A simple optimally unbiased MA filter for timekeeping

In this paper, we address the design of an optimally unbiased moving average (MA) filter for time error online estimating and synchronization in Global Positioning System (GPS)-based timekeeping. We proceed from the slowly changing nature of a time error generated by a local clock, assuming its function to be linear for N points in the average. Employing the inherent property of a simple MA to produce the lowest noise for the given averaging interval and using linear regression as a proper stochastic approximation to evaluate the bias, we find the optimal weighting coefficients. The designed optimally unbiased MA filter and its improved modification produce two times more noise than a simple MA when N >> 1. Both the numerical simulation and the filtering of the real GPS-based time error processes are provided and discussed in detail.