New Time Scale Algorithm: AT1 Plus Frequency Variance

摘要

The algorithm which generates the AT1 time scale at the National Institute of Standards and Technology (NIST) has generated a scale with many desirable properties since 1968. Five of these are as follows: 1. The fractional frequency variation of the scale is smaller than any clock in the scale for all integration times. 2. The algorithm adaptively estimates the weights of clocks in real time. 3. The scale is much more reliable than any individual clock. 4. One can add or remove clocks from the scale easily, with a minimum impact on the scale. 5. One can correct the ensemble for calibrations against a primary reference. There are three other properties we would like to obtain: 1. Automatic frequency step detection. 2. A scale optimized for post- processing, including running both forwards and backwards in time. 3. A scale that can run with minimal supervision for use in non-technical environments. It turns out that simply estimating a variance of the frequency state of the clocks facilitates all three of these new properties. We report here a new algorithm which uses techniques from Kalman filtering to estimate this variance. Results from simulation and applications to real clocks are presented also.