Mihailo Kolundzija

Related publications (16)

Blind as a Bat: Audible Echolocation on Small Robots

Frederike Dümbgen, Adrien Guillaume Olivier Hoffet, Mihailo Kolundzija, Adam James Scholefield, Martin Vetterli

For safe and efficient operation, mobile robots need to perceive their environment, and in particular, perform tasks such as obstacle detection, localization, and mapping. Although robots are often equipped with microphones and speakers, the audio modality is rarely used for these tasks. Compared to the localization of sound sources, for which many practical solutions exist, algorithms for active echolocation are less developed and often rely on hardware requirements that are out of reach for small robots. We propose an end-to-end pipeline for sound-based localization and mapping that is targeted at, but not limited to, robots equipped with only simple buzzers and low-end microphones. The method is model-based, runs in real time, and requires no prior calibration or training. We successfully test the algorithm on the e-puck robot with its integrated audio hardware, and on the Crazyflie drone, for which we design a reproducible audio extension deck. We achieve centimeter-level wall localization on both platforms when the robots are static during the measurement process. Even in the more challenging setting of a flying drone, we can successfully localize walls, which we demonstrate in a proof-of-concept multi-wall localization and mapping demo.

2022

Multi-Modal Probabilistic Indoor Localization on a Smartphone

Serge Ayer, Frederike Dümbgen, Emmanuel Girardin, Mihailo Kolundzija, Johan Leuenberger, Cynthia Oeschger, Adam James Scholefield

IEEE2019

Spatial sound rendering methods that use B-format have moved from static to signal-dependent, making B-format signal analysis a crucial part of B-format decoders. In the established B-format signal analysis methods, the acquired sound field is commonly modeled in terms of a single plane wave and diffuse sound, or in terms of two plane waves. We present a B-format analysis method that models the sound field with two direct sounds and diffuse sound, and computes the three components' powers and direct sound directions as a function of time and frequency. We show the effectiveness of the proposed method with experiments using artificial and realistic signals.

2018

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Systems with hundreds of microphones for acoustic field acquisition, or hundreds of loudspeakers for rendering, have been proposed and built. To analyze, design, and apply such systems requires a framework that allows us to leverage the vast set of tools available in digital signal processing in order to achieve intuitive and efficient algorithms. We thus propose a discrete space–time framework, grounded in classical acoustics, which addresses the discrete nature of the spatial and temporal sampling. In particular, a short-space/time Fourier transform is introduced, which is the natural extension of the localized or short-time Fourier transform. Processing in this intuitive domain allows us to easily devise algorithms for beam-forming, source separation, and multi-channel compression, among other useful tasks. The essential space band-limitedness of the Fourier spectrum is also used to solve the spatial equalization task required for sound field rendering in a region of interest. Examples of applications are shown.

2014

Beyond Moore-Penrose: Sparse Pseudoinverse

Ivan Dokmanic, Mihailo Kolundzija, Martin Vetterli

Frequently, we use the Moore-Penrose pseudoinverse (MPP) even in cases when we do not require all of its defining properties. But if the running time and the storage size are critical, we can do better. By discarding some constraints needed for the MPP, we gain freedom to optimize other aspects of the new pseudoinverse. A sparser pseudoinverse reduces the amount of computation and storage. We propose a method to compute a sparse pseudoinverse and show that it offers sizable improvements in speed and storage, with a small loss in the least-squares performance. Differently from previous approaches, we do not attempt to approximate the MPP, but rather to produce an exact but sparse pseudoinverse. In the underdetermined (compressed sensing) scenario we prove that the rescaled sparse pseudoinverse yields an unbiased estimate of the unknown vector, and we demonstrate its potential in iterative sparse recovery algorithms, pointing out directions for future research.

2013

Multi-channel low-frequency room equalization using perceptually motivated constrained optimization

Christof Faller, Mihailo Kolundzija, Martin Vetterli

We consider the problem of multiple-loudspeaker low-frequency room equalization for a wide listening area, where the equalized loudspeaker is helped using the remaining ones. Using a spatial discretization of the listening area, we formulate the problem as a multipoint error minimization between desired and synthesized magnitude frequency responses. The desired response and cost function are formulated with a goal of capturing the room's spectral power profile, and penalizing strong resonances. Considering physical and psychoacoustical observations, we argue for the use of gain-limited, short, and well-localized equalization filters, with an additional delay for loudspeakers that help the equalized one. We propose a convex optimization framework for computing room equalization filters, where the mentioned filter requirements are incorporated as convex constraints. We verify the effectiveness of our equalization approach through simulations.

Ieee2012

Spatial Acoustic Signal Processing

Mihailo Kolundzija

A sound field on a line or in a plane has an effectively limited spatial bandwidth determined by the temporal frequency. Similar can be said for sound fields from far-field sources when analyzed on circular and spherical apertures. Namely, for a given frequency and aperture size, a sound field is effectively composed of a finite number of circular or spherical harmonic components. Based on these two observations, it follows that if adequately sampled, sound fields can be represented and manipulated in a digital domain with negligible loss of information. The optimal sampling surface depends on the problem geometry, and the set of sampling points needs to be in accordance with the Nyquist criterion relative to the mentioned effective sound field bandwidth. In this thesis, we address the problems of sound field capture and reproduction from a practical perspective. More specifically, we present approaches that do not depend on acoustical models, but rely instead on obtaining an acoustic MIMO channel between transducers (microphones or loudspeakers) and a set of sampling (or control) points. Subsequently, sound field capture and reproduction are formulated as constrained optimization problems in a spatially discrete domain and solved using conventional numerical optimization tools. The first part of the thesis deals with spatial sound capture. We present a framework for analyzing and designing differential microphone arrays based on spatiotemporal sound field gradients. We also show how to record two- and three-dimensional sound fields with differential, circular, and spherical microphone arrays. Finally, we use the mentioned discrete optimization for computing filters for directional and sound field microphone arrays. In the second part of the thesis, we focus on spatial sound reproduction. We first present a design of a baffled loudspeaker array for reproducing sound with high directivity over a wide frequency range, which combines beamforming at low, and scattering from a rigid baffle at high frequencies. We next present Sound Field Reconstruction (SFR), which is an approach for optimally reproducing a desired sound field in a wide listening area by inverting a discrete, MIMO acoustic channel. In the end, we propose a single- and multi-channel low-frequency room equalization method, formulated as a discrete constrained optimization problem, with constraints designed to prevent excessive equalization filter gains, localization bias, and temporal distortions in the form of pre- and post-echos.

EPFL2012

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Building acoustic beamformers is a problem whose solution is hindered by the wide-band nature of audible sound. In order to achieve a consistent directional response over a wide range of frequencies, a conventional acoustic beamformer needs a high number of discrete loudspeakers and be large enough to achieve a desired low-frequency performance. The acoustic beamformer design described in this paper uses measurement-based optimized beamforming for loudspeakers mounted on a rigid cylindrical baffle. Super-directional beamforming enables achieving desired directivity with multiple loudspeakers at low frequencies. High frequencies are reproduced with a single loudspeaker, whose highly directional reproduction---due to the cylindrical baffle---matches the design goals. In addition to the beamformer filter design procedure, it is shown how such loudspeaker array can be used for spatial sound reproduction.

2011

Reproducing Sound Fields Using MIMO Acoustic Channel Inversion

Christof Faller, Mihailo Kolundzija, Martin Vetterli

Sound fields are essentially band-limited phenomena, both temporally and spatially. This implies that a spatially sampled sound field respecting the Nyquist criterion is effectively equivalent to its continuous original. We describe Sound Field Reconstruction (SFR)---a technique that uses the previously stated observation to express the reproduction of a continuous sound field as an inversion of the discrete acoustic channel from a loudspeaker array to a grid of control points. The acoustic channel is inverted using truncated singular value decomposition (SVD) in order to provide optimal sound field reproduction subject to a limited effort constraint. Additionally, a detailed procedure for obtaining loudspeaker driving signals that involves selection of active loudspeakers, coverage of the listening area with control points, and frequency domain FIR filter design is described. Extensive simulations comparing SFR with Wave Field Synthesis show that on average, SFR provides higher sound field reproduction accuracy.

2011

Spatiotemporal Gradient Analysis of Differential Microphone Arrays

Christof Faller, Mihailo Kolundzija, Martin Vetterli

The literature on gradient and differential microphone arrays makes a distinction between the two types, and nevertheless shows how both types can be used to obtain the same directional responses. A more theoretically sound rationale for using delays in differential microphone arrays has not yet been given. This paper presents a gradient analysis of the sound field viewed as a spatio-temporal phenomenon, and gives a theoretical interpretation of the working principles of gradient and differential microphone arrays. It shows that both types of microphone arrays can be viewed as devices for approximately measuring spatio-temporal derivatives of the sound field. Furthermore, it also motivates the design of high-order differential microphone arrays using the aforementioned spatio-temporal gradient analysis.

2011