An Efficient Maximum Likelihood Method for Direction-of-Arrival Estimation via Sparse Bayesian Learning

Liu, Zhang‐Meng; Huang, Zhitao; Zhou, Yiyu

doi:10.1109/twc.2012.090312.111912

Cited by 226 publications

(167 citation statements)

References 35 publications

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“…For a given set of active DOAs M, stochastic maximum likelihood [14], [16] provides an asymptotically efficient estimate of σ 2 . Let Γ M = diag(γ γ new M ) be the covariance matrix of the K active sources obtained above with corresponding active steering matrix A M which maximizes (17).…”

Section: F Noise Variance Estimation (Hyperparameter σmentioning

confidence: 99%

Multisnapshot Sparse Bayesian Learning for DOA

Gerstoft

Mecklenbräuker

Xenaki

et al. 2016

IEEE Signal Process. Lett.

226

178

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Abstract-March 1, 2016 The directions of arrival (DOA) of plane waves are estimated from multi-snapshot sensor array data using Sparse Bayesian Learning (SBL). The prior source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters the unknown variances (i.e. the source powers). For a complex Gaussian likelihood with hyperparameter the unknown noise variance, the corresponding Gaussian posterior distribution is derived. For a given number of DOAs, the hyperparameters are automatically selected by maximizing the evidence and promote sparse DOA estimates. The SBL scheme for DOA estimation is discussed and evaluated competitively against LASSO ( 1-regularization), conventional beamforming, and MUSIC.

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Section: F Noise Variance Estimation (Hyperparameter σmentioning

confidence: 99%

Multisnapshot Sparse Bayesian Learning for DOA

Gerstoft

Mecklenbräuker

Xenaki

et al. 2016

IEEE Signal Process. Lett.

226

178

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“…23 Figure 1 compares the DOA power spectra of CBF, MVDR, and SBL beamformer [Eq. (6) and b n, respectively] on a simple configuration with a ULA.…”

Section: Sparse Bayesian Learning Beamformingmentioning

confidence: 99%

“…17,20 The hierarchical formulation of SBL inference offers both a computationally convenient Gaussian posterior distribution for adaptive processing (type-I maximum likelihood) and automatic regularization towards robust sparse estimates determined by the hyperparameters which maximize the evidence (type-II maximum likelihood). 21 In array signal processing, SBL is shown to improve significantly the resolution in beamforming 22 and in general the accuracy of DOA estimation, [23][24][25][26][27][28] 26 and multifrequency 23,24,27,28 SBL inference exploits the common sparsity profile across snapshots for stationary signals and frequencies for broadband signals to provide robust estimates by alleviating the ambiguity in the spatial mapping between sources and sensors due to noise and frequency-dependent spatial aliasing, respectively. Accounting for the statistics of modelling errors in SBL estimation, e.g., due to sensor position, sound speed uncertainty or basis mismatch, further improves support recovery.…”

mentioning

confidence: 99%

Sound source localization and speech enhancement with sparse Bayesian learning beamforming

Xenaki

Boldt

Christensen

2018

The Journal of the Acoustical Society of America

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Speech localization and enhancement involves sound source mapping and reconstruction from noisy recordings of speech mixtures with microphone arrays. Conventional beamforming methods suffer from low resolution, especially with a limited number of microphones. In practice, there are only a few sources compared to the possible directions-of-arrival (DOA). Hence, DOA estimation is formulated as a sparse signal reconstruction problem and solved with sparse Bayesian learning (SBL). SBL uses a hierarchical two-level Bayesian inference to reconstruct sparse estimates from a small set of observations. The first level derives the posterior probability of the complex source amplitudes from the data likelihood and the prior. The second level tunes the prior towards sparse solutions with hyperparameters which maximize the evidence, i.e., the data probability. The adaptive learning of the hyperparameters from the data auto-regularizes the inference problem towards sparse robust estimates. Simulations and experimental data demonstrate that SBL beamforming provides high-resolution DOA maps outperforming traditional methods especially for correlated or non-stationary signals. Specifically for speech signals, the high-resolution SBL reconstruction offers not only speech enhancement but effectively speech separation.

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“…One solution is to increase the number of grids adaptively during the iteration [7]. But here we perform a post-processing whose computational cost is lower [8]. Denote θ k as the set which consists of two adjacent grids relating to the kth peak location ofγ, Θ −k as the grid set obtained by removing…”

Section: Sparse Bayesian Learning Formentioning

confidence: 99%

“…The narrowband DOA estimation algorithms 1-SVD [7] based on 1-norm and RVM-DOA [8] based on SBL are the two well-known algorithms. The abbreviations SVD and RVM denotes the singular value decomposition and relevance vector machine, respectively.…”

Section: Introductionmentioning

confidence: 99%

Wideband DOA Estimation via Sparse Bayesian Learning over a Khatri-Rao Dictionary

Pan¹,

Tai²,

Yuan³

2015

RADIOENGINEERING

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Abstract. This paper deals with the wideband directionof-arrival (DOA) estimation by exploiting the multiple measurement vectors (MMV) based sparse Bayesian learning (SBL) framework. First, the array covariance matrices at different frequency bins are focused to the reference frequency by the conventional focusing technique and then transformed into the vector form. Then a matrix called the Khatri-Rao dictionary is constructed by using the KhatriRao product and the multiple focused array covariance vectors are set as the new observations. DOA estimation is to find the sparsest representations of the new observations over the Khatri-Rao dictionary via SBL. The performance of the proposed method is compared with other wellknown focusing based wideband algorithms and the CramerRao lower bound (CRLB). The results show that it achieves higher resolution and accuracy and can reach the CRLB under relative demanding conditions. Moreover, the method imposes no restriction on the pattern of signal power spectral density and due to the increased number of rows of the dictionary, it can resolve more sources than sensors.

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An Efficient Maximum Likelihood Method for Direction-of-Arrival Estimation via Sparse Bayesian Learning

Cited by 226 publications

References 35 publications

Multisnapshot Sparse Bayesian Learning for DOA

Multisnapshot Sparse Bayesian Learning for DOA

Sound source localization and speech enhancement with sparse Bayesian learning beamforming

Wideband DOA Estimation via Sparse Bayesian Learning over a Khatri-Rao Dictionary

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