The PANDA experiment at FAIR offers unique possibilities for performing hyperon physics. The detector will enable the reconstruction of both hyperon and antihyperon, which will be created together in proton-antiproton collisions. This enables investigations of the strong interaction in the non-perturbative regime. Due to their relatively long-lived nature, the hyperons impose a particular challenge on the track reconstruction and event building. In order to exploit the large expected reaction rates to the fullest, PANDA will utilize a fully software-based event filtering. Therefore, reconstructing hyperons for such a filter requires online track reconstruction that can handle particles created a measurable distance away from the interaction point and, at the same time, operate on free streaming data is needed. Until antiprotons are available at PANDA, a part of the hyperon program can be carried out with the predecessor, PANDA@HADES using a proton beam. In this thesis, investigations of the detector signatures from the decay channels Λ → pπ-, Ξ- → Λπ- and Ω- → Λ K- produced in YbarY reactions are presented. The detector signatures guide the subsequent track reconstruction algorithms. A candidate for online track reconstruction algorithms on free streaming data based on a 4D Cellular Automaton has been developed and is benchmarked. It utilizes information from the PANDA straw tube tracker and is agnostic to the point of origin of the particle. The track reconstruction quality assurance procedure and results from the tracking at different event rates are also presented. Finally, extrapolation algorithms for including hit information from additional detectors in the tracks are outlined. In order to maximize the potential of the predecessor experiment PANDA@HADES, a kinematic fitting procedure has been developed for HADES that combines geometric the decay vertex information of neutral particles and track parameters such as momentum. Benchmark studies on simulated data from the channel p(3.5 GeV)p → ΛK+p are presented as well as tests of the kinematic fit on experimental data from 2007.