Proceedings of CHEP2013 - In 2018 data taking for hadronphysics facility PANDA is planned to commence. It will be build at the antiproton accelerator HESR, which itself is a part of the FAIR complex (GSI, Darmstadt, Germany). The luminosity at PANDA will be measured by a dedicated subdetector, which will register scattered antiproton tracks from ̄pp elastic scattering. From a software point of view, the Luminosity Detector is a tracking system. Therefore the most of its offline software parts are typical for a track reconstruction. The basic concept and Monte Carlo based performance studies of each reconstruction step is presented in this paper.