AI 中文总结
本研究针对空间目标跟踪的非高斯分布挑战，开发了双滤波器自适应高斯混合平滑算法，经Molniya和地月晕轨道验证，可显著降低估计误差与不确定性。
AI 中文摘要
空间目标跟踪因可能出现的显著非高斯分布而带来极具挑战性的估计问题，尤其在高度非线性动态环境或测量不可用期间。自适应高斯混合滤波器可动态调整其混合分辨率以系统地近似这些非高斯分布，但极具挑战性的估计问题仍可能产生高度不确定或不准确的估计值，尤其是在观测间隙较长时。平滑算法可通过整合未来测量信息显著改进滤波估计值，适用于对实时性要求不高的应用场景，但在非线性、非高斯环境下进行平滑会带来额外的理论和计算挑战。本研究开发了一种用于非线性系统的新型递归贝叶斯平滑算法，该算法可优化由前向自适应高斯混合滤波器生成的高斯混合后验分布。双滤波器平滑方法通过状态变量中的信息形式高斯混合来近似未来测量信息，同时整合了非线性高斯混合滤波中的分裂、合并及递归测量更新等技术，以提升该近似过程的准确性和计算效率。所提出的平滑器在Molniya轨道和地月晕轨道的空间目标跟踪问题上验证了其估计能力，结果显示与前向滤波器相比，其能显著降低估计误差和不确定性。
英文摘要
Space object tracking poses challenging estimation problems due to the significantly non-Gaussian distributions that can arise, particularly under highly nonlinear dynamics or during periods of measurement unavailability. Adaptive Gaussian mixture filters can dynamically adjust their mixture resolution to systematically approximate these non-Gaussian distributions, but challenging estimation problems can still produce highly uncertain or inaccurate estimates, especially during prolonged observation gaps. Smoothing algorithms can significantly improve filtered estimates by incorporating future measurement information for applications where immediacy is not required, but smoothing in nonlinear, non-Gaussian settings poses additional theoretical and computational challenges. This work develops a new recursive Bayesian smoothing algorithm for nonlinear systems that refines Gaussian mixture posteriors produced by a forward adaptive Gaussian mixture filter. A two-filter smoothing approach approximates the future measurement information by an information-form Gaussian mixture in the state variable. Techniques from nonlinear Gaussian mixture filtering including splitting, merging, and recursive measurement updating are also incorporated to improve the accuracy and computational efficiency of this approximation. The proposed smoother's estimation capabilities are demonstrated on space object tracking problems for Molniya and Earth-Moon halo orbits and shown to significantly reduce estimation error and uncertainty compared to the forward filter.
