Can anyone help me in curve fitting problem of Magic Formula?

I have a set of 25 values of x and y and this predefined equation. I have to fit the values in this and find the coefficients

 f (x)= D.sin[C tg-1{(1- E).B.x + E.tg-1(B.x)}]              tg-1 = inverse tg function

I have to write a MATLAB algorithm to find the optimum fit for the data shown above and find the parameters B, C, D, and E. I even have to plot the curve

[Walter Roberson]

Unfortunately between the "]" and the "tg-1" you have a series of 14 unicode characters that fall into the "private use" range, meaning that any particular printable representation assigned to them is for use only within one program. U+F0BD U+F0D7 U+F0E9 U+F0D7 and so on. We do not know if those are important for our understanding ?

When you say "inverse tg" is that "inverse tan" ?

[Walter Roberson]

Your expression appears to correspond to

D .* sin(C .* atan((1-E) .* B .* x + E .* atan(B .* x)))

Could you confirm that you want the arctan of B*x to be inside another arctan expression? It is not at all common to want to arctan an arctan.

If you had something more like

D .* sin(C .* atan((1-E) .* atan(B .* x) + E .* atan(B .* x)))

or

D .* sin(C .* (atan((1-E) .* B .* x) + atan(E .* B .* x)))

then it would make more sense, as it would be finding a mixing coefficient E between two possibilities.

[Akshay Apte]

I have to use the magic formula and compute it. I think it should be arctan. Not sure!

[Walter Roberson]

When you say "magic formula" are you referring to "magic formula investing" or something like that ???

[John BG]

magic=science?

[Torsten]

https://en.wikipedia.org/wiki/Hans_B._Pacejka

Best wishes

Torsten.

Answer 1

[Walter Roberson]

I suggest that you use cftool to create a custom model

Answer 2

[Marco Furlan]

Another approach can be to use lsqcurvefit

Link here