A Computationally Efficient Unscented Kalman Smoother for Ameliorated Tracking of Subatomic Particles in High Energy Physics Experiments

The focus of this paper is to discuss improvements with respect to smoothing and its efficient implementation with the Unscented Kalman Filter (UKF) for particle tracking in High Energy Physics (HEP) experiments. At present, in almost all of the HEP experiments, smoothing is typically achieved using the Rauch-Tung-Striebel smoother or Kalman smoother that works naturally with the existing particle tracking algorithm, the Extended Kalman Filter. However, it does not work directly with the UKF that has recently been shown to improve particle tracking in the Muon Ionization Cooling Experiment due to the fact that Jacobian matrices are not available in the UKF framework. Although a smoother, the Unscented Rauch-Tung-Striebel (URTS) smoother, exists that naturally works with the UKF, it is not computationally efficient provided that particle tracking is a large dimensional problem. Therefore, the existing smoothers do not provide an efficient solution to improve the overall particle tracking process for such problems where computational complexity is one of the main challenges. In this paper, an alternative to the URTS method is presented that does not only implement directly with the UKF but also requires less computational effort. We name it as Jacobian Equivalent Rauch-Tung-Striebel smoother.