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

TL;DR

This paper addresses distributed state estimation in sensor networks with communication constraints, proposing a greedy algorithm based on weak submodularity that achieves near-optimal performance, validated through extensive simulations.

Contribution

It introduces a novel formulation for minimizing estimation error under communication limits and develops an efficient greedy algorithm with provable approximation guarantees.

Findings

The greedy algorithm achieves a constant factor approximation of the optimal solution.

Simulation results demonstrate the effectiveness of the proposed approach.

The formulation balances individual sensor performance and overall estimation accuracy.

Abstract

We study the problem of distributed state estimation in a network of sensing units that can exchange their measurements but the rate of communication between the units is constrained. The units collect noisy, possibly only partial observations of the unknown state; they are assisted by a relay center which can communicate at a higher rate and schedules 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.