Estimating the Instabilities of N Clocks by Means of Comparison Measurements

Amedeo Premoli, Patrizia Tavella

Abstract:	The estimation of individual instabilities of N clocks, compared by measuring the differences of their readings, is here considered without assuming a priori any hypotheses on their uncorrelation. Instabilities of the N clocks are described by a complete (non-diagonal) NxN covariance matrix R Only differences of clock readings are available in order to estimate R Statistical processing of these data allows one to calculate the (N-1)x(N-1) covariance matrix S of the differences relative to the N-th(reference) clock. By analyzing the relationships tying R and S, several pieces of information can be inferred and, in particular, the conditions for the validity of the uncorrelation hypothesis are established. The estimation of R from S is not unique: in any case R must be positive definite. A theorem states that R is positive definite if and only if its determinant is positive. Nevertheless infinitely many acceptable choices of R still fulfill the condition of positive definiteness. This paper shows that, by increasing the number N of compared clocks, the amount of arbitrariness in estimating R is reduced. The analysis of some experimental dale illustrates the capability of the method.
Published in:	Proceedings of the 24th Annual Precise Time and Time Interval Systems and Applications Meeting December 1 - 3, 1992 Ritz-Carlton Hotel McLean, Virginia
Pages:	385 - 398
Cite this article:	Premoli, Amedeo, Tavella, Patrizia, "Estimating the Instabilities of N Clocks by Means of Comparison Measurements," Proceedings of the 24th Annual Precise Time and Time Interval Systems and Applications Meeting, McLean, Virginia, December 1992, pp. 385-398.
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