[time-nuts] Curve fitting

Bruce Griffiths bruce.griffiths at xtra.co.nz
Wed Dec 23 22:06:18 UTC 2009


Mark Sims wrote:
> Hello Tom,
>
> I have added (and am still adding) a bunch of new features to Lady Heather.  It (she?) can calculate the min, max, average, rms value,  standard deviation,  variance of the data covered by any plot window,  plus a linear regression trend line and FFT.  It can also subtract a constant slope (default=trend line slope) from any plot.
>
> I have also added on oscillator "autotune" function.  This steps the DAC voltage +/- 0.1V from the current setting and calculates the oscillator EFC gain (in Hz/volt).   It then sets the oscillator values (gain,  damping, time constant,  sat elevation mask, and signal level mask) to more time-nutty values than the defaults.
>
> Testing has shown that the osc gain calculated this way is excellent... certainly better than you get eyeballing a 5370 counter.
>
> It would not be difficult to  step the DAC over a larger range to get the EFC linearity curve (except the GPS loses lock if you are too far out of range and the osc freq error may not be available).
>
> I can easily calculate the osc tempco and drift rate using the active temperature control.  I would like to do it using just the raw data...  hence the need for curve fitting to untangle the osc drift rate and tempco from the raw measurements provided by the Tbolt.
>
> Heather has a record stored of all GPSDO parameters going back (default 3 days,  max=1year) since the program was started.   I can use that data to calculate the oscillator parameters (if I can come up with a reasonable curve fitting routine)
>
>    
Mark

Instead of using a traditional least squares fit to a large data set it 
may be more prudent to use robust fitting techniques which are far less 
sensitive to the inevitable outliers.
However unless you are fitting a simple straight line this is much more 
involved than a least squares fit.
One method is to do a least squares fit and use these results as initial 
values in a more robust fitting procedure.


Bruce





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