The goal of the research is to improve space situational awareness (SSA) for space debris objects, and to make space operations more sustainable and remain possible in the future. Vital to this awareness is understanding which objects are present, through space surveillance and tracking (SST), and where these objects will be in the future, through orbit prediction and analysis. Therefore, the research specifically focusses on supporting conjunction analysis, which aims to predict which satellites have a high risk of collisions, and improving re-entry predictions, which indicate possible ranges of impact locations and epochs for satellites returning back to Earth.@en

Verified interval orbit propagation provides mathematically guaranteed solutions of satellite position and velocity over time. These verified solutions are useful for conjunction analysis and other space-situational-awareness activities. Unfortunately, verified methods suffer from overestimation and explosive interval growth, limiting the possible propagation time and thus their applicability. Different orbital-element state models have been shown to increase the maximum propagation time to a degree, but at the expense of significant overestimation introduced by the state transformations. This paper proposes the Dromo state model for verified integration. Dromo is a regularized variation-of-parameter formulation of the perturbed two-body equations of motion. Taylor models are implemented for both integration and transformation. Moreover, a technique is developed for dealing with time uncertainty resulting from verified regularized propagation. Dromo significantly prolongs the maximum forecasting window, producing verified trajectories of days up to weeks in duration for the low Earth orbit regime. A sensitivity analysis of the integrator settings identifies combinations that produce stable and computationally efficient solutions. A sensitivity study of the orbital parameters shows that the method is applicable to a large orbital regime, especially for low Earth orbit regions that contain high densities of space debris.

@en

Satellite reentry predictions are used to determine the time and location of impacts of decaying objects. These predictions are complicatedby uncertainties in the initial state and environment models, and the complex evolution of the attitude. Typically, the aerodynamic and error propagation are done in a simplistic fashion. Full six-degrees-of-freedom modeling and attitude control is proposed for studying the historic reentry case of the Gravity Field and Steady-State Ocean Circulation Explorer satellite. Improved error modeling and estimation of the initial state and atmospheric density are introduced for both Global Positioning System and two-line elements states. A sensitivity analysis is performed to identify the driving parameters for several models and epochs. The predictions are compared against Tracking And Impact Predictions, and predictions by the European Space Agency Space Debris Office. The performed predictions are consistently closer to the true decay epoch for several starting epochs, while providing narrower windows than other predictions with higher confidence.

@en

Predictions of the impact time and location of space debris in a decaying trajectory are highly influenced by uncertainties. The traditional Monte Carlo (MC) method can be used to perform accurate statistical impact predictions, but requires a large computational effort. A method is investigated that directly propagates a Probability Density Function (PDF) in time, which has the potential to obtain more accurate results with less computational effort. The decaying trajectory of Delta-K rocket stages was used to test the methods using a six degrees-of-freedom state model. The PDF of the state of the body was propagated in time to obtain impact-time distributions. This Direct PDF Propagation (DPP) method results in a multi-dimensional scattered dataset of the PDF of the state, which is highly challenging to process. No accurate results could be obtained, because of the structure of the DPP data and the high dimensionality. Therefore, the DPP method is less suitable for practical uncontrolled entry problems and the traditional MC method remains superior. Additionally, the MC method was used with two improved uncertainty models to obtain impact-time distributions, which were validated using observations of true impacts. For one of the two uncertainty models, statistically more valid impact-time distributions were obtained than in previous research.

@en

Two-Line Elements (TLEs) resulting from the Space Surveillance Network (SSN) are often the only available source for many Space Situational Awareness (SSA) activities such as conjunction analyses and re-entry predictions. The network consists of many different radar and optical stations, contributing in either a dedicated, collateral and contributing fashion. For low-Earth orbit radar stations are primarily employed. Radar station can be further distinct into phased-array and mechanically steered radars. Uncertainties in TLEs are primarily a product of sensor capabilities, model deficiencies, network geometry and configuration, and orbit determination setup. The aim of the paper is to separate and analyse the individual contributions and identify potential areas of improvement. Specifically, the configuration and geometry of the network is investigated. Only the LEO satellites are considered. Further, although mechanically steered radars are generally much more accurate, only phased-array radar stations, capable of tracking many object, are considered. The SSN is simulated as a collection of present and hypothetical dedicated and collateral radar stations. An investigation into the current state of the SSN is performed. The location and coverage of each station is accurately estimated and modelled. Range and range-rate measurements are generated for several setups over a number of revolutions. Noise is introduced to individual observations to account for sensor capabilities (e.g. power and resolution) and secondary disturbances. Lastly, observations are edited out to account for sensor availability, viewing conditions, and other limitations. TLEs are estimated from the simulated measurements using Simplified General Perturbations (SGP4) model. GOCE during its re-entry phase is used as the reference satellite. During this final phase the thruster was switched off. GPS derived orbits are considered as truth for assessing TLE accuracy. The optimal number of measurement and passes are investigated to achieve the best state estimates. The resulting simulated TLEs are compared against actual historical TLE estimates. Several network configuration consisting of different combinations of stations are investigated, including historical, present, proposed and hypothetical scenarios. Individual sensors are shown to be the primary factor in the overall accuracy of the initial state. Sensor accuracy, however, is difficult to improve, due to the associated cost and trade-off between accuracy and capacity. The network itself is found to be underrepresented in large regions of the world. The new proposed space fence, with sites in the Marshall Islands and Western Australia, improves the geometry and overall accuracy significantly. @en

TLEs are important for many Space Situational Awareness (SSA) studies, because of their widespread availability. For many objects such as rocket bodies, stages, and defunct satellites TLEs present the only source of orbital states. Despite their importance, TLEs suffer from some major drawbacks: they are of limited accuracy (especially compared to GPS/TIRA), are often mistagged, miss manoeuvres, and lack covariance information. Although the TLEs are openly available, their observations and corresponding covariance are not. The proper understanding and subsequent modeling and estimation of these uncertainties is paramount for previously mentioned SSA activities. The aim of the paper is to present uncertainty models and estimation techniques, focusing on improving re-entry predictions using TLEs of low-earth orbit (LEO) satellites. Only the uncertainties in the initial translational state and deficiencies in atmospheric density and spacecraft aerodynamic modeling are considered. GOCE, during its re-entry phase, is used as the reference object for this study. Probability distributions are presented for modeling uncertainties in the translational and rotational state, and atmospheric density. A new robust weighted differencing method for estimating the uncertainty of TLEs is introduced. For GOCE during the period of investigation, two types of TLEs are present, namely of the classic and enhanced type. The latter TLEs are obtained from pseudo observations derived from a numerical higher-order fit and propagation. The proposed method is validated using GPS orbit solutions. Moreover, the estimation of the ballistic coefficient through retrofitting is discussed and executed for both TLE types. The obtained estimates of the uncertainty in the initial translational state and atmospheric density are applied to re-entry time predictions of GOCE. Specifically, decay time distributions are obtained using six degree-of-freedom statistical re-entry simulations. The effects of the different environment and spacecraft models is investigated, especially the proper modeling of the attitude control that was present almost entirely throughout re-entry. Moreover, GPS and TLE-derived translational-state inputs are compared. The developed methods and findings are then applied to re-entry predictions of several Delta-K rocket bodies. Enhanced TLEs are shown to have a reduced uncertainty and improved forward propagation stability compared to the older classic type. In fact, enhanced TLEs states are found to be most accurate after their associated epoch, due to the inclusion of propagated pseudo measurements. The ballistic coefficient of enhanced TLEs is found to differ from classic TLEs and is shown to be consistent with retrofit estimates of the ballistic coefficient. This suggests that the coefficient is obtained directly from the numerical fitting process, rather than co-estimated with the mean elements of the TLE themselves, as is the case for classic TLEs. This finding positively affects re-entry predictions. The attitude control and atmospheric density bias are the two major factors on the mean decay epoch. While the atmospheric density uncertainty is by far the most important factor in the decay-time uncertainty. The uncertainty in initial state is shown to have only minor influence on the final decay-time distributions, despite GPS being up to four orders of magnitude more accurate than TLEs. This illustrates the importance of improving atmospheric density modeling for re-entry predictions. @en

Accurate knowledge of satellite orbit errors is essential for many types of analyses. Unfortunately, for two-line elements (TLEs) this is not available. This paper presents a weighted differencing method using robust least-squares regression for estimating many important error characteristics. The method is applied to both classic and enhanced TLEs, compared to previous implementations, and validated using Global Positioning System (GPS) solutions for the GOCE satellite in Low-Earth Orbit (LEO), prior to its re-entry. The method is found to be more accurate than previous TLE differencing efforts in estimating initial uncertainty, as well as error growth. The method also proves more reliable and requires no data filtering (such as outlier removal). Sensitivity analysis shows a strong relationship between argument of latitude and covariance (standard deviations and correlations), which the method is able to approximate. Overall, the method proves accurate, computationally fast, and robust, and is applicable to any object in the satellite catalogue (SATCAT).

@en