>Thank you for your help. What you have described is exactly what I'm >currently doing, however its not very robust when noisy data is >introduced into the algorithm. Do you know how to do a least squares >fit of data to the equation of a circle? (I suppose: f(x,y)=x^2+y^2) >I have a suspicion that this is a multivariate regression problem. I'm >rather a newbie to this sort of thing. > >Thanks, >Marc
Hello, it's me again! You told me that my solution to your problem was the same as the one you were already using. Then I believe that your original description was a bit wrong, but that won't help you any further. I spent some time on a least squares method and I found one. I will not repeat the derivation here since that would give me a headache typing it, but I will give you the final result:
Suppose that you have datapoints (x1,y1), (x2,y2), ..., (xN,yN). Now form the following sums:
Now I hope I didn't make any mistakes typing it. I've checked this formula for the data points (2,1), (-3,-4), (1,-2) and (-6,5). It does indeed give X=-3, Y=1 and R=5, as it should. I believe that my derivation is correct. Use it, try it out and tell me when anything is wrong with it.