[time-nuts] exponential+linear fit

Volker Esper ailer2 at t-online.de
Mon Oct 7 08:31:40 EDT 2013


very cool

Am 07.10.2013 09:46, schrieb Ulrich Bangert:
> 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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