A Gradient Method for Clock Weighting in an Ensemble Timescale Filter

Michael J. Coleman

Abstract:	When using a Kalman Filter implementation of a timescale, it is common to assign clock weights based on the variance of the clocks’ state estimates. Filters can be tailored to constrain the weights so that: no one clock dominates the ensemble; certain groups of clocks maintain various weight levels; and/or, particular clocks are barred from the ensemble. The filters in question here compute weights based on current variances and utilize a set of constraints to protect a timescale from domination by one clock. By design, the clock weights are inversely related to the clock state variances; i.e., lower variance yields higher weight . Sudden changes in the variances and/or weights can affect each other in a Kalman Filter and occasionally cause unstable behavior. Timescale weighting in a Kalman Filter can be numerically sensitive, particularly if the weights are computed using an inverse of the variance. The inverse relation tends to amplify numerical errors in the weights when the variances are small. A clock whose stability is different from other clocks in a timescale ensemble, will disturb the timescale upon entry (going from zero to positive weight). If the weight distribution is changed substantially, the ensemble may be sufficiently disturbed that other filter features may invoke drastic actions such as phase break corrections. The approach considered in this report is to compute a desired weight distribution at each epoch, and move the weights towards that distribution. This is mathematically similar to following the gradient of a function V(w) where the function V computes a total variance of the ensemble for a given weight vector w. A trade between the current ensemble weight distribution and a more desirable distribution has been shown in several tests to yield greater continuity to the aposteriori variances. We investigate the performance of this weighting method using a variety of clock data. The use of a gradient–type approach is thought to be more effective when the number of clocks in the ensemble is relatively small (about or fewer than 12). This approach is also beneficial to ensembles that contain clock members experiencing periodic breaks and/or outages. The goal is to determine how well this method will weigh an ensemble of clocks in a timescale such that the dynamics of the timescale are void of severe changes and corrections thereby improving stability.
Published in:	Proceedings of the 46th Annual Precise Time and Time Interval Systems and Applications Meeting December 1 - 4, 2014 Seaport Boston Hotel Boston, Massachusetts
Pages:	86 - 92
Cite this article:	Coleman, Michael J., "A Gradient Method for Clock Weighting in an Ensemble Timescale Filter," Proceedings of the 46th Annual Precise Time and Time Interval Systems and Applications Meeting, Boston, Massachusetts, December 2014, pp. 86-92.
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