MATLAB: Fitting data to a limaçon curve

Question

I have data in the form of two column vectors x and y containing the x and y coordinates of measurements. The data forms a limaçon curve that can be described by the equation (x^2+y^2-a*x)^2 = b^2*(x^2+y^2). How can I fit a curve of that type to my data yielding a and b as results?

Answer 1

Here's a poor man's method, assuming you don't have the Optimization or Curve Fit Toolboxes

 z=x.^2+y.^2;
 %Cheesy initial guess of p=[a,sqrt(b)]
 p= [x, sqrt(z)]\z;
 p(2)=max(p(2),0);   %b must be positive
 %Re-optimize
 p0=p;
 p=fminsearch(@(p) norm( (z-p(1).*x).^2 - z.*p(2).^2  ), p0 );
 a=p(1);
 b=p(2)^2;