Distributed Tracking in Multihop Sensor Networks With Communication Delays

We describe distributed tracking of a nonlinear dynamical system via networked sensors. The sensors communicate with each other by means of a multihop protocol over a communication network. We derive in-network processing algorithms to deal with arbitrary network topology and then extend these results to account for communication delays and packet losses. We show that these algorithms are optimal in the linear setting and achieve centralized performance. The proposed techniques differ from existing techniques in two important aspects: a) there is no designated leader/fusion node and each sensor attempts to optimally track the system trajectory based on its local observations and time-dependent information available from other sensors in the network; b) the message computation at each sensor is structurally identical. Consequently, the sensor network can be queried at any time and at any node to obtain optimal estimates for the state of the dynamical system. We then present two multihop protocols - one based on gossip and another token-based - for distributed implementation of the in-network processing techniques. We show several advantages of token-based schemes over gossip protocols: a) message complexity is significantly smaller for achieving the same performance; b) they are well-suited for situations where target and network data aggregation time-scales are comparable; and c) they are well-suited for random geometric graphs with nodes having small communication-connectivity radius - a scenario typical of ad-hoc wireless networks. This is because they can fuse data only from the set of nodes that can be visited in any time period.