Abstract
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.
Highlights
The advent of wireless sensor networks (WSNs) has created renewed interest in the field of distributed computing, calling for collaborative solutions that enable low-cost estimation of stationary signals as well as reduced-complexity tracking of nonstationary processes
Different from WSN topologies that include a fusion center (FC), ad hoc ones are devoid of hierarchies and rely on in-network processing to effect agreement among sensors on the estimate of interest
The present paper develops a fully distributed (D-) least mean-square- (LMS-)type algorithm, which performs consensus-based, innetwork, adaptive estimation for linear regression applications
Summary
The advent of wireless sensor networks (WSNs) has created renewed interest in the field of distributed computing, calling for collaborative solutions that enable low-cost estimation of stationary signals as well as reduced-complexity tracking of nonstationary processes. Often times sensors need to perform estimation in a constantly changing environment without having available a (statistical) model for the underlying processes of interest This has motivated the development of distributed adaptive estimation schemes, generalizing the notion of adaptive filtering to a setup involving networked sensing/processing devices [2, Section I.B]. Relative to the D-LMS variant in [16], the present reformulation of the LMS cost circumvents the requirement of the special type of sensors comprising the so-called bridge sensor subset; see [13, 17] As a byproduct, this approach results in a fully distributed algorithm whereby all sensors perform identical tasks, without introducing hierarchies that may require intricate recovery protocols to cope with sensor failures.
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