title: A simple optimally unbiased MA filter for timekeeping.
abstract: 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.
authors.affiliation: FIMEE, Guanajuato University, Salamanca Gto., Mexico. shmaliy@salamanca.ugto.mx
authors.forename: Yuriy S
authors.initials: YS
authors.lastname: Shmaliy