Re: fitting parameters to a differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg108411] Re: fitting parameters to a differential equation
- From: dh <dh at metrohm.com>
- Date: Wed, 17 Mar 2010 04:37:41 -0500 (EST)
- References: <hnnk2g$cgs$1@smc.vnet.net>
Hi Eric,
I think your idea of usein the DE is sound. Nonlinear Fits are usually nasty.
I assume that "I have a noise measurement" actually means: "I have a
noisy measurement". Otherwise we are out of luck.
To get the derivative I would use digital filters (assuming the data is
equidistant) that at the same time smooth and calculate the derivative.
Which filter you need depends on the amount of noise in your data. A
very simple to calculate type are called Golay Savitzky filters.
Daniel
On 16.03.2010 10:46, eric g wrote:
> Hello Group,
>
> does this make sense to you?:
>
> Suppose I have an second order differential equation on y[t]:
> y''+ay'+by=0, and I have a noise measurement of {y[t], @t1,t2,....tN}, I
> would like to fit 'a' and 'b' using the differential equation rather
> than using the solution.
>
> I will proceed like this:
>
> * take my y[t1],...,y[tN] measuremenst and do b-splines interpolation (I
> dont know what is the best way to do this), named yi[t], then find
> yi'[t], and yi''[t]
>
> * then I have an algebraic system on 'a,b' with N-equations (N is a big
> number) ayi'[t1]+by[t1]=-y''[t1],.....
>
> * how to use pseudoinverse to fit 'a' and 'b'? do you think this way may
> be better that a nonlinear fit (weighted nonlinear regression) using the
> solution of the equation? Do you think that this way may avoid the
> problem of finding the appropriate guess for the nonlinear fits
> algorithms with is ussually an issue?
>
> best regards,
> Eric
>
>
>
--
Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>
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