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Identification of Room Boundaries for Sound Field Estimation
Abstract and Figures
Echoes generated by the sound reflected off the walls of a room carry information about the geometry of the enclosure. Capitalization of this acoustic property could lead to improvements in current state-of-the-art methods for sound field estimation, where prior information can be used to improve the conditioning of the problem. In this thesis, robust and computational efficient methods are developed for identifying first order reflections to estimate the room geometry using small microphone arrays. Furthermore, as the estimation of such reflections becomes even more challenging in actual audio reproduction systems, this work aims to develop methods capable to deal with complications that might arise due to the employed drivers. This is done by considering the estimation problem in two different scenarios. Firstly, the first order reflections estimation problem is posed as a sorting problem. For this case, a set of echoes, received at different microphones, must be grouped accordingly to the wall which originated them. This problem is solved by using a greedy subspace-based algorithm. The proposed approach provides similar performance compared with the state-of-the-art method at a reduced computational cost. For the second scenario, instead of echoes, only raw microphones measurements are available. This instance of the problem is posed under an estimation theory framework, and solved by sequential minimization of a non-linear cost function based on the propagation of waves. Experimental results, evaluated in simulated shoe-box shaped rooms, demonstrate the performance and applicability of the proposed methods for room geometry estimation.
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Radio astronomy is known for its very large telescope dishes, but is currently making a transition towards the use of large numbers of small elements. For example, the Low Frequency Array, commissioned in 2010, uses about 50 stations, each consisting of at least 96 low band antennas and 768 high band antennas. For the Square Kilometre Array, planned for 2024, the numbers will be even larger. These instruments pose interesting array signal processing challenges. To present some aspects, we start by describing how the measured correlation data is traditionally converted into an image, and translate this into an array signal processing framework. This paves the way for a number of alternative image reconstruction techniques, such as a Weighted Least Squares approach. Self-calibration of the instrument is required to handle instrumental effects such as the unknown, possibly direction dependent, response of the receiving elements, as well a unknown propagation conditions through the Earth’s troposphere and ionosphere. Array signal processing techniques seem well suited to handle these challenges. The fact that the noise power at each antenna element may be different motivates the use of Factor Analysis, as a more appropriate alternative to the eigenvalue decomposition that is commonly used in array processing. Factor Analysis also proves to be very useful for interference mitigation. Interestingly, image reconstruction, calibration and interference mitigation are often intertwined in radio astronomy, turning this into an area with very challenging signal processing problems.
Numerical methods applied to room acoustics are usually employed to predict the sound pressure at certain positions generated by a known source. In this paper the inverse problem is studied: given a number of microphones placed in a room, the sound pressure is known at these positions and this information may be used to perform a localization and signal reconstruction of the sound source. The source is assumed to be spatially sparse meaning it can be modeled as a point source. The finite difference time domain method is used to model the acoustics of a simple two dimensional square room and its matrix formulation is presented. A two step method is proposed. First a convex optimization problem is solved to localize the source while exploiting its spatial sparsity. Once its position is known the source signal can be reconstructed by solving an overdetermined system of linear equations.
Microphone arrays have attracted a lot of interest in the last two decades. The reason behind this is that they have the potential to solve many important problems in both human-machine and human-human interfaces for different kinds of communications. But before microphone arrays can be deployed broadly, there is a strong need for a deep understanding of the problems encountered in the real world and their clear formulation in order that useful algorithms can be developed to process the sensor signals.
While there are many manuscripts on antenna arrays from a narrowband perspective (narrowband signals and narrowband processing), the literature is quite scarce when it comes to sensor arrays explained from a truly broadband perspective. Many algorithms for speech applications were simply borrowed from narrowband antenna arrays. However, a direct application of narrowband ideas to broadband speech processing may not be necessarily appropriate and can lead to many misunderstandings. Therefore, the main objective of this book is to derive and explain the most fundamental algorithms from a strictly broadband (signals and/or processing) viewpoint. Thanks to the approach taken here, new concepts come in light that have the great potential of solving several, very difficult problems encountered in acoustic and speech applications.
Microphone Array Signal Processing is a timely and important professional reference for researchers and practicing engineers from universities and a wide range of industries. It is also an excellent text for graduate students who are interested in this promising and exciting field
In many spectral estimation and array processing problems, the process of finding estimates of model parameters often involves the optimisation of a cost function containing multiple peaks and dips. Such non-convex problems are hard to solve using traditional optimisation algorithms developed for convex problems, and computationally intensive grid searches are therefore often used instead. In this paper, we establish an analytical connection between the grid size and the parametrisation of the cost function so that the grid size can be selected as coarsely as possible to lower the computation time. Additionally, we show via three common examples how the grid size depends on parameters such as the number of data points or the number of sensors in DOA estimation. We also demonstrate that the computation time can potentially be lowered by several orders of magnitude by combining a coarse grid search with a local refinement step.
Recent works on reconstruction of room geometry from echoes assume that the geometry of the sensor array is known. In this paper, we show that such an assumption is not essential; echoes provide sufficient clues to reconstruct the room’s and the array’s geometries jointly, even from a single acoustic event. Rather than focusing on the combinatorial problem of matching the walls and the recorded echoes, we provide algorithms for solving the joint estimation problem in practical cases when this matching is known and the number of microphones is small. We then explore intriguing connections between this problem and simultaneous localization and mapping (SLAM), and show that SLAM can be solved by the same methods. Finally, we demonstrate how effective the proposed methods are by numerical simulations and experiments with real measured room impulse responses.
We address the problem of jointly localizing a robot in an unknown room and estimating the room geometry from echoes. Unlike earlier work using echoes, we assume a completely autonomous setup with (near) collocated microphone and the acoustic source. We first introduce a simple, easy to analyze estimator, and prove that the sequence of room and trajectory estimates converges to the true values. Next, we approach the problem from a Bayesian point of view, and propose a more general solution which does not require any assumptions on motion and measurement model of the robot. In addition to theoretical analysis, we validate both estimators numerically.