Estimation in the presence of fractionally integrated noise: An application to atomic timescales

The U.S. Naval Observatory (USNO) maintains the world's largest ensemble of atomic clocks, and is the largest contributor to the world's official timescale, UTC. As such, the accuracy and precision of the USNO timescale is of the utmost importance. This dissertation evaluates traditional clock analysis and modeling techniques such as those based on power-law noises, also called 1fa noises for the shape of their power spectral density. In addition, the class of long-memory processes, frequently employed in the economics genre yet applicable to many physical noises, is investigated in the atomic clock setting. An alternative clock noise model is developed using these long-memory or fractionally integrated noises. Estimation in the presence of such noise is studied, and comparisons to the current atomic clock modeling methodology are made. Several potential estimation techniques are evaluated including ordinary least squares, prewhitening techniques, and maximum likelihood estimation. A fractional difference prewhitening estimator is developed and shown to perform quite well in the presence of several additive long-memory noises. This estimator is evaluated in terms of atomic clock rate and drift determination, and ultimately upon its effects on the accuracy and stability of the USNO timescale.