## 1 Introduction  
Orbit uncertainty propagation (OUP) and orbit determination (OD) are essential in space missions such as near-Earth missions [1; 2; 3], asteroid exploration missions [4; 5; 6], lunar exploration missions [7], Venus exploration missions [8], and Jupiter exploration missions [9; 10]. Among these space missions, deep space exploration missions rely on extremely accurate OUP and OD techniques. The OUP involves predicting the orbital states (and the associated uncertainties), whereas the OD involves determining the precise position and velocity of a space target, such as a spacecraft or an asteroid, with respect to a reference frame [11; 12; 13]. Accurate OUP and OD are crucial for many deep space missions, including spacecraft navigation, design of trajectory correction maneuvers, planetary exploration, and more [14; 15]. High accuracy helps to optimize and design robust trajectories that consider uncertainties, which is particularly important for mission planning and execution [16; 17]. Additionally, it enables the prediction of future spacecraft positions and velocities [18; 19], which is useful for coordinating operations and avoiding collisions with other objects in deep space [20; 21; 22]. Classic OUP methods include Monte Carlo simulation [23], unscented transform (UT) [24; 25; 26], cubature rule [27], state transition matrix [28; 29], state transition tensor (STT) [30; 31; 32], and Gaussian mixture model (GMM) [34]. [PERSON] and [PERSON] investigated the OUP problem of a spacecraft on a Sun-Earth L1 orbit [32; 33]. [PERSON] and [PERSON] derived an STM for OUP of a fly-by spacecraft [35]. [PERSON] and [PERSON] analyzed the stability of the Europa Lander orbit using STT [36]. [PERSON] et al proposed a semi-analytical uncertainty propagation method for a heliocentric constellation based on STT techniques [31]. In general, OD can be performed for a deep space probe using optical [37], pulsar-based [10], and doppler-Range radio [35] measurements. [PERSON] et al. investigated the possibility of optical navigation during the approach of an asteroid [5]. They performed observability analysis for the optical navigation and proposed an observability improvement method based on maneuvers. [PERSON] and [PERSON] proposed a weighted least squares method for state estimation of interplanetary orbits using multi-angle measurements [38]. [PERSON] investigated the possibility of deep-space optical navigation using a planet's centroid and apparent diameter in images [39]. Compared with angle-only measurements, the use of the apparent diameter can improve the observability of optical navigation. [PERSON] further investigated the pose estimation and optical navigation methods using the features of the rotating celestial bodies (e.g., asteroids) and spheroidal planets with banded atmospheres (e.g., Jupiter) [9]. [PERSON] et al. analyzed the performance of optical navigation of a CubeSat in an Earth-Mars transfer [11]. [PERSON] et al. reviewed deep space navigation methods and concluded that the conventional doppler-rRange radio navigation method can hardly satisfy the deep space mission requirement of high performance in real-time accuracy and coverage [10]. In addition, they found that the higher frequency of pulsars leads to a better navigation solutions compared to optical navigation. [PERSON] et al. compared deep-space navigation methods using optical, pulsar-based, and radiometric measurements and concluded that significant pulsar time-of-arrival measurement noise limits its utility for approach and entry navigation [40]. The least squares (LS) and Kalman filter are two basic methods for OD [41; 42]. In LS-based OD, a set of measurements, such as range and angle measurements, is used to estimate the initial state vector of a spacecraft. The basic idea of LS is to minimize the difference between the observed and predicted measurements by adjusting the initial state vector [43].