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Description

These statistical properties generally cannot be measured independently. Variances, covariances and Allan variances can, however, be determined indirectly if three or more clocks are intercompared, by removing biasses due to intercomparisons. Realistic simulation experiments show that the indirect methods are valid only if there are no sample cross-correlations between clocks.;The Standard International (SI) unit of time interval is the second, defined as 9192631770 oscillations of a certain transition in the cesium atom. Atomic clocks realize the definition to a few parts in 10('12), or 10('14) in some laboratory versions. An atomic time scale is formed by counting the number of seconds produced by atomic clocks since a conventional starting point. Specific algorithms are used by different institutions for averaging results from several clocks, to improve time scale stability, continuity and reliability since clocks have inherent correlated noise.;Time scale algorithms employ weights according to unbiassed variances of the clocks averaged. Rejection rules are applied to delete poor clocks, and new clocks may be added. To overcome resulting discontinuities, a condition requiring the weighted sum of prediction errors to be zero at any given time is imposed, which also removes a rank deficiency in the observation equations. The actual methods used by several establishments are discussed in detail, including those that "steer" the resulting scales towards external standards when available.;Some background material on the need for and nature of time is presented, leading to a review of modern methods of intercomparing clocks. The operating principles of atomic clocks are also described, as are the statistical properties of their random noise processes which the algorithms attempt to filter out.;Extensive tests on three simulated data sets compare the effects of the different algorithm principles. Using relative whiteness of the results as criteria, it is found that predictions should be unbiassed; that weights should be assigned on full results, rather than prediction errors, over the desired stability interval; that optimisation for both short and long term stability is not feasible, nor is complete filtering; and that five clocks, preferably many more, are necessary. The conclusions are verified on real data.