Parametrized Kalman filter for downstream tracks

This master’s thesis presents the developments necessary for a parametrized Kalman filter for downstream track reconstruction in the LHCb experiment’s High-Level Trigger 1 (HLT1) system, implemented on GPUs within the Allen framework. The primary objective was to split the existing Kalman filter kernel into modular sub-kernels, allowing their reorganization to extend Kalman filtering to downstream tracks. Downstream tracks are particle trajectories originating outside the Vertex Locator (VELO). This enhancement aims to improve the efficiency of event selection for long-lived particle decays.
A secondary focus was the exploration of Carlson’s square-root filter as a more numerically robust alternative to the traditional Kalman filter, addressing potential instability issues arising from single-precision arithmetic. Initial results indicate promising improvements in numerical stability, although more research is required to resolve anomalies in specific prediction steps. Additionally, critical bugs in the parametrized Kalman filter similarity functions were identified and fixed, leading to measurable gains in momentum resolution. Deprecated code structures were also modernized, reducing technical debt and improving maintainability.