Distributed Estimation over Wireless Sensor Networks with Packet Losses

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.

💡 Research Summary

The paper presents a fully decentralized adaptive algorithm for estimating a time‑varying signal using a wireless sensor network (WSN) in which both measurement noise and communication packet losses are present. Unlike many existing distributed estimation schemes that rely on a central coordinator or pre‑defined static weights, each node in the proposed framework independently computes a set of adaptive combination weights that minimize the local mean‑square estimation error. The algorithm proceeds in discrete time steps. At each step a node i forms a local estimate (\hat{x}i(k)) by linearly combining its own noisy measurement (y_i(k)=x(k)+v_i(k)) with the most recent estimates received from its neighboring nodes. The combination weights (w{i,j}(k)) are obtained by solving a local quadratic optimization problem that explicitly minimizes (\mathbb{E}