Structure from Sound with Incomplete Data

Kreković, Miranda; Baechler, Gilles; Vetterli, Martin

doi:10.1109/icassp.2018.8462559

“…Multidimensional unfolding [21], [22], ML optimization [14] Distances between nodes/events -Requires full synchronization, Bad local minima SDP relaxations [23], [24], [25], [26], [27], [28], [29] Distances/TDOA/FDOA -Requires anchor nodes or positions of the sensor nodes Majorization [30], Two-stage [31], [32], [33], [34] TDOA Source or receiver offsets Bad local minima, cannot handle near-minimal configurations Two-stage [16] TDOA Source & receiver offsets Slow, cannot handle near-minimal configurations Proposed TOA/TDOA Source & receiver offsets -A more common situation in audio applications is that the nodes can only receive or only send. The "sending" nodes need not be real devices; they can be any acoustic events or signals of opportunity.…”

Section: Approachmentioning

confidence: 99%

“…Early work of Pollefeys and Nister [38] exploits the low rank of a certain matrix of squared TOA differences. Their work is a near-field generalization of the work of Thrun [33], which was also adapted to work with missing measurements [34]. Heusdens and Gaubitch propose a more robust scheme based on structured total-least-squares [39] to reconstruct the times.…”

Section: Approachmentioning

confidence: 99%

Localizing Unsynchronized Sensors With Unknown Sources

Badawy

¹

,

Larsson

²

,

Pollefeys

³

2023

IEEE Trans. Signal Process.

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We propose a method for sensor array selflocalization using a set of sources at unknown locations. The sources produce signals whose times of arrival are registered at the sensors. We look at the general case where neither the emission times of the sources nor the reference time frames of the receivers are known. Unlike previous work, our method directly recovers the array geometry, instead of first estimating the timing information. The key component is a new loss function which is insensitive to the unknown timings. We cast the problem as a minimization of a non-convex functional of the Euclidean distance matrix of microphones and sources subject to certain non-convex constraints. After convexification, we obtain a semidefinite relaxation which gives an approximate solution; subsequent refinement on the proposed loss via the Levenberg-Marquardt scheme gives the final locations. Our method achieves state-of-the-art performance in terms of reconstruction accuracy, speed, and the ability to work with a small number of sources and receivers. It can also handle missing measurements and exploit prior geometric and temporal knowledge, for example if either the receiver offsets or the emission times are known, or if the array contains compact subarrays with known geometry.

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“…Early work of Pollefeys and Nister [28] exploits the low rank of a certain matrix of squared TOA differences. Their work is a near-field generalization of the work of Thrun [29], which was also adapted to work with missing measurements [30], [31]. Heusdens and Gaubitch propose a more robust scheme based on structured total-least-squares [32] to reconstruct the times.…”

Section: A Related Workmentioning

confidence: 99%

Localizing Unsynchronized Sensors with Unknown Sources

Badawy¹,

Larsson²,

Pollefeys³

2021

Preprint

0

View full text Add to dashboard Cite

We propose a method for sensor array selflocalization using a set of sources at unknown locations. The sources produce signals whose times of arrival are registered at the sensors. We look at the general case where neither the emission times of the sources nor the reference time frames of the receivers are known. Unlike previous work, our method directly recovers the array geometry, instead of first estimating the timing information. The key component is a new loss function which is insensitive to the unknown timings. We cast the problem as a minimization of a non-convex functional of the Euclidean distance matrix of microphones and sources subject to certain non-convex constraints. After convexification, we obtain a semidefinite relaxation which gives an approximate solution; subsequent refinement on the proposed loss via the Levenberg-Marquardt scheme gives the final locations. Our method achieves state-of-the-art performance in terms of reconstruction accuracy, speed, and the ability to work with a small number of sources and receivers. It can also handle missing measurements and exploit prior geometric and temporal knowledge, for example if either the receiver offsets or the emission times are known, or if the array contains compact subarrays with known geometry.

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“…Prior work on localization from point-to-plane distances has so far been mostly computational [2], [3]. Although several papers point out problems with uniqueness [4], [5], a complete study was up to now absent.…”

Section: Introductionmentioning

confidence: 99%

Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

Kreković

¹

,

Vetterli

²

2020

IEEE Trans. Signal Process.

Self Cite

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We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the notable "structure from sound" approach to microphone localization with unknown sources. In our earlier work we proposed computational methods for localization from point-to-plane distances and noted that such localization suffers from various ambiguities beyond the usual rigid body motions; in this paper we provide a complete characterization of uniqueness. We enumerate equivalence classes of configurations which lead to the same distance measurements as a function of the number of planes and points, and algebraically characterize the related transformations in both 2D and 3D. Here we only discuss uniqueness; computational tools and heuristics for practical localization from point-to-plane distances using sound will be addressed in a companion paper.Index Terms-point-to-plane distance matrix, inverse problem in the Euclidean space, uniqueness of the reconstruction, collocated source and receiver, indoor localization and mapping.

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Structure from Sound with Incomplete Data

Cited by 4 publications

References 17 publications

Localizing Unsynchronized Sensors With Unknown Sources

Localizing Unsynchronized Sensors With Unknown Sources

Localizing Unsynchronized Sensors with Unknown Sources

Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

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