Initial-Condition Estimation in Network Synchronization Processes: Algebraic and Graphical Characterizations of the Estimator
Mengran Xue
Department of Electrical Engineering and Computer Science
University of Michigan
Ann Arbor, MI
mxue@umich.edu
Enoch Yeung
Department of Computing and Mathematical Sciences
California Institute of Technology
Pasadena, CA
Anurag Rai
Department of Electrical Engineering
Massachusetts Institute of Technology
Cambridge, MA
Sandip Roy
Department of Electrical Engineering
Washington State University
Pullman, WA
Yan Wan
Department of Electrical Engineering
University of North Texas
Denton, TX
Sean Warnick
Information and Decision Algorithms Laboratories
Brigham Young University
Provo, UT
Abstract
A graph-theoretic analysis of state inference for a class of network synchronization (or diffusive) processes is pursued. Precisely, estimation is studied for a nonrandom initial condition of a canonical synchronization dynamic 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, graph properties are identified (e.g., symmetries, interconnection strengths, spectral measures) that determine (1) whether or not estimation is possible and (2) the quality of the estimate.