Clock current state estimation with a Kalman-like algorithm employing measurement of time errors

To meet the needs of the IEEE Standard 1139-1999 in part of the estimations of clock state, we propose using a fast recursive p-shift unbiased estimation algorithm employing measurement of the time interval error. A special feature of this algorithm is that it has the Kalman-like form, although ignores both the clock and measurement noise sources and allows for any initial clock state. The algorithm can straightforwardly be applied to provide unbiased filtering (p = 0) and smoothing (p <; 0) of clock state, also to predict (p > 0) its future behavior. An application is given for a master clock.