Atmospheric Density Uncertainty Research Articles

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 test-bed 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.

Orbital error propagation considering atmospheric density uncertainty

Due to the influence of various errors, the orbital uncertainty propagation of artificial celestial objects while orbit prediction is required, especially in some applications such as conjunction analysis. In the orbital error propagation of artificial celestial objects in low Earth orbits (LEOs), atmospheric density uncertainty is one of the important factors that require special attention. In this paper, on the basis of considering the uncertainties of position and velocity, the atmospheric density uncertainty is also taken into account to further investigate the orbital error propagation of artificial celestial objects in LEOs. Artificial intelligence algorithms are introduced, the MC Dropout neural network and the heteroscedastic loss function are used to realize the correction of the empirical atmospheric density model, as well as to provide the quantification of model uncertainty and input uncertainty for the corrected atmospheric densities. It is shown that the neural network we built achieves good results in atmospheric density correction, and the uncertainty quantization obtained from the neural network is also reasonable. Moreover, using the Gaussian mixture model - unscented transform (GMM-UT) method, the atmospheric density uncertainty is taken into account in the orbital uncertainty propagation, by adding a sampled random term to the corrected atmospheric density when calculating atmospheric density. The feasibility of the GMM-UT method considering atmospheric density uncertainty is proved by the further comparison of abundant sampling points and GMM-UT results (with and without considering atmospheric density uncertainty).

Nonsingular Fixed-Time Tracking Guidance for Mars Aerocapture With Neural Compensation

Mars aerocapture is one of the most concerned technologies for future Mars sample-return and manned exploration missions. This article investigates the challenging problem of the reference trajectory tracking guidance for Mars aerocapture under uncertainties. Based on an integral sliding surface, a fixed-time neural adaptive tracking guidance law is synthesized by incorporating the neural network (NN) approximation into the fixed-time integral sliding mode control approach. Benefiting from the integral sliding surface design, the proposed tracking guidance law has no singularity problem inherently existing in terminal sliding mode control. By adopting the NN approximation to compensate for the lumped uncertain term in the feedforward loop, the proposed tracking guidance law is strongly robust against aerodynamic coefficient uncertainties and atmospheric density uncertainty. Stability analysis shows that the radial distance tracking error and its time derivative can stabilize to the small neighborhoods around the origin in fixed time under the proposed tracking guidance law. Finally, the effectiveness and advantages of the proposed tracking guidance law are illustrated through simulations and comparisons.

창정 5B호 발사체의 재진입 시점 예측 분석

This paper represents a reentry time prediction analysis of CZ-5B rocket-body in China, subject to analysis of the Inter-Agency Space Debris Coordination Committee Reentry (IADC) reentry test campaign conducted in May 2021. Predicting the reentry of space objects is difficult to accurately predict due to the lack of accurate physical information about target, and uncertainty in atmospheric density. Therefore, IADC conducts annual re-entry campaigns to verify analysis techniques by each agency, and the Korea Aerospace Research Institute has also participated in them since 2015. Ballistic coefficient estimation method proposed to predict target reentry time and the result confirmed the difference of 73 seconds, which confirms the accuracy of the proposed method.

Adaptive Gaussian Mixture based orbit determination with combined atmospheric density uncertainty consideration

Large initial uncertainties in the semi-major axis or force-model uncertainties, such as atmospheric density uncertainty are key drivers of the along-track uncertainty growth. Long propagation times may result in the need to use filtering algorithms for orbit determination that do not reside to the assumption of Gaussianity for state errors but estimate the entire probability density function. Adaptive Gaussian mixture based filters have shown promising results in the past. Previous research in the field of orbit determination using Gaussian mixture filters has restricted its attention to initial uncertainties in the semi-major axis direction. The present paper focuses on the consequences of including realistic, physics-based descriptions of atmospheric density uncertainty into the covariance propagation of the mixture kernels.It is shown that the neglect of process noise, as has been customary for many years, can lead to undesired characteristics of the probability density function (pdf) estimates and that the inclusion of atmospheric density uncertainty process noise, even in cases where it is not the dominant driver of along-track uncertainty growth, is able to correct these deficiencies. For low orbiting satellites with increased ballistic coefficients or small initial uncertainties in the semi-major axis direction, density uncertainty is the dominant driver of the along-track uncertainty increase. Due to its growth that evolves at least cubic in time, situations may arise which require the usage of Gaussian mixtures also for the process noise when working in Cartesian coordinates. The theoretical foundation for this case is elaborated and an algorithm capable of dynamically switching between a single Gaussian and a Gaussian mixture for the density uncertainty process noise is presented.

Propagation of grid-scale density model uncertainty to orbital uncertainties

Accurate knowledge of the orbital state-vector uncertainty is required for the computation of reliable collision probabilities, the association of tracks, as well as the optimal planning of sensor resources. In low Earth Orbits (LEO) neutral atmospheric density uncertainty is the main contributor to orbital state vector uncertainty. Grid-scale model uncertainty on the other hand is, in most cases, the dominating component of atmospheric density uncertainty.Prior research in the field of density uncertainty has been broad. Nowadays multiple authors seem to agree that a first-order stochastic Gauss-Markov process, also known as Ornstein-Uhlenbeck process (OUP), is an appropriate stochastic representation for density model uncertainties. While many have studied orbital variations due to stochastic grid-scale density uncertainty, it is believed that the work at hand provides for the first time explicit analytic equations for the estimation of orbital uncertainties due to an underlying Ornstein-Uhlenbeck process that has been optimized for the representation of atmospheric density. It is shown that the long-term in-track position error due to this modified OUP grows with ~t3.The presented derivations and their validation build upon prior work by Emmert et al. and Sagnières and Sharf. Numerical Monte-Carlo simulations are used to validate the findings with two different semi-empirical density models. We also demonstrate that the resulting orbital uncertainty due to the modified OUP in atmospheric density can be estimated using a classical OUP in the relative density error.

Robust adaptive divided difference filter based on forgetting factors and its applications

SummaryThis paper proposes robust and adaptive divided difference filters (RADDFs) based on forgetting factors which are robust to dynamic systems with biases or uncertainties. The RADDFs are founded on the principle of covariance matching. The robustness of RADDFs is reflected in that it amplifies the innovation covariance to compensate the effect of dynamic biases or uncertainties. The forgetting factor is adjusted adaptively. Then, the scalar forgetting factor is further extended to multiple forgetting factors. The proposed RADDFs are illustrated by Mars entry navigation system with atmospheric density uncertainty, lift over drag ratio uncertainty, and ballistic coefficient uncertainty. To validate the filter performance by multiple forgetting factors, a typical tight coupling nonlinear system with abrupt biases is used.

Least squares orbit estimation including atmospheric density uncertainty consideration

Density uncertainty is the major driver of unrealistic covariances for objects in low Earth orbits. The analytic propagation of uncertainties in the neutral atmospheric density to resulting uncertainties in the orbital position and velocity has only received little attention in the literature so far.The main contribution of the paper at hand is the analytic development of an orbital state-vector error variance-covariance matrix that models the propagation of uncertainties in atmospheric density to the orbital state-vector error in the Geocentric Celestial Reference Frame (GCRF). Also extensions of the classical batch weighted least squares (WLS) and the sequential batch weighted least squares algorithms, which allow to incorporate this covariance matrix as process-noise, are presented.Numerical simulations with three different semi-empirical models are provided to validate the derivations. It is shown that the extension of the WLS-algorithm in combination with the density uncertainty GCRF covariance matrix is able to consistently perform orbit and covariance estimation, which is not the case without density uncertainty consideration in a classical WLS algorithm.

Spacecraft relative guidance via spatio-temporal resolution in atmospheric density forecasting

Spacecraft equipped with the capability to vary their ballistic coefficient can use differential drag as the control force to perform propellant-less relative maneuvers. Because atmospheric drag is proportional to atmospheric density, uncertainty in atmospheric density makes the generation and tracking of drag-based guidances difficult. Spatio-temporal resolution, or the mapping of density information to altitude and time, is shown in this work to improve atmospheric density estimation from forecasted density for spacecraft in LEO. This is achieved by propagating simulated orbits for two spacecraft using forecasted density. Additionally, a receding-horizon control algorithm is introduced, with the goal of improving the tracking of guidances. Using a simulated perfect forecast of the atmospheric density for propagation of the orbits, relative guidance trajectories are generated and tracked, establishing the benefit of adding spatio-temporal resolution. Next, imperfect density forecasting is added, indicating that the benefit of spatio-temporal resolution is retained in the presence of imperfect forecasting. Finally, a receding-horizon control algorithm is used with imperfect forecasting, demonstrating that receding-horizon control improves the tracking of guidances compared to single-horizon control.

Mars atmospheric entry guidance for reference trajectory tracking

To improve the accuracy of Mars landing, a new nonlinear entry guidance law for low lift landers has been developed. A novel Terminal Sliding Mode Control (TSMC) for tracking a reference trajectory is proposed. The guidance method is based on TSMC theory adapted to the problem of entry guidance. The TSMC has been adapted to account for the specific sliding mode exhibited by the longitudinal motion of the entry vehicle, with bank angle control following a reference trajectory. The finite-time stability nature of the TSMC law is proven by using a Lyapunov-based approach. Extended state observer (ESO) is applied to estimate Mars atmospheric density uncertainty and lift-to-drag ratio disturbance existing in the spacecraft system, by which terminal sliding mode controllers are designed combining the two approaches respectively to force the state variables of the closed loop system to converge to the reference trajectory. Also, simulation results are presented to illustrate the effectiveness of the control strategy.

Stochastic stability of a satellite influenced by aerodynamic and gravity gradient torques

Quantitative as well as qualitative results dealing with stochastic stability of a satellite influenced by aerodynamic and gravity gradient torques are presented. In particular, parameter regions denoting that the solution process is stable with probability one are found, along with estimates of the probability of convergence to equilibrium positions. The atmospheric density uncertainty introduces the randomness into the system. Stochastic Liapunov functions are used to obtain the stability results, and probability estimates of convergence to equilibrium positions are found by applying supermartingale inequalities. As a prelude of the satellite application, a heuristic explanation of the theory of stochastic Liapunov functions and the techniques of applying this theory to design problems are presented. A complete treatment of the satellite application with its impact on design considerations is provided.

Global properties of diffusion processes on cylindrical type phase space

A diffusion process on a multi-dimensional cylinder is developed that can be used to study stochastic processes defining states in physical systems having angular measurements. Stochastic Liapunov functions and supermartingales are used to investigate asymptotic stability and related properties of the process. A model for a satellite under the influence of aerodynamic and gravitational torques is developed as a canonical diffusion process on a cylinder; the atmospheric density uncertainty introduces the randomness into the system. Stochastic stability of this system, along with general pendulum systems, is investigated.