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

Source localization and denoising: a perspective from the TDOA space

In this manuscript, we formulate the problem of denoising Time Differences of Arrival (TDOAs) in the TDOA space, i.e. the Euclidean space spanned by TDOA measurements. The method consists of pre-processing the TDOAs with the purpose of reducing the measurement noise. The complete set of TDOAs (i.e., TDOAs computed at all microphone pairs) is known to form a redundant set, which lies on a linear subspace in the TDOA space. Noise, however, prevents TDOAs from lying exactly on this subspace. We therefore show that TDOA denoising can be seen as a projection operation that suppresses the component of the noise that is orthogonal to that linear subspace. We then generalize the projection operator also to the cases where the set of TDOAs is incomplete. We analytically show that this operator improves the localization accuracy, and we further confirm that via simulation.Comment: 25 pages, 9 figure

The algebro-geometric study of range maps

Localizing a radiant source is a widespread problem to many scientific and technological research areas. E.g. localization based on range measurements stays at the core of technologies like radar, sonar and wireless sensors networks. In this manuscript we study in depth the model for source localization based on range measurements obtained from the source signal, from the point of view of algebraic geometry. In the case of three receivers, we find unexpected connections between this problem and the geometry of Kummer's and Cayley's surfaces. Our work gives new insights also on the localization based on range differences.Comment: 38 pages, 18 figure

Who Said That? Towards a Machine-Prediction-Based Approach to Tursiops Truncatus Whistle Localization and Attribution in a Reverberant Dolphinarium

Dolphin communication research is an active period of growth. Many researchers expect to find significant communicative capacity in dolphins given their known sociality and large and complex brains. Moreover, given dolphins’ known acoustic sensitivity, serving their well-studied echolocation ability, some researchers have speculated that dolphin communication is mediated in large part by a sophisticated “vocal” language. However, evidence supporting this belief is scarce. Among most dolphin species, a particular tonal class of call, termed the whistle, has been identified as socially important. In particular, for the common bottlenose dolphin, Tursiops truncatus – arguably the focal species of most dolphin cognitive and communication research – research has fixated on “signature whistles,” individuallydistinctive whistles that seem to convey an individual’s identity to conspecifics, can be mimicked, and can be modulated under certain circumstances in ways that may or may not be communicative. Apart from signature whistles, most studies of dolphin calls concern group-based repertoires of whistles and other, pulse-form call types. However, studies of individual repertoires of non-signature whistles, and the phenomenon of combined signature and non-signature vocal exchanges among dolphins, are conspicuously rare in the literature, tending to be limited by either extreme subject confinement or sparse attributions of vocalizer identity. Nevertheless, such studies constitute a logical prerequisite to an understanding of the communicative potential of whistles. This absence can be explained by a methodological limitation in the way in which dolphin sounds are recorded. In particular, no established method exists for recording the whistles of an entire social group of dolphins so as to reliably attribute them to their vocalizers. This thesis proposes a dolphinarium-based system for achieving audio recording with whistle attribution, as well as visual behavioral tracking. Towards achieving the proposed system, I present foundational work involving the installation of permanent hydrophone arrays and cameras in a dolphinarium that enforces strict animal safety regulations. Attributing tonal sounds via the process of sound localization – estimation of a sound’s point of origin based on the physical properties of its propagation – in a highly reverberant environment is a notoriously difficult problem, resistant to many conventional signal processing techniques. This thesis will provide evidence of this difficulty, and also a demonstration of a highly e↵ective machine-learning-based solution to the problem. This thesis also provides miscellaneous hardware and the pieces of a computational pipeline towards completion of the full proposed, automated system. Once completed, the proposed system will provide an enormous data stream that will lend itself to large-scale studies of individual repertoires of non-signature whistles and combined signature and non-signature vocal exchanges among an invariant group of socializing dolphins, representing a unique and necessary achievement in dolphin communication research

Ambisonics

This open access book provides a concise explanation of the fundamentals and background of the surround sound recording and playback technology Ambisonics. It equips readers with the psychoacoustical, signal processing, acoustical, and mathematical knowledge needed to understand the inner workings of modern processing utilities, special equipment for recording, manipulation, and reproduction in the higher-order Ambisonic format. The book comes with various practical examples based on free software tools and open scientific data for reproducible research. The book’s introductory section offers a perspective on Ambisonics spanning from the origins of coincident recordings in the 1930s to the Ambisonic concepts of the 1970s, as well as classical ways of applying Ambisonics in first-order coincident sound scene recording and reproduction that have been practiced since the 1980s. As, from time to time, the underlying mathematics become quite involved, but should be comprehensive without sacrificing readability, the book includes an extensive mathematical appendix. The book offers readers a deeper understanding of Ambisonic technologies, and will especially benefit scientists, audio-system and audio-recording engineers. In the advanced sections of the book, fundamentals and modern techniques as higher-order Ambisonic decoding, 3D audio effects, and higher-order recording are explained. Those techniques are shown to be suitable to supply audience areas ranging from studio-sized to hundreds of listeners, or headphone-based playback, regardless whether it is live, interactive, or studio-produced 3D audio material