Theoretical analysis of the DAMAS algorithm and efficient implementation of the covariance matrix fitting method for large-scale problems

Chardon, Gilles; Picheral, José; Ollivier, François

doi:10.1016/j.jsv.2021.116208

Cited by 13 publications

(3 citation statements)

References 24 publications

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“…As above, when the theoretical covariance matrix is used in (10), B U (α) is maximal at the actual position of the source. In noiseless cases, the power of the source can be estimated by ρ = B U ( α).…”

Section: Beamforming and Steering Vectorsmentioning

confidence: 92%

“…CLEAN and CLEAN-SC [7]) can use beamforming as a selection step to add a new source to a set of identified sources. Also, deconvolution can be used to improve the resolution of beamforming maps, with the DAMAS algorithm [8] being one of the most famous examples of such methods (note however that the DAMAS algorithm was shown to solve the Covariance Matrix Fitting problem [9], which does not involve beamforming, and can be solved using more efficient numerical algorithms [10]).…”

Section: Introductionmentioning

confidence: 99%

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Theoretical analysis of beamforming steering vector formulations for acoustic source localization

Chardon

2022

Journal of Sound and Vibration

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In three-dimensional acoustic source localization, setting the steering vector is an important choice. Four steering vector formulations are frequently used. In the noiseless case, two of them yield a correct estimation of the position, the two others yielding correct estimation of the amplitude of the source, assuming its position is known. Here, noisy measurements are considered, and the steering vector formulations are compared in terms of bias and variance of the estimated position and amplitude, allowing a more informative assessment of their performances. An approximated value of the position bias of the biased formulations is given. Maximum likelihood estimation of the parameters of the source is derived, showing that it involves the combination of two steering vector formulations, for position estimation, followed by amplitude estimation. This analysis does not rely on the specific form of the Green function, and remains relevant for general propagation media.

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Section: Beamforming and Steering Vectorsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Theoretical analysis of beamforming steering vector formulations for acoustic source localization

Chardon

2022

Journal of Sound and Vibration

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“…Using the specific structure of those matrix products, the computation can be accelerated compared to a straightforward matrix multiplication. For a detailed discussion of this aspect within the context of acoustic source power reconstruction, we refer to [5].…”

Section: Vectorized Fista Formulationmentioning

confidence: 99%

Wavenumber spectrum determination for aeroacoustic applications using FISTA

Raumer

Spehr

2023

inter noise

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This conference paper deals with computational methods to determine the wavenumber spectrum of acoustic data measured by a phased microphone array. Such problems occur e.g. within the analysis of pressure fluctuations due to a turbulent boundary layer on a surface such as a wind-tunnel wall or the skin of an aircraft. The problem is closely related to the deconvolution of dirty beamforming maps in wavenumber domain, which seeks to determine the wavenumber spectrum by removing the influence of the shift-invariant point spread function from the beamforming result. Firstly, we recall how this task can be formulated as a minimization problem and then discuss a specific solver for this problem, provided by the framework of the generalized FISTA algorithm. The resulting method takes advantage of the convolutional structure of the gradient of the data misfit functional and allows further for a flexible regularization with L1 and L2 penalties as well as a nonnegativity constraint. Finally, the presented algorithmic framework is demonstrated with numerical examples.

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