Fitting data to a limaçon curve
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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?
采纳的回答
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;
3 个评论
Frederik
2013-3-1
Matt J
2013-3-1
Then you could use lsqnonlin, for example.Or, here's a modification of my code
z=x.^2+y.^2;
fun=@(p) norm( (z-p(1).*x).^2 - z.*p(2).^2 );
%Cheesy initial guess of p=[a,b]
p1 = [x, sqrt(z)]\z;
p2 = [-x, sqrt(z)]\(-z);
f1=fun(p1);
f2=fun(p2);
p0=p1*(f1<=f2) + p2*(f2<f1);
%Re-optimize
p=fminsearch(fun, p0 );
a=p(1);
b=p(2);
Frederik
2013-3-1
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