Information fusion strategies and performance bounds in packet-drop networks

In this paper we discuss suboptimal distributed estimation schemes for stable stochastic discrete time linear systems under the assumptions that (i) distributed sensors have computation capabilities, (ii) the communication between the sensors and the estimation center is subject to random packet loss, and (iii) there is no communication between sensors. We consider strategies which are based on raw measurement fusion (MF) as well as on fusing local estimates, such as local Kalman filters or other pre-processing rules. We show that the optimal mean square estimation error that can be achieved under packet loss, referred as infinite bandwidth filter (IBF), cannot be reached using a limited bandwidth channel; we also compare these strategies under specific noise regimes. We also propose novel mathematical tools to derive analytical upper and lower bounds for the expected estimation error covariance of the MF and the IBF strategies assuming identical sensors. The theoretical findings are complemented with simulation results.