Distributed Kalman Filtering Under Model Uncertainty

We study the problem of distributed Kalman filtering for sensor networks in the presence of model uncertainty. More precisely, we assume that the actual state-space model belongs to a ball, in the Kullback-Leibler topology, about the nominal state-space model and whose radius reflects the mismatch modeling budget allowed for each time step. We propose a distributed Kalman filter with a diffusion step which is robust with respect to the aforementioned model uncertainty. Moreover, we derive the corresponding least favorable performance. Finally, we check the effectiveness of the proposed algorithm in the presence of uncertainty through a numerical example.