Optimal Oscillator Modelling for GNSS-Disciplined Clock Holdover

An important part of GNNS Disciplined Clock (GDC) design is to optimally estimate the oscillator’s current frequency and drift, as that will determine the performance of the GDC under holdover. The simplest method is make a parabolic fit to a batch of the most recent GNSS data used by the GDC, after removing the effects of all steering that had been applied. The steering would then be applied to the derived parabola (phase, frequency, and drift) so as to extrapolate into the future. The accuracy of this extrapolation determines the capability of the GDC under holdover. It is dependent on the noise characteristics of the oscillator. An insightful paper by Vernotte et al. (2001) shows how the time interval error (TIE) of an oscillator depends on the amount of its white phase noise, white frequency noise (random walk phase noise, RW), flicker frequency noise, and the amount of its random walk frequency noise (integrated random walk phase noise, IRW, or RR). This paper uses those results to derive the optimal baseline for any linear combination of RR and IRW, mostly under the assumption that the phase noise is negligible. For brevity, flicker frequency noise is ignored; its characteristics are intermediate between the two noise types covered. The rule of thumb for the parabolic fit is that the optimal baseline is about ten times the prediction distance for pure RW, but only 1.06 times the prediction distance for IRW. The optimal baseline distance of a linear combination more closely approximates that of RWFM as the fourth power of the prediction distance distances. Some analysis for white phase noise is also included. Finally, it is shown that a perfectly tuned Kalman filter outperforms even the optimal quadratic fits, and the relative accuracy of the two algorithms is assessed.