Optimal decentralized estimation through self-synchronizing networks in the presence of propagation delays

In this paper we focus on a sensor network scheme whose nodes are locally coupled oscillators that evolve in time according to a differential equation, whose parameters depend on the local estimate. The proposed system is capable, by self-synchronization, to reach the network consensus that coincides with the globally optimum maximum likelihood estimate, even though each sensor is only locally coupled with nearby nodes. Our main contribution is to study the effect of propagation delay on both the synchronization capability of the system and the final estimate. We provide delay-independent conditions for the proposed system to synchronize, and we derive closed-form expression of the synchronized state. Interestingly, the effect of propagation delays is simply to introduce a bias on the final estimate, that depends on the network topology and on the values of the delays. The analysis of this bias, suggest us how to design the coupling mechanism in order to alleviate it or even remove it.