Nonlinear orbital uncertainty propagation with differential algebra and Gaussian mixture model

Nonlinear uncertainty propagation is of critical importance in many application fields of astrodynamics. In this article, a framework combining the differential algebra technique and the Gaussian mixture model method is presented to accurately propagate the state uncertainty of a nonlinear system. A high-order Taylor expansion of the final state with respect to the initial deviations is firstly computed with the differential algebra technique. Then the initial uncertainty is split to a Gaussian mixture model.With the high-order state transition polynomial, each Gaussian mixture element is propagated to the final time, forming the final Gaussian mixture model. Through this framework, the final Gaussian mixture model can include the effects of high-order terms during propagation and capture the non-Gaussianity of the uncertainty, which enables a precise propagation of probability density. Moreover, the manual derivation and integration of the high-order variational equations is avoided, which makes the method versatile. The method can handle both the application of nonlinear analytical maps on any domain of interest and the propagation of initial uncertainties through the numerical integration of ordinary differential equation. The performance of the resulting tool is assessed on some typical orbital dynamic models, including the analytical Keplerian motion, the numerical J_2 perturbed motion,and a nonlinear relative motion.

Message from the Guest Editors of the Special Issue on Astrodynamics for Space Situational Awareness

The term space situational awareness(SSA),in a broad sense,refers to the comprehensive knowledge of the near-Earth space environment.It has gained increasing attention as the number of space objects,including the natural and artificial,continues to grow rapidly in recent years and several collisions between them have occurred.One of the main objectives of SSA is to maintain awareness of potentially adversarial space events,in particular collisions,and avoid them.This typically involves tracking and identification of orbiting space objects,predicting their future locations,assessing the collision risk,and removing harmful objects such as debris to improve safety.

Real-time space object tracklet extraction from telescope survey images with machine learning

In this study,a novel approach based on the U-Net deep neural network for image segmentation is leveraged for real-time extraction of tracklets from optical acquisitions.As in all machine learning(ML)applications,a series of steps is required for a working pipeline:dataset creation,preprocessing,training,testing,and post-processing to refine the trained network output.Online websites usually lack ready-to-use datasets;thus,an in-house application artificially generates 360 labeled images.Particularly,this software tool produces synthetic night-sky shots of transiting objects over a specified location and the corresponding labels:dual-tone pictures with black backgrounds and white tracklets.Second,both images and labels are downscaled in resolution and normalized to accelerate the training phase.To assess the network performance,a set of both synthetic and real images was inputted.After the preprocessing phase,real images were fine-tuned for vignette reduction and background brightness uniformity.Additionally,they are down-converted to eight bits.Once the network outputs labels,post-processing identifies the centroid right ascension and declination of the object.The average processing time per real image is less than 1.2 s;bright tracklets are easily detected with a mean centroid angular error of 0.25 deg in 75%of test cases with a 2 deg field-of-view telescope.These results prove that an ML-based method can be considered a valid choice when dealing with trail reconstruction,leading to acceptable accuracy for a fast image processing pipeline.