A Non-Linear Kalman Filter for track parameters estimation in High Energy Physics

The Kalman Filter is a widely used approach for the linear estimation of dynamical systems and is frequently employed within nuclear and particle physics experiments for the reconstruction of charged particle trajectories, known as tracks. Implementations of this formalism often make assumptions on the linearity of the underlying dynamic system and the Gaussian nature of the process noise, which is violated in many track reconstruction applications. This paper introduces an implementation of a Non-Linear Kalman Filter (NLKF) within the ACTS track reconstruction toolkit. The NLKF addresses the issue of non-linearity by using a set of representative sample points during its track state propagation. In a typical use case, the NLKF outperforms an Extended Kalman Filter in the accuracy and precision of the track parameter estimates obtained, with the increase in CPU time below a factor of two. It is therefore a promising approach for use in applications where precise estimation of track parameters is a key concern.