In 1971 Hafele and Keating carried portable atomic clocks east and then west around the world and verified the Sagnac effect, a special relativity effect attributable to the earth's rotation. In the study reported here observations of the effect were made by using electromagnetic signals instead of portable clocks to make clock comparisons. Global Positioning System satellites transmit signals that can be viewed simultaneously from remote stations on the earth; thus an around-the-world Sagnac experiment can be performed with electromagnetic signals. The effect is larger than that occurring when portable clocks are used. The average error over a 3-month experiment was only 5 nanoseconds.
We have estimated the relativistic redshift correction due to gravity, necessary to reference to the geoid the measurements of the new frequency standards at the National Institute of Standards and Technology (NIST) in Boulder, Colorado, USA, using a new local survey and various methods and models. We referenced the frequency offsets computed from different methods to the same geoid surface, one defined with respect to the current best estimate of an ideal mean-Earth ellipsoid. The new fractional frequency results are (1) −1797.61 × 10 −16 , based on the global gravitational model EGM96; (2a) −1798.72 × 10 −16 , based on the regional, high-resolution geoid model G96SSS; (2b) −1798.49 × 10 −16 , based on the regional, high-resolution geoid model G99SSS; and (3) −1798.91 × 10 −16 , based on the value for the geopotential number provided in the National Geodetic Survey's data sheet for the NIST reference marker. The minus sign implies that clocks run faster in the laboratory in Boulder than a standard clock located on the geoid. The values from (2b) and (3) are expected to be the most accurate and are also independent. Based on these results, we estimate the frequency shift at the reference point at NIST to be −1798.7 × 10 −16 , with an estimated standard uncertainty of ±0.3 × 10 −16 .
A theory is presented for estimating the uncertainty of a frequency comparison in the presence of distributed dead time or measurement interval offset using an extension of the method of Douglas and Boulanger (1997 Proc. 11th European Frequency and Time Forum pp 345-9). The uncertainties due to the distributed dead time and lumped dead time with mixed power law noise type are calculated and compared. It is shown that the use of distributed measurements of frequencies can greatly reduce the uncertainty as compared with that of lumped measurements. When a measurement interval offset is present, two different methods are possible for the frequency estimation and uncertainty evaluation. We compare and discuss the different results for the different methods.
Abstract-Frequency differences between major national timing centers are being resolved with uncertainty of less than 1 part in 1014',using satellites of the Global Positioning System (GPS) in common-view. Portable clock and GPS time differences are in excellent agreement. Around the world GPS measurement between three laboratories had a time residual of 5.1 ns.
The National Bureau of Standards (NBS) Time and Frequency Division now performs precision time and frequency transfer using common view measurements of Global Positioning System (GPS) satellites as a calibration service. Using this service, we have been able to transfer time with time stabilities of a few nanoseconds, time accuracies of the order of 10 ns, and frequency stabilities of one part in 10 1 4, or better, for measurement times of about four days and longer. The full accuracy of the NBS primary frequency standard is now available at a remote site. This paper describes the technique used for weighting and smoothing the data to produce these levels of stability and accuracy. All of the primary frequency standards used in the generation of International Atomic Time (TAl) now use this technique.
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