On inference of network time constants from impulse response data: graph-theoretic Cramer-Rao bounds

We examine the role played by a linear dynamical network´s topology in inference of its eigenvalues from noisy impulse-response data. Specifically, for a canonical linear time-invariant network dynamics, we relate the Cramer-Rao bounds on eigenvalue estimator performance (from impulse-response data) to structural properties of the transfer function, and in turn to the network´s topological structure. We focus especially on networks with a slow-coherence structure, in which case we find that stimulus and observation in each strongly-connected network component is needed for high-fidelity estimation.