Team-Optimal Distributed MMSE Estimation in General and Tree Networks
This addresses a gap in distributed state estimation for networks, offering optimal performance in specific topologies, though it is incremental as it builds on existing MMSE frameworks.
The paper tackles the problem of achieving team-optimal distributed minimum mean-square error (MMSE) estimation in general and tree networks, showing that exchanging local estimates suffices for oracle performance only in certain topologies and proposing recursive algorithms that achieve this with reduced complexity through time-windowing.
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.