MATLAB: Parameter Estimation (help)

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Has anyone come across with the following:

I need to calculate parameters a1, n1 ... a3, n3 of the following equation (linear, say):

a1, a2, a3 are coefficients;
n1, n2, n3 are exponential ones.

Y = X1 (a1 * V^{n1} + a2 * V^{n2} + a3 * V^{n3})

where Y, X1, and V are known values.

Will it be possible to do so in MATLAB? if so, I would highly appreciate if you could let me know the procedure.

Else, any other approach will be warmly welcomed.

Thx in advance.

Last edited: 08-Sep-09 05:12 AM

GuitarDaku

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Do "lookfor parameter".
Looks like something which should be done in matlab.
If you can linearize that equation and change into matrix form, that could be one way.

F22

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I think you need the Curve Fitting Toolbox, or may be try statistical model fitting in JMP or Minitab

Samayayatri

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Aiya!!!

This is a linear combination of exponential functions! I wonder if the fminsearch function will come in handy. I've never used it though.

You'll have to set up your function as follows:

Y = X1 (a1 * V^{n1} + a2 * V^{n2} + a3 * V^{n3})

Let P=Y./X1;

So now you'll have:

P=a1*V^{n1} + a2*V^{n2}+a3*V^{n3};

Beyond that, I can't say much.

If you could provide the scenario in which you're trying to estimate this, perhaps it would help?

samaeBajii

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It would still be degenerate, I think.

More detail might help.

Neural

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Yeap, I thought the same, f22.
Either CFT or system identification approach might work.

Is any one using Siemens PTI PSS/E tool for power systems dynamic simulation??

--

thx guys for your inputs.

nepaliraja

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Try least square. Here is a nonlinear solver

help lsqnonlin
LSQNONLIN solves non-linear least squares problems.
    LSQNONLIN attempts to solve problems of the form:
    min sum {FUN(X).^2}    where X and the values returned by FUN can be
              x             vectors or matrices.

choose FUN = Y - X1 (a1 * V^{n1} + a2 * V^{n2} + a3 * V^{n3}) and put known constants Y, X1 and V. The x vectors would be [a1, a2, a3, n1, n2, n3]. It will find the least square i.e. FUN^2 for different possible of x. Minimum FUN^2 will be 0 so you will get Y = X1 (a1 * V^{n1} + a2 * V^ + {n2}a3 * V^{n3}) by changing a's and n's.

Samayayatri

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Neural

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.
Thx nepaliraja for the valuable info. (sorry for the late response).

I used "polyfit" to calculate the coefficients and keeping it 3rd degree polynomial. Meanwhile,
this is working.

Cheers !

Happy Dashain to you all Sajha friends.

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