Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

The development of a new Kalman-filter time scale at NIST



Jian Yao, Thomas E. Parker, Judah Levine


We report on a preliminary design of a new Kalman-filter Hydrogen-maser time scale at NIST. The time scale is composed of a few Hydrogen masers and a Cs clock. The Cs clock is used as a reference clock, just for easy operations with the existing data. All the data used in this paper are real measurement data, except mentioned specifically. Unlike most other time scales, this time scale uses three basic time-scale equations, instead of only one equation. Also, this time scale can detect a clock error (i.e., time error, frequency error, or frequency drift error) automatically. A frequency step of 6.8×10-15 s/s (which typically corresponds to ~ 20C temperature change of a H-maser chamber) in a clock only leads to ~ 2.5 ns change in the time scale in 100 days, thanks to the advanced error-detection technique. A frequency-drift step of 5.4×10-21 s/s2 in a clock only leads to ~ 11 ns change in the time scale in 100 days. These features make the new time scale stiff and less likely to be affected by a bad clock. Tests show that the time scale deviates from the UTC by less than ± 5 ns for ~100 days, when the time scale is initially aligned to the UTC and then is completely free running. Once the time scale is steered to an external frequency standard (such as a Cs fountain), it can maintain the time with little error even if the external frequency standard stops working for tens of days. At NIST, we have the Cs fountain running in 2015 September (23 days), 2015 December (14 days) and 2016 February (18 days). Although the Cs fountain runs for only 55 days in total, the time scale steered to the Cs fountain has a deviation of less than 4 ns (peak-to- peak) from the UTC, during MJD 57265 – 57500 (235 days). This can be helpful when we do not have a continuously-running fountain, or when the continuously-running fountain accidentally stops, or when we have the optical clocks running occasionally.
Conference Dates
January 30-February 2, 2017
Conference Location
Monterey, CA
Conference Title
2017 PTTI


kalman filter, time scale


Yao, J. , Parker, T. and Levine, J. (2017), The development of a new Kalman-filter time scale at NIST, 2017 PTTI, Monterey, CA (Accessed April 14, 2024)
Created January 31, 2017, Updated June 2, 2021