Methods to extract information from the tracking of mobile objects/
particles have broad interest in biological and physical sciences.
Techniques based on the simple criterion of proximity in
time-consecutive snapshots are useful to identify the trajectories
of the particles. However, they become problematic as the motility
and/or the density of the particles increases because of the
uncertainties on the trajectories that particles have followed during
the acquisition time of the images. Here, we report efficient
methods for learning parameters of the dynamics of the particles
from their positions in time-consecutive images. Our algorithm
belongs to the class of message-passing algorithms, also known
in computer science, information theory and statistical physics
under the name of Belief Propagation. The algorithm is distributed,
thus allowing parallel implementation suitable for computations
on multiple machines without significant inter-machine
overhead. We test our method on the model example of particle
tracking in turbulent flows, which is particularly challenging due
to the strong transport that those flows produce. Our numerical
experiments show that the BP algorithm compares in quality with
exact Markov Chain Monte-Carlo algorithms, yet BP is far superior
in speed. We also suggest and analyze a random-distance model
that provides theoretical justification for BP accuracy. Methods
developed here systematically formulate the problem of particle
tracking and provide fast and reliable tools for its extensive range
of applications.