Re: Re: fitting parameters to a differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg108541] Re: [mg108411] Re: fitting parameters to a differential equation
- From: Virgil Stokes <vs at it.uu.se>
- Date: Mon, 22 Mar 2010 02:41:05 -0500 (EST)
- References: <hnnk2g$cgs$1@smc.vnet.net> <201003170937.EAA27589@smc.vnet.net>
On 17-Mar-2010 10:37, dh wrote:
> 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
>>
>>
>>
>>
>
>
I wrote a Mathematica notebook about a year ago on LS smoothing for
teaching purposes. This notebook gives some background on the SG
smoother and contains code that can be used to estimate smoothed values
(0th derivative) and derivatives of noisy TS data --- several examples
of smoothing are included. If anyone is interested in this notebook,
then just drop me an email with "SG Smoother" in the subject.
--V
- References:
- Re: fitting parameters to a differential equation
- From: dh <dh@metrohm.com>
- Re: fitting parameters to a differential equation