Bob Fisher
Given a set of N data points 
we would like to find the parameters 
of the circle
that best fits these points.
Given the parameter vector 
,
the circle center is at
and has radius 
.
To improve numerical stability, you will probably want to subtract the mean point position and scale by the range of values before doing the estimation. You need to unscale the parameter vector afterwards.
There are several different distance measures that one can use when defining the error. The most common three are the Euclidean, approximated Euclidean and algebraic distance measures.