[time-nuts] exponential+linear fit

Alan Melia alan.melia at btinternet.com
Mon Oct 7 14:17:35 UTC 2013


I agree a fit to an equation that has no physical meaning is a bit spurious. 
You can fit almost anything to a polynomial, but it doesnt mean that the 
coefficients mean anything or that an interpolation between data points is 
even sensible!! I have been the victim of a clever maths graduate (with no 
physics knowledge!)

Alan
G3NYK


----- Original Message ----- 
From: "Tim Shoppa" <tshoppa at gmail.com>
To: "Discussion of precise time and frequency measurement" 
<time-nuts at febo.com>
Sent: Monday, October 07, 2013 2:03 PM
Subject: Re: [time-nuts] exponential+linear fit


> 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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