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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