# The USNO 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 and cesium clocks. 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.