Search Results (30)

Real-Time Precise Orbit Determination (RTPOD) of Low Earth Orbit (LEO) satellites relies primarily on onboard GNSS observations and may suffer from degraded performance when observation geometry weakens or tracking conditions deteriorate within satellite formations. To enhance the robustness and accuracy of RTPOD under such conditions, a cooperative Extended Kalman Filter (EKF) framework that fuses onboard GNSS and inter-satellite link (ISL) range measurements is established, integrated with an iterative Detection, Identification, and Adaptation (DIA) quality control algorithm. By introducing high-precision ISL range measurements, the strategy increases observation redundancy, improves the effective observation geometry, and provides strong relative position constraints among LEO satellites. This constraint strengthens solution stability and convergence, while simultaneously enhancing the sensitivity of the DIA-based quality control to observation outliers. The proposed strategy is validated in a simulated real-time environment using Centre National d’Etudes Spatiales (CNES) real-time products and onboard observations of the GRACE-FO mission. The results demonstrate comprehensive performance enhancements for both satellites over the experimental period. For the GRACE-D satellite, which suffers from about 17% data loss and a cycle slip ratio several times higher than that of GRACE-C, the mean orbit accuracy improves by 39% (from 13.1 cm to 8.0 cm), and the average convergence time is shortened by 44.3%. In comparison, the GRACE-C satellite achieves a 4.2% mean accuracy refinement and a 1.3% reduction in convergence time. These findings reveal a cooperative stabilization mechanism, where the high-precision spatiotemporal reference is transferred from the robust node to the degraded node via inter-satellite range measurements. This study demonstrates the effectiveness of the proposed method in enhancing the robustness and stability of formation orbit determination and provides algorithmic validation for future RTPOD of LEO satellite formations or large-scale constellations. Full article

This paper presents a novel approach to address the problem of intercepting non-cooperative targets with multiple satellites in Earth orbit. The multi-satellite interception problem is formulated as a multi-player pursuit–evasion game that explicitly accounts for stochastic disturbances and control constraints. By combining differential game theory with stochastic optimization techniques, the paper derives optimal interception trajectories that ensure safety and performance under modeling uncertainties. A linear exponential quadratic cost functional is established, and corresponding Nash equilibrium strategies are obtained to determine the optimal control laws. Numerical simulations validate the effectiveness and robustness of the proposed approach in achieving reliable interception performance. Full article

In this paper, a predator–prey model with hunting cooperation and maturation delay is studied. Through theoretical analysis, we investigate the existence of multiple stability switches of the positive equilibrium. By applying Hopf bifurcation theory, the conditions for Hopf bifurcation are derived, indicating the emergence of periodic solutions as the maturation delay passes through critical values. Utilizing center manifold theory and normal form analysis, we determine the stability and direction of the bifurcating orbits. Numerical simulations are performed to validate the theoretical results. Furthermore, the simulations vividly demonstrate the appearance of period-doubling bifurcations, which is the onset of chaotic behavior. Bifurcation diagrams and phase portraits are employed to precisely characterize the transition processes from a stable equilibrium to periodic, period-doubling solutions and chaotic states under different maturation delay values. The study reveals the significant influence of maturation delay on the stability and complex dynamics of predator–prey systems with hunting cooperation. Full article

Continuous low thrust is widely used in orbit transfer maneuvers. If the unknown maneuvers are not correctly compensated, the orbiting accuracy will be seriously affected. We propose a rapid method for pre-identifying thrust acceleration based on single-arc orbit determination in order to determine the orbit of non-cooperative continuous low-thrust maneuvering spacecraft. The single-arc orbit determination results of two ground-based radar observations with a certain time interval are used to inversely determine the direction and magnitude of acceleration of the spacecraft under continuous thrust based on their relationship with satellite orbit parameters. The solution error is relatively small when using this method, even over a short period of time when data are sparse. The results can then be applied to the orbital adjustment of a satellite. The results show that when the satellite climbs with maximum tangential acceleration, the interval between the two radar observations is greater than 7 h, and the proposed method can rapidly pre-identify tangential thrust acceleration with a solution error of less than 5%. When the satellite adjusts the orbital plane with the maximum normal acceleration, the average relative measurement error of the normal acceleration is about 20% when the time interval between two observations is 24 h. The longer the observation interval and the greater the thrust acceleration, the smaller the relative error. The calculation results can be used as the initial value for precision orbit determination of continuous low-thrust maneuvering spacecraft. Full article

Orbit determination for non-cooperative low Earth orbit (LEO) objects undergoing continuous low-thrust maneuvers remains a significant challenge, particularly for large satellite constellations like Starlink. This paper presents a method that integrates the unscented transformation into a batch filtering framework with an optimized rho-minimum sigma points sampling strategy. The proposed approach uses a reduced dynamics model that considers Earth’s non-spherical gravity and models the combined effects of low-thrust and atmospheric drag as an equivalent along-track acceleration. Numerical simulations under different measurement noise levels, initial state uncertainties, and across multiple satellites confirm the method’s reliable convergence and favorable accuracy, even in the absence of prior knowledge of the along-track acceleration. The method consistently converges within 10 iterations and achieves 24 h position predictions with root mean square errors of less than 3 km under realistic noise conditions. Additional validation using a higher-fidelity model that explicitly accounts for atmospheric drag demonstrates improved accuracy and robustness. The proposed method can provide accurate orbit knowledge for space situational awareness associated with continuously maneuvering Starlink satellites. Full article

The analysis and processing of active radar image information is an important method for determining the payload orientation of non-cooperative targets. However, a challenge for spacecraft carrying parabolic antenna payloads is that active radar imaging is susceptible to defocus, making it difficult to achieve a reliable estimate of the orientation of such payloads. As such, this paper proposes a method for estimating the orientation of spacecraft parabolic antenna payloads based on radar-measured radar cross section (RCS) sequence data. By utilizing the step effect produced when the ground-based radar observes the parabolic antenna payload, the mathematical model for estimating the orientation of the parabolic antenna payload is established through the analysis of the geometric relationship between the radar observation vector and the antenna payload orientation in the orbital coordinate system. This method employs an optimized model and particle swarm optimization to achieve the pointing estimation of the parabolic antenna payload. The simulation results demonstrate that the proposed algorithm can accurately estimate the pointing direction of the antenna payload, with the maximum error being better than three degrees, and it has good robustness. The results of real data processing further verify the effectiveness of the algorithm. Full article

Axial estimation is an important task for detecting non-cooperative space targets in orbit, with inverse synthetic aperture radar (ISAR) imaging serving as a fundamental approach to facilitate this process. However, most of the existing axial estimation methods usually rely on manually extracting and matching features of key corner points or linear structures in the images, which may result in a degradation in estimation accuracy. To address these issues, this paper proposes an axial estimation method for spaceborne targets via ISAR image sequences based on a regression network. Firstly, taking the ALOS satellite as an example, its Computer-Aided Design (CAD) model is constructed through a prior analysis of its structural features. Subsequently, target echoes are generated using electromagnetic simulation software, followed by imaging processing, analysis of imaging characteristics, and the determination of axial labels. Finally, in contrast to traditional classification approaches, this study introduces a straightforward yet effective regression network specifically designed for ISAR image sequences. This network transforms the classification loss into a loss function constrained by the minimum mean square error, which can be utilized to adaptively perform the feature extraction and estimation of axial parameters. The effectiveness of the proposed method is validated through both electromagnetic simulations and experimental data. Full article

In this paper, we propose a Bayesian Optimization (BO)-based strategy using the Gaussian Process (GP) for feature detection of a known but non-cooperative space object by a chaser with a monocular camera and a single-beam LIDAR in a close-proximity operation. Specifically, the objective of the proposed Space Object Chaser-Resident Assessment Feature Tracking (SOCRAFT) algorithm is to determine the camera directional angles so that the maximum number of features within the camera range is detected while the chaser moves in a predefined orbit around the target. For the chaser-object spatial incentive, rewards are assigned to the chaser states from a combined model with two components: feature detection score and sinusoidal reward. To calculate the sinusoidal reward, estimated feature locations are required, which are predicted by Gaussian Process models. Another Gaussian Process model provides the reward distribution, which is then used by the Bayesian Optimization to determine the camera directional angles. Simulations are conducted in both 2D and 3D domains. The results demonstrate that SOCRAFT can generally detect the maximum number of features within the limited camera range and field of view. Full article

Orbital maneuver detection for non-cooperative targets in space is a key task in space situational awareness. This study develops a passive maneuver detection algorithm using line-of-sight angles measured by a space-based optical sensor, especially for targets in high-altitude orbit. Emphasis is placed on constructing a new characterization for maneuvers as well as the corresponding detection method. First, the concept of relative angular momentum is introduced to characterize the orbital maneuver of the target quantitatively, and the sensitivity of the proposed characterization is analyzed mathematically. Second, a maneuver detection algorithm based on the new characterization is designed in which sliding windows and correlations are utilized to determine the mutation of the maneuver characterization. Subsequently, a numerical simulation system composed of error models, reference missions and trajectories, and computation models for estimating errors is established. Then, the proposed algorithm is verified through numerical simulations for both long-range and close-range targets. The results indicate that the proposed algorithm is effective. Additionally, the sensitivity of the proposed algorithm to the width of the sliding window, accuracy of the optical sensor, magnitude and number of maneuvers, and different relative orbit types is analyzed, and the sensitivity of the new characterization is verified using simulations. Full article

Accurately determining the attitude of non-cooperative spacecraft in on-orbit servicing (OOS) has posed a challenge in recent years. In point cloud-based spatial non-cooperative target attitude estimation schemes, high-precision point clouds, which are more robust to noise, can offer more accurate data input for three-dimensional registration. To enhance registration accuracy, we propose a noise filtering method based on moving least squares microplane projection (mpp-MLS). This method retains salient target feature points while eliminating redundant points, thereby enhancing registration accuracy. Higher accuracy in point clouds enables a more precise estimation of spatial target attitudes. For coarse registration, we employed the Random Sampling Consistency (RANSAC) algorithm to enhance accuracy and alleviate the adverse effects of point cloud mismatches. For fine registration, the J-ICP algorithm was utilized to estimate pose transformations and minimize spacecraft cumulative pose estimation errors during movement transformations. Semi-physical experimental results indicate that the proposed attitude parameter measurement method outperformed the classic ICP registration method. It yielded maximum translation and rotation errors of less than 1.57 mm and 0.071°, respectively, and reduced maximum translation and rotation errors by 56% and 65%, respectively, thereby significantly enhancing the attitude estimation accuracy of non-cooperative targets. Full article

To find superior guidance strategies for preventing possible interception threats from space debris, out-of-control satellites, etc., this paper investigates an orbital pursuit–evasion–defense game problem with three players called the pursuer, the evader, and the defender, respectively. In this game, the pursuer aims to intercept the evader, while the evader tries to escape the pursuer. A defender accompanying the evader can protect the evader by actively intercepting the pursuer. For such a game, a linear-quadratic duration-adaptive (LQDA) strategy is first proposed as a basic strategy for the three players. Later, an advanced pursuit strategy is designed for the pursuer to evade the defender when they are chasing the evader. Meanwhile, a cooperative evasion–defense strategy is proposed for the evader and the defender to build their cooperation. Simulations determined that the proposed LQDA strategy has higher interception accuracy than the classic LQ strategy. Meanwhile, the proposed two-sided pursuit strategy can improve the interception performance of the pursuer against a non-cooperative defender. But if the evader and defender employ the proposed cooperation strategy, the pursuer’s interception will be much more difficult. Full article

Space-based opportunistic positioning is a crucial component of resilient positioning, navigation, and timing (PNT) systems, and it requires the acquisition of orbit information for non-cooperative low Earth orbit (LEO) satellites. Traditional methods for orbit determination (OD) of non-cooperative LEO satellites have difficulty in achieving a balance between reliability, hardware costs, and availability duration. To address these challenges, this study proposes a framework for single-station orbit determination of non-cooperative LEO satellites. By utilizing signals of opportunity (SOPs) captured by a single ground station, the system performs initial orbit determination (IOD), precise orbit determination (POD), and orbit prediction (OP), enabling the long-term determination of satellite positions and velocities. Under the proposed framework, the reliability and real-time performance are dependent on the initial orbit determination and the orbit calculation based on the dynamical model. To achieve initial orbit determination, a three-step algorithm is designed. (1) An improved search method is employed to estimate a coarse orbit using single-pass Doppler measurements. (2) Data association is conducted to obtain multi-pass Doppler observations. (3) The least squares (LS) is implemented to determine the initial orbit using the associated multi-pass Doppler measurements and the coarse orbit. Additionally, to enhance computational efficiency, two fast orbit calculation algorithms are devised. These algorithms leverage the numerical stability of the Runge–Kutta integrator to reduce computations and exploit the strong correlation among nearby time intervals of orbits with small eccentricities to minimize redundant calculations, thereby achieving orbit calculation efficiently. Finally, through positioning experiments, the determined orbits are demonstrated to have accuracy comparable to that of two-line elements (TLE) updated by the North American Aerospace Defense Command (NORAD). Full article

Difference schemes that approximate dynamic systems are considered discrete models of the same phenomena that are described by continuous dynamic systems. Difference schemes with t-symmetry and midpoint and trapezoid schemes are considered. It is shown that these schemes are dual to each other, and, from this fact, we derive theorems on the inheritance of quadratic integrals by these schemes (Cooper’s theorem and its dual theorem on the trapezoidal scheme). Using examples of nonlinear oscillators, it is shown that these schemes poses challenges for theoretical research and practical application due to the problem of extra roots: these schemes do not allow one to unambiguously determine the final values from the initial values and vice versa. Therefore, we consider difference schemes in which the transitions from layer to layer in time are carried out using birational transformations (Cremona transformations). Such schemes are called reversible. It is shown that reversible schemes with t-symmetry can be easily constructed for any dynamical system with a quadratic right-hand side. As an example of such a dynamic system, a top fixed at its center of gravity is considered in detail. In this case, the discrete theory repeats the continuous theory completely: (1) the points of the approximate solution lie on some elliptic curve, which at $\Delta t\to 0$ turns into an integral curve; (2) the difference scheme can be represented using quadrature; and (3) the approximate solution can be represented using an elliptic function of a discrete argument. The last section considers the general case. The integral curves are replaced with closures of the orbits of the corresponding Cremona transformation as sets in the projective space over $\mathbb{R}$. The problem of the dimension of this set is discussed. Full article

In the realm of non-cooperative space security and on-orbit service, a significant challenge is accurately determining the pose of abandoned satellites using imaging sensors. Traditional methods for estimating the position of the target encounter problems with stray light interference in space, leading to inaccurate results. Conversely, deep learning techniques require a substantial amount of training data, which is especially difficult to obtain for on-orbit satellites. To address these issues, this paper introduces an innovative binocular pose estimation model based on a Self-supervised Transformer Network (STN) to achieve precise pose estimation for targets even under poor imaging conditions. The proposed method generated simulated training samples considering various imaging conditions. Then, by combining the concepts of convolutional neural networks (CNN) and SIFT features for each sample, the proposed method minimized the disruptive effects of stray light. Furthermore, the feedforward network in the Transformer employed in the proposed method was replaced with a global average pooling layer. This integration of CNN’s bias capabilities compensates for the limitations of the Transformer in scenarios with limited data. Comparative analysis against existing pose estimation methods highlights the superior robustness of the proposed method against variations caused by noisy sample sets. The effectiveness of the algorithm is demonstrated through simulated data, enhancing the current landscape of binocular pose estimation technology for non-cooperative targets in space. Full article

Autonomous, anti-jamming, and high-precision satellite navigation are of great importance to current and future space technologies. This paper proposes a cooperative constellation navigation system for low Earth orbit (LEO) satellites that use only the optical measurements of cooperative satellites. Based on photometry, an optical transmission link model of the system is built. With the pixel coordinates of the cooperative satellites on the optical images, the line of sight (LoS) vectors of the cooperative satellites with respect to the LEO spacecraft are first calculated, and a single-point positioning method based on the LoS vectors’ inner products is proposed. The single-point positioning results are then fed into a least square batch filter to estimate a high-precision spacecraft orbit. Simulations are conducted to evaluate the potential navigation accuracy. With a cooperative satellite ephemeris error of 100 m and an optical measurement noise level of 5 arcsecs, position accuracies of single-point positioning and dynamic orbit determination in the order of hundreds of meters and eight meters, respectively, are realized. In addition, the influences of the orbital altitude of the cooperative constellation, the ephemeris error of the cooperative satellite, the noise level of the optical measurements, and the Earth’s gravitational model on navigation accuracy are investigated via comparative simulations. Full article