Estimating Time from Atomic Clocks

A Kalman recursive algorithm for estimating time from an ensemble of atomic clocks has been developed. The algorithm allows for the addition or deletion of clocks at any time, and provides automatic error detection and correction. The observations consist of time differences between clocks and may be taken at unequally spaced time points. Maximum likelihood estimates of the unknown parameters are obtained with confidence intervals, as well as hypothesis tests to determine whether the estimated parameters are significantly different from zero. The program is operational on the National Bureau of Standards' Time and Frequency Division's PDP 11/70.