Stochastic models of stable frequency and time sources and their relationship

Author

Audoin, Claude ; Dimarcq, Noël

Author_Institution

CNRS, Univ. Paris Sud, Orsay, France

Volume

42

Issue

3

fYear

1993

fDate

6/1/1993 12:00:00 AM

Firstpage

682

Lastpage

688

Abstract

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

Keywords

Kalman filters; filtering and prediction theory; frequency measurement; frequency stability; measurement standards; measurement theory; random processes; stochastic processes; time measurement; white noise; ARIMA; Allan variance; Kalman models; continuous time model; phase fluctuations; power law model; random walk; relative frequency fluctuations; sampled phase derivations; stable frequency; stochastic models; time sources; white frequency noise; white phase noise; 1f noise; Fluctuations; Frequency; Kalman filters; Phase noise; Predictive models; Stability; Stochastic processes; Stochastic resonance; White noise;

fLanguage

English

Journal_Title

Instrumentation and Measurement, IEEE Transactions on

Publisher

ieee

ISSN

0018-9456

Type

jour

DOI

10.1109/19.231590

Filename

231590