  Ellipse and ellipsoid fitting has been extensively researched and widely
applied. Although traditional fitting methods provide accurate estimation of
ellipse parameters in the low-noise case, their performance is compromised when
the noise level or the ellipse eccentricity are high. A series of robust
fitting algorithms are proposed that perform well in high-noise,
high-eccentricity ellipse/spheroid (a special class of ellipsoid) cases. The
new algorithms are based on the geometric definition of an ellipse/spheroid,
and improved using global statistical properties of the data. The efficacy of
the new algorithms is demonstrated through simulations.
