Distributed Tracking in Multi-hop Networks

We describe distributed tracking of a linear dynamical system via networked sensors. The networked sensors communicate with each other by means of a multihop protocol over a communication network. MMSEoptimal solution is Kalman filtering when measurements are available centrally, but new methods are required to account for communication constraints. We derive optimal algorithms to deal with arbitrary network topology and then extend these results to account for communication delays and packet losses. The proposed techniques differ from related techniques proposed 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, where the computed message from each sensor is the innovation in the state conditioned on all the information available upto that time at each sensor. 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.