An iterative method for track-based global alignment is proposed. It is derived from the Kalman filter and designed to avoid the inversion of large matrices. The update formulas for the alignment parameters and for the associated covariance matrix are described. The implementation and the computational complexity are discussed, and we show how to limit the latter to an acceptable level by restricting the update to detectors that are close in the sense of a certain metric. The performance of the

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... Kalman filter in terms of precision and speed of convergence is studied with simulated tracks. Results from an implementation in the CMS reconstruction program CMSSW are presented, using two sections of the barrel part of the CMS Tracker.