The localization and tracking of artists on stage enables theatre spotlights to automatically follow the artist’s movements. The company Sendrato utilizes Ultra-Wideband (UWB) systems for this purpose, but the position estimation accuracy decreases when the sensors operate in a Non-Line-of-Sight (NLOS) environment. To prevent the body from blocking the UWB signals, Sendrato places two UWB tags on the hips of the artist and averages the two estimated tag positions. Inertial Measurement Units (IMUs) offer an additional means for location tracking, providing inputs to calculate position, velocity, and orientation estimates independent of the environment, but suffer from accumulative error due to integration drift. This thesis studies how Sendrato can improve position tracking accuracy with UWB data by incorporating IMU sensor data. Additionally, the thesis investigates how the two tags can be coupled to correct for each other’s inaccuracies. Hence the thesis studies how the sensor fusion of two coupled UWB/IMU sensors, attached to a person’s hips, can be used to improve position tracking accuracy compared to using two separate UWB tags. This gives rise to a research approach consisting of two parts. To investigate the potential of UWB/IMU sensor fusion for position tracking accuracy, an Extended Kalman Filter (EKF) fusing IMU and UWB measurements is implemented and compared to UWB-only position tracking algorithms. Additionally, it is investigated whether IMU bias state estimation, Zero Velocity Update (ZUPT) implementation and NLOS detection and mitigation can further improve the UWB/IMU EKF tracking accuracy. The second part researches the potential of coupling two UWB/IMU tags for position tracking accuracy. Previous methods inspired to use knowledge of the fixed relative distance between the tags to correct position estimates from each tag. This research developed this approach by including an equality constraint on the distance between the tags into the EKF. An experiment is conducted where the joint UWB/IMU EKF is tested on a known walked trajectory containing several stationary points. The results show that the tightly coupled UWB/IMU EKF can help smooth faulty UWB measurements, correct stationary points with a ZUPT, and identify IMU bias. Moreover, enforcing a fixed distance between joint tags allows for mutual correction of their trajectories, though the impact on the averaged trajectory may be less significant. All of these techniques show potential for improving position tracking accuracy compared to a loosely coupled UWB-only algorithm. However, the methods all showed limitations, presumably caused by the data quality. An important direction for future work would be to continue this research with better calibrated UWB data.

In this thesis max-plus algebra is introduced and applied to the problem of controlling train delays. Two control strategies for the propagation of delays are discussed. The first is by letting certain trains run faster when a delay is detected, the second is by breaking connections between trains that have to wait for each other in order to enable passengers to changeover from one train to the other. The goal is to understand how to model the propagation of delays when different control strategies are applied, in order to provide train operators tools for making quick decisions on how to intervene when a delay is detected.
The models provided in the report are in the form of max-plus-linear systems and switching max-plus linear systems. These can be programmed in Python to automate the decision making. The report starts with providing a basic understanding of max-plus algebra, where also max-plus linear systems and switching max-plus linear systems are explained. Subsequently, a railway network is designed that serves as an example during this thesis. This railway network is modelled into a max-plus linear system and, additionally, a desirable train timetable for passengers is designed for this network by means of the power algorithm. The main results are two switching max-plus linear systems that model the propagation of delays when the two control strategies are applied. The report ends with a larger railway network at which all acquired knowledge is applied. It can be concluded that the models in this thesis provide methods to calculate exactly how the delay propagates through the network when certain control strategies are applied and, based on that, decisions can be made quicker. Moreover, it is possible to calculate the consecutive departure times. As a result the passengers can be informed quickly about the new departure times as a consequence of the delay and how long it will take for the trains to run according to timetable again. This thesis adds the modelling of faster running trains to existing literature. We have seen that speeding up trains is also a control strategy to solve delays and can be modelled systematically.