Near-Optimal Distributed Estimation for a Network of Sensing Units Operating Under Communication Constraints

We study the problem of distributed state estimation in a network of sensing units that can exchange their measurements but the communication between the units is constrained. The units collect noisy, possibly only partial observations of the unknown state; they are assisted by a scheduler which organizes the exchange of measurements between the units. We consider the task of minimizing the total mean-square estimation error of the network while promoting balance between the individual units' performances. This problem is formulated as the maximization of a monotone objective function subject to a cardinality constraint. By leveraging the notion of weak submodularity, we develop an efficient greedy algorithm for the proposed formulation and show that the greedy algorithm achieves a constant factor approximation of the optimal objective. Our extensive simulation studies illustrate the efficacy of the proposed formulation and the greedy algorithm.