Clustering is performed by combining determinations on the positional relationships at several iterations. From this geometrical basis, unlike the conventional clustering algorithms using simple thresholding method, the proposed algorithm can perform clustering accurately in various multitask environments. Simulation results show that the proposed algorithm has more accurate estimation accuracy than the conventional algorithms, and is insensitive to parameter selection.
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