On November 22, 2019, Rico Mendrzik successfully defended his Ph.D. thesis Position Estimation in Networks with Sparse Infrastructure. The Ph.D. examination committee was formed by Prof. Volker Turau (Institute of Telematics) and the two reviewers Prof. Gerhard Bauch and Prof. Henk Wymeersch (Chalmers University, Göteborg).
In my thesis I study the problem of self-position estimation in wireless networks with sparse infrastructure from a stochastic perspective. Self-position estimation refers to the ability to conclude the own geometric location from a number of noisy measurements. In wireless networks, these measurements are derived from the radio signals that are received from one or more transmitting nodes. Measurements such as the distances or angles to the transmitting nodes enable the receiver to infer its position. Some nodes, so-called anchors, have global knowledge of their positions. Anchors are usually considered as part of the infrastructure of a wireless network. Measurements with respect to anchors translate the relative position information into global position information. If receiving nodes with unknown positions, so-called agents, attempt to estimate their own positions unambiguously, they generally require measurements to multiple anchors. Networks that employ only a small number of anchors per unit area are classified as networks with sparse infrastructure. Simple positioning methods such as trilateration or triangulation fail in these networks and more sophisticated positioning strategies are required. Most of these strategies require tools from the domain of statistical signal processing. In that domain, the statistical models of the measurement errors are used to determine position information that inherently contains the uncertainties of the positions of agents.
Two approaches have been considered in my thesis. Both enable unambiguous positioning in wireless networks with sparse infrastructure, and they rely heavily on statistical signal processing. Particularly, the framework of belief propagation was considered in both approaches. The first approach that was studied compensates the lack of anchors by cooperation among agents. In particular, agents derive cooperative distance measurements from the signals received from other agents in addition to those from anchors. These measurements must be considered carefully, though, since other agents – in contrast to anchors – have imperfect position information. In the second approach that was studied, large antenna arrays are used to overcome the lack of infrastructure by deriving more measurements from the received signal of a single anchor. These measurements include angular measurements such as the angle-of-arrival and angle-of-departure. Moreover, every multipath component of the received signal can be harnessed in these approaches, providing even more measurements. With such a large number of measurements per anchor, agents can position themselves using only a single anchor.
Advances in the field of cooperative positioning were made on the algorithmic frontier. A method has been developed which allows agents to confine their locations to small areas. Embedding the constraints into the position estimation problems assists the actual estimator by steering its focus to the relevant regions. The usage of constraints is shown to improve the performance of cooperative position estimators in terms of accuracy, computational complexity, and speed of convergence. In contrast to the advances in the domain of cooperative positioning, theoretical and algorithmic advances have been made in the field of single anchor positioning. Analytical studies of the estimation problems in that field have revealed that many other parameters can be estimated on top of the positions of agents. Those parameters include agent states (orientation and clock offset to the anchor) as well as the positions of reflecting or scattering objects in the agent’s radio environment. Driven by the theoretical insights, a belief propagation-based estimator was developed that enables an agent to jointly estimate its position, orientation, and clock offset with respect to an anchor along with the positions of reflecting or scattering objects in its radio environment in a static scenario.