Koopman-operator Observer-based Estimation of Pedestrian Crowd Flows

We present here some preliminary results on the problem of estimating pedestrian crowds from limited measurements. More specifically, we focus on a data-driven operator-based approach. We use the Koopman operator and its approximation with the kernel dynamic mode decomposition kDMD, to design a dynamical observer, which allows us to estimate the full crowd flow, based on a partial-view of a sensing camera. We explain the dynamical observer design, discuss its limitations, and propose some numerical simulations to validate the proposed approach.