Distributed algorithms are developed for optimal estimation of stationary random signals and smoothing of (even nonstationary) dynamical processes based on generally correlated observations collected by ad hoc wireless sensor networks (WSNs). Maximum a posteriori (MAP) and linear minimum mean-square error (LMMSE) schemes, well appreciated for centralized estimation, are shown possible to reformulate for distributed operation through the iterative (alternating-direction) method of multipliers. Sensors communicate with single-hop neighbors their individual estimates as well as multipliers measuring how far local estimates are from consensus. When iterations reach consensus, the resultant distributed (D) MAP and LMMSE estimators converge to their centralized counterparts when inter-sensor communication links are ideal. The D-MAP estimators do not require the desired estimator to be expressible in closed form, the D-LMMSE ones are provably robust to communication or quantization noise and both are particularly simple to implement when the data model is linear-Gaussian. For decentralized tracking applications, distributed Kalman filtering and smoothing algorithms are derived for any-time MMSE optimal consensus-based state estimation using WSNs. Analysis and corroborating numerical examples demonstrate the merits of the novel distributed estimators.
Bibliographical noteFunding Information:
Manuscript received March 7, 2007; revised July 23, 2007. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Aleksandar Dogandzic. Work in this paper was supported by the USDoD ARO Grant No. 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. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies of the Army Research Laboratory or the U. S. Government. Part of the paper was presented in the Fortieth Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, October 29–November 1, 2006; the 2007 IEEE Workshop on Signal Processing Advances Wireless Communication (SPAWC) Conference, Helsinki, Finland, June 17–20, 2007; and the 2007 SSP Workshop, Madison, WI, August 26–29, 2007.
- Distributed estimation
- Kalman smoother
- Nonlinear optimization
- Wireless sensor networks (WSNs)