Interpolating measured data, by specific function

Hello, I'm looking for ideal method, how to interpolate measured data by function looks like y(x)=D*sin{C*atan[B*x-E*(B*x-atan(B*x)]}.

I need to get constants B,C,D,E. Can anybody help me, with solution of this problem?? Thank you.

Answer 1

[Andrei Bobrov]

Please try it:

fm = @(B,C,D,E,x)D*sin(C*atan(B*x-E*(B*x-atan(B*x)));

F = fit(x,y,fm,'StartPoint', [1,1,1,1]);

example of using:

out = F(x(1:8));
plot(F,x,y);