Team-Optimal Distributed MMSE Estimation in General and Tree Networks

TL;DR

This paper develops and analyzes distributed algorithms for team-optimal state estimation in networks, achieving oracle performance in finite-horizon MSE by exchanging local estimates, with practical complexity reductions demonstrated through numerical examples.

Contribution

It introduces recursive algorithms that attain team-optimal finite-horizon MMSE in distributed networks, identifying network conditions for optimal information exchange.

Findings

Algorithms achieve oracle performance in finite-horizon MSE.

Exchange of local estimates suffices over certain network topologies.

Numerical results show superior estimation accuracy with proposed methods.

Abstract

We construct team-optimal estimation algorithms over distributed networks for state estimation in the finite-horizon mean-square error (MSE) sense. Here, we have a distributed collection of agents with processing and cooperation capabilities. These agents observe noisy samples of a desired state through a linear model and seek to learn this state by interacting with each other. Although this problem has attracted significant attention and been studied extensively in fields including machine learning and signal processing, all the well-known strategies do not achieve team-optimal learning performance in the finite-horizon MSE sense. To this end, we formulate the finite-horizon distributed minimum MSE (MMSE) when there is no restriction on the size of the disclosed information, i.e., oracle performance, over an arbitrary network topology. Subsequently, we show that exchange of local estimates is sufficient to achieve the oracle performance only over certain network topologies. By inspecting these network structures, we propose recursive algorithms achieving the oracle performance through the disclosure of local estimates. For practical implementations we also provide approaches to reduce the complexity of the algorithms through the time-windowing of the observations. Finally, in the numerical examples, we demonstrate the superior performance of the introduced algorithms in the finite-horizon MSE sense due to optimal estimation.