  The problem of fitting concentric ellipses is a vital problem in image
processing, pattern recognition, and astronomy. Several methods have been
developed but all address very special cases. In this paper, this problem has
been investigated under a more general setting, and two estimators for
estimating the parameters have been proposed. Since both estimators are
obtained iterative fashion, several numerical schemes are investigated and the
best initial guess is determined. Furthermore, the constraint Cram\'{e} Rao
lower bound for this problem is derived and it is compared with the variance of
each estimator. Finally, our theory is assessed and validated by a series of
numerical experiments on both real and synthetic data.
