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In this paper, we present a generalized Japan Standard Time algorithm(JST-algo) for higher-order atomic clock ensembles and mathematically clarifythe relations of the (generalized) JST-algo and the conventional Kalmanfiltering algorithm (CKF-algo) in the averaged atomic time and the clockresiduals for time scale generation. In particular, we reveal the fact that theaveraged atomic time of the generalized JST-algo does not depend on theobservation noise even though the measurement signal is not filtered in thealgorithm. Furthermore, the prediction error of CKF- algo is rigorously shownby using the prediction error regarding an observable state space. It ismathematically shown that when the covariance matrices of system noises areidentical for all atomic clocks, considering equal averaging weights for theclocks is a necessary and sufficient condition to ensure equivalence betweenthe generalized JST-algo and CKF-algo in averaged atomic time. In suchhomogeneous systems, a necessary and sufficient condition for observationnoises is presented to determine which algorithm can generate the clockresiduals with smaller variances. A couple of numerical examples comparing thegeneralized JST-algo and CKF-algo are provided to illustrate the efficacy ofthe results.

Relations Between Generalized JST Algorithm and Kalman Filtering Algorithm for Time Scale Generation