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

We present an expression for the covariance matrix of 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 χ2 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.