Stochastic Sensor Scheduling for Energy Constrained Estimation in Multi-Hop Wireless Sensor Networks

Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central fusion center. The fusion center computes an estimate of the process state by means of a Kalman filter. In this paper we assume that the WSN admits a tree topology with fusion center at the root. At each time step only a subset of sensors can be selected to transmit observations to the fusion center due to a limited energy budget. We propose a stochastic sensor selection algorithm that randomly selects a subset of sensors according to certain probability distribution, which is opportunely designed to minimize the asymptotic expected estimation error covariance matrix. We show that the optimal stochastic sensor selection problem can be relaxed into a convex optimization problem and thus solved efficiently. We also provide a possible implementation of our algorithm which does not introduce any communication overhead. The paper ends with some numerical examples that show the effectiveness of the proposed approach.

💡 Research Summary

This paper addresses the problem of sensor scheduling in wireless sensor networks (WSNs) where energy resources are limited and the network topology is a directed tree rooted at a fusion center. The authors consider a discrete‑time linear dynamical system observed by m sensors, each providing noisy measurements. Because transmitting all sensor data at every sampling instant would quickly exhaust the battery, only a subset of sensors may be active at each time step. In a tree topology, the selected sensors must form a connected subtree that includes the fusion center, otherwise the data cannot reach the estimator.

The central contribution is a stochastic sensor selection scheme. At each time instant a transmission subtree T is drawn randomly according to a probability distribution π over the set of all admissible subtrees. The marginal probability that sensor i is active is denoted p_i = Σ_{T∋i} π_T. The Kalman filter applied at the fusion center evolves according to a random Riccati map g_T that depends on the chosen subtree. By defining the operator g_π that averages over the random choice, the error covariance evolves as P_k = g_π(P_{k‑1}). The long‑run performance is captured by the deterministic limit g_∞^π(Σ) = lim_{k→∞} E