A sequential approach for distributed set-membership estimation to exploit redundant information

This manuscript proposes a novel approach for the distributed set-membership estimation of linear time-invariant plants. The method is based on sequentially exploiting the information that the agents receive from their neighbourhood in an adequate manner, so that redundant information is not discarded, but used to further shrink the sets. To do so, they need to build the innovation-routing table, which integrates routing information and concepts of subspace observability. Then, sequential filtering steps are performed over the sets that contain the different modes in which the state vector is locally decomposed. The method is presented for sets described as zonotopes and takes advantage of the developments of well-known centralized zonotopic observers. Simulation results show that the use of redundant information reduces the uncertainty of the estimation, and the increment of computational cost is minor. Furthermore, the sensitivity of the method with respect to different parameters is analysed with numerical simulations and compared to similar estimators in the literature.