In this paper, we examine one of the possible approaches to design an optimally unbiased moving average (MA) filter intended for the time error online estimating and synchronization in timekeeping. The approach is based on the slowly changing nature of a time error generated by the local clock and has led to a simple formula for the optimally unbiased MA filter, which does not require any a priori knowledge about the time error process. When filtering the various GPS-based time error processes, we found out that, of the filters with the same time constant, the designed filter demonstrates an error intermediate between the three-state and two-state Kalman filters. The filter has been examined for numerically simulated data and some practical situations of the GPS-based time errors generated with the crystal and rubidium oscillators.
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