Summary The Kalman filter is a fundamental process in the reconstruction of particle collisions in high‐energy physics detectors. At the LHCb detector in the Large Hadron Collider, this reconstruction happens at an average rate of 30 million times per second. Due to iterative enhancements in the detector's technology, together with the projected removal of the hardware filter, the rate of particles that will need to be processed in software in real‐time is expected to increase in the coming years by a factor 40. In order to cope with the projected data rate, processing and filtering software must be adapted to take into account cutting‐edge hardware technologies. We present Cross Kalman, a cross‐architecture Kalman filter optimized for low‐rank problems and SIMD architectures. We explore multi‐ and many‐core architectures and compare their performance on single and double precision configurations. We show that under the constraints of our mathematical formulation, we saturate the architectures under study. We validate our results and integrate our filter in the LHCb framework. Our work will allow to better use the available resources at the LHCb experiment and enables us to evaluate other computing platforms for future hardware upgrades. Finally, we expect that the presented algorithm and data structures can be easily adapted to other applications of low‐rank Kalman filters.