On 10/04/2013 11:16 PM, Jim Lux wrote: > On 10/4/13 1:18 PM, Joseph Gwinn wrote: >> On Fri, 04 Oct 2013 14:30:40 -0400, time-nuts-requ...@febo.com wrote: >>> ------------------------------ >>> >>> Message: 4 >>> Date: Fri, 04 Oct 2013 10:38:07 -0700 >>> From: Jim Lux <jim...@earthlink.net> >>> To: Discussion of precise time and frequency measurement >>> <time-nuts@febo.com> >>> Subject: [time-nuts] exponential+linear fit >>> Message-ID: <524efcff.8000...@earthlink.net> >>> Content-Type: text/plain; charset=ISO-8859-1; format=flowed >>> >>> 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. >> >> How many measured data points do you have? If you have enough data, >> you can use the MatLab nlinfit() (nonlinear fit) function to fit the >> data directly to the y(t) equation. > > > I'm removing a slowly varying bias term from fairly noisy data. Maybe > several 10s of thousands of data points, > And I want to do it quickly on a slow processor. ... and a simple high-pass filter won't do it for you?
Can you store all samples in memory and iterate over them? Just trying to figure out your limits. > > > >> >> Because nlinfit uses a least-squares approach, and there are many >> coefficients to be found, a reasonable starting point is required. The >> fit on the derivative, while probably too noisy to yield a useful final >> answer, would be one way to get some of the initial values. > > I've done that and it works.. but I'm looking for a more "basic" sort > of approach, given that I actually know something about the underlying > model. Least-square do require you to know something about the underlying model. If you can build the Jacobian, that helps. Least-square isn't all that hard to do incremental, which means that there is very little data to be held in memory compared to the straight-forward way. You only need to hold the data-series in memory if you need it for other purposes. Cheers, Magnus _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
