[time-nuts] Digital temperature compensation

[Dan Drown]

I'm experimenting with using a temperature sensor to estimate local  
oscillator frequency changes.  My goal is to have a decent holdover  
clock for a NTP server with not so great GPS antenna placement.

I've been sampling temperature every minute, measured by a DS18B20.   
I've been measuring local clock frequency differences, using chronyd's  
logs from the GPS's PPS.  At 28C through 21C, I get a pretty good  
result that fits a quadratic polynomial decently (0.117 ppm stddev).   
I've attached the graph of that as "temp-clock-warmer.png".

With the colder temperatures, there's a sudden drop off in frequency  
that I'm having a hard time finding a equation that fits as nicely.   
All the examples I can find on the web look like third degree  
polynomials, while my data doesn't seem to fit that exactly.  The best  
result I've had so far (0.198 ppm stddev) is attached as  
"temp-clock.png" and uses the function:

f(x) = -abs(a * (x - 20.88)) + b * ((x - 20.88)**2) + c * ((x - 20.88)**3)
a = 0.888582
b = 0.113806
c = -0.00445763

Does anyone have any advice on how to better model this?  Has anyone  
seen this behavior?

I can provide the raw data if that would help any.
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