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A Distributed Algorithm for In-Network Adaptive Estimation Using Incremental Aggregated Gradient

Authors:
Wael Bazzi
Amir Rastegarnia
Azam Khalili
Saeid Sanei

Keywords: Adaptive networks; incremental; least mean square; estimation

Abstract:
In this paper, we consider the distributed estimation problem where a set of nodes is deployed to estimate a parameter of interest when the statistical model (or information) for the underlying processes is not available, or it varies in time. Such a scenario appears in many real-world applications e.g. in sensor networks. The estimation problem can be expressed mathematically as the minimization of a cost function, which is the sum of continuously differentiable local cost functions. The paper aims to develop an iterative, fully distributed and adaptive solution for the optimization problem. Similar to the existing Incremental Least Mean-Squares (ILMS) algorithm, in the proposed algorithm we use steepest-descent method to generate an approximation of the descent direction at every node. However, unlike the ILMS, the proposed algorithm uses the aggregate gradient at each node which is the average of the previously computed gradients by other nodes. The resultant algorithm which is called Incremental Aggregated Gradient-LMS (IAG-LMS) outperforms the ILMS algorithm in terms of the steady-state error. Moreover, its stability bound (in terms of the step-size parameter) is also wider than the ILMS algorithm. We present numerical simulations to support the mentioned claims and illustrate the results.

Pages: 142 to 146

Copyright: Copyright (c) IARIA, 2014

Publication date: June 22, 2014

Published in: conference

ISSN: 2308-4219

ISBN: 978-1-61208-347-6

Location: Seville, Spain

Dates: from June 22, 2014 to June 26, 2014