Stochastic Cramér-Rao Bound Analysis for DOA Estimation in Spherical Harmonics Domain

Kumar, Lalan; Hegde, Rajesh M.

doi:10.1109/lsp.2014.2381361

Cited by 31 publications

(16 citation statements)

References 20 publications

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“…With the time domain smoothing, PWD is implemented here as: (34) The output energy of the time-domain beamformer at is given as where is the estimated array covariance matrix, given in Eq. (31).…”

Section: Beamformingmentioning

confidence: 99%

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Direction of Arrival Estimation of Reflections from Room Impulse Responses Using a Spherical Microphone Array

Tervo

Politis

2015

IEEE/ACM Trans. Audio Speech Lang. Process.

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This paper studies the direction of arrival estimation of reflections in short time windows of room impulse responses measured with a spherical microphone array. Spectral-based methods, such as multiple signal classification (MUSIC) and beamforming, are commonly used in the analysis of spatial room impulse responses. However, the room acoustic reflections are highly correlated or even coherent in a single analysis window and this imposes limitations on the use of spectral-based methods. Here, we apply maximum likelihood (ML) methods, which are suitable for direction of arrival estimation of coherent reflections. These methods have been earlier developed in the linear space domain and here we present the ML methods in the context of spherical microphone array processing and room impulse responses. Experiments are conducted with simulated and real data using the em32 Eigenmike. The results show that direction estimation with ML methods is more robust against noise and less biased than MUSIC or beamforming.Index Terms-Direction of arrival (DOA), room acoustics, spatial room impulse response, spherical microphone arrays.

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Section: Beamformingmentioning

confidence: 99%

“…These partial derivatives are available in the literature and, for example, in MATHEMATICA. In[34], the CRLB for a single stochastic source in the SH domain is presented.…”

mentioning

confidence: 99%

Direction of Arrival Estimation of Reflections from Room Impulse Responses Using a Spherical Microphone Array

Tervo

Politis

2015

IEEE/ACM Trans. Audio Speech Lang. Process.

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“…Firstly, we demonstrate the capability of resolution to SH-ANM method and the super resolution method on the sphere in [34] for single snapshot and noiseless case. Then, the comparison of the DOA estimation performance in noisy case between SH-ANM method in Section V-A and l 1 norm based method in [16], the SHESPRIT in [10], TSDA (estimate elevations with U-SHESPRIT and estimate azimuths with U-SHRMUSIC) in [11], CV-VSBL in [17] and Cramer-Rao Bound (CRB) in [49] is presented. Here, we refer to the SH-ANM method with SH-ESPRIT in Section V-A as ANM-SHESPRIT.…”

Section: Simulationsmentioning

confidence: 99%

Spherical Harmonic Atomic Norm and its Application to DOA Estimation

Pan

2019

IEEE Access

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Signal processing in the spherical harmonic (SH) domain has the advantages of analyzing a signal on the sphere with equal resolution in the whole space and of decomposite the frequency-and location-dependent components of the signal. Therefore, it finds recent applications in signal recovery and localization. In this paper, we consider the gridless sparse signal recovery problem in the SH domain with atomic norm minimization (ANM). Due to the absence of Vandermonde structure for spherical harmonics, the Vandermonde decomposition theorem, which is the mathematic foundation of conventional ANM approaches, is not applicable in the SH domain. To address this issue, a low-dimensional semidefinite programming (SDP) method to implement the spherical harmonic atomic norm minimization (SH-ANM) approach is proposed. This method does not rely on the Vandermonde decomposition and can recover the atomic decomposition in the SH domain directly. As an application, we develop the direction-of-arrival estimation approach based on the proposed SH-ANM method, and computer simulations demonstrate that its performance is superior to the state-of-the-art counterparts. Furthermore, we validate the results in real-life acoustics scenes for multiple speakers localization using measured data in LACATA challenge. INDEX TERMS Spherical harmonic domain, atomic norm, gridless sparse signal recovery, semidefinite programming, direction-of-arrive estimation.

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“…Here s(t) and Ψ are the linear and nonlinear parameters of our optimization problem, respectively. Minimizing the objective function in (20) requires an exhaustive search in (2L + LN s )-dimension space. To decrease the computational complexity of such joint optimization problems, an iterative process is proposed based on [28] as follows: 1) Initialize Ψ and find the optimal estimator of s(t) as:…”

Section: A Uniform Noisementioning

confidence: 99%

Robust Stochastic Maximum Likelihood Algorithm for DOA Estimation of Acoustic Sources in the Spherical Harmonic Domain

Lolaee

Akhaee

2018

2018 26th European Signal Processing Conference (EUSIPCO)

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The direction of arrival (DOA) estimation of sound sources has been a popular signal processing research topic due to its widespread applications. Using spherical microphone arrays (SMA), DOA estimation can be applied in the spherical harmonic (SH) domain without any spatial ambiguity. However, the environment reverberation and noise can degrade the estimation performance. In this paper, we propose a new expectation maximization (EM) algorithm for deterministic maximum likelihood (ML) DOA estimation of L sound sources in the presence of spatially nonuniform noise in the SH domain. Furthermore a new closed-form Cramer-Rao bound (CRB) for the deterministic ML DOA estimation is derived for the signal model in the SH domain. The main idea of the proposed algorithm is considering the general model of the received signal in the SH domain, we reduce the complexity of the ML estimation by breaking it down into two steps: expectation and maximization steps. The proposed algorithm reduces the complexity from 2L-dimensional space to L 2-dimensional space. Simulation results indicate that the proposed algorithm shows at least an improvement of 6dB in robustness in terms of root mean square error (RMSE). Moreover, the RMSE of the proposed algorithm is very close to the CRB compared to the recent methods in reverberant and noisy environments in the large range of signal to noise ratio.

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Stochastic Cramér-Rao Bound Analysis for DOA Estimation in Spherical Harmonics Domain

Cited by 31 publications

References 20 publications

Direction of Arrival Estimation of Reflections from Room Impulse Responses Using a Spherical Microphone Array

Direction of Arrival Estimation of Reflections from Room Impulse Responses Using a Spherical Microphone Array

Spherical Harmonic Atomic Norm and its Application to DOA Estimation

Robust Stochastic Maximum Likelihood Algorithm for DOA Estimation of Acoustic Sources in the Spherical Harmonic Domain

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