[time-nuts] exponential+linear fit

Jim Lux jimlux at earthlink.net
Fri Oct 4 13:38:07 EDT 2013


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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