[time-nuts] exponential+linear fit

[Tim Shoppa]

Proposing a random fitting with various curves without an underlying
physical (e.g. Eureqa) model seems... odd. That's more voodoo
engineering/science than anything real. It doesn't surprise me that
computer scientists would propose that as an approach to data, making it
even more inappropriate.

Having well-versed engineers and physical scientists looking at curves and
striving to understand the various features with underlying well-understood
and used physical models (including abnormalities in measurements), that
seems appropriate.

The originally proposed model of long term linear drift trend plus
exponential decay of initial thermal conditions is very well understood and
accepted.


On Mon, Oct 7, 2013 at 3:46 AM, Ulrich Bangert <df6jb at ulrich-bangert.de>wrote:

> Jim,
>
> most if not all fitting strategies make use of an assumption concerning the
> underlying model.
>
> For those who are not sure what the underlying model is this one
>
> http://creativemachines.cornell.edu/eureqa
>
> is the hottest tool that I have ever seen. Give it a try.
>
> Best regards
>
> Ulrich
>
> > -----Ursprungliche Nachricht-----
> > Von: time-nuts-bounces at febo.com
> > [mailto:time-nuts-bounces at febo.com] Im Auftrag von Jim Lux
> > Gesendet: Freitag, 4. Oktober 2013 19:38
> > An: Discussion of precise time and frequency measurement
> > Betreff: [time-nuts] exponential+linear fit
> >
> >
> > I'm trying to find a good way to do a combination
> > exponential/linear fit
> > (for baseline removal).  It's modeling phase for a moving
> > source plus a
> > thermal transient, so the underlying physics is the linear term (the
> > phase varies linearly with time, since the velocity is constant) plus
> > the temperature effect.
> >
> > the general equation is y(t) = k1 + k2*t + k3*exp(k4*t)
> >
> > Working in matlab/octave, but that's just the tool, I'm
> > looking for some
> > numerical analysis insight.
> >
> > I could do it in steps.. do a straight line to get k1 and k2,
> > then fit
> > k3& k4 to the residual; or fit the exponential first, then do the
> > straight line., but I'm not sure that will minimize the
> > error, or if it
> > matches the underlying model (a combination of a linear trend and
> > thermal effects) as well.
> >
> > I suppose I could do something like do the fit on the
> > derivative, which
> > would be
> >
> > y'(t) = k2 + k3*k4*exp(k4*t)
> >
> > Then solve for the the k1.  In reality, I don't think I care as much
> > what the numbers are (particularly the k1 DC offset) so
> > could probably
> > just integrate (numerically)
> >
> > y'()-k2-k3*k4*exp(k4*t) and get my sequence with the DC term, linear
> > drift, and exponential component removed.
> >
> >
> > The fear I have is that differentiating emphasizes noise.
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