Direction of Arrival Estimation in the Spherical Harmonic Domain using Subspace Pseudo-Intensity Vectors

Direction of Arrival (DOA) estimation is a fundamental problem in acoustic signal processing. It is used in a diverse range of applications, including spatial filtering, speech dereverberation, source separation and diarization. Intensity vector-based DOA estimation is attractive, especially for spherical sensor arrays, because it is computationally efficient. Two such methods are presented which operate on a spherical harmonic decomposition of a sound field observed using a spherical microphone array. The first uses Pseudo-Intensity Vectors (PIVs) and works well in acoustic environments where only one sound source is active at any time. The second uses Subspace Pseudo-Intensity Vectors (SSPIVs) and is targeted at environments where multiple simultaneous sources and significant levels of reverberation make the problem more challenging. Analytical models are used to quantify the effects of an interfering source, diffuse noise and sensor noise on PIVs and SSPIVs. The accuracy of DOA estimation using PIVs and SSPIVs is compared against the state-of-the-art in simulations including realistic reverberation and noise for single and multiple, stationary and moving sources. Finally, robust performance of the proposed methods is demonstrated using speech recordings in real acoustic environments

Multiple source localization using spherical microphone arrays

Direction-of-Arrival (DOA) estimation is a fundamental task in acoustic signal processing and is used in source separation, localization, tracking, environment mapping, speech enhancement and dereverberation. In applications such as hearing aids, robot audition, teleconferencing and meeting diarization, the presence of multiple simultaneously active sources often occurs. Therefore DOA estimation which is robust to Multi-Source (MS) scenarios is of particular importance. In the past decade, interest in Spherical Microphone Arrays (SMAs) has been rapidly grown due to its ability to analyse the sound field with equal resolution in all directions. Such symmetry makes SMAs suitable for applications in robot audition where potential variety of heights and positions of the talkers are expected. Acoustic signal processing for SMAs is often formulated in the Spherical Harmonic Domain (SHD) which describes the sound field in a form that is independent of the geometry of the SMA. DOA estimation methods for the real-world scenarios address one or more performance degrading factors such as noise, reverberation, multi-source activity or tackled problems such as source counting or reducing computational complexity. This thesis addresses various problems in MS DOA estimation for speech sources each of which focuses on one or more performance degrading factor(s). Firstly a narrowband DOA estimator is proposed utilizing high order spatial information in two computationally efficient ways. Secondly, an autonomous source counting technique is proposed which uses density-based clustering in an evolutionary framework. Thirdly, a confidence metric for validity of Single Source (SS) assumption in a Time-Frequency (TF) bin is proposed. It is based on MS assumption in a short time interval where the number and the TF bin of active sources are adaptively estimated. Finally two analytical narrowband MS DOA estimators are proposed based on MS assumption in a TF bin. The proposed methods are evaluated using simulations and real recordings. Each proposed technique outperforms comparative baseline methods and performs at least as accurately as the state-of-the-art.Open Acces

Online DOA estimation using real eigenbeam ESPRIT with propagation vector matching

International audienceThe Eigenbeam estimation of signal parameters via rotational invariance technique (EB-ESPRIT) [1] is a method to estimate multiple directions-of-arrival (DOAs) of sound sources from a spherical microphone array recording in the spherical harmonics domain (SHD). The method, first, constructs a signal subspace from the SHD signal and then makes use of the fact that, for plane-wave sources, the signal subspace is spanned by the (complex conjugate) spherical harmonic vectors at the source directions. The DOAs are then estimated from the signal subspace using recurrence relations of spherical harmonics.In recent publications, the singularity and ambiguity problems of the original EB-ESPRIT have been solved by jointly combining several types of recurrence relations. The state-of-the-art EB-ESPRIT, denoted as DOA-vector EB-ESPRIT, is based on three recurrence relations [2,3]. This EB-ESPRIT variant can estimate the source DOAs with significantly higher accuracy compared to the other EB-ESPRIT variants [3]. However, a permutation problem arises, which can be solved by using, for example, a joint diagonalization method [3].For parametric spatial audio signal processing purposes in the short-time Fourier transform (STFT) domain, DOA estimates are usually needed per time-frame and frequency bin. In principle, one can use the DOA-vector EB-ESPRIT method to estimate the source DOAs per time-frequency bin in an online manner. However, due to the eigendecompostion of the PSD matrix and the joint diagonalization procedure, the computational cost might be too large for many real-time applications.In this work, we propose a computationally more efficient version of the DOA-vector EB-ESPRIT based on real spherical harmonics recurrence relations. First, we separate the real and imaginary parts of the real SHD signal in the STFT domain and then construct a real signal subspace thereof, which can be recursively estimated using the deflated projection approximation subspace tracking (PASTd) [4] method. For the case of one source per time-frequency bin, the joint diagonalization is not necessary and we can simplify the EB-ESPRIT equations. For the case of two sources, the plane-wave propagation vectors can directly be estimated from the signal subspace eigenvectors by employing properties of the propagation vectors. This method can be seen as a higher order ambisonics extension of the robust B-format DOA estimation in [5]. The proposed method for estimating two DOAs can be summarized as follows:1. Separate real and imaginary parts of the real SHD signal in the STFT domain.2. Recursively estimate the signal subspace eigenvectors using PASTd.3. Estimate the two plane-wave propagation vectors from the signal subspace eigenvectors by using that they span the same subspace and by using properties of the propagation vectors (subspace-propagation vector matching).4. Estimate the DOAs by using three types of real spherical harmonics recurrence relations.Alternatively, one can estimate the DOAs analogously to the complex DOA-vector EB-ESPRIT using the joint diagonalization method proposed in [3].For the evaluation, we simulate SHD signals up to third order with one and two speech sources in reverberant and noisy environments. For the one-source scenarios, we compare the real DOA-vector EB-ESPRIT with subspace estimation based on singular value decomposition (SVD) against PASTd. For the two-source scenarios, we compare the real DOA-vector EB-ESPRIT with joint diagonalization against subspace-propagation vector matching and the robust B-format DOA estimation method.We analyze the angular distributions of the DOA estimates and find, that the DOA estimation using PASTd for the signal subspace estimation is slightly less accurate than the SVD based method but computationally much more efficient. For the estimation of two DOAs, the EB-ESPRIT based methods outperform the robust B-format estimation method when higher SHD orders are considered. The joint diagonalization method is more accurate than the subspace-propagation vector matching method. However, the latter is computationally more efficient.References:[1] H. Teutsch and W. Kellermann, “Detection and localization of multiple wideband acoustic sources based on wavefield decomposition using spherical apertures,” in Proc. IEEE Intl. Conf. Acoust., Speech Signal Proc. (ICASSP), Mar. 2008, pp. 5276–5279.[2] B. Jo and J. W. Choi, “Nonsingular EB-ESPRIT for the localization of early reflections in a room,” J. Acoust. Soc. Am., vol. 144, no. 3, p. 1882, Sep. 2018.[3] A. Herzog and E. A. P. Habets, “Eigenbeam-ESPRIT for DOA-vector estimation,” IEEE Signal Process. Lett., vol. 26, no. 4, pp. 572-576, April 2019.[4] B. Yang – “Projection Approximation Subspace Tracking, IEEE Trans. Sig. Proc.,” vol. 43, no. 1, Jan. 1995.[5] O. Thiergart and E.A.P. Habets, “Robust direction-of-arrival estimation of two simultaneous plane waves from a B-format signal,” IEEE 27th Conv. of Electrical and Electronics Engineers in Israel, Nov. 2012

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

Broadband DOA estimation using Convolutional neural networks trained with noise signals

A convolution neural network (CNN) based classification method for broadband DOA estimation is proposed, where the phase component of the short-time Fourier transform coefficients of the received microphone signals are directly fed into the CNN and the features required for DOA estimation are learnt during training. Since only the phase component of the input is used, the CNN can be trained with synthesized noise signals, thereby making the preparation of the training data set easier compared to using speech signals. Through experimental evaluation, the ability of the proposed noise trained CNN framework to generalize to speech sources is demonstrated. In addition, the robustness of the system to noise, small perturbations in microphone positions, as well as its ability to adapt to different acoustic conditions is investigated using experiments with simulated and real data.Comment: Published in Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA) 201