This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits—namely the orbit set—that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus allowing for a compact analytical description of the orbit set. The automatic domain splitting tool controls the truncation error of the polynomial approximation by patching the uncertainty domain with different polynomial expansions, effectively creating a mesh. The algorithm is tested for different observing strategies to understand the working boundaries, thus defining the region for which the admissible region is necessary to extract meaningful information from observations and highlight where the new method can achieve a smaller uncertainty region, effectively showing that for some observing strategies it is possible to extract more information from a tracklet than the attributable. Consequently, the method enables comparison of orbit sets avoiding sampling when looking for correlation of different observations. Linear regression is also implemented to improve the uncertainty estimation and study the influence of the confidence level on the orbit set size. This is shown both for simulated and real observations obtained from the TFRM observatory.

中文翻译：

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概率数据关联：轨道集

本文提出了一种新的方法来解决光学观测的初始轨道确定问题作为轨道的连续体——即轨道集——在规定的精度内拟合采集的观测集。利用微分代数将观测中的不确定性与具有截断幂级数的轨道天体的状态分析联系起来，从而允许对轨道集进行紧凑的分析描述。自动域分割工具通过用不同的多项式展开修补不确定域来控制多项式近似的截断误差，从而有效地创建网格。该算法针对不同的观察策略进行了测试，以了解工作边界，因此定义了允许区域从观测中提取有意义信息所必需的区域，并突出显示新方法可以实现更小的不确定性区域的区域，有效地表明对于某些观测策略，可以从轨迹中提取比可归因信息更多的信息. 因此，该方法能够在寻找不同观测的相关性时避免采样的轨道集的比较。还实施了线性回归以改进不确定性估计并研究置信水平对轨道集大小的影响。从 TFRM 天文台获得的模拟和真实观测都显示了这一点。有效地表明，对于某些观察策略，可以从轨迹中提取比可归因信息更多的信息。因此，该方法能够在寻找不同观测的相关性时避免采样的轨道集的比较。还实施了线性回归以改进不确定性估计并研究置信水平对轨道集大小的影响。从 TFRM 天文台获得的模拟和真实观测都显示了这一点。有效地表明，对于某些观察策略，可以从轨迹中提取比可归因信息更多的信息。因此，该方法能够在寻找不同观测的相关性时避免采样的轨道集的比较。还实施了线性回归以改进不确定性估计并研究置信水平对轨道集大小的影响。从 TFRM 天文台获得的模拟和真实观测都显示了这一点。还实施了线性回归以改进不确定性估计并研究置信水平对轨道集大小的影响。从 TFRM 天文台获得的模拟和真实观测都显示了这一点。还实施了线性回归以改进不确定性估计并研究置信水平对轨道集大小的影响。从 TFRM 天文台获得的模拟和真实观测都显示了这一点。