  The various algorithms used to extrapolate particle trajectories from
measurements are often very time-consuming with computational complexities
which are typically quadratic. In this article, we propose a new algorithm
called GEM with a lower complexity and reasonable performance on linear tracks.
It is an extension of the EM algorithm used to fit Gaussian mixtures. It works
in arbitrary dimension and with an arbitrary number of simultaneous particles.
In a second part, we extend it to circular tracks (for charged particles) and
even a mix of linear and circular tracks. This algorithm is implemented in an
open-source library called libgem and two applications are proposed, based on
data-sets from two kind of particle trackers.
