Analytic Technique for Statistically Modeling Random Atomic Clock Errors in Estimation

Patrick J. Fell

Abstract: Minimum variance estimation requires that the statistics of random observation errors be modeled properly. If measurements are derived through the use of atomic frequency standards, then one source of error affecting ble is random fluctuation in frequency. This is the case, for example, with range and integrated Doppler measurements from Satellites of the Positioning System used for precise geodetic point positioning and baseline determination for geodynamic applications. In this paper an analytic method is presented which approximates the statistics of this random process. The procedure starts with a model of the Allan variance for a particular oscillator and develops the statistics of range and integrated Doppler measurements. A series of five first order Markov processes is used to approximate the power spectral density obtained from the Allan variance. Range and Doppler error statistics are obtained from the integration of the corresponding auto correlation function. Statistics for residuals to polynomial clock models are then obtained by linear transformation. Examples are given for rubidium and cesium clocks.
Published in: Proceedings of the 12th Annual Precise Time and Time Interval Systems and Applications Meeting
December 2 - 4, 1980
Goddard Space Flight Center
Greenbelt, Maryland
Pages: 551 - 580
Cite this article: Fell, Patrick J., "Analytic Technique for Statistically Modeling Random Atomic Clock Errors in Estimation," Proceedings of the 12th Annual Precise Time and Time Interval Systems and Applications Meeting, Greenbelt, Maryland, December 1980, pp. 551-580.
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