  This study introduces a Kalman Filter tailored for homogeneous gas Time
Projection Chambers (TPCs), adapted from the algorithm utilized by the ALICE
experiment. In order to describe semi-circular paths in the plane perpendicular
to the magnetic field, we introduce a novel mirror rotation technique into the
Kalman Filter algorithm, enabling effective tracking of trajectories of varying
lengths, including those with multiple circular paths within the detector, also
known as "loopers". Demonstrated relative improvements of up to 80\% in
electron momentum resolution and up to 50\% in muon and pion momentum
resolution underscore the significance of this enhancement. Such advancements
hold promise not only for the future of the ALICE TPC but also for neutrino
high-pressure gas TPCs, where loopers become significant owing to the
randomness of production points and their relatively low energies in neutrino
interactions.
