more….

Early GPS designs treated one of the clocks as a master, “correct” by definition and dropped from the problem. Although such artificial reliance on a particular clock was obviously undesirable, suggestions of clock ensembling were inhibited by a lack of theory. The combined orbit/clock problem clearly required a Kalman filter or the equivalent, and that seemed to demand a completely observable system.

Composite clock presents the solution (in use since June 1990). Essentially it is a Kalman filter applied to the original orbit/clock problem, including all clocks, treating none as master. There are no explicit ensembling equations, and the system is not completely observable, but a series of new theorems shows that

(a) The Kalman filter implicitly creates an ensemble time from all the clocks, and

(b) The unobservability can be handled in any of several acceptable ways.

A concept of transparent variations is developed to show the role of unobservable dimensions, and permit a dynamic separation of covariance into unobservable and observable parts. The observable part is recognized as the covariance of the various clocks about an implicit ensemble mean of them all, and the unobservable part as the covariance of the implicit ensemble mean relative to an ideal clock. To within the small error levels of the observable parts of the system, every corrected clock (physical clock corrected by its estimated error) behaves as if controlled by the implicit ensemble mean. Thus a corrected clock represents the implicit ensemble mean (to within such errors) and has the same long-term stability. For example, long term Allan variances are typically reduced, relative to stand-alone values, by a factor of the effective number of clocks.

Leave a comment