Scalable Network Parameter Estimation in the Presence of Anomalies

This paper considers the problem of parameter estimation in a network in which the stochastic model of its measurements can change due to disruption in an unknown subset of sensors. This uncertainty in the measurements model introduces a new dimension to the estimator design. On one hand, the estimation quality depends on the successful isolation of anomalous sensors, and on the other hand, the detection performance is imperfect because of noisy measurements. Motivated by these two observations, this paper models the problem as a composite hypothesis testing problem and analyzes an optimal estimation framework. In large networks, the dimension of the hypotheses testing problem increases exponentially with the size of the network, and also finding the optimal estimate becomes computationally prohibitive. To counter this, this paper provides a scalable solution that consists of detecting and isolating anomalous sensors followed by a sensor-level estimation routine, and establishes asymptotic optimality of the scalable approach. This paper also formulates the decision rules to establish the reliability of the local estimates formed by each sensor, and the local estimates deemed to be reliable are aggregated to form a global estimate. The optimal and scalable schemes are evaluated and compared in a case study.