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This paper addresses an unbiased p-step predictive finite impulse response (FIR) filter of the local clock K-degree time interval error (TIE) polynomial model with applications to the global positioning system (GPS)-based clock synchronization. Generic coefficients are derived for a 2-parameter family of the polynomial filter gains. A generalization is provided for the p-step linear (ramp) gain allowing for close to optimal predictive filtering of the TIE. Basic holdover algorithms are discussed along with their most critical properties. Efficiency of the proposed filter in holdover is demonstrated by simulation and in real applications to GPS-based (sawtooth and sawtoothless) measurements of the TIE of a crystal clock.

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An investigation of the optimal time step (sampling interval) is provided for the time interval error (TIE) model of a local crystal clock in GPS-based timekeeping. For the sawtooth noise of a receiver, the local clock states are estimated employing an unbiased finite impulse response (FIR) filtering algorithm. We exploit the local crystal clock imbedded to the Stanford Frequency Counter SR620. The measurements are provided using the SynPaQ III GPS Sensor as a timing receiver and rubidium clock (SR625) as a reference source of time for the crystal clock.