The global covariance matrix of tracks fitted with a Kalman filter and an application in detector alignment

TL;DR

This paper derives a covariance matrix expression for Kalman filter-fitted tracks, enabling improved detector alignment and vertex constraint integration without refitting, enhancing tracking accuracy in particle physics experiments.

Contribution

It introduces a novel covariance matrix expression for Kalman filter tracks, facilitating detector alignment and vertex constraint incorporation without additional refitting.

Findings

Enables detector alignment using Kalman filter tracks

Allows vertex constraints to be included without refitting

Improves accuracy of tracking detector calibration

Abstract

We present an expression for the covariance matrix for the set of state vectors describing a track fitted with a Kalman filter. We demonstrate that this expression facilitates the use of a Kalman filter track model in a minimum $\chi^2$ algorithm for the alignment of tracking detectors. We also show that it allows to incorporate vertex constraints in such a procedure without refitting the tracks.