A Kalman Filter approach for track reconstruction in a neutrino telescope

In high energy neutrino telescopes, the detection principle relies on the detection of Cherenkov light emitted from an up-going muon induced by ν μ that have penetrated the Earth. In the muon energy range of interest for astrophysical searches (namely from about 100 GeV to about 1 PeV), the electromagnetic showers accompanying the muon track generate Cherenkov light emitted within a few degrees of the cone associated to the primary particle. Furthermore, because of photon scattering in the water, the measurement is affected by non-Gaussian noise. Consequently, the track reconstruction in underwater Cherenkov neutrino telescopes is strongly complicated. Moreover, environmental background originates large noise counting rate. In an undersea neutrino detector, in fact, the decay of radioactive elements, mainly the β - decay of potassium isotope 40K, generates electrons that produce Cherenkov light leading an isotropic background of photons. Therefore, the hit-pattern identification of neutrino induced event is non-trivial and the track reconstruction has to deal with a non-linear problem due to this non-Gaussian measurement noise. In this paper a method, based on the Gaussian Sum Filter algorithm to take into account non-Gaussian process noise, for track reconstruction in a km3 underwater neutrino telescope, is presented.