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.

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.

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.

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).