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: [email protected] > [mailto:[email protected]] 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. > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
