Estimation of the clock TIE state space model using a thinning unbiased FIR filtering algorithm

A thinning algorithm is proposed for real-time unbiased finite impulse response (FIR) estimation of the local clock time interval error (TIE) model (time error, fractional frequency offset, linear frequency drift rate, etc.) employing GPS-based sawtooth measurements. We show that the approach allows obtaining practically optimal estimates of the clock states, by large horizons (number of the points in the average). The algorithm is applied to the TIE measurements allowing for different time steps and averaging horizons for each of the clock states and compared to the three state Kalman filter. It is demonstrated that, in the presence of the sawtooth noise induced by the GPS receiver, the unbiased FIR estimates with thinning out fit the clock states better than the Kalman filter, in terms of the Allan deviation and precision time protocol deviation.