Initial-Condition Estimation in Network Synchronization Processes: Algebraic and Graphical Characterizations of the Estimator

Abstract

We pursue a graph-theoretic analysis of state inference in network synchronization (or diffusive) processes. Precisely, we study estimation of a non-random initial condition of a canonical synchronization dynamics defined on a graph, from noisy observations at a single network node. By characterizing the maximum-likelihood estimation of the initial condition and the associated Cramer-Rao bound, we identify graph properties (e.g., symmetries, interconnection strengths, spectral measures) that determine 1) whether or not estimation is possible and 2) the quality of the estimate.