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The number of resident space objects (RSOs) has been steadily increasing over time, posing significant risks to the safe operation of on-orbit assets. The accurate prediction of potential collision events and implementation of effective and nonredundant avoidance maneuvers require the precise estimation of the orbit positions of objects of interest and propagation of their associated uncertainties. Previous research mainly focuses on striking a balance between accurate propagation and efficient computation. A recently proposed approach that integrates uncertainty propagation with different coordinate representations has the potential to achieve such a balance. This paper proposes combining the generalized equinoctial orbital elements (GEqOE) representation with an adaptive Gaussian mixture model (GMM) for uncertainty propagation. Specifically, we implement a reformulation for the orbital dynamics so that the underlying state and the moment feature of the GMM are propagated under the GEqOE coordinates. Starting from an initial Gaussian probability distribution function (PDF), the algorithm iteratively propagates the uncertainty distribution using a detection-splitting module. A differential entropy-based nonlinear detector and a splitting library are utilized to adjust the number of GMM components dynamically. Component splitting is triggered when a predefined threshold of differential entropy is violated, generating several GMM components. The final probability density function (PDF) is obtained by a weighted summation of the component distributions at the target time. Benefiting from the nonlinearity reduction caused by the GEqOE representation, the number of triggered events largely decreases, causing the necessary number of components to maintain uncertainty realism also to decrease, which enables the proposed approach to achieve good performance with much more efficiency. As demonstrated by the results of propagation in three scenarios with different degrees of complexity, compared with the Cartesian-based approach, the proposed approach achieves comparable accuracy to the Monte Carlo method while largely reducing the number of components generated during propagation. Our results confirm that a judicious choice of coordinate representation can significantly improve the performance of uncertainty propagation methods in terms of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

The airborne hyperspectral remote sensing systems (AHRSSs) acquire images with high spectral resolution, high spatial resolution, and high temporal dimension. While the AHRSS captures more detailed information from the terrain objects, the computational complexity of data processing is greatly increased. As an important application technology in the hyperspectral domain, anomaly detection (AD) processing must be real-time and high-precision in many cases, such as post-disaster rescue, military battlefield search, and natural disaster detection. In this paper, the real-time AD technology for the push-broom AHRSS is studied, the mathematical model is established, and a novel implementation framework is proposed. Firstly, the optimized kernel minimum noise fraction (OP-KMNF) transformation is employed to extract informative and discriminative features between the background and anomalies. Secondly, the Nyström method is introduced to reduce the computational complexity of OP-KMNF transformation by decomposing and extrapolating the sub-kernel matrix to estimate the eigenvector of the entire kernel matrix. Thirdly, the extracted features are transferred to hard disks for data storage. Then, taking the extracted features as input data, the background separation model-based CEM anomaly detector (BSM-CEMAD) is imported to detect anomalies. Finally, graphics processing unit (GPU) parallel computing is utilized in the Nyström-based OP-KMNF (NOP-KMNF) transformation and the BSM-CEMAD to improve the execution efficiency, and the real-time AD for the push-broom AHRSS could be realized. To test the feasibility of the implementation framework proposed in this paper, the experiment is carried out with the Airborne Multi-Modular Imaging Spectrometer (AMMIS) developed by the Shanghai Institute of Technical Physics as the data acquisition platform. The experimental results show that the proposed method outperforms many other state-of-the-art AD methods in anomalies detection and background suppression. Moreover, under the condition that the downlink data could retain most of the hyperspectral data information, the proposed method achieves real-time detection of pixel-level anomalies, with the initial delay not exceeding 1 s, the false alarm rate (FAR) less than 5%, and the true positive rate (TPR) close to 98%. [ABSTRACT FROM AUTHOR]