Measuring Adjoint-invariance of Neighborhoods in Solvable Lie Groups

In this thesis, we derive a lower bound on a quantity appearing in a Fourier multiplier inequality on solvable Lie groups.<br/>In Caspers, Janssens, Krishnaswamy-Usha and Miaskiwskyi (2022), a classical result by de Leeuw about the restriction of Fourier multipliers on $\mathbb{R}^n$ to a discrete subgroup is extended to a noncommutative setting...

Comparative Evaluation of Invariant and Multiplicative EKF for 3D Pose Estimation with IMU Sensors and GPS or Landmark Measurements

This thesis investigates the performance of the invariant extended Kalman filter (IEKF) compared to the multiplicative extended Kalman filter (MEKF) in the context of nonlinear state estimation on matrix Lie groups. The IEKF, a relatively recent variant of the EKF, is particularly suitable for systems with group-affine process models and...

Multivariate generalisations of classical hypergeometric polynomials from Lie theory

In this thesis, we will be studying Lie groups and their connection to certain orthogonal polynomials. We will look into the classical Krawtchouk, Meixner and Laguerre polynomials, and the multivariate Krawtchouk and Meixner polynomials as defined by Iliev. Using representations of the Lie groups SU(2) and SU(1,1), it will be shown that the...

Representation theory of SU(2) and SU(3) with applications to spin and quark models

In this thesis we provide an elementary introduction in finite dimensional representation theory of the Lie groups SU(2) and SU(3) for undergraduate students in physics and mathematics. We will also give two application of representation theory of these two groups in physics: the spin and quark models. We begin with first discussing...

Attitude and rate estimation without rate sensors: A Lie group approach

Attitude estimation is one of the basic processes of the attitude and orbit control system hosted by every satellite. The spacecraft should be orientated properly during the orbit, according to the mission objectives. The estimation is based on a plethora of sensors, like rate gyroscopes, star trackers, sun and earth sensors, magnetometers (for...

De wortelsystemen in E8

In dit verslag wordt besproken hoe je deelwortelsystemen in het wortelsysteem E8 kan vinden. In het begin wordt er algemene theorie over wortelsystemen gegeven. Vervolgens worden er twee manieren besproken hoe je deelwortelsystemen in wortelsystemen kan vinden. Uiteindelijk worden de twee manieren toegepast op E8 om deelwortelsystemen in E8 te...

Fixed-Wing UAV Integrated Navigation with Low-Cost IMU/GPS

Today, there is an increase in the use of Unmanned Aerial Vehicles (UAV's), for applications that can be considered dull, dirty or dangerous when compared to those applications of conventional aircraft or helicopters. To further increase the use of UAV's, their navigation filters must be robust and reliable. The trend in current autopilot...