Adaptive algorithms based on in-network processing of distributed observations are well-motivated for online parameter estimation and tracking of (non)stationary signals using ad hoc wireless sensor networks (WSNs). To this end, a fully distributed least mean-square (D-LMS) algorithm is developed in this paper, offering simplicity and flexibility while solely requiring single-hop communications among sensors. The resultant estimator minimizes a pertinent squared-error cost by resorting to i) the alternating-direction method of multipliers so as to gain the desired degree of parallelization and ii) a stochastic approximation iteration to cope with the time-varying statistics of the process under consideration. Information is efficiently percolated across the WSN using a subset of "bridge" sensors, which further tradeoff communication cost for robustness to sensor failures. For a linear data model and under mild assumptions aligned with those considered in the centralized LMS, stability of the novel D-LMS algorithm is established to guarantee that local sensor estimation error norms remain bounded most of the time. Interestingly, this weak stochastic stability result extends to the pragmatic setup where intersensor communications are corrupted by additive noise. In the absence of observation and communication noise, consensus is achieved almost surely as local estimates are shown exponentially convergent to the parameter of interest with probability one. Mean-square error performance of D-LMS is also assessed. Numerical simulations: i) illustrate that D-LMS outperforms existing alternatives that rely either on information diffusion among neighboring sensors, or, local sensor filtering; ii) highlight its tracking capabilities; and iii) corroborate the stability and performance analysis results.
Bibliographical noteFunding Information:
Manuscript received January 17, 2008; accepted January 06, 2009. First published February 24, 2009; current version published May 15, 2009. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Aleksandar Dogandzic. Work in this paper was supported by the USDoD ARO Grant W911NF-05-1-0283; and also through collaborative participation in the C&N Consortium sponsored by the U.S. ARL under the CTA Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. Part of the paper was presented at the Forty-Fifth Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, September 26–28, 2007 and at the International Conference on Acoustics, Speech and Signal Processing, Las Vegas, NV, March 30–April 4, 2008.
- Distributed estimation
- LMS algorithm
- Wireless sensor networks (WSNs)