The clock model and its relationship with the Allan and related variances

IEEE Trans Ultrason Ferroelectr Freq Control. 2005 Feb;52(2):289-96. doi: 10.1109/tuffc.2005.1406554.


The clock errors are modeled by stochastic differential equations (SDE) and the relationships between the diffusion coefficients used in SDE and the Allan variance, a typical tool used to estimate clock noise, are derived. This relationship is fundamental when a mathematical clock model is used, for example in Kalman filter, noise estimation, and clock prediction activities.