  A distributed adaptive algorithm to estimate a time-varying signal, measured
by a wireless sensor network, is designed and analyzed. One of the major
features of the algorithm is that no central coordination among the nodes needs
to be assumed. The measurements taken by the nodes of the network are affected
by noise, and the communication among the nodes is subject to packet losses.
Nodes exchange local estimates and measurements with neighboring nodes. Each
node of the network locally computes adaptive weights that minimize the
estimation error variance. Decentralized conditions on the weights, needed for
the convergence of the estimation error throughout the overall network, are
presented. A Lipschitz optimization problem is posed to guarantee stability and
the minimization of the variance. An efficient strategy to distribute the
computation of the optimal solution is investigated. A theoretical performance
analysis of the distributed algorithm is carried out both in the presence of
perfect and lossy links. Numerical simulations illustrate performance for
various network topologies and packet loss probabilities.
