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.

Asteroid missions stand at the forefront of space exploration endeavours. These face a number of challenges, with safe navigation being one of the main issues. The irregular nature of these bodies creates highly perturbed gravity fields that, if modelled incorrectly, can be a danger to the safe navigation of the spacecraft. Therefore, improving the gravity field modelling of asteroids is of key importance.

This research aims to improve the gravity field estimation of asteroids through the use of a satellite constellation consisting of a mothership and a set of CubeSats. In particular, it focuses on the modelling and estimation of the gravity field with spherical harmonics (SH), which makes the research only applicable to the navigation of the spacecraft outside of the Brillouin sphere.

The system design is based on a CubeSat constellation orbiting the asteroid that relays measurements back to a mothership that estimates its state and gravity field through an Unscented Kalman Filter (UKF). The research is centered around 433 Eros asteroid for the model implementation, being an irregular body with known characteristics from the Near-Shoemaker mission.

An end-to-end simulation environment is implemented for the system research. This allows for simulating the orbits of the satellites in a real-world environment considering SH gravity field up to degree and order 15, the perturbation effect of the Sun point mass, and the solar radiation pressure. Additionally, it includes a realistic polyhedral shape of the asteroid including its landmarks. The asteroid model is used together with the modelling of the satellite sensors to estimate the measurements that can be obtained in a realistic scenario including sensor errors, visibility, and communications constraints. Furthermore, the simulation environment contains a UKF filter capable of conducting the gravity-field estimates from the measured states of the constellation satellites.

The research conducts a thorough sensitivity analysis of the scenario evaluating how the constellation design impacts the estimates obtained. This analysis evaluates a number of filter designs, and determines that better performance is achieved when the design models the dynamics of several satellites at the same time. This is followed by an analysis of variance, conducted to obtain a better understanding of the constellation characteristics' effects on the filter estimates.


From the results obtained, a design synthesis is conducted to test the system implemented with an optimised constellation design. Furthermore, the filter design is re-evaluated and improved through the addition of better covariance matrix tuning and the addition of a degree-by-degree estimation procedure that allows to reduce computational load, a main constraint of the system. The results obtained show that the model is capable of accurately estimating the gravity field spherical harmonic coefficients with an error lower than 15% when the filter is tuned properly for SH up to degree and order nine. Additional verification of its applicability has been conducted by testing the system with extreme case asteroids, which show that the system requires a thruster and control system for the satellites to be capable of maintaining stable orbits around the asteroids when these have extremely irregular gravity fields.

The origin of the Martian dichotomy is subject to question and no substantial evidence exists. Some surface and interior features that are not visible in, e.g., topography data, can show up in gravity data. Therefore, this research inverts gravity data to find a crustal and mantle global density model. Previous research performed a one-layer inversion, assuming equal mass in all columns. Also, missions like InSight do not provide global interior information, but only at the landing site. The aim of this research is to provide a global density model of both the Martian crust and upper mantle. The inversion is performed using a weighted, regularized least-squares algorithm. The gravity input consists of the residual between the MRO120F data set and the state-of-the-art gravity field model of the TU Delft. The design matrix is built using Green’s functions, which define the influence of a mass element in all different directions on a measurement point. Using this least-squares algorithm, three different methods for inversion are used. The separate two-layer inversion, the combined independent two-layer inversion and the combined dependent two-layer inversion. All three inversion methods are performed on synthetic planets as well, for verification purposes. By performing all inversions on the synthetic planets, it was found that the combined independent two-layer inversion results in a strong decoupling of short and long wavelength signals, but is not able to attribute gravity signals to different features in the crust and mantle. The combined dependent two-layer inversion does lead to a result that shows decoupling of crust and mantle features. The hypothesis is that adding different gravity components to the combined dependent two-layer inversion will further increase its accuracy. The results of the inversion methods applied to Mars are in agreement with existing research in terms of standard deviations of the crust and mantle density anomalies. The maps were also analysed geologically, where the most important conclusion is the evidence of potential impact basins in the north polar region. These can be evidence to accept the several impact theory for the origination of the Martian dichotomy. Increasing the resolution and refining the third inversion method with multiple gravity components will increase the potential of gravity inversion to define geological features of Mars.

Recent years have seen the exponential growth of the number of artificial objects orbiting the Earth. Since space debris can cause substantial damage, measures are investigated to make space operations more sustainable. Amongst these, there is an interest in the development of methods to detect possible collisions between objects in space. Traditional methods require highly accurate propagations with large computational times, so the focus of this thesis is the modelling of faster and more accurate algorithms to enhance collision risk assessment. To avoid long propagations, neural networks have been trained for orbit prediction and uncertainty estimation, with the main goal of calculating the collision probability between two objects. Different analyses have been made to assess the accuracy, stability, applicability and generalisation of the methods developed. The results show much faster collision risk calculations than traditional methods with a similar level of accuracy. It is also demonstrated how a tool which can generalise to satellites with different geometries can be built.

The Jovian system is one of the most attractive destinations for scientific space exploration, with many missions having flown to Jupiter and its moons. Among the latter, Io stands out due to its intense volcanic activity, with plumes extending up to hundreds of kilometers above its surface. Scientists believe that sampling, returning, and analyzing the particles ejected from Io’s volcanoes has the potential to unlock valuable information about Earth’s formation, and the history of the Solar System. For this reason, the concept of an Io Sample Return mission was born at the Jet Propulsion Laboratory, California Institute of Technology, where this thesis was carried out.
The project focuses on the mission design and trajectory optimization of a Discovery-class Io Sample Return concept. It investigates which geometry, maneuvers sequence, and flyby trajectories, can enable the sampling of Io’s Prometheus plume through a single flyby, before returning the material back to Earth.
Firstly, a broad-search of feasible patched-conics round-trip trajectories to Jupiter is conducted, using a simplified two-bodies model. The search incorporates launch, entry, time of flight, mission delta-V, and Io encounter constraints. Two algorithms for the reconstruction of ballistic and targeted flybys are developed and integrated within the trajectories-search workflow. This phase highlights the infeasibility of the 14 years flight time constraint and the 8 km/s maximum Io-relative speed during sampling. The two thresholds are increased to 18 years and 10 km/s, respectively. The solutions-space is progressively filtered with the aid of a primer-vector optimizer, and a single candidate trajectory is chosen for further studies. The solutions from the broad-search are also used to conduct a sensitivity study on alternative plume targets, which highlights Prometheus’ ideal position for sampling missions that avoid Jupiter orbit insertion.
The selected patched-conics candidate is used as initial guess for the numerical propagation and optimization of the end-to-end mission. A high-level trade-off is conducted to select the most suitable approach to propagate the trajectory. Two optimization approaches are then compared. An arc-wise scheme, in which each interplanetary transfer is optimized individually, and an all-arcs method, where the Earth-Jupiter and Jupiter-Earth journeys are each optimized in their entirety. Self-Adaptive Differential Evolution (SADE) and Generational Multi-Objective Evolutionary Algorithm by Decomposition (GMOEA/D) are the two optimizers of choice.
Optimization runs conducted using the patched-conics initial guess prove unable to converge to acceptable solutions. Moreover, single-objective optimization struggles to satisfy position discontinuities requirements, when adopting the all-arcs approach. The patched-conics solution is therefore extended to multi-conic, leading to significant performance improvements. Final results show that GMOEA/D outperforms SADE using the all-arcs approach, and finds a solution that satisfies delta-V, launch C3, entry speed, and position discontinuities constraints. It also improves the total delta-V of the baseline multi-conic solution by about 70 m/s, leaving over 700 m/s of margin on the mission delta-V budget.

The GRACE mission has provided unprecedented insights into mass redistribution processes in the Earth system. Following a strong call for continuation of the mass observations, the GRACE-Follow On (GRACE-FO) mission was launched in May 2018, leaving a coverage gap of ca. 1 year between GRACE and GRACE-FO. Geopotential solutions derived from data of the Swarm mission (2013-present) are candidate data to potentially bridge this gap, as well as bridge the minor discontinuities in the current GRACE time series. This study aims to validate the sensitivity of the Swarm measurement system to mass rates, by comparing GRACE and Swarm observations of the gravity trend induced by glacial isostatic adjustment (GIA). Studies inverting GIA observations (e.g., relative sea level change, surface deformation, [time variable] gravity) into mantle viscosity estimates suggest relatively high viscosity in the Hudson Bay area. This suggests that the North American GIA-induced gravity trend is linear on a multi-decadal time scale, which means we can extrapolate the GRACE-derived GIA observations into the Swarm time period for this area. We find that the Swarm-derived GIA observations correspond well in amplitude and spatial distribution to GRACE observations and conclude that both systems have a similar sensitivity to gravity trends at spatial scales to which Swarm is sensitive to (ca. 1500 km). We validate our findings via geopotential solutions of GRACE-FO and provide a brief analysis of the benefits of adding Swarm-derived information to the combined GRACE / GRACE-FO time series.