Fitting an ellipsoid to 3D data points

here you go:

This paper describes fitting an ellipsoid to multiple dimensions AS WELL AS finding the center for the ellipois. Hope this helps,

http://www.physics.smu.edu/~scalise/SMUpreprints/SMU-HEP-10-14.pdf

(btw, I'm assuming this answer is a bit late, but I figured I would add this solution for anyone who stumbles across your question in search for the same thing :)

If you want the minimum-volume enclosing ellipsoid, check out this SO answer for a bounding ellipsoid.

If you want the best fitting ellipse in a least-squares sense, check out this MATLAB code for error ellipsoids where you find the covariance matrix of your mean-shifted 3D points and use that to construct the ellipsoid.