In order to profit from the largely increased instantaneous luminosity provided by the accelerator in Run III (2021-2023), the upgraded LHCb detector will make usage of a fully software based trigger, with a real-time event reconstruction and selection performed at the bunch crossing rate of the LHC (~30 MHz). This assumption implies much tighter timing constraints for the event reconstruction than currently used in Run II (2015-2018). The reconstruction of particles’ trajectories passing through the LHCb detector uses, already at an early stage, the Kalman Filter, a linear quadratic estimator for the tracks parameters. In the present configuration, the Kalman Filter is one of the most time-consuming parts of the reconstruction. For this reason, different approaches are currently being explored in order to reduce its execution time while keeping high reconstruction performances. The latest developments and their impact will be presented. These include vectorization, use of different computer architectures, simplifications of the algorithm, use of a parametrized approach and changes in the formalism.