The 2020 upgrade of the LHCb detector will vastly increase the rate of collisions the Online system needs to process in software, in order to filter events in real time. 30 million collisions per second will pass through a selection chain, where each step is executed conditional to its prior acceptance. The Kalman Filter is a fit applied to all reconstructed tracks which, due to its time characteristics and early execution in the selection chain, consumes 40% of the whole reconstruction time in the current trigger software. This makes the Kalman Filter a time-critical component as the LHCb trigger evolves into a full software trigger in the Upgrade. I present a new Kalman Filter algorithm for LHCb that can efficiently make use of any kind of SIMD processor, and its design is explained in depth. Performance benchmarks are compared between a variety of hardware architectures, including x8664 and Power8, and the Intel Xeon Phi accelerator, and the suitability of said architectures to efficiently perform the LHCb Reconstruction process is determined.