[time-nuts] Re: 3-Cornered Hat fails with negative variances, is there anything I can to to improve?

[AC0XU (Jim)]

I published a couple of papers on Tri-Cornered Hat and Grosslambert. 

https://ieeexplore.ieee.org/document/9234829

https://www.ion.org/publications/abstract.cfm?articleID=17805

My position is that this is a statistical problem, and it is best to analyze the results statistically. In particular, you can estimate the distributions of the measurements and the computed ADEV estimates. You never end up with unphysical results because even if the simple tri-cornered hat formula produces a negative result for some time scale, the estimate includes an uncertainty interval that includes positive values. Unfortunately, the usual ADEV apps don't perform this analysis. Some day I hope to publish one but that hasn't happened yet. The algorithm I use is described in the first paper.

Sadly, no manufacturer of stable timing devices makes much of an effort to capture the statistical properties of their devices. The most that most manufacturers do is post ADEV values at a few time scales. I haven't seen any datasheets with confidence intervals for ADEV. Also, manufacturers can be cavalier with temperature sensitivity, which can be huge even for OCXOs and  "atomic clock on a chip" devices. So you have the right idea - testing is super important.