Ah the Kernel
The original kernel is vulnerable to input signals that are not at the nominal 1-PPS frequency or are excessively noisy. In the new kernel a frequency discriminator is used to suppress samples that are outside a tolerance range of ±500 PPM. As in the original kernel, a three-stage median filter is used to suppress outlyer time samples and second order time differences are used to suppress outlyer frequency samples. In the new kernel the outlyer thresholds have been changed to 500 ms for time (jitter) adjustments and between 500 PPM and about 2 PPM, depending on the calibration interval, for frequency adjustments.
While the new design allows for much larger tolerances and is much more resilient to noise and incorrect signal sources, there are specific limits due to the inherent ambiguity of the PPS signal itself when the pulse occurs approximately midway between two adjacent seconds. In order to prevent ambiguity errors, the sum of the maximum time offset and maximum frequency offset, expressed in microseconds over one second, must not exceed 500 ms. In practice with NTP, these limits cannot even be approached, due to the conservative design of the protocol daemon.
The original kernel modifications average the PPS time over a 64-s interval and average the PPS frequency over intervals that start at 8 s and eventually grow to 256 s. As determined by experiment and simulation, these intervals are too large for typical room temperature quartz oscillators. The design of the new kernel reflects the choice of Allan intercept, which depends on the intrinsic phase noise of the PPS signal and the intrinsic stability of the oscillator.
As determined by simulation and experiment, an appropriate value for the Allan intercept is 128 s. The time offset is averaged each second with weight factor equal to the reciprocal of this value, while the frequency offset is measured over an interval equal to the same value.
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