Whatever method is used in the "Calculate Circle Approximation" does not do well if there are not points around an arc which is close to 360°. I suspect the Kasa method, or something similar is used (link to Matlab code: http://blogs.mathworks.com/pick/2008/03/14/fitting-a-circle-easily/). This method works well if there are points all around the 360° of a circle, but not so well if the data only covers an arc. If you go to Chernov's page ( http://www.math.uab.edu/~chernov/cl/) you can find a link to Matlab code for the Pratt Method ( http://www.math.uab.edu/~chernov/cl/MATLABcircle.html), which works great for arcs. Although I have not tested it, I suspect the Pratt Method works well for data distributed across 360° as well. If that is the case, I would recommend that you either add an "arc fitting" function using the Pratt Method or replace the method used in the "Calculate Circle Approximation" with the Pratt Method.
Attached is an image of an example of latitude and longitude data. Note that, because this is lat & lon data, the circles look like ovals, but they really are circles. I was trying to fit a circle to the red curve between the two vertical black cursor lines. The green circle was obtained by using the "Calculate Circle Approximation" function while the blue circle was calculated via the Pratt Method.
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