The growing space debris environment poses a significant threat to operational satellites and the future of spaceflight. To assess the collision risk between space objects, often probabilistic methods are used, which suffer from the fact that very uncertain states will lead to a low probability of collision, described as the dilution effect. Apart from this drawback, satellite operators are required to decide whether to mitigate a risk well before the time of closest approach. However, the time horizon available for this is often too short. This research aimed at studying whether novel risk assessment metrics could increase the reliability of risk quantification and extend the time horizon available for decision making. Outer probability measures have proven to be a reliable method for mitigating the dilution effect, whereas a geometry-based metric has proven more challenging to use. Together with the theoretical analysis of the metrics, their operational application has been studied.

The modern day growth in satellites and debris in orbit around Earth is resulting in ever increasing requirements for state estimation systems used to avoid collisions and ensure safe operations as part of space situational awareness initiatives. While there are many methods to perform state estimation, the optimal control based estimator (OCBE) provides unique benefits, such as the ability to perform in the presence of mis-modelled accelerations while allowing for reconstruction of unknown maneuvers from the target spacecraft.
However, the method suffers from high computational costs. This thesis covers the implementation of a new variant of the OCBE, focused on propagation and estimation of state in terms of regularized "EDromo" elements.
The method showcases benefits in terms of estimated state error, and reduced sensitivity to the time gaps between measurements, at the cost of further computational complexity. For future work, suggestions to improve efficiency of the method are also presented.

This thesis investigates methods to enhance the robustness of space object cataloguing pipelines, focusing on tracklet correlation and orbit estimation using angular measurements from short observation arcs. The cataloguing robustness is defined as achieving high true positive and negative rates for tracklet correlation to allow for the build-up of an accurate object catalogue. The study addresses the main research question: How can the robustness of the cataloguing pipeline be improved when applying orbit estimation methods to the full angle set of short observation arcs?

A baseline tracklet correlation approach, based on the Boundary Value Problem (BVP) within the Admissible Region framework, is implemented. This method uses angular observations and hypothesized ranges to estimate an object's state, with correlations evaluated via a cost function based on the Mahalanobis distance. Classical IOD methods are employed to investigate their application toward validation of tracklet correlation when reconsidering the full angle set. The considered methods include the angles-only Gauss method, a multiple angles least-squares Gauss approach, Gooding’s method, as well as a Batch Least Squares (BLS) orbit determination (OD) method. The BVP and IOD methods consider two-body dynamics, and the BLS Earth's zonal harmonics and third body effects from the Sun and Moon. Simulated measurements are derived from Two Line Element sets (TLE) for initial reference states for LEO, MEO, and GEO objects, propagated with the SGP4 model accounting for Earth's atmospheric drag, zonal harmonics and third body Sun and Moon effects, providing the test data.

Results show that the BVP method performs best for GEO, achieving ~90% true positive rates with reasonable uncertainty gating. For LEO and MEO, higher thresholds and cost-function minima are required due to greater observation complexity and force-model discrepancy. Gooding’s method, making use of a Lambert solver, demonstrated robust performance across multiple orbital revolutions, while Gauss’ methods were less effective for large time gaps. Additionally, BLS struggled with sparse data and large time steps, offering limited state refinement despite higher computational expense.

The findings suggest gating based on chi-squared distribution thresholds for GEO and higher magnitudes for LEO and MEO to optimize true negative rates. While the BVP method provides sufficient accuracy for re-observation scenarios, classical IOD methods and BLS exhibit limitations under sparse tracklet conditions. This work highlights challenges in cataloguing lower-altitude objects, for ground-based optical observations, and suggests the application of the BVP method on lower altitudes requires inclusion of force models for the primary perturbations.

This thesis addresses the issue of space debris tracking through the development and evaluation of advanced radar-based Initial Orbit Determination (IOD) algorithms and optimised measurement strategies. Space debris presents a challenge to space missions, necessitating tracking methods that do not require cooperation from the objects being tracked. The batch least squares estimator (BLSE), extended Kalman filter (EKF), unscented Kalman filter (UKF), and unscented batch estimator (UBE) were evaluated using both simulated and real radar data from the Sentinel-1A satellite. The UBE algorithm showed the lowest root-mean-square error (RMSE) and fastest convergence, effectively managing the non-linear complexities of orbit determination.
Four radar measurement strategies were examined to determine the minimum number of observations required for accurate orbit prediction and reacquisition. Strategies that provided full coverage and focused on the closest point of approach (CPA) demonstrated the most reliable results such as the inbound-CPA-outbound method and the changing radar update time. The study also investigated the impact of excluding specific radar measurements, such as range, radial velocity, azimuth, or elevation, on the accuracy of orbit estimation. It was found that a combination of range and angle measurements provided the most accurate results.

The congestion of orbits around the Earth, particularly in Low Earth Orbit (LEO), necessitates the implementation of space-based Space Situational Awareness (SSA) missions. This increasing orbital congestion, driven by the proliferation of mega constellations, poses significant challenges to satellite operations and collision avoidance. In response, commercial entities are beginning to plan and launch space-based SSA missions. Despite this emerging interest, there is a notable gap in the literature regarding the scheduling of operations for these missions, which are characterised by the inclusion of multiple operational modes.

Additionally, existing literature on operational scheduling often lacks high-fidelity modelling of onboard resource dynamics. This research addresses this gap by focusing on energy-constrained scenarios, developing novel operational scheduling frameworks suitable for assigning data collection and data downlink tasks for optical space-based SSA missions under such constraints.

To enhance the fidelity of the scheduling process, this research employs both low-fidelity and high-fidelity simulators to model the dynamic behaviour of onboard resources. The developed frameworks are tested in various scenarios to validate their practicality and effectiveness. A significant contribution of this research is the open-source availability of part of the developed scheduling frameworks, utilising software accessible under the TU Delft license. This open-source approach ensures that the research can be extended and built upon by future researchers, fostering ongoing advancements in the field of space-based SSA operations.