Orbit determination (OD) is a fundamental problem in space surveillance and tracking, crucial for ensuring the safety of space assets. Real-world ground-based optical tracking scenarios often involve challenges such as limited measurement time, short visible arcs, and the presence of outliers, leading to sparse and non-Gaussian observational data. Additionally, the highly perturbative and nonlinear orbit dynamics of resident space objects (RSOs) in low Earth orbit (LEO) add further complexity to the OD problem. This paper introduces a novel variant of the higher-order unscented Kalman estimator (HOUSE) called $w$-HOUSE, which employs a square-root formulation and addresses the challenges posed by nonlinear and non-Gaussian OD problems. The effectiveness of $w$-HOUSE was demonstrated through synthetic and real-world measurements, specifically outlier-contaminated angle-only measurements collected for the Sentinel 6A satellite flying in LEO. Comparative analyses are conducted with the original HOUSE (referred to as $\delta$-HOUSE), unscented Kalman filters (UKF), conjugate unscented transformation (CUT) filters, and precise orbit determination solutions estimated via onboard global navigation satellite systems measurements. The results reveal that the proposed $w$-HOUSE filter exhibits greater robustness when dealing with varying values of the dependent parameter compared to the original $\delta$-HOUSE. Moreover, it surpasses all other filters in terms of positioning accuracy, achieving three-dimensional root-mean-square errors of less than 60 m in a three-day scenario. This research suggests that the new $w$-HOUSE filter represents a viable alternative to UKF and CUT filters, offering improved positioning performance in handling the nonlinear and non-Gaussian OD problem associated with LEO RSOs.

翻译：轨道确定（OD）是空间监视与跟踪领域的基础问题，对于确保空间资产安全至关重要。实际地基光学跟踪场景常面临观测时间有限、可视弧段短、存在异常值等挑战，导致观测数据稀疏且呈现非高斯分布。此外，低地球轨道（LEO）空间物体（RSO）的高扰动非线性轨道动力学特性进一步增加了OD问题的复杂性。本文提出一种名为 $w$-HOUSE 的新型高阶无迹卡尔曼估计器（HOUSE）变体，该变体采用平方根形式，能够应对非线性、非高斯OD问题带来的挑战。通过合成数据与实测数据（特别是针对LEO飞行的Sentinel 6A卫星采集的含异常值纯角度测量数据）验证了 $w$-HOUSE 的有效性。与原始HOUSE（记作 $\delta$-HOUSE）、无迹卡尔曼滤波器（UKF）、共轭无迹变换（CUT）滤波器以及基于星载全球导航卫星系统测量数据估算的精密轨道确定结果进行了对比分析。结果表明，与原始 $\delta$-HOUSE 相比，所提出的 $w$-HOUSE 滤波器在处理不同依赖参数取值时展现出更强的鲁棒性。此外，该滤波器在定位精度方面超越所有其他滤波器，在三日仿真场景下实现了均方根误差小于60米的三维定位精度。本研究表明，新型 $w$-HOUSE 滤波器可作为UKF与CUT滤波器的有效替代方案，在处理LEO空间物体相关非线性、非高斯OD问题时具有更优的定位性能。