发表机构
Texas A& M University; The Ohio State University（德克萨斯农工大学; 俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对莫尔尼亚轨道短弧仅测角定轨问题，证明传统GLSDC在高噪声下不可靠，通过兰伯特初始化与非线性优化揭示多解性，并提出物理约束作为轨道族选择工具。
AI 中文摘要
本文以莫尔尼亚轨道为案例，研究了噪声短弧仅测角轨道确定的不确定性。首先表明，在高噪声短弧条件下，传统的高斯初轨确定后接高斯最小二乘微分校正方法不可靠，经常无法收敛或收敛到双曲局部解。为了探索候选解空间，采用基于兰伯特的初始化过程，在假设距离和角度观测对的网格上进行，并使用非线性最小二乘优化对所得状态进行精化。无约束解集揭示了多个轨道族，包括再入椭圆、有界椭圆、xGEO椭圆和双曲轨迹，所有这些都能以相当的残差重现观测到的角度弧。解表现出结构化的距离-速度关系，表明角度测量主要约束视线的视运动，而非绝对距离。最后，引入物理动机的约束以隔离类似莫尔尼亚的有界椭圆解。结果表明，在没有先验信息的情况下，短弧仅测角轨道确定从根本上是不唯一的，约束应被解释为轨道族选择工具，而非唯一性的证明。
英文摘要
This paper investigates the ambiguity of noisy short-arc angles-only orbit determination for a Molniya-orbit case study. Conventional Gauss Initial Orbit Determination followed by Gaussian Least-Squares Differential Correction is first shown to be unreliable under high-noise short-arc conditions, frequently failing to converge or converging to hyperbolic local solutions. To explore the candidate solution space, a Lambert-based initialization procedure is used over a grid of assumed ranges and angular-observation pairs, and the resulting states are refined using nonlinear least-squares optimization. The unconstrained solution set reveals multiple orbit families, including reentry elliptic, bounded elliptic, xGEO elliptic, and hyperbolic trajectories, all of which can reproduce the observed angular arc with comparable residuals. The solutions exhibit a structured range-velocity relationship, indicating that the angular measurements primarily constrain apparent line-of-sight motion rather than absolute range. Finally, physically motivated constraints are introduced to isolate Molniya-like bounded elliptic solutions. The results demonstrate that short-arc angles-only orbit determination is fundamentally non-unique without a priori information and that constraints should be interpreted as orbit-family selection tools rather than proof of uniqueness.
