  The paper addresses the problem of distributed filtering with guaranteed
convergence properties using minimum-energy filtering and $H_\infty$ filtering
methodologies. A linear state space plant model is considered observed by a
network of communicating sensors, in which individual sensor measurements may
lead to an unobservable filtering problem. However, each filter locally shares
estimates, that are subject to disturbances, with its respective neighboring
filters to produce an estimate of the plant state. The minimum-energy strategy
of the proposed local filter leads to a locally optimal time-varying filter
gain facilitating the transient and the asymptotic convergence of the
estimation error, with guaranteed $H_\infty$ performance. The filters are
implementable using only the local measurements and information from the
neighboring filters subject to disturbances. A key idea of the proposed
algorithm is to locally approximate the neighboring estimates, that are not
directly accessible, considering them as disturbance contaminated versions of
the plant state. The proposed algorithm imposes minimal communication load on
the network and is scalable to larger sensor networks.
