When an asteroid has a few observations over a short time span the information contained in the observational arc could be so little that a full orbit determination may be not possible. One of the methods developed in recent years to overcome this problem is based on the systematic ranging and combined with the Admissible Region theory to constrain the poorly-determined topocentric range and range-rate. The result is a set of orbits compatible with the observations, the Manifold Of Variations, a 2-dimensional compact manifold parametrized over the Admissible Region. Such a set of orbits represents the asteroid confidence region and is used for short-term hazard predictions. In this paper we review the Manifold Of Variations method and make a detailed analysis of the related probabilistic formalism.

中文翻译：

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变异的多样性：短期撞击物的危害评估

当小行星在短时间内进行几次观测时，观测弧中包含的信息可能非常少，以至于无法确定完整的轨道。近年来为克服这一问题而开发的一种方法是基于系统测距并结合容许区域理论来约束确定不佳的地心距和距距率。结果是一组与观测兼容的轨道，即变流流形，这是一个在可接受区域上参数化的二维紧凑流形。这样一组轨道代表了小行星置信区域，用于短期危险预测。在本文中，我们回顾了 Manifold Of Variations 方法，并对相关的概率形式主义进行了详细分析。