## 1 Introduction  
In recent years, the rapid deployment of low Earth orbit (LEO) satellite mega-constellations, typically represented by Starlink, has led to a marked increase in the number of low-orbit space targets. As of 28 April 2025, the number of operational Starlink satellites in orbit was reported to be 7239 according to Jonathan's Space Pages at [[https://planet4589.org/space/con/star/stats.html](https://planet4589.org/space/con/star/stats.html)]([https://planet4589.org/space/con/star/stats.html](https://planet4589.org/space/con/star/stats.html)) (accessed on 28 April 2025). In addition to their large population, Starlink satellites are characterized by frequent orbital maneuvers. Most Starlink satellites are initially injected into orbits at an approximate altitude of 300 km. Subsequently, the satellites ascend to operational altitudes above 500 km using continuous low-thrust electric propulsion. This process often involves several temporary parking phases. Both the orbit-raising and orbit-lowering phases generally last several months, while the on-station phase can extend for several years. Compared to infrequently maneuvering space targets, Starlink satellites experience substantially larger orbit determination (OD) and prediction errors. According to the statistical results presented in [1], for uncontrolled LEO satellites, the 7-day orbit prediction error using TLE data with SGP4 is approximately 10 km, mainly in the along-track direction. For Starlink satellites during the orbit-raising phase, the 1-day prediction error for the V1 version satellites can reach several tens of kilometers [2]. For the V2 mini version satellites, which are equipped with higher thrust, the 1-day prediction error can be even larger, reaching several tens or even over a hundred kilometers. This is primarily due to the difficulty in accurately characterizing their thrust force models and maneuvering schedules. This consequently gives rise to a set of challenges concerning space situational awareness, such as tracking and cataloging space targets and collision warning. In the domain of satellite orbit determination, estimation algorithms play an important role. Among the most widely employed are batch processing methods, which include the least squares method (LSM) [3; 4; 5; 6; 7], and sequential processing methods, represented by the Kalman filtering (KF) and its variants [8; 9; 10; 11]. The Batch Least Squares (BLS) method is a classical OD approach. This method linearizes the nonlinear dynamical system and measurement equations through a Taylor series expansion, neglecting higher-order terms. The OD procedure involves computing partial derivatives of both the dynamics system and measurement equations with respect to the state variables. By simultaneously processing a complete set (or a substantial portion) of observations collected over a defined time span, BLS can estimate the orbital parameters with high accuracy under good initial guesses. However, as system nonlinearity and the number of state variables increase, the calculation of the required partial derivatives becomes more complex. In situations with strong nonlinearity and sparse or limited observations, the BLS method may encounter convergence issues, potentially resulting in OD failure. Among the various Kalman filter variants, the Unscented Kalman Filter (UKF) distinguishes itself from traditional linearization-based approaches by applying the unscented transformation (UT) within the standard Kalman filtering framework. Employing a set of sigma points, the UKF approximates the posterior state distribution, allowing it to address nonlinear system and measurement models directly without computing partial derivatives. This approach can capture higher-order statistics and enhance filtering performance under nonlinear conditions. However, the performance of the UKF is sensitive to the choice of sigma points, weighting parameters, and initial assumptions, including prior variance and process noise [11; 12].