Methods for Optimal Recursive Estimation of Non-Stationary Time Series, Applications to Atomic Time and Frequency Metrology,
PARIS-6 UNIV (FRANCE)
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In time and frequency metrology, the problems of characterization, prediction, approximation and modelization are of fundamental importance for theoretical and experimental studies. In this paper, an improved unified approach is proposed and developed, which is based on the optimal estimation theory and the digital recursive processing methods. For two different models of non-stationary time series, the digital recursive methods of optimal estimation are presented. By these unified methods one can synthesize some digital filters and digital differentiators. These digital estimators are used to characterize the frequency instabilities of atomic clocks, to predict the random variations of atomic time scales, and to smooth the time series data. For the modelization of the statistics of frequency and phase fluctuations some analytical procedures are proposed. Then the Markov models of atomic clock instabilities can be deduced. In order to emphasize the utility of the theory, application examples are given for some time comparison data between commercial cesium atomic clocks.