Probabilistic Solar Proxy Forecasting with Neural Network Ensembles

Space weather indices are used commonly to drive forecasts of thermosphere density, which directly affects objects in low-Earth orbit (LEO) through atmospheric drag. One of the most commonly used space weather proxies, $F_{10.7 cm}$, correlates well with solar extreme ultra-violet (EUV) energy deposition into the thermosphere. Currently, the USAF contracts Space Environment Technologies (SET), which uses a linear algorithm to forecast $F_{10.7 cm}$. In this work, we introduce methods using neural network ensembles with multi-layer perceptrons (MLPs) and long-short term memory (LSTMs) to improve on the SET predictions. We make predictions only from historical $F_{10.7 cm}$ values, but also investigate data manipulation to improve forecasting. We investigate data manipulation methods (backwards averaging and lookback) as well as multi step and dynamic forecasting. This work shows an improvement over the baseline when using ensemble methods. The best models found in this work are ensemble approaches using multi step or a combination of multi step and dynamic predictions. Nearly all approaches offer an improvement, with the best models improving between 45 and 55\% on relative MSE. Other relative error metrics were shown to improve greatly when ensembles methods were used. We were also able to leverage the ensemble approach to provide a distribution of predicted values; allowing an investigation into forecast uncertainty. Our work found models that produced less biased predictions at elevated and high solar activity levels. Uncertainty was also investigated through the use of a calibration error score metric (CES), our best ensemble reached similar CES as other work.Comment: 23 pages, 12 figures, 5 Table

Advanced Ensemble Modeling Method For Space Object State Prediction Accounting For Uncertainty In Atmospheric Density

For objects in the low Earth orbit region, uncertainty in atmospheric density estimation is an important source of orbit prediction error, which is critical for space traffic management activities such as the satellite conjunction analysis. This paper investigates the evolution of orbit error distribution in the presence of atmospheric density uncertainties, which are modeled using probabilistic machine learning techniques. The recently proposed HASDM-ML, CHAMP-ML, and MSIS-UQ machine learning models for density estimation (Licata and Mehta, 2022b; Licata et al., 2022b) are used in this work. The investigation is convoluted because of the spatial and temporal correlation of the atmospheric density values. We develop several Monte Carlo methods, each capturing a different spatiotemporal density correlation, to study the effects of density uncertainty on orbit uncertainty propagation. However, Monte Carlo analysis is computationally expensive, so a faster method based on the Kalman filtering technique for orbit uncertainty propagation is also explored. It is difficult to translate the uncertainty in atmospheric density to the uncertainty in orbital states under a standard extended Kalman filter or unscented Kalman filter framework. This work uses the so-called consider covariance sigma point (CCSP) filter that can account for the density uncertainties during orbit propagation. As a testbed for validation purposes, a comparison between CCSP and Monte Carlo methods of orbit uncertainty propagation is carried out. Finally, using the HASDM-ML, CHAMP-ML, and MSIS-UQ density models, we propose an ensemble approach for orbit uncertainty quantification for four different space weather conditions

Debris re-entry modeling using high dimensional derivative based uncertainty quantification

Well-known tools developed for satellite and debris re-entry perform break-up and trajectory simulations in a deterministic sense and do not perform any uncertainty treatment. In this paper, we present work towards implementing uncertainty treatment into a Free Open Source Tool for Re-entry of Asteroids and Space Debris (FOSTRAD). The uncertainty treatment in this work is limited to aerodynamic trajectory simulation. Results for the effect of uncertain parameters on trajectory simulation of a simple spherical object is presented. The work uses a novel uncertainty quantification approach based on a new derivation of the high dimensional model representation method. Both aleatoric and epistemic uncertainties are considered in this work. Uncertain atmospheric parameters considered include density, temperature, composition, and free-stream air heat capacity. Uncertain model parameters considered include object flight path angle, object speed, object mass, and direction angle. Drag is the only aerodynamic force considered in the planar re-entry problem. Results indicate that for initial conditions corresponding to re-entry from a circular orbit, the probabilistic distributions for the impact location are far from the typically used Gaussian or ellipsoids and the high probability impact location along the longitudinal direction can be spread over ∼2000 km, while the overall distribution can be spread over ∼4000 km. High probability impact location along the lateral direction can be spread over ∼400 km

Surrogate model for probabilistic modeling of atmospheric entry for small NEO's

Near Earth Objects (NEOs) enter the Earths atmosphere on a regular basis. Depending on the size, object and entry parameters; these objects can burn-up through ablation (complete evaporation), undergo fragmentation of varying nature, or impact the ground unperturbed. Parameters that influence the physics during entry are either unknown or highly uncertain. In this work, we propose a probabilistic approach for simulating entry. Probabilistic modeling typically requires an expensive Monte Carlo approach. In this work, we develop and present a novel engineering approach of developing surrogate models for simulation of the atmospheric entry accounting for drag, ablation, evaporation, fragmentation, and ground impact

Sensitivity analysis and probabilistic re-entry modeling for debris using high dimensional model representation based uncertainty treatment

Well-known tools developed for satellite and debris re-entry perform break- up and trajectory simulations in a deterministic sense and do not perform any uncertainty treatment. The treatment of uncertainties associated with the re-entry of a space object requires a probabilistic approach. A Monte Carlo campaign is the intuitive approach to performing a probabilistic analysis, however, it is computationally very expensive. In this work, we use a recently developed approach based on a new derivation of the high dimensional model representation method for implementing a computationally efficient probabilistic analysis approach for re-entry. Both aleatoric and epistemic uncertainties that affect aerodynamic trajectory and ground impact location are considered. The method is applicable to both controlled and uncontrolled re-entry scenarios. The resulting ground impact distributions are far from the typically used Gaussian or ellipsoid distributions

Updates And Improvements To The Satellite Drag Coefficient Response Surface Modeling Toolkit

For satellites in the Low Earth Orbit (LEO) region, the drag coefficient is a primary source of uncertainty for orbit determination and prediction. Researchers at the Los Alamos National Laboratory (LANL) have created the so-called Response Surface Modeling (RSM) toolkit to provide the community with a resource for simulating and modeling satellite drag coefficients for satellites with complex geometries (modeled using triangulated facets) in the free molecular flow (FMF) regime. The toolkit fits an interpolation surface using non-parametric Gaussian Process Regression (GPR) over drag coefficient data computed using the numerical Test Particle Monte Carlo (TPMC) method. The fitted response surface provides a substantial computational benefit over numerical approaches for calculating drag coefficients. In this work, the RSM toolkit is further developed into a versatile software with extended capabilities. The capabilities are specifically expanded to include uncertainty quantification and adaptation for automatic development of regression models for satellites with non-stationary components (e.g., rotating solar panels). Furthermore, the toolkit uses Python 3.x and C programming languages to provide an open-source software package with a OSI approved GPL license. To assist the end user, the new RSM toolkit has been developed to have a user-friendly installation process and is provided with extensive documentation. The analysis of two different conceptual satellites is performed during this work: a simple cube and a CubeSat consisting of a simple cube body with 2 rotating solar panels. During the creation of the regression model for each satellite for different atmospheric species, it is found that the cube\u27s minimum Root Mean Squared Error (RMSE) is 0.00211 and the maximum RMSE is 0.00350. The CubeSat has a minimum RMSE of 0.00304 and the maximum is 0.00498. These results are overall conducive of a well performing regression model

Stochastic Modeling Of Physical Drag Coefficient – Its Impact On Orbit Prediction And Space Traffic Management

Ambitious satellite constellation projects by commercial entities and the ease of access to space in recent times have led to a dramatic proliferation of low-Earth space traffic. It jeopardizes space safety and long-term sustainability, necessitating better space domain awareness (SDA). Correct modeling of uncertainties in force models and orbital states, among other things, is an essential part of SDA. For objects in the low-Earth orbit (LEO) region, the uncertainty in the orbital dynamics mainly emanate from limited knowledge of the atmospheric drag-related parameters and variables. In this paper, which extends the work by Paul et al. (2021), we develop a feed-forward deep neural network model for the prediction of the satellite drag coefficient for the full range of satellite attitude (i.e., satellite pitch ∈ (-90°, +90°) and satellite yaw ∈ (0°, +360°)). The model simultaneously predicts the mean and the standard deviation and is well-calibrated. We use numerically simulated physical drag coefficient data for training our neural network. The numerical simulations are carried out using the test particle Monte Carlo method using the diffuse reflection with incomplete accommodation gas-surface interaction model. Modeling is carried out for the well-known Challenging Minisatellite Payload (CHAMP) satellite. Finally, we use the Monte Carlo approach to propagate CHAMP over a three-day period under various modeling scenarios to investigate the distribution of radial, along-track, and cross-track orbital errors caused by drag coefficient uncertainty. The key takeaways of this paper are - (a) a constant drag coefficient cannot be used for reliable SDA purposes, and (b) stochastic machine learning models allow for the computation of drag coefficients in a timely manner while providing reliable uncertainty estimates