  This paper provides a detailed description of a vertex fitting algorithm
designed for precision measurements in low-energy particle physics experiments.
An accurate reconstruction of low-momentum trajectories is facilitated by
reducing the material budget of the detector to a few per mill of the radiation
length. This decreases the multiple scattering experienced by particles within
the detector, thereby enhancing vertex fitting accuracy. However, in the case
of light detection systems, the intrinsic spatial resolution of the sensors
imposes further constraints on the final vertex resolution that require careful
consideration. The algorithm developed in this study addresses both multiple
scattering and spatial resolution aspects in the context of vertex fitting,
specifically tailored for light pixel detectors. Furthermore, this works
presents a detailed examination of the vertex reconstruction within the
low-material budget pixel detector of the Mu3e experiment.
