Analytical computation of process noise matrix in Kalman filter for fitting curved tracks in magnetic field within dense, thick scatterers

TL;DR

This paper derives the functional forms of the process noise matrix for Kalman filter-based track fitting in dense, thick materials within magnetic fields, enhancing the accuracy of particle trajectory estimation.

Contribution

It provides a detailed analytical derivation of the process noise matrix elements for complex tracking environments, complementing previous work by Mankel.

Findings

Derived explicit forms of process noise matrix elements for dense materials

Improved accuracy in Kalman filter track fitting in complex environments

Enhanced understanding of noise modeling in magnetic fields

Abstract

In the context of track fitting problems by a Kalman filter, the appropriate functional forms of the elements of the random process noise matrix are derived for tracking through thick layers of dense materials and magnetic field. This work complements the form of the process noise matrix obtained by Mankel[1].