Relationship Between Allan Variances and Kalman Filter Parameters

A.J. Van Dierendonck, J.B. McGraw

Abstract:	In this paper we construct a relationship between the Allan variance parameters (h2, h1, h0, h-1 and h-2) and a Kalman Filter model that would be used to estimate and predict clock phase, frequency and frequency drift. To start with we review the meaning of those Allan Variance parameters and how they are arrived at for a given frequency source. Although a subset of these parameters is arrived at by measuring phase as a function of time rather than as a spectral density, they all represent phase noise spectral density coefficients, though not necessarily that of a rational spectral density. The phase noise spectral density is then transformed into a time domain covariance model which can then be used to derive the Kalman Filter model parameters. Simulation results of that covariance model are presented and compared to clock uncertainties predicted by Allan variance parameters. A two state Kalman Filter model is then derived and the significance of each state is explained.
Published in:	Proceedings of the 16th Annual Precise Time and Time Interval Systems and Applications Meeting November 27 - 29, 1984 NASA Goddard Space Flight Center Greenbelt, Maryland
Pages:	273 - 293
Cite this article:	Van Dierendonck, A.J., McGraw, J.B., "Relationship Between Allan Variances and Kalman Filter Parameters," Proceedings of the 16th Annual Precise Time and Time Interval Systems and Applications Meeting, Greenbelt, Maryland, November 1984, pp. 273-293.
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