Optimal Discrete-Time Distributed Kalman Filter With Reduced Communication

This article proposes and analyzes a distributed filter where the consensus term is a virtual output rather than the local state estimate. This feature allows for reducing the data transmitted among nodes at each intermediate step, namely, instead of exchanging a vector of the dimension of the state, nodes exchange a vector of the dimension of the rank of the total output matrix. The main finding is that the convergence to the performance of the centralized Kalman filter and mean-square boundedness of the estimation error are not lost despite an increase in the number of consensus steps. Simulations show that the total communication overhead is reduced without performance degradation with respect to the original distributed filter, where nodes exchange local state estimates.