James A. Barnes

Abstract: A linear drift in frequency is an important element in most stochastic models of oscillator performance. Quartz crystal oscillators often have drifts in excess of a part in ten to the tenth power per day. Even commercial cesium beam devices often show drifts of a few parts in ten to the thirteenth per year. There are many ways to estimate the drift rates from data samples (e.8., regress the phase on a quadratic; regress the frequency on a linear; compute the simple mean of the first difference of frequency: use Kalman filters with a drift term as one element in the state vector; and others). Although most of these estimators are unbiased, they vary in efficiency (1.2., confidence intervals). Further, the estimation of confidence intervals using the standard analysis of variance (typically associated with the specific estimation technique) can give amazingly optimistic results. The source of these problems is not an error in, say, the regressions techniques, but rather the problems arise from correlations within the residuals. That is, the oscillator model is often not consistent with constraints on the analysis technique or, in other words, some specific analysis techniques are often inappropriate for the task at hand. The appropriateness of a specific analysis technique is critically dependent on the oscillator model and can often be checked with a simple "whiteness" test on the residuals. Following a brief review of linear regression techniques, the paper provides guidelines for appropriate drift estimation for various oscillator models, including estimation of realistic confidence intervals for the drift.
Published in: Proceedings of the 15th Annual Precise Time and Time Interval Systems and Applications Meeting
December 6 - 8, 1983
Naval Research Laboratory
Washington, DC
Cite this article: Barnes, James A., "THE MEASUREMENT OF LINEAR FREQUENCY DRIFT IN OSCILLATORS," Proceedings of the 15th Annual Precise Time and Time Interval Systems and Applications Meeting, Washington, DC, December 1983, pp. -.
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