结合 Kolmogorov-Arnold 网络的高轨目标初轨确定

Objective Initial orbit determination(IOD)estimates a spacecraft’s orbit by using a limited set of observations, providing rapid trajectory insights and essential initial estimates for subsequent orbit refinement. As a fundamental component of space situational awareness(SSA), an efficient and accurate IOD method is crucial for downstream tasks such as track association, satellite cataloging, and anomaly detection. Optical observations are the primary means of acquiring space object data, but they lack direct range measurements, posing a major challenge for IOD. Traditional IOD methods typically rely on iterative range estimation to improve accuracy, leading to high computational costs and a strong dependence on precise dynamical models and sufficient observations. These challenges are exacerbated in short-arc scenarios, where limited physical constraints often result in trivial solutions or convergence failures. For high-earth-orbit objects, orbital dynamics are influenced by multiple perturbation factors, including the earth’s non-spherical gravitational field, solar radiation pressure, and lunar gravitational effects, making orbit determination significantly more complex than in low-earth orbit. While deep learning has demonstrated strong nonlinear fitting capabilities, conventional neural networks function as black-box models and struggle to incorporate underlying physical laws governing orbital motion. In contrast, the Kolmogorov-Arnold network(KAN), inspired by the Kolmogorov-Arnold representation theorem, offers an interpretable alternative. Unlike traditional multilayer perceptron(MLP), KAN replaces fixed-weight parameters with learnable univariate functions, parameterized as splines, enabling adaptive activation functions and a more flexible topology. This design preserves strong fitting capabilities while improving interpretability. To overcome the limitations of traditional IOD techniques and conventional deep learning models in short-arc IOD tasks, we propose a novel IOD method of high-earth-orbit objects via short-arc observations using KAN. By leveraging short-arc space-based optical observations, our method integrates deep learning with orbital physics, enhancing accuracy and computational efficiency synergistically. Method In this study, we developed a model based on KAN for short-arc IOD tasks of high-earth-orbit objects. The model architecture consists of five interconnected KAN layers, employing a design strategy of dimensionality increase followed by dimensionality reduction. The model processes angular observation data of target objects acquired from space-based observers. Through its hierarchical structure, the network effectively extracts complex nonlinear relationships from the input data while focusing on the most critical features. Ultimately, the model outputs accurate predictions for the position vector and the velocity vector of the target object at the initial moment of the observation arc. Furthermore, we constructed a large-scale dataset of short-arc space-based optical observations for high-earth-orbit objects. This dataset is derived from real on-orbit satellite data provided by CelesTrak, selecting 581 high-orbit active satellites from its database as target objects. We further designed seven satellites to serve as space-based observers. We generated a total of 258 741 observation samples by simulation, which were split into training(70%), validation(15%), and test(15%)sets. Each observation arc spans 300 seconds with a sampling interval of 60 seconds, recording the observation angles and their rates of change of the target satellites relative to the observer. The selected dataset features a diverse range of orbits for the satellites, providing a reliable data foundation for model training and performance evaluation. Using this dataset, we trained our model. To address inconsistencies in parameter units and magnitudes, we first applied data normalization before feeding the data into the model as a preprocessing step. The model employs a composite loss function that incorporates both positional and velocity errors, regulated by a weighting coefficient λ to prevent over-optimization toward either metric. For training, we adopted the Adam optimizer with an initial learning rate of 0. 001, supplemented by a dynamic learning rate scheduler;if the validation loss failed to decrease for 100 consecutive epochs, then the learning rate was halved. This approach ensures rapid and stable convergence while improving training efficiency considerably. With a batch size of 512 and training performed on an NVIDIA GeForce RTX 3090 GPU, the entire training process took approximately five hours to complete 2 000 training epochs. Result We evaluated our approach by comparing our model with four traditional IOD methods:the Laplace method, the Gauss method, the Double-R method, and the circle-orbit tracking method. The experiment was conducted on the dataset that we constructed. Quantitative evaluation metrics included the average position error(E_p), average velocity error(E_v), and speed evaluation metric arcs per second(APS). Experimental results demonstrate that our method outperforms all other methods across multiple performance dimensions. In terms of accuracy, our model’s E_p is 27. 458 km, which is only 0. 24%, 0. 58%, 0. 49%, and 0. 50% of those achieved by the four traditional IOD methods, respectively. Similarly, our model’s E_v is 3. 904 m/s, which is only 0. 46%, 1. 14%, 0. 95%, and 0. 98% of the E_v values of the corresponding methods. Moreover, with regard to processing speed, our method’s APS is 154, 212, 822, and 132 times higher than that of the competing methods, demonstrating crucial advantages in both accuracy and efficiency. In addition, our approach exhibits outstanding stability. It produces no unsolvable cases and generates erroneous solutions at a rate less than 0. 08% of that observed with traditional IOD methods. Furthermore, when compared with the conventional deep learning method MLP, our method achieves E_p and E_v values that are only 25. 01% and 19. 58% of those of the MLP, respectively, highlighting KAN’s superior nonlinear fitting capability over conventional deep learning methods. Conclusion In this study, we proposed a KAN-based model for short-arc IOD tasks of high-earth-orbit objects. Experiment results show that our model demonstrates superior accuracy and efficiency compared with several traditional IOD methods while also outperforming conventional deep learning approaches. It exhibits exceptional stability and effectively solves the problem of short-arc initial orbit determination.