Time and the Kalman Filter

This article reviews applications of the Kalman filter to atomic timing. The objectives of the article are twofold - present diverse applications and concepts in a consistent fashion, both in regard to notation and mathematical concepts. and develop the key ideas in a tutorial form by introducing the basic concepts and then applications.we apply the Kalman filter to clock estimation, clock monitoring, and time-scale definition. Furthermore, the GPS composite clock algorithm along with numerical simulations is described. Finally, the advantages and criticalities of the application of the Kalman filter to atomic timing, highlighting issues that are worth investigating are pointed out and on which the time and frequency community is currently working.