Dear Umar Faruk Aminu ,

You can use nonlinear least-square only if you know the general structure of the spectral density function in advance. For example, consider you have "y" array as experimental data related to spectral density and u1, u2, and u3 arrays are the experimental data related to system inputs and you want to define y as a multi-variable function of them (there is no limitation in the number of defined inputs). Also, consider your function is in the following form:

y = A + B*sin(C*u1) + D*(u2)^E + F*exp(G*u3)

So such a code can estimate your required parameters: (The "p" vector has seven elements because you have seven parameters to be estimated)

minres = @(p)( p(1) + p(2)*sin(p(3)*u1) + p(4)*(u2)^p(5) + p(6)*exp(p(7)*u3) - y ) ;

par0 = [1 1 1 1 1 1 1] ;

for i = 1 : 30

par = lsqnonlin(minres, par0) ;

par0(1:7) = par(1:7) ;

end

You can replace "1" values in the elements of par0 with any better starting points of estimation if you have. Increasing the number of iterations of "for" loop is effective for increasing the accuracy up to a particular limit for each estimation which can be reduced by choosing better starting points.

Best regards

Thank you for taking your time to respond to my question sir Kianoosh Karimi,

The answer you provided is helpful to me.

Best regards

Hi Umar,

What are you exactly trying todo::you work for the chinese gov or what?

-Chinese Trunk Track Irregularity??? Never heard of it.

-Non Linear Least Square Optimization never heard of it.

You are loosing too much time with that matlab TimeIsBaraka.

-> well i am working on the hyperbolic space for space jump and using only PI for it. And watching BattleStarGalaktika on my own version of iMovie build with HTMLCSSJS.

So what is PI?

And Why is PI equal to 3,14..

PI is Pithon