How to find the best fit coefficients for an equation which is dependant on more than one varying input parameters?

Hi

I am working on finding the coefficients of an equation which is dependant on 3 parameters.

Example: y(t)=exp(a(t)).x(1)+b(t).x(2)+exp(c(t)).exp(c(t)).x(3);

a,b,c are parameters and x(1),x(2),x(3) are coefficients. Parameters are form of a matrix. I need to find the best fit for the coefficients x(1),x(2),x(3).

which function should I use?

Thanks in advance

[Walter Roberson]

Are the periods multiplications ?

[Nadia A]

Parameters are dependant on time. They are stored as matrix. It is not periodic, If that is what you meant?

[Walter Roberson]

In the code fragment

b(t).x(2)

what does the character between the ")" and the "x" mean?

[Nadia A]

Yes it is multiplication that I meant here. Sorry for the confusion.

I am not able to use the curve fitting toolbox. Shows this error when I tried using it:

To use 'fittype', you might need: fittype - Curve Fitting Toolbox

Is ther any other function I can use to find the coefficients?

Thanks

Answer 1

[Walter Roberson]

If you have the curve fitting toolbox, use fittype() to create the fit parameters and then use fit()

[Nadia A]

Okay. Thank You. I will try that.

[Walter Roberson]

Form two matrix

A = [exp(a(:)), b(:), exp(c(:)).^2];
b = y(:);

Now you can use

x = A \ b;

This can work because your expression is linear in your variables to be solved for.

[Nadia A]

Okay. But will this give the best fit coefficients for y?

I have samples of required y and a(t) which is input. b(t) samples are also available. c(t) is a complex parameter dependant on input and needs to be calculated on the input at that instant. Can I use lsqcurvefit to find coefficients? If so, how do I pass B,C since only A is input.

[Walter Roberson]

Yes it will calculate the best fit coefficients using least squares.

At any one time, you know the a, b, and c up to now. You can use those to find the best fit of everything that has come so far. If you only want to consider a window of samples ("sliding best fit" so to speak) then you would only put the ones in the window into A and b.

You will need at least 3 samples to do a fitting.

[Nadia A]

Thank You

[Muhammet Mammetkuliyev]

Hi Nadia

so how did you solve this fitting problem? I have the same type of fitting to do but dont know how to do it.

thanks

[Muhammet Mammetkuliyev]

I am wondering what if equation is not linear in x1, x2 and x3 which are fit parameters?

specifically, I have such equation that I want to fit.

y(t) = abs( a(t)*(x1*exp(1i*x2)+x3/(t-x4+ix5)) )^2

How can I proceed?

Answer 2

[Muhammet Mammetkuliyev]

and one like this

y(t) = abs( x1*exp(1i*x2)+a(t)(x3/(t-x4+ix5)) + b(t)*(x6/(t-x7+ix8)))^2

[Nadia A]

Hi

I had used fmincon to find the best fit for the parameters. Hope this helps.