Kalman filter tracking in a Cherenkov neutrino telescope

The reconstruction of tracks in underwater Cherenkov neutrino telescopes is strongly complicated due to large background counting rate originates from ⁴⁰K beta decay and to the electromagnetic showers accompanying high energy muons together with the effects of light propagation in the water, in particular the photon scattering. These two effects lead to a non-linear problem with a non-Gaussian measurement noise. A method for track reconstruction based on Kalman filter approach in this situation is presented. We use Gaussian Sum Filter algorithm to take into account non-Gaussian process noise. While usual Kalman filter estimators based on linear least-square method are optimal in case all observations are Gaussian distributed, the Gaussian Sum Filter offers a better treatment of non-Gaussian process noise and/or measurement errors when these are modeled by Gaussian mixtures. As an example of the application, the results of muon track reconstruction in NEMO underwater neutrino telescope are presented as well as the comparison of its capability with other standard track reconstruction methods.