Confidence on the second difference estimation of frequency drift: a study based on simulation

Simulation is used to compare the confidence in estimating frequency drift in the presence of stochastic noise between two different estimators: (1) a mean second difference using neighbouring data, and (2) a single second difference over the entire data set. In each case 100-s data sampling and 10000 samples (11.5 days of data) are simulated. The two estimators show a similar confidence when the noise is purely random walk frequency modulation, but when there is also white frequency modulation, as is common in oscillators, method (2) is more efficient. An advantage of (1) is that it provides an internal confidence to an estimate on a single data set. When a typical rubidium gas cell frequency standard is simulated, the confidence of the drift estimate is ten times better for method (2) as compared to method (1)