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Graph-Theoretic Analysis of Estimators for Stochastically-Driven Diffusive Network Processes

Abstract:

Monitoring of a linear diffusive network dynamics that is subject to a stationary stochastic input is considered, from a graph-theoretic perspective. Specifically, the performance of minimum mean square error (MMSE) estimators of the stochastic input and network state, based on remote noisy measurements, is studied. Using a graph-theoretic characterization of frequency responses in the diffusive network model, we show that the performance of an off-line (noncausal) estimator exhibits an exact topological pattern, which is related to vertex cuts and paths in the network's graph. For on-line (causal) estimation, graph-theoretic results are obtained for the case where the measurement noise is small.