Stochastic Models for Atomic Clocks

J.A. Barnes, R.H. Jones, P.V. Tryon, D.W. Allan

Abstract: Most workers in the field of atomic clocks encounter frequency and time instabilities which can be characterized (or model led) as random fluctuations. These random fluctuations typically display a power spectral density which varies as a power-law over some significant range of (Fourier) frequencies (e. q. , 5 (f) = h f , where Y denotes the normalized, instantaneous frequency and f denotes the Fourier frequency). Typical oscillators and/or clocks may have regions where one specific power-laws predominates and other regions where other power-laws predominate. In general, various combinations of five different power-laws seem to be adequate to describe almost all observed random behavior in atomic clocks. In addition to the random components, oscillators and clocks often show systematic, (i.e.deterministic) trends such as offsets in frequency and time, as well as linear drifts in frequency. For the atomic clocks used in the NBS Time Scales, an adequate model is the superposition of white FM, random walk FM, and linear frequency drift for times longer than about one minute. The model has been tested on several clocks using maximum likelihood techniques for parameter estimation and the residuals have been "acceptably random. " Conventional diagnostics indicate that additional model elements contribute no significant improvement to the model even at the expense of the added model complexity.
Published in: Proceedings of the 14th Annual Precise Time and Time Interval Systems and Applications Meeting
November 30 - 3, 1982
NASA Goddard Space Flight Center
Greenbelt, Maryland
Pages: 295 - 306
Cite this article: Barnes, J.A., Jones, R.H., Tryon, P.V., Allan, D.W., "Stochastic Models for Atomic Clocks," Proceedings of the 14th Annual Precise Time and Time Interval Systems and Applications Meeting, Greenbelt, Maryland, November 1982, pp. 295-306.
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