Minimal Structure and Motion Problems for TOA and TDOA Measurements with Collinearity Constraints

Structure from sound can be phrased as the problem of determining the position of a number of microphones and a number of sound sources given only the recorded sounds. In this paper we study minimal structure from sound problems in both TOA (time of arrival) and TDOA (time difference of arrival) settings with collinear constraints on e.g. the microphone positions. Three such minimal cases are analyzed and solved with efficient and numerically stable techniques. An experimental validation of the solvers are performed on both simulated and real data. In the paper we also show how such solvers can be utilized in a RANSAC framework to perform robust matching of sound features and then used as initial estimates in a robust non-linear leastsquares optimization

Euclidean Distance Matrices: Essential Theory, Algorithms and Applications

Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness. We show how various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. Matlab code for all the described algorithms, and to generate the figures in the paper, is available online. Finally, we suggest directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine - change of title in the last revisio

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

Implementation of an Autonomous Impulse Response Measurement System

Data collection is crucial for researchers, as it can provide important insights for describing phenomena. In acoustics, acoustic phenomena are characterized by Room Impulse Responses (RIRs) occurring when sound propagates in a room. Room impulse responses are needed in vast quantities for various reasons, including the prediction of acoustical parameters and the rendering of virtual acoustical spaces. Recently, mobile robots navigating within indoor spaces have become increasingly used to acquire information about its environment. However, little research has attempted to utilize robots for the collection of room acoustic data. This thesis presents an adaptable automated system to measure room impulse responses in multi-room environments, using mobile and stationary measurement platforms. The system, known as Autonomous Impulse Response Measurement System (AIRMS), is divided into two stages: data collection and post-processing. To automate data collection, a mobile robotic platform was developed to perform acoustic measurements within a room. The robot was equipped with spatial microphones, multiple loudspeakers and an indoor localization system, which reported real time location of the robot. Additionally, stationary platforms were installed in specific locations inside and outside the room. The mobile and stationary platforms wirelessly communicated with one another to perform the acoustical tests systematically. Since a major requirement of the system is adaptability, researchers can define the elements of the system according to their needs, including the mounted equipment and the number of platforms. Post-processing included extraction of sine sweeps and the calculation of impulse responses. Extraction of the sine sweeps refers to the process of framing every acoustical test signal from the raw recordings. These signals are then processed to calculate the room impulse responses. The automatically collected information was complemented with manually produced data, which included rendering of a 3D model of the room, a panoramic picture. The performance of the system was tested under two conditions: a single-room and a multiroom setting. Room impulse responses were calculated for each of the test conditions, representing typical characteristics of the signals and showing the effects of proximity from sources and receivers, as well as the presence of boundaries. This prototype produces RIR measurements in a fast and reliable manner. Although some shortcomings were noted in the compact loudspeakers used to produce the sine sweeps and the accuracy of the indoor localization system, the proposed autonomous measurement system yielded reasonable results. Future work could expand the amount of impulse response measurements in order to further refine the artificial intelligence algorithms

A self-calibrating system for finger tracking using sound waves

In this thesis a system for tracking the fingers of a user using sound waves is developed. The proposed solution is to attach a small speaker to each finger and then have a number of microphones placed ad hoc around a computer monitor listening to the speakers. The system should then be able to track the positions of the fingers so that the coordinates can be mapped to the computer monitor and be used for human-computer interfacing. The thesis focuses on the proof-of-concept of the system. The system pipeline consists of three parts: signal processing, system self-calibration and real-time sound source tracking. In the signal processing step four different signal methods are constructed and evaluated. It is shown that multiple signals can be used in parallel. The signal method with the best performance uses a number of dampened sine waves stacked on top of each other, with each sound wave having a different frequency within a specified frequency band. The goal was to use ultrasound frequency bands for the system but experimenting showed that they gave rise to a lot of aliasing, thus rendering the higher frequency bands unusable. The second step, the system self-calibration, aims to do a scene reconstruction to find the positions of the microphones and the sound source path using only the received signal transmissions. First the time-difference of arrival (TDOA) values are estimated using robust techniques centred around a GCC-PHAT. The time offsets are then estimated in order to convert the TDOA problem into a time-of-arrival (TOA) problem so that the positions of the receivers and sound events can be calculated. Finally a "virtual screen" is fitted to the sound source path to be used for coordinate projection. The scene reconstruction was successful in 80 % of the test cases, in the sense that it managed to estimate the spatial positions at all. The estimates for the microphones had errors of 11.8 +/- 5 centimetres on average for the successful test cases, which is worse than the results presented in previous research. However, the best test case outperformed the results of another paper. The newly developed and implemented technique for finding the virtual screen was far from robust and only found a reasonable virtual screen in 12.5 % of the test cases. In the third step the sound events were estimated, one sound event at a time, using the SRP-PHAT method with the CFRC improvement. Unfortunate choices of the search volumes made the calculations very computationally heavy. The results were comparable to those of the system self-calibration when using the same data and the estimated microphone positions

Computer Vision without Vision : Methods and Applications of Radio and Audio Based SLAM

The central problem of this thesis is estimating receiver-sender node positions from measured receiver-sender distances or equivalent measurements. This problem arises in many applications such as microphone array calibration, radio antenna array calibration, mapping and positioning using ultra-wideband and mapping and positioning using round-trip-time measurements between mobile phones and Wi-Fi-units. Previous research has explored some of these problems, creating minimal solvers for instance, but these solutions lack real world implementation. Due to the nature of using different media, finding reliable receiver-sender distances is tough, with many of the measurements being erroneous or to a worse extent missing. Therefore in this thesis, we explore using minimal solvers to create robust solutions, that encompass small erroneous measurements and work around missing and grossly erroneous measurements.This thesis focuses mainly on Time-of-Arrival measurements using radio technologies such as Two-way-Ranging in Ultra-Wideband and a new IEEE standard 802.11mc found on many WiFi modules. The methods investigated, also related to Computer Vision problems such as Stucture-from-Motion. As part of this thesis, a range of new commercial radio technologies are characterised in terms of ranging in real world enviroments. In doing so, we have shown how these technologies can be used as a more accurate alternative to the Global Positioning System in indoor enviroments. Further to these solutions, more methods are proposed for large scale problems when multiple users will collect the data, commonly known as Big Data. For these cases, more data is not always better, so a method is proposed to try find the relevant data to calibrate large systems

Acoustical Ranging Techniques in Embedded Wireless Sensor Networked Devices

Location sensing provides endless opportunities for a wide range of applications in GPS-obstructed environments; where, typically, there is a need for higher degree of accuracy. In this article, we focus on robust range estimation, an important prerequisite for fine-grained localization. Motivated by the promise of acoustic in delivering high ranging accuracy, we present the design, implementation and evaluation of acoustic (both ultrasound and audible) ranging systems.We distill the limitations of acoustic ranging; and present efficient signal designs and detection algorithms to overcome the challenges of coverage, range, accuracy/resolution, tolerance to Doppler’s effect, and audible intensity. We evaluate our proposed techniques experimentally on TWEET, a low-power platform purpose-built for acoustic ranging applications. Our experiments demonstrate an operational range of 20 m (outdoor) and an average accuracy 2 cm in the ultrasound domain. Finally, we present the design of an audible-range acoustic tracking service that encompasses the benefits of a near-inaudible acoustic broadband chirp and approximately two times increase in Doppler tolerance to achieve better performance

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