Stochastic models of stable frequency and time sources and theirrelationship

Different stochastic models of a stable frequency and time sources showing white phase noise, white frequency noise, and random walk of frequency noise are considered. A continuous time model of phase fluctuations is associated with the power law model of relative frequency fluctuations. The ARIMA (0,2,2) and the Kalman models of the sampled phase derivations are derived from the continuous model. Equations relating the characteristic parameters of these three representations of the source behavior are given. The Allan variance of relative frequency fluctuations is expressed as a function of the characteristic parameters. The approximation inherent to the simplified Kalman model is discussed, and the limit of validity of this model is stated