Running consensus in wireless sensor networks

Wireless sensor networks are valid candidate to monitor environmental parameters in dangerous areas. In many such applications, the sensors first sense the environment and then average their measurements to compute the final estimator in a completely distributed fashion. Usually, there is no meaningful way to decide when the sensing stage should be terminated to start the average procedure. What happens if the network is impaired before that the distributed estimator is computed? Oppositely, what happens if the sensing stage is too short (i.e., the network has collected only a small amount of data when the averaging step starts)? We propose a scheme - and call it running consensus - where the sensing and the averaging stages are simultaneous: The network continues collecting data while computing on-the-fly the distributed estimator. The asymptotic behavior of the running consensus is investigated and compared with that of the classical consensus algorithms, the impact of the network topology is discussed, and examples of applications are presented.