  We present a novel method for estimating the circulations and positions of
point vortices using trajectory data of passive particles in the presence of
Gaussian noise. The method comprises two algorithms: the first one calculates
the vortex circulations, while the second one reconstructs the vortex
trajectories. This reconstruction is done thanks to a hierarchy of optimization
problems, involving the integration of systems of differential equations, over
time sub-intervals all with the same amplitude defined by the autocorrelation
function for the advected passive particles' trajectories. Our findings
indicate that accurately tracking the position of vortices and determining
their circulations is achievable, even when passive particle trajectories are
affected by noise.
