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：同心椭圆拟合问题是图像处理、模式识别和天文学中的一个关键问题。已有多种方法被提出，但均仅适用于非常特殊的情况。本文在更通用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。由于这两种估计量均通过迭代方式获得，因此探讨了多种数值方案，并确定了最佳初始猜测值。此外，推导了该问题的约束克拉美-罗下界，并将其与各估计量的方差进行了比较。最后，通过一系列基于真实数据和合成数据的数值实验，对理论进行了评估和验证。