131 research outputs found
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
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
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
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
Frequency-Sliding Generalized Cross-Correlation: A Sub-band Time Delay Estimation Approach
The generalized cross correlation (GCC) is regarded as the most popular
approach for estimating the time difference of arrival (TDOA) between the
signals received at two sensors. Time delay estimates are obtained by
maximizing the GCC output, where the direct-path delay is usually observed as a
prominent peak. Moreover, GCCs play also an important role in steered response
power (SRP) localization algorithms, where the SRP functional can be written as
an accumulation of the GCCs computed from multiple sensor pairs. Unfortunately,
the accuracy of TDOA estimates is affected by multiple factors, including
noise, reverberation and signal bandwidth. In this paper, a sub-band approach
for time delay estimation aimed at improving the performance of the
conventional GCC is presented. The proposed method is based on the extraction
of multiple GCCs corresponding to different frequency bands of the cross-power
spectrum phase in a sliding-window fashion. The major contributions of this
paper include: 1) a sub-band GCC representation of the cross-power spectrum
phase that, despite having a reduced temporal resolution, provides a more
suitable representation for estimating the true TDOA; 2) such matrix
representation is shown to be rank one in the ideal noiseless case, a property
that is exploited in more adverse scenarios to obtain a more robust and
accurate GCC; 3) we propose a set of low-rank approximation alternatives for
processing the sub-band GCC matrix, leading to better TDOA estimates and source
localization performance. An extensive set of experiments is presented to
demonstrate the validity of the proposed approach.Comment: Article accepted in IEEE/ACM Transactions on Audio, Speech, and
Language Processin
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