Performance bounds for information fusion strategies in packet-drop networks

In this paper we provide some analytical performance bounds for different distributed estimation schemes for stochastic discrete time linear systems where the communication between the sensors and the estimation center is subject to random packet loss. In particular, we analyze three different strategies. The first, named measurement fusion (MF) optimally fuses the raw measurements received so far from all sensors. The second strategy, named infinite bandwidth filter (IBF), computes the optimal mean square estimator assuming that each node can send all measurements observed up to its current time in a single packet. The last strategy, named open loop partial estimate fusion (OLPEF), simply sums local state estimates received from each sensor and replace the lost ones with their open loop counterpart. In particular, we propose novel mathematical tools to derive analytical upper and lower bounds for expected estimation error covariance the MF and the IBF strategies in the scenario of identical sensors and we compare their values with the empirical performance obtained via simulations.