Collaborative scalar-gain estimators for potentially unstable social dynamics with limited communication

In this paper, we study the estimation of potentially unstable social dynamics-e.g., social and political movements, environmental and health hazards, and global brands; when they are observed by a geographically distributed set of agents. We are interested in scenarios when the information exchange among the agents is limited. This paper considers a generalization of distributed estimation to vector (non-scalar) and dynamic (non-static) cases. As we will show, when the state-vector evolves over time, the information flow over the communication network may not be fast enough to track this evolution. In this context, the key questions we address are: (i) can a distributed estimator with limited communication track an unstable system? and; (ii) what is the cutoff point beyond which the given observations and the agent topology may not result into a bounded estimation error? To address these questions, we present a scalar-gain estimator and characterize the relation between the system instability and communication/observation infrastructure. We derive and analyze the aforementioned cutoff point as the Scalar Tracking Capacity, and further show that unstable vector systems can be distributedly estimated with bounded error.

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