A new optimally unbiased moving average (MA) filter is examined being intended for the time error online estimating and synchronization in GPS-based timekeeping. The approach proceeds from the slowly changing nature of a time error generated by a local clock assuming its function to be linear for the number N of points in the average. The filter and its improved modification produces an unbiased estimate with two times more noise than a simple MA for N 1. Both the numerical simulation and the filtering of the real GPS-based time error processes are provided and discussed in detail.
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