A comprehensive analysis of the geometry of TDOA maps in localisation problems

In this manuscript we consider the well-established problem of TDOA-based source localization and propose a comprehensive analysis of its solutions for arbitrary sensor measurements and placements. More specifically, we define the TDOA map from the physical space of source locations to the space of range measurements (TDOAs), in the specific case of three receivers in 2D space. We then study the identifiability of the model, giving a complete analytical characterization of the image of this map and its invertibility. This analysis has been conducted in a completely mathematical fashion, using many different tools which make it valid for every sensor configuration. These results are the first step towards the solution of more general problems involving, for example, a larger number of sensors, uncertainty in their placement, or lack of synchronization.Comment: 51 pages (3 appendices of 12 pages), 12 figure

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

Experimental evaluation of a UWB-based cooperative positioning system for pedestrians in GNSS-denied environment

Cooperative positioning (CP) utilises information sharing among multiple nodes to enable positioning in Global Navigation Satellite System (GNSS)-denied environments. This paper reports the performance of a CP system for pedestrians using Ultra-Wide Band (UWB) technology in GNSS-denied environments. This data set was collected as part of a benchmarking measurement campaign carried out at the Ohio State University in October 2017. Pedestrians were equipped with a variety of sensors, including two different UWB systems, on a specially designed helmet serving as a mobile multi-sensor platform for CP. Different users were walking in stop-and-go mode along trajectories with predefined checkpoints and under various challenging environments. In the developed CP network, both Peer-to-Infrastructure (P2I) and Peer-to-Peer (P2P) measurements are used for positioning of the pedestrians. It is realised that the proposed system can achieve decimetre-level accuracies (on average, around 20 cm) in the complete absence of GNSS signals, provided that the measurements from infrastructure nodes are available and the network geometry is good. In the absence of these good conditions, the results show that the average accuracy degrades to meter level. Further, it is experimentally demonstrated that inclusion of P2P cooperative range observations further enhances the positioning accuracy and, in extreme cases when only one infrastructure measurement is available, P2P CP may reduce positioning errors by up to 95%. The complete test setup, the methodology for development, and data collection are discussed in this paper. In the next version of this system, additional observations such as the Wi-Fi, camera, and other signals of opportunity will be included

Experimental Evaluation of a UWB-Based Cooperative Positioning System for Pedestrians in GNSS-Denied Environment

Cooperative positioning (CP) utilises information sharing among multiple nodes to enable positioning in Global Navigation Satellite System (GNSS)-denied environments. This paper reports the performance of a CP system for pedestrians using Ultra-Wide Band (UWB) technology in GNSS-denied environments. This data set was collected as part of a benchmarking measurement campaign carried out at the Ohio State University in October 2017. Pedestrians were equipped with a variety of sensors, including two different UWB systems, on a specially designed helmet serving as a mobile multi-sensor platform for CP. Different users were walking in stop-and-go mode along trajectories with predefined checkpoints and under various challenging environments. In the developed CP network, both Peer-to-Infrastructure (P2I) and Peer-to-Peer (P2P) measurements are used for positioning of the pedestrians. It is realised that the proposed system can achieve decimetre-level accuracies (on average, around 20 cm) in the complete absence of GNSS signals, provided that the measurements from infrastructure nodes are available and the network geometry is good. In the absence of these good conditions, the results show that the average accuracy degrades to meter level. Further, it is experimentally demonstrated that inclusion of P2P cooperative range observations further enhances the positioning accuracy and, in extreme cases when only one infrastructure measurement is available, P2P CP may reduce positioning errors by up to 95%. The complete test setup, the methodology for development, and data collection are discussed in this paper. In the next version of this system, additional observations such as the Wi-Fi, camera, and other signals of opportunity will be included

Analysis and Accuracy Improvement of UWB-TDoA-Based Indoor Positioning System

Positioning systems are used in a wide range of applications which require determining the position of an object in space, such as locating and tracking assets, people and goods; assisting navigation systems; and mapping. Indoor Positioning Systems (IPSs) are used where satellite and other outdoor positioning technologies lack precision or fail. Ultra-WideBand (UWB) technology is especially suitable for an IPS, as it operates under high data transfer rates over short distances and at low power densities, although signals tend to be disrupted by various objects. This paper presents a comprehensive study of the precision, failure, and accuracy of 2D IPSs based on UWB technology and a pseudo-range multilateration algorithm using Time Difference of Arrival (TDoA) signals. As a case study, the positioning of a 4×4m2 area, four anchors (transceivers), and one tag (receiver) are considered using bitcraze’s Loco Positioning System. A Cramér–Rao Lower Bound analysis identifies the convex hull of the anchors as the region with highest precision, taking into account the anisotropic radiation pattern of the anchors’ antennas as opposed to ideal signal distributions, while bifurcation envelopes containing the anchors are defined to bound the regions in which the IPS is predicted to fail. This allows the formulation of a so-called flyable area, defined as the intersection between the convex hull and the region outside the bifurcation envelopes. Finally, the static bias is measured after applying a built-in Extended Kalman Filter (EKF) and mapped using a Radial Basis Function Network (RBFN). A debiasing filter is then developed to improve the accuracy. Findings and developments are experimentally validated, with the IPS observed to fail near the anchors, precision around ±3cm, and accuracy improved by about 15cm for static and 5cm for dynamic measurements, on average

RF signal sensing and source localisation systems using Software Defined Radios

Radio frequency (RF) source localisation is a critical technology in numerous location-based military and civilian applications. In this thesis, the problem of RF source localisation has been studied from the perspective of the system implementation for real-world applications. Commercial off-the-shelf Software Defined Radio (SDR) devices are used to demonstrate the practical RF source localisation systems. Compared to the conventional localisation systems, which rely on dedicated hardware, the SDR-based system is developed using general-purpose hardware and software-defined components, offering great flexibility and cost efficiency in system design and implementation. In this thesis, the theoretical results of source localisation are evaluated and put into practice. To be specific, the practical localisation systems using different measurement techniques, including received-signal-strength-indication (RSSI) measurements, time-difference-of-arrival (TDOA) measurements and joint TDOA and frequency-difference-of-arrival (FDOA) measurements, are demonstrated to localise the stationary RF signal sources using the SDRs. The RSSI-based localisation system is demonstrated in small indoor and outdoor areas with a range of several metres using the SDR-based transceivers. Furthermore, interests from the defence area motivated us to implement the time-based localisation systems. The TDOA-based source localisation system is implemented using multiple spatially distributed SDRs in a large outdoor area with the sensor-target range of several kilometres. Moreover, they are implemented in a fully passive way without prior knowledge of the signal emitter, so the solutions can be applied in the localisation of non-cooperative signal sources provided that emitters are distant. To further reduce the system cost, and more importantly, to deal with the situation when the deployment of multiple SDRs, due to geographical restrictions, is not feasible, a joint TDOA and FDOA-based localisation system is also demonstrated using only one stationary SDR and one mobile SDR. To improve the localisation accuracy, the methods that can reduce measurement error and obtain accurate location estimates are studied. Firstly, to obtain a better understanding of the measurement error, the error sources that affect the measurement accuracy are systematically analysed from three aspects: the hardware precision, the accuracy of signal processing methods, and the environmental impact. Furthermore, the approaches to reduce the measurement error are proposed and verified in the experiments. Secondly, during the process of the location estimation, the theoretical results on the pre-existing localisation algorithms which can achieve a good trade-off between the accuracy of location estimation and the computational cost are evaluated, including the weight least-squares (WLS)-based solution and the Extended Kalman Filter (EKF)-based solution. In order to use the pre-existing algorithms in the practical source localisation, the proper adjustments are implemented. Overall, the SDR-based platforms are able to achieve low-cost and universal localisation solutions in the real-world environment. The RSSI-based localisation system shows tens of centimetres of accuracy in a range of several metres, which provides a useful tool for the verification of the range-based localisation algorithms. The localisation accuracy of the TDOA-based localisation system and the joint TDOA and FDOA-based localisation system is several tens of metres in a range of several kilometres, which offers potential in the low-cost localisation solutions in the defence area

Localisation and tracking of people using distributed UWB sensors

In vielen Überwachungs- und Rettungsszenarien ist die Lokalisierung und Verfolgung von Personen in Innenräumen auf nichtkooperative Weise erforderlich. Für die Erkennung von Objekten durch Wände in kurzer bis mittlerer Entfernung, ist die Ultrabreitband (UWB) Radartechnologie aufgrund ihrer hohen zeitlichen Auflösung und Durchdringungsfähigkeit Erfolg versprechend. In dieser Arbeit wird ein Prozess vorgestellt, mit dem Personen in Innenräumen mittels UWB-Sensoren lokalisiert werden können. Er umfasst neben der Erfassung von Messdaten, Abstandschätzungen und dem Erkennen von Mehrfachzielen auch deren Ortung und Verfolgung. Aufgrund der schwachen Reflektion von Personen im Vergleich zum Rest der Umgebung, wird zur Personenerkennung zuerst eine Hintergrundsubtraktionsmethode verwendet. Danach wird eine konstante Falschalarmrate Methode zur Detektion und Abstandschätzung von Personen angewendet. Für Mehrfachziellokalisierung mit einem UWB-Sensor wird eine Assoziationsmethode entwickelt, um die Schätzungen des Zielabstandes den richtigen Zielen zuzuordnen. In Szenarien mit mehreren Zielen kann es vorkommen, dass ein näher zum Sensor positioniertes Ziel ein anderes abschattet. Ein Konzept für ein verteiltes UWB-Sensornetzwerk wird vorgestellt, in dem sich das Sichtfeld des Systems durch die Verwendung mehrerer Sensoren mit unterschiedlichen Blickfeldern erweitert lässt. Hierbei wurde ein Prototyp entwickelt, der durch Fusion von Sensordaten die Verfolgung von Mehrfachzielen in Echtzeit ermöglicht. Dabei spielen insbesondere auch Synchronisierungs- und Kooperationsaspekte eine entscheidende Rolle. Sensordaten können durch Zeitversatz und systematische Fehler gestört sein. Falschmessungen und Rauschen in den Messungen beeinflussen die Genauigkeit der Schätzergebnisse. Weitere Erkenntnisse über die Zielzustände können durch die Nutzung zeitlicher Informationen gewonnen werden. Ein Mehrfachzielverfolgungssystem wird auf der Grundlage des Wahrscheinlichkeitshypothesenfilters (Probability Hypothesis Density Filter) entwickelt, und die Unterschiede in der Systemleistung werden bezüglich der von den Sensoren ausgegebene Informationen, d.h. die Fusion von Ortungsinformationen und die Fusion von Abstandsinformationen, untersucht. Die Information, dass ein Ziel detektiert werden sollte, wenn es aufgrund von Abschattungen durch andere Ziele im Szenario nicht erkannt wurde, wird als dynamische Überdeckungswahrscheinlichkeit beschrieben. Die dynamische Überdeckungswahrscheinlichkeit wird in das Verfolgungssystem integriert, wodurch weniger Sensoren verwendet werden können, während gleichzeitig die Performanz des Schätzers in diesem Szenario verbessert wird. Bei der Methodenauswahl und -entwicklung wurde die Anforderung einer Echtzeitanwendung bei unbekannten Szenarien berücksichtigt. Jeder untersuchte Aspekt der Mehrpersonenlokalisierung wurde im Rahmen dieser Arbeit mit Hilfe von Simulationen und Messungen in einer realistischen Umgebung mit UWB Sensoren verifiziert.Indoor localisation and tracking of people in non-cooperative manner is important in many surveillance and rescue applications. Ultra wideband (UWB) radar technology is promising for through-wall detection of objects in short to medium distances due to its high temporal resolution and penetration capability. This thesis tackles the problem of localisation of people in indoor scenarios using UWB sensors. It follows the process from measurement acquisition, multiple target detection and range estimation to multiple target localisation and tracking. Due to the weak reflection of people compared to the rest of the environment, a background subtraction method is initially used for the detection of people. Subsequently, a constant false alarm rate method is applied for detection and range estimation of multiple persons. For multiple target localisation using a single UWB sensor, an association method is developed to assign target range estimates to the correct targets. In the presence of multiple targets it can happen that targets closer to the sensor induce shadowing over the environment hindering the detection of other targets. A concept for a distributed UWB sensor network is presented aiming at extending the field of view of the system by using several sensors with different fields of view. A real-time operational prototype has been developed taking into consideration sensor cooperation and synchronisation aspects, as well as fusion of the information provided by all sensors. Sensor data may be erroneous due to sensor bias and time offset. Incorrect measurements and measurement noise influence the accuracy of the estimation results. Additional insight of the targets states can be gained by exploiting temporal information. A multiple person tracking framework is developed based on the probability hypothesis density filter, and the differences in system performance are highlighted with respect to the information provided by the sensors i.e. location information fusion vs range information fusion. The information that a target should have been detected when it is not due to shadowing induced by other targets is described as dynamic occlusion probability. The dynamic occlusion probability is incorporated into the tracking framework, allowing fewer sensors to be used while improving the tracker performance in the scenario. The method selection and development has taken into consideration real-time application requirements for unknown scenarios at every step. Each investigated aspect of multiple person localization within the scope of this thesis has been verified using simulations and measurements in a realistic environment using M-sequence UWB sensors