- Research Article
- Open Access
Performance Analysis of the Consensus-Based Distributed LMS Algorithm
© Gonzalo Mateos et al. 2009
Received: 15 May 2009
Accepted: 8 October 2009
Published: 23 November 2009
Low-cost estimation of stationary signals and reduced-complexity tracking of nonstationary processes are well motivated tasks than can be accomplished using ad hoc wireless sensor networks (WSNs). To this end, a fully distributed least mean-square (D-LMS) algorithm is developed in this paper, in which sensors exchange messages with single-hop neighbors to consent on the network-wide estimates adaptively. The novel approach does not require a Hamiltonian cycle or a special bridge subset of sensors, while communications among sensors are allowed to be noisy. A mean-square error (MSE) performance analysis of D-LMS is conducted in the presence of a time-varying parameter vector, which adheres to a first-order autoregressive model. For sensor observations that are related to the parameter vector of interest via a linear Gaussian model and after adopting simplifying independence assumptions, exact closed-form expressions are derived for the global and sensor-level MSE evolution as well as its steady-state (s.s.) values. Mean and MSE-sense stability of D-LMS are also established. Interestingly, extensive numerical tests demonstrate that for small step-sizes the results accurately extend to the pragmatic setting whereby sensors acquire temporally correlated, not necessarily Gaussian data.
To access the full article, please see PDF.
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.