Nowadays, space-based systems for navigation, communication, Earth observation, meteorology and many other applications are indispensable for services critical for society. In order to preserve these vital applications among the increased risks in space, the Space Surveillance and Tracking segment of the Space Situational Awareness program has been set up in the last decade by the European Space Agency. This segment is occupied with one core activity: maintaining and building up a space object catalog. The object states within it can be used for conjunction assessment, collision avoidance and fragmentation event detection, allowing active satellites to be protected.

For objects in Low Earth Orbit, the Space Surveillance and Tracking segment primarily employs radar, which uses active signals, whose signal strength degrades with the fourth power of the distance. Beyond this orbit regime, passive optical sensors are primarily used, because they do not require an active signal and are therefore able to observe beyond Low Earth Orbit without large power requirements. As a consequence of the sparse optical sensors which have to track the large population of space objects, the optical observing arcs are typically very short: minutes at most. These short optical arcs are called tracklets.

Determining an orbit from a short arc is a challenging problem and is commonly referred to as the too short arc problem. Specifically, this problem entails that a single short arc tracklet is insufficient to construct an orbit with realistic state estimates. In order to obtain accurate state estimates, the object corresponding to the tracklet must be re-observed during a later pass to obtain six independent parameters of high quality. The initial problem to solve, however, is to identify which tracklets are correlated and thus associated with the same object. Thus, tracklet correlation is a critical step in the cataloging of objects. Evaluating and improving the performance of tracklet correlation methods is the key subject of this thesis. The performance is assessed on three key metrics: the association accuracy, the computational efficiency and the robustness.

In the first part of this thesis, tracklet correlation methods are evaluated. The most promising ones have been identified to be the Adapted Gooding method, the BVP optimization and IVP optimization. The performance of these methods is evaluated for different data distribution characteristics and orbit regimes, first without incorporating perturbations in the tracklet correlation methods.

In the second part, the tracklet correlation methods are modified to improve the performance. A major gap in the state of the art has been successfully addressed, namely to incorporate perturbations in the tracklet correlation methods. Results have shown a significant increase in association accuracy. Specifically, tracklet pairs with arbitrary time gap can be associated with the same true positive rate. Moreover, tracklet pairs from different orbit regimes can be associated with a similar true positive rate if the most important perturbations are incorporated.

Finally, the BVP and IVP optimization are found to be robust to noise, while the Adapted Gooding method severely suffers from the perfect measurement assumption. The performance of the latter has been improved by improving the accuracy of the angles through a Least Squares fit. Although the BVP and IVP optimization are robust to noise, the performance is limited by the accuracy of the angle rates, according to the Chi-squared distribution. A novel tracklet correlation method called the BVP-DC2-DC3 is developed to overcome this limitation, achieving an excellent TPR of 100% and a TNR of 99% for the analyzed objects in GEO for tracklets with a measurement noise of one arcsecond. This accuracy is superior to literature. Moreover, the computational efficiency is superior or comparable to literature. Additionally, the BVP-DC2-DC3 has a high robustness, because for the analyzed GEO tracklets with a measurement noise of five arcseconds, a TPR of 100% and a TNR of 95% can still be achieved.

In preparation of a large-scale nulling interferometry mission aiming to detect and characterize Earth-like exoplanets, it is required that key technologies are demonstrated in a space environment. Design trade-offs for a large mission have assumed long, reconfigurable baselines. However, it is uncertain that the same design performs best for a smaller mission with shorter, fixed baselines.
This research aims to compare the performance of three possible nulling configurations, a linear double Bracewell, a rectangular double Bracewell and a off-center kite shaped kernel nuller, on their ability to constrain the temperature, radius, and position of an exoplanet during the mission detection phase.
The configurations are compared by planetary signal simulations performed using the simulation software SCIFYsim. The configurations are compared based on three categories (1) performance for a single planet case, (2) the introduced correlations between planetary parameters, and (3) the performance in a two planet case.
The analysis indicates that the configurations performed similarly when modeling a single planet system, with the linear configuration showing a slight advantage. Regarding the parameter correlations, the kernel configuration exhibits the least correlations between fitted parameters. In the two-planet system, both the rectangular and kernel configurations achieve the highest accuracy in retrieving planetary parameters, though the overall performance remains relatively similar across configurations. Notably, despite the blurry signature of the two planet system in the matched filter map for the linear configuration, the fitting process is able to retrieve the planetary parameters.

For this Thesis a weighted spherical harmonic analysis is performed on the intensity distribution of Io's hotspots to find potential long wavelength patterns. Unfortunately, no definitive conclusion can be drawn as to whether the primary signal (Loki Patera) is caused by a long wavelength signal originating from deep within Io, or whether it is caused by a local phenomenon. This is because the spectral power associated with the analysis does not just have significant power in one or a few degrees. Instead all harmonic degrees return a strong signal. This has been checked up to at least degree 30 which is well into the shorter wavelengths.

Comparing the weighted spherical harmonic analysis of Io’s hotspot intensity distribution to an unweighted spherical harmonic analysis of the hotspot distribution (so without intensities), the location of the primary signal(s) is different between the two analyses, but both still point towards the asthenospheric heating model or magma ocean heating model as the explanation for Io’s heat flow pattern.