Journal Quest

Main task today: Working on some write-up of my recent analysis for the journal paper.

Gordon came by and I showed him the recent stuff. We looked at how to determine the time uncertainty from the Allan deviation. That would be a good thing to include in the paper.

Met with Ray, we went over the status of everything in the COSMICi system (HW at least).

Emailed Brian Stearns (contact at DeLorme) to ask him if the 0.2 ppm frequency instability we are seeing could be attributable to the TCXO used in the kit, requested part # for datasheet lookup. Also told him about the (10/20/200/400) millisecond glitches.

I'm wondering now if it is really a good assumption for us to say that quantization errors of neighboring phase readings are independent. Suppose the real OCXO frequency is close to an integer; the the quantization errors will be almost totally correlated, and will vanish from the y values. Or, if the OCXO frequency is close to a half-integer, then the quantization errors will be offset from each other by 0.5, and will tend to add up constructively in the y value, but then will tend to cancel again in the d (deviation) determination.

I'm thinking I need to make a more detailed model of the quantization error. Some parameters:

a - quantization error for first (x1) phase measurement, in cycles, in range [-0.5, +0.5). (That is, actual phase at the time of the PPS edge was the measured value minus a.)

f1 - fractional part of actual average frequency (phase accum. btw. PPS edges) during 1st second, in range [0, 1).

b - can be derived from f1 and a

f2 - fractional part of actual average frequency (phase accum. btw. PPS edges) during 2nd second, in range [0, 1). This can be derived from f1 and a model of the "real" instability, as a normal distribution.

c - can be derived from f2 and b.

Then, y1 and y2 can be derived from this, their error (relative to f1 and f2) can be derived, and the d=y2-y1 can be derived, and the error between this and the real delta of f2-f1 can be derived.

We can sweep through values of f1 and a, and plot the distribution of deviation measurement, including the effect of quantization error, as a function of the "real" underlying deviation.

This is all well and good, but I think the argument for phase offsets being pretty well independent for larger window sizes is pretty strong, otherwise I think we'd see some variation in the adjusted Allan deviation measurements depending on the window size, which we don't see except for very small window sizes. Still, doing the above more detailed calculation would be a good sanity check on our earlier calculations.