Modeling of Magnetic Fields and Extended Objects for Localization Applications

Abstract: The level of automation in our society is ever increasing. Technologies like self-driving cars, virtual reality, and fully autonomous robots, which all were unimaginable a few decades ago, are realizable today, and will become standard consumer products in the future. These technologies depend upon autonomous localization and situation awareness where careful processing of sensory data is required. To increase efficiency, robustness and reliability, appropriate models for these data are needed.In this thesis, such models are analyzed within three different application areas, namely (1) magnetic localization, (2) extended target tracking, and (3) autonomous learning from raw pixel information.Magnetic localization is based on one or more magnetometers measuring the induced magnetic field from magnetic objects. In this thesis we present a model for determining the position and the orientation of small magnets with an accuracy of a few millimeters. This enables three-dimensional interaction with computer programs that cannot be handled with other localization techniques. Further, an additional model is proposed for detecting wrong-way drivers on highways based on sensor data from magnetometers deployed in the vicinity of traffic lanes. Models for mapping complex magnetic environments are also analyzed. Such magnetic maps can be used for indoor localization where other systems, such as GPS, do not work.In the second application area, models for tracking objects from laser range sensor data are analyzed. The target shape is modeled with a Gaussian process and is estimated jointly with target position and orientation. The resulting algorithm is capable of tracking various objects with different shapes within the same surveillance region.In the third application area, autonomous learning based on high-dimensional sensor data is considered. In this thesis, we consider one instance of this challenge, the so-called pixels to torques problem, where an agent must learn a closed-loop control policy from pixel information only. To solve this problem, high-dimensional time series are described using a low-dimensional dynamical model. Techniques from machine learning together with standard tools from control theory are used to autonomously design a controller for the system without any prior knowledge.System models used in the applications above are often provided in continuous time. However, a major part of the applied theory is developed for discrete-time systems. Discretization of continuous-time models is hence fundamental. Therefore, this thesis ends with a method for performing such discretization using Lyapunov equations together with analytical solutions, enabling efficient implementation in software.