  Modern semiconductor detectors allow for charged particle tracking with ever
increasing position resolution. Due to the reduction of the spatial hit
uncertainties, multiple Coulomb scattering in the detector layers becomes the
dominant source for tracking uncertainties. In this case long distance effects
can be ignored for the momentum measurement, and the track fit can consequently
be formulated as a sum of independent fits to hit triplets. In this paper we
present an analytical solution for a three-dimensional triplet(s) fit in a
homogeneous magnetic field based on a multiple scattering model. Track fitting
of hit triplets is performed using a linearization ansatz. The momentum
resolution is discussed for a typical spectrometer setup. Furthermore the track
fit is compared with other track fits for two different pixel detector
geometries, namely the Mu3e experiment at PSI and a typical high-energy
collider experiment. For a large momentum range the triplets fit provides a
significantly better performance than a single helix fit. The triplets fit is
fast and can easily be parallelized, which makes it ideal for the
implementation on parallel computing architectures.
