## THE U.S. NAVAL OBSERVATORY Time Scale

* "The clock does strike, by algebra."
--- Samuel Butler (1600-1680)
*

The **ensemble ** of clocks upon which
UTC(USNO), the USNO Mean time scale, is based,
consists of ** hydrogen masers** ,
**cesium clocks**, and Rubidium fountains.
The various atomic clocks are included in the actual
ensemble, or rejected, on the basis of their long-term and short-term
**performance ** .

The **USNO timescale** is generated as described by L. A. Breakiron, 1991,
Proceedings of the 23rd Annual Time and Time Interval (PTTI)
Applications and Planning Meeting, pp. 297-305, except for revisions in
the weighting and steering.

The ** mean timescale ** is generated by the following algorithm:

z(t) = z(t-T) + SUM_i {w(t,i) * [x(t,i) - x(t-T,i) + T * r(t,i)
- 1/2 * (T**2 * d(t-T,i) ) ] }

where ` z(t) ` is the difference between the readings of the
**Master Clock ** .
and the mean timescale, ` x(t,i) ` is the difference between
the readings of the Master Clock and clock * i *, ` w(t,i) ` is
the weight of clock * i *, ` r(t,i) ` is the rate (frequency
in time gained per time interval * T *), and ` d(t,i) ` is the
frequency drift of clock * i * relative to the mean of the original clock
ensemble, all at time * t *.
The weights change with time relative to the present such that the
masers dominate the mean timescale in the recent past, but are completely
deweighted by 75 days in the past in order to prevent
any residual drift from affecting the timescale. This weighting scheme
allows us to combine the short-term stability of our hydrogen masers with
the long-term accuracy of our cesium clocks. The Master Clock
is steered in frequency (at a rate of no more than 150 ps/day and with a time
constant currently set at 50 days) until its time is synchronized as closely
as possible with that of the mean timescale.

The Master Clock (MC) is the source of UTC(USNO) and designated lead reference to which all measurements can be
corrected if necessary. However, most of the time, the differences between these systems are about 1 nanosecond or less. Measurements between all
clocks are made every hour; a second, independent high precision system
measures the high performance clocks every 100 seconds. The various clock
vaults are located in several buildings that are separated by as much as
300 meters. The connecting cables are either low loss coaxial cables or fiber
optic links. All are installed underground.