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.

翻译：共心椭圆拟合问题在图像处理、模式识别和天文学中是一个关键问题。目前已发展出多种方法，但均仅针对非常特殊的情形。本文在更一般的设定下对该问题进行了研究，并提出了两种参数估计方法。由于这两种估计器均通过迭代方式获取，因此考察了多种数值方案，并确定了最佳初始猜测值。此外，推导了该问题的约束Cramér Rao下界，并将其与各估计器的方差进行了比较。最后，通过在真实数据与合成数据上的一系列数值实验，对我们的理论进行了评估与验证。