Robust Distributed Kalman Filtering: On the Choice of the Local Tolerance

We propose a distributed Kalman filter for a sensor network under model uncertainty. The distributed scheme is characterized by two communication stages in each time step: in the first stage, the local units exchange their observations and then they can compute their local estimate; in the final stage, the local units exchange their local estimate and compute the final estimate using a diffusion scheme. Each local estimate is computed in order to be optimal according to the least favorable model belonging to a prescribed local ambiguity set. The latter is a ball, in the Kullback-Liebler topology, about the corresponding nominal local model. We propose a strategy to compute the radius, called local tolerance, for each local ambiguity set in the sensor network, rather than keep it constant across the network. Finally, some numerical examples show the effectiveness of the proposed scheme.