Optimal sensor scheduling for remote estimation over 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 lossy channel to a central base station. The base station computes an estimate of the process state. We consider this remote estimation problem for wireless single-hop communication with the widely used IEEE 802.15.4 Media Access Control (MAC) protocol. Using a Markov chain model for the MAC protocol, we derive an expression for the probability of successful packet transmission λ (N). We show that λ (N) is a monotone decreasing function of the number of sensors N attempting to access the channel. State estimation is better served by having data from more sensor nodes, but this results in decreased probability of successful packet transmission. As a consequence, we are faced with a design trade-off in determining how many sensors should attempt to communicate their observations to the base station and which sensors are most informative for the purpose of state estimation. We show that this problem of optimal sensor selection can be cast as an optimization problem which can be solved approximately using convex programming. The optimal selection of sensors is dynamic and leads, in turn, to the problem of optimal sensor scheduling. We offer a synthetic example to illuminate our ideas.