A Comparison of GPS Clock Models For the Next Generation GPS System Timescale

Michael J. Coleman and Ken Senior

Abstract:	The on-orbit GPS satellite clock signals demonstrate signi?cant periodic ?uctuations for periods of 2.003 and 4.006 cycles/day. A timescale algorithm which includes the on-orbit GPS clocks should account for these periodic variations in order to mitigate their in?uence on the timescale. This is accomplished in a Kalman ?lter by introducing the periodics as independent states which evolve in a discrete–time algorithm alongside four other clock dynamic states. However, there is some freedom in the choice of how these harmonic states are coupled to the other states depending on the application at hand. A typical model of a clock’s dynamics is a four state clock model, including the phase of the clock, its ?rst derivative (frequency) and its second derivative (drift), each perturbed by an independent random walk; one additional phase state is also included in order to model a pure white phase noise. Four additional states are joined with the typical clock states in order to accommodate the periodic processes, where each of the four harmonic states are also perturbed by stochastic noises of some type (e.g., random walks) in order to account for any random change in the harmonic amplitude or phase over time. In general, a Kalman ?lter will grow in complexity with the number of states and the number of non-trivial correlations between them. Since the process noise covariance matrix will have o?–diagonal entries for the discrete model, including those between the typical clock dynamic states and the harmonic states, reducing unnecessary correlations can lead to reduced complexity and improved processing time for the ?lter implementation. If the process noise covariance between the harmonic states and the clock dynamic states are small, then a ?lter algorithm that neglects these small cross-correlations (and hence simpli?es the state covariance matrix) is preferable and can be exploited to reduce processing time. This work investigates the performance of the fully coupled model in comparison with the reduced covariance model, where performance is measured in terms of both timescale stability, model accuracy, and processing time. The bene?ts and costs of coupling the harmonics only to the phase state versus coupling them fully to the drift and frequency states is also investigated.
Published in:	Proceedings of the 43rd Annual Precise Time and Time Interval Systems and Applications Meeting November 14 - 17, 2011 Hyatt Regency Long Beach Long Beach, California
Pages:	501 - 520
Cite this article:	Coleman, Michael J., Senior, Ken, "A Comparison of GPS Clock Models For the Next Generation GPS System Timescale," Proceedings of the 43rd Annual Precise Time and Time Interval Systems and Applications Meeting, Long Beach, California, November 2011, pp. 501-520.
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