Application of Kalman Filters and ARIMA Models to Frequency and Phase Lock Loops Digital

J.A. Barnes, S.R. Stein

Abstract: The problem of controlling the phase and frequency of atomic clocks is analyzed in two stages. The first step requires estimating the state (time and frequency) of the clock at the time of the last measurement and forecasting the future state. The second step is the design of a control algorithm for steering the slave clock to the reference. This division of the overall control problem is useful because different design requirements are utilized for each step. We apply the Kalman filter to perform optimum state estimation and forecasting. The Kalman filter is advantageous for this application because it provides minimum least squares error estimates and forecasts both during transients and for steady state operation. It also provides internal estimates of the variances of its outputs. Analytic solutions have been found for steady state performance.
Published in: Proceedings of the 19th Annual Precise Time and Time Interval Systems and Applications Meeting
December 1 - 3, 1989
Sheraton Hotel
Redondo Beach, California
Pages: 311 - 323
Cite this article: Barnes, J.A., Stein, S.R., "Application of Kalman Filters and ARIMA Models to Frequency and Phase Lock Loops Digital," Proceedings of the 19th Annual Precise Time and Time Interval Systems and Applications Meeting, Redondo Beach, California, December 1987, pp. 311-323.
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