This is a study of three timescales formed from a Kalman filter operating on a model of a clock ensemble. The raw Kalman scale is unstable at short averaging times. The Kalman-plus-weights and reduced Kalman scales are stable at all averaging times. An optimality property is proved for the reduced Kalman scale.

Total variance is a statistical tool developed for improved estimates of frequency stability at averaging times up to one-half the test duration. As a descriptive statistic, total variance performs an exact decomposition of the sample variance of the frequency residuals into components associated with increasing averaging times. As an estimator of Allan variance, total variance has greater equivalent degrees of freedom and lesser mean square error than the standard unbiased estimator has.

No abstract

NPL has developed a Kalman-filter-based clock algorithm for combining measurements from its three active hydrogen masers. The algorithm is designed to produce a near optimal composite when the dominant noise process present is flicker frequency modulation (FFM). The FFM is modelled approximately by a linear combination of Markov noise processes. Each Markov process is included in the Kalman filter and contributes an additional component to its state vector. Both the validity of the model and the effectiveness of adding these additional components to the state vector are examined. The performance of the new algorithm is examined when applied to simulated measurements and also to measurements obtained from NPL's hydrogen masers.

This work gives an algorithm for combining the readings of an ensemble of clocks in which noisy pairwise comparisons are admitted. It extends and generalizes a previously published Kalman filter algorithm that is useful only for an ensemble of clocks within the same laboratory. The present algorithm may be useful for an ensemble of clocks distributed among several remote laboratories.