Situational Awareness for Dynamical Network Processes Using Incidental Measurements

Increasingly, incidental sensing capabilities are being leveraged for wide-area situational awareness of complex network processes. For instance, sensors embedded on miners´ body suits are envisioned for sensing for chemical hazards, blog data is being used to track disease spread, and autonomous vehicle platforms can incidentally measure environmental conditions while engaging in mission tasks. This paper explores how sparse incidental measurements can be used in tandem with models for the network processes, to gain situational awareness. Specifically, we study reconstruction and forecasting of a network diffusion process by a single stochastically-transitioning observer (where the transition process is not necessarily Markov). Conditions are obtained on the observer´s transition model and the diffusion process, such that the process state (scene) can be recovered from the incidental-measurement sequence. Additionally, the minimum-variance scene estimator and its performance are characterized, when the measurements are subject to additive white Gaussian noise. Two illustrative examples are also developed. The formal analyses and examples indicate that incidental measurements can permit effective reconstruction of network processes under broad conditions, albeit with some delay and error cost.