Clock state estimation with the Kalman-like UFIR algorithm via TIE measurement

We show that recently designed the p-shift unbiased finite impulse response (UFIR) iterative algorithm is highly efficient in applications to clock state estimation via measurement of the time interval error (TIE). The algorithm is Kalman-like, but does not involve noise statistics and initial errors. Its crucial property is that the estimate becomes optimal in the minimum mean square error sense when the estimator memory is large that is typical for clocks. Examples are given for state estimation in an ovenized crystal clock and error prediction in a master clock. Based upon the experimental studies, we show that this algorithm outperforms the Kalman filter requiring the clock noise covariance matrix that is hard to specify correctly even in white Gaussian approximation.

► Clock state is estimated using the p-shift UFIR algorithm.
► The clock noise covariance cannot be described correctly for optimal estimators.
► The UFIR algorithm does not involve the noise covariances and initial errors.
► UFIR algorithm is more accurate than the Kalman one for clock state estimation.
► UFIR Predictor of clock errors produce smaller errors than the Kalman filter.