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

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

Timbre transfer using image-to-image denoising diffusion implicit models

Timbre transfer techniques aim at converting the sound of a musical piece generated by one instrument into the same one as if it was played by another instrument, while maintaining as much as possible the content in terms of musical characteristics such as melody and dynamics. Following their recent breakthroughs in deep learning-based generation, we apply Denoising Diffusion Models (DDMs) to perform timbre transfer. Specifically, we apply the recently proposed Denoising Diffusion Implicit Models (DDIMs) that enable to accelerate the sampling procedure. Inspired by the recent application of DDMs to image translation problems we formulate the timbre transfer task similarly, by first converting the audio tracks into log mel spectrograms and by conditioning the generation of the desired timbre spectrogram through the input timbre spectrogram. We perform both one-to-one and many-to-many timbre transfer, by converting audio waveforms containing only single instruments and multiple instruments, respectively. We compare the proposed technique with existing state-of-the-art methods both through listening tests and objective measures in order to demonstrate the effectiveness of the proposed model

Synthesis of Soundfields through Irregular Loudspeaker Arrays Based on Convolutional Neural Networks

Most soundfield synthesis approaches deal with extensive and regular loudspeaker arrays, which are often not suitable for home audio systems, due to physical space constraints. In this article we propose a technique for soundfield synthesis through more easily deployable irregular loudspeaker arrays, i.e. where the spacing between loudspeakers is not constant, based on deep learning. The input are the driving signals obtained through a plane wave decomposition-based technique. While the considered driving signals are able to correctly reproduce the soundfield with a regular array, they show degraded performances when using irregular setups. Through a Convolutional Neural Network (CNN) we modify the driving signals in order to compensate the errors in the reproduction of the desired soundfield. Since no ground-truth driving signals are available for the compensated ones, we train the model by calculating the loss between the desired soundfield at a number of control points and the one obtained through the driving signals estimated by the network. Numerical results show better reproduction accuracy both with respect to the plane wave decomposition-based technique and the pressure-matching approach

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

On the problem of the existence for connecting trajectories under the action of gravitational and electromagnetic fields

AbstractWe give sufficient conditions assuring the existence of timelike trajectories connecting two prescribed events in a Lorentzian manifold. They represent the trajectories of a free falling massive particle under the action of a gravitational and electromagnetic fiel

Dictionary-based Equivalent Source Method for Near-Field Acoustic Holography

In this paper, we propose a modification of the standard Equivalent Source Method (ESM) for Near-Field Acoustic Holography (NAH). As in EMS, we aim at modeling the acoustic pressure radiated from a vibrating object, and its surface velocity, as the joint effect of a set of equivalent sources located within or close to the object itself. The estimation of the equivalent source strengths (weigths) comes from the solution of a highly ill-conditioned problem. Rather than solving this problem in the least-squares sense, we exploit the 3D model of the vibrating object, along with a rough estimate of its physical parameters, to restrict the space of the solutions. More specifically, we make use of Finite Element Analysis for populating a compressed dictionary of possible equivalent source weights. NAH is then approached by seeking a sparse linear combination of the entries of the dictionary. Experiments carried on a public database prove the effectiveness of the proposed technique, especially when the number of available microphones is limited, and in the presence of a significant level of measurement noise