Localization using Distance Geometry : Minimal Solvers and Robust Methods for Sensor Network Self-Calibration

In this thesis, we focus on the problem of estimating receiver and sender node positions given some form of distance measurements between them. This kind of localization problem has several applications, e.g., global and indoor positioning, sensor network calibration, molecular conformations, data visualization, graph embedding, and robot kinematics. More concretely, this thesis makes contributions in three different areas.First, we present a method for simultaneously registering and merging maps. The merging problem occurs when multiple maps of an area have been constructed and need to be combined into a single representation. If there are no absolute references and the maps are in different coordinate systems, they also need to be registered. In the second part, we construct robust methods for sensor network self-calibration using both Time of Arrival (TOA) and Time Difference of Arrival (TDOA) measurements. One of the difficulties is that corrupt measurements, so-called outliers, are present and should be excluded from the model fitting. To achieve this, we use hypothesis-and-test frameworks together with minimal solvers, resulting in methods that are robust to noise, outliers, and missing data. Several new minimal solvers are introduced to accommodate a range of receiver and sender configurations in 2D and 3D space. These solvers are formulated as polynomial equation systems which are solvedusing methods from algebraic geometry.In the third part, we focus specifically on the problems of trilateration and multilateration, and we present a method that approximates the Maximum Likelihood (ML) estimator for different noise distributions. The proposed approach reduces to an eigendecomposition problem for which there are good solvers. This results in a method that is faster and more numerically stable than the state-of-the-art, while still being easy to implement. Furthermore, we present a robust trilateration method that incorporates a motion model. This enables the removal of outliers in the distance measurements at the same time as drift in the motion model is canceled

Scalable positioning of commodity mobile devices using audio signals

This thesis explores the problem of computing a position map for co-located mobile devices. The positioning should happen in a scalable manner without requiring specialized hardware and without requiring specialized infrastructure (except basic Wi-Fi or cellular access). At events like meetings, talks, or conferences, a position map can aid spontaneous communication among users based on their relative position in two ways. First, it enables users to choose message recipients based on their relative position, which also enables the position-based distribution of documents. Second, it enables senders to attach their position to messages, which can facilitate interaction between speaker and audience in a lecture hall and enables the collection of feedback based on users’ location. In this thesis, we present Sonoloc, a mobile app and system that, by relying on acoustic signals, allows a set of commodity smart devices to determine their relative positions. Sonoloc can position any number of devices within acoustic range with a constant number of acoustic signals emitted by a subset of devices. Our experimental evaluation with up to 115 devices in real rooms shows that – despite substantial background noise – the system can locate devices with an accuracy of tens of centimeters using no more than 15 acoustic signals.Diese Dissertation befasst sich mit dem Problem, eine Positionskarte von sich am gleichen Ort befindenden mobilen Geräten zu berechnen. Dies soll skalierbar, ohne Verwendung von spezialisierter Hardware oder Infrastruktur (ausgenommen einfache WLAN- oder Mobilfunkzugang) erfolgen. Bei Veranstaltungen wie Meetings, Diskussionen oder Konferenzen kann eine Positionskarte die Benutzer bei spontaner Kommunikation mithilfe der relativen Positionen in zweierlei Hinsicht unterstützen. Erstens ermöglicht sie den Benutzern, die Empfänger von Nachrichten aufgrund deren Position zu wählen, was auch eine positionsabhängige Verteilung von Unterlagen erlaubt. Zweitens ermöglicht sie den Sendern, ihre Position in die Nachrichten zu integrieren, was eine Interaktion zwischen Referent und Zuhörer in einem Hörsaal und die Sammlung von positionsabhängigen Rückmeldungen erlaubt. In dieser Dissertation stellen wir die Mobile-App und das System Sonoloc vor, das mithilfe von Tonsignalen erlaubt, die relative Position handelsüblicher, intelligenter Geräte zu bestimmen. Sonoloc kann eine beliebige Zahl von Geräten innerhalb des Hörbereichs durch eine gleichbleibende Zahl von Tonsignalen, die von einer Teilmenge der Geräte gesendet werden, lokalisieren. Unsere experimentelle Analyse mit bis zu 115 Geräten in echten Räumen zeigt, dass das System trotz signifikanter Hintergrundgeräusche unter Verwendung von bis zu 15 Tonsignalen mit einer Genauigkeit von wenigen Dezimetern Geräte lokalisieren kann.This work was supported in part by the European Research Council (ERC Synergy imPACT 610150), the German Science Foundation (DFG CRC 1223), the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (A), KAKENHI Grant Number 16H01735), and the National Science Foundation (NSF Awards CNS 1526635 and CNS 1314857)

Mapping and Merging Using Sound and Vision : Automatic Calibration and Map Fusion with Statistical Deformations

Over the last couple of years both cameras, audio and radio sensors have become cheaper and more common in our everyday lives. Such sensors can be used to create maps of where the sensors are positioned and the appearance of the surroundings. For sound and radio, the process of estimating the sender and receiver positions from time of arrival (TOA) or time-difference of arrival (TDOA) measurements is referred to as automatic calibration. The corresponding process for images is to estimate the camera positions as well as the positions of the objects captured in the images. This is called structure from motion (SfM) or visual simultaneous localisation and mapping (SLAM). In this thesis we present studies on how to create such maps, divided into three parts: to find accurate measurements; robust mapping; and merging of maps.The first part is treated in Paper I and involves finding precise – on a subsample level – TDOA measurements. These types of subsample refinements give a high precision, but are sensitive to noise. We present an explicit expression for the variance of the TDOA estimate and study the impact that noise in the signals has. Exact measurements is an important foundation for creating accurate maps. The second part of this thesis includes Papers II–V and covers the topic of robust self-calibration using one-dimensional signals, such as sound or radio. We estimate both sender and receiver positions using TOA and TDOA measurements. The estimation process is divided in two parts, where the first is specific for TOA or TDOA and involves solving a relaxed version of the problem. The second step is common for different types of problems and involves an upgrade from the relaxed solution to the sought parameters. In this thesis we present numerically stable minimal solvers for both these steps for some different setups with senders and receivers. We also suggest frameworks for how to use these solvers together with RANSAC to achieve systems that are robust to outliers, noise and missing data. Additionally, in the last paper we focus on extending self-calibration results, especially for the sound source path, which often cannot be fully reconstructed immediately. The third part of the thesis, Papers VI–VIII, is concerned with the merging of already estimated maps. We mainly focus on maps created from image data, but the methods are applicable to sparse 3D maps coming from different sensor modalities. Merging of maps can be advantageous if there are several map representations of the same environment, or if there is a need for adding new information to an already existing map. We suggest a compact map representation with a small memory footprint, which we then use to fuse maps efficiently. We suggest one method for fusion of maps that are pre-aligned, and one where we additionally estimate the coordinate system. The merging utilises a compact approximation of the residuals and allows for deformations in the original maps. Furthermore, we present minimal solvers for 3D point matching with statistical deformations – which increases the number of inliers when the original maps contain errors