In this work, we consider direction-of-arrival (DoA) estimation in the presence of extreme noise using Deep Learning (DL). In particular, we introduce a Convolutional Neural Network (CNN) that is trained from mutli-channel data of the true array manifold matrix and is able to predict angular directions using the sample covariance estimate. We model the problem as a multi-label classification task and train a CNN in the low-SNR regime to predict DoAs across all SNRs. The proposed architecture demonstrates enhanced robustness in the presence of noise, and resilience to a small number of snapshots. Moreover, it is able to resolve angles within the grid resolution. Experimental results demonstrate significant performance gains in the low-SNR regime compared to state-of-the-art methods and without the requirement of any parameter tuning. We relax the assumption that the number of sources is known a priori and present a training method, where the CNN learns to infer the number of sources jointly with the DoAs. Simulation results demonstrate that the proposed CNN can accurately estimate off-grid angles in low SNR, while at the same time the number of sources is successfully inferred for a sufficient number of snapshots. Our robust solution can be applied in several fields, ranging from wireless array sensors to acoustic microphones or sonars.
This paper investigates the accuracy of various Generalized Cross-Correlation with Phase Transform (GCC-PHAT) methods for a close pair of microphones. We investigate interpolation-based methods and also propose another approach based on Singular Value Decomposition (SVD). All investigated methods are implemented in C code, and the execution time is measured to determine which approach is the most appealing for real-time applications on low-cost embedded hardware.
The recently proposed subspace pseudointensity method for direction of arrival estimation is applied in the context of Tasks 1 and 2 of the LOCATA Challenge using the Eigenmike recordings. Specific implementation details are described and results reported for the development dataset, for which the ground truth source directions are available. For both single and multiple source scenarios, the average absolute error angle is about 9 degrees.
Tampere University of Technology（坦佩雷理工大学）；Aalto University（阿尔托大学）
This paper proposes a deep neural network for estimating the directions of arrival (DOA) of multiple sound sources. The proposed stacked convolutional and recurrent neural network (DOAnet) generates a spatial pseudo-spectrum (SPS) along with the DOA estimates in both azimuth and elevation. We avoid any explicit feature extraction step by using the magnitudes and phases of the spectrograms of all the channels as input to the network. The proposed DOAnet is evaluated by estimating the DOAs of multiple concurrently present sources in anechoic, matched and unmatched reverberant conditions. The res…
In this paper, we present a new model for Direction of Arrival (DOA) estimation of sound sources based on an Icosahedral Convolutional Neural Network (CNN) applied over SRP-PHAT power maps computed from the signals received by a microphone array. This icosahedral CNN is equivariant to the 60 rotational symmetries of the icosahedron, which represent a good approximation of the continuous space of spherical rotations, and can be implemented using standard 2D convolutional layers, having a lower computational cost than most of the spherical CNNs. In addition, instead of using fully connected laye…
We present a novel learning-based approach to estimate the direction-of-arrival (DOA) of a sound source using a convolutional recurrent neural network (CRNN) trained via regression on synthetic data and Cartesian labels. We also describe an improved method to generate synthetic data to train the neural network using state-of-the-art sound propagation algorithms that model specular as well as diffuse reflections of sound. We compare our model against three other CRNNs trained using different formulations of the same problem: classification on categorical labels, and regression on spherical coor…
IIIT Hyderabad（海得拉巴国际信息技术学院）；Queen Mary University of London（伦敦玛丽女王大学）
Sound source localization is crucial in acoustic sensing and monitoring-related applications. In this paper, we do a comprehensive analysis of improvement in sound source localization by combining the direction of arrivals (DOAs) with their derivatives which quantify the changes in the positions of sources over time. This study uses the SALSA-Lite feature with a convolutional recurrent neural network (CRNN) model for predicting DOAs and their first-order derivatives. An update rule is introduced to combine the predicted DOAs with the estimated derivatives to obtain the final DOAs. The experime…
NTT Media Intelligence Laboratories（NTT媒体情报实验室）；University of Padova（帕多瓦大学）
In this paper, we propose a novel data augmentation method for training neural networks for Direction of Arrival (DOA) estimation. This method focuses on expanding the representation of the DOA subspace of a dataset. Given some input data, it applies a transformation to it in order to change its DOA information and simulate new potentially unseen one. Such transformation, in general, is a combination of a rotation and a reflection. It is possible to apply such transformation due to a well-known property of First Order Ambisonics (FOA). The same transformation is applied also to the labels, in …
We propose a generalized formulation of direction of arrival estimation that includes many existing methods such as steered response power, subspace, coherent and incoherent, as well as speech sparsity-based methods. Unlike most conventional methods that rely exclusively on grid search, we introduce a continuous optimization algorithm to refine DOA estimates beyond the resolution of the initial grid. The algorithm is derived from the majorization-minimization (MM) technique. We derive two surrogate functions, one quadratic and one linear. Both lead to efficient iterative algorithms that do not…
Range estimation of a far field sound source in a reverberant environment is known to be a notoriously difficult problem, hence most localization methods are only capable of estimating the source's Direction-of-Arrival (DoA). In an earlier work, we have demonstrated that, under certain restrictive acoustic conditions and given the orientation of a reflecting surface, one can exploit the dominant acoustic reflection to evaluate the DoA \emph{and} the distance to a static sound source in Ambisonic domain. In this article, we leverage the recently presented Generalized Time-domain Velocity Vector…
An approach to the estimation of the Direction of Arrival (DOA) of wide-band signals with a planar microphone array is presented. Our algorithm estimates an unambiguous DOA using a single planar array in which the microphones are placed fairly close together and the sound source is expected to be in the far field. The algorithm uses the ambiguous DOA estimates obtained from microphone pairs in the array to determine an unambiguous DOA estimate for the array as a whole. The required pair-wise DOAs may be calculated using Time Delay Estimations (TDEs), which may in turn be calculated using cross…
Neural-network (NN)-based methods show high performance in sound event localization and detection (SELD). Conventional NN-based methods use two branches for a sound event detection (SED) target and a direction-of-arrival (DOA) target. The two-branch representation with a single network has to decide how to balance the two objectives during optimization. Using two networks dedicated to each task increases system complexity and network size. To address these problems, we propose an activity-coupled Cartesian DOA (ACCDOA) representation, which assigns a sound event activity to the length of a cor…
Assisted RTF-Vector-Based Binaural Direction of Arrival Estimation Exploiting a Calibrated External Microphone Array
University of Oldenburg, Department of Medical Physics and Acoustics（奥尔登堡大学医学物理与声学系）；Cluster of Excellence Hearing4all, Oldenburg, Germany（卓越中心Hearing4all）
In this paper, we primarily explore the improvement of single stream audio systems using Angle of Arrival calculations in both simulation and real life gathered data. We wanted to learn how to discern the direction of an audio source from gathered signal data to ultimately incorporate into a multi modal security system. We focused on the MUSIC algorithm for the estimation of the angle of arrival but briefly experimented with other techniques such as Bartlett and Capo. We were able to implement our own MUSIC algorithm on stimulated data from Cornell. In addition, we demonstrated how we are able…
In this paper we consider a binaural hearing aid setup, where in addition to the head-mounted microphones an external microphone is available. For this setup, we investigate the performance of several relative transfer function (RTF) vector estimation methods to estimate the direction of arrival (DOA) of the target speaker in a noisy and reverberant acoustic environment. More in particular, we consider the state-of-the-art covariance whitening (CW) and covariance subtraction (CS) methods, either incorporating the external microphone or not, and the recently proposed spatial coherence (SC) meth…
Noise Suppression for Time Difference of Arrival: Performance Evaluation of a Generalized Cross-Correlation Method Using Mean Signal and Inverse Filter
Machine learning is a promising technique for angle-of-arrival (AOA) estimation of waves impinging a sensor array. However, the majority of the methods proposed so far only consider a known, fixed number of impinging waves, i.e., a fixed source number. This paper proposes a machine-learning-based estimator designed for the case when the source number is variable and hence unknown a priori. The proposed estimator comprises a framework of single-label classifiers. Each classifier predicts if waves are present within certain randomly selected segments of the array's field of view (FOV), resulting…
MUltiple SIgnal Classification (MUSIC) and Estimation of signal parameters via rotational via rotational invariance (ESPRIT) has been widely used in super resolution direction of arrival estimation (DoA) in both Uniform Linear Arrays (ULA) or Uniform Circular Arrays (UCA). However, problems become challenging when the number of source signal increase, MUSIC suffer from computation complexity when finding the peaks, while ESPRIT may not robust to array geometry offset. Therefore, Neural Network become a potential solution. In this paper, we propose a neural network to estimate the azimuth and e…
A vector sensor, a type of sensor array with six collocated antennas to measure all electromagnetic field components of incident waves, has been shown to be advantageous in estimating the angle of arrival and polarization of the incident sources. While angle estimation with machine learning for linear arrays has been well studied, there has not been a similar solution for the vector sensor. In this paper, we propose neural networks to determine the number of the sources and estimate the angle of arrival of each source, based on the covariance matrix extracted from received data. Also, we provi…
Polyphonic sound event detection and direction-of-arrival estimation require different input features from audio signals. While sound event detection mainly relies on time-frequency patterns, direction-of-arrival estimation relies on magnitude or phase differences between microphones. Previous approaches use the same input features for sound event detection and direction-of-arrival estimation, and train the two tasks jointly or in a two-stage transfer-learning manner. We propose a two-step approach that decouples the learning of the sound event detection and directional-of-arrival estimation s…
In this paper, we present a novel approach to compute ambiguities in thinned uniform linear arrays, i.e., sparse non-uniform linear arrays, via a mixed-integer program. Ambiguities arise when there exists a set of distinct directions-of-arrival, for which the corresponding steering matrix is rank-deficient and are associated with nonunique parameter estimation. Our approach uses Young tableaux for which a submatrix of the steering matrix has a vanishing determinant, which can be expressed through vanishing sums of unit roots. Each of these vanishing sums then corresponds to an ambiguous set of…
The estimation of direction of arrivals with help of $TV$-minimization is studied. Contrary to prior work in this direction, which has only considered certain antenna placement designs, we consider general antenna geometries. Applying the soft-recovery framework, we are able to derive a theoretic guarantee for a certain direction of arrival to be approximately recovered. We discuss the impact of the recovery guarantee for a few concrete antenna designs. Additionally, numerical simulations supporting the findings of the theoretical part are performed.
High-performance computing of array signal processing problems is a critical task as real-time system performance is required for many applications. Noise subspace-based Direction-of-Arrival (DOA) estimation algorithms are popular in the literature since they provide higher angular resolution and higher robustness. In this study, we investigate various optimization strategies for high-performance DOA estimation on GPU and comparatively analyze alternative implementations (MATLAB, C/C++ and CUDA). Experiments show that up to 3.1x speedup can be achieved on GPU compared to the baseline multi-thr…
In contrast to other spread-spectrum techniques, wideband pulse trains with relatively low pulse arrival rates may be considered unsuitable for covert communications. The high crest factor of such trains can be extremely burdensome for the transmitter hardware, and it makes the pulse trains easily detectable even at very low signal-to-noise ratios. In addition, it may appear that sharing the wideband channel by multiple users would require explicit allocation of the pulse arrival times for each sub-channel, which would be impractical in most cases. On the other hand, messaging by wideband puls…
Super-resolution Multi-signal Direction-of-Arrival Estimation by Hankel-structured Sensing and Decomposition
Center for Connected Autonomy and AI（连接自主与人工智能中心）；Dept. of Electrical Engineering and Computer Science（电气工程与计算机科学系）；Florida Atlantic University（佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）；AFRL/RI（空军研究实验室/RI）
In this paper, a deep learning approach is presented for direction of arrival estimation using automotive-grade ultrasonic sensors which are used for driving assistance systems such as automatic parking. A study and implementation of the state of the art deterministic direction of arrival estimation algorithms is used as a benchmark for the performance of the proposed approach. Analysis of the performance of the proposed algorithms against the existing algorithms is carried out over simulation data as well as data from a measurement campaign done using automotive-grade ultrasonic sensors. Both…
This work analyses the performance-complexity tradeoff for different direction of arrival (DoA) estimation techniques. Such tradeoff is investigated taking into account uniform linear array structures. Several DoA estimation techniques have been compared, namely the conventional Delay-and-Sum (DS), Minimum Variance Distortionless Response (MVDR), Multiple Signal Classifier (MUSIC) subspace, Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Unitary-ESPRIT and Fourier Transform method (FT-DoA). The analytical formulation of each estimation technique as well the compar…
The problem of off-grid direction-of-arrival (DOA) estimation is investigated. We develop a grid-based method to jointly estimate the closest spatial frequency (the sine of DOA) grids, and the gaps between the estimated grids and the corresponding frequencies. By using a second-order Taylor approximation, the data model under the framework of joint-sparse representation is formulated. We point out an important property of the signals of interest in the model, namely the proportionality relationship, which is empirically demonstrated to be useful in the sense that it increases the probability o…
Institute of Digital Communication Systems, Ruhr University Bochum（鲁尔大学波鸿数字通信系统研究所）；Department of Electrical and Computer Engineering, Purdue University（普渡大学电气与计算机工程系）
We present a MUSIC-based Direction of Arrival (DOA) estimation strategy using small antenna arrays, via employing deep learning for reconstructing the signals of a virtual large antenna array. Not only does the proposed strategy deliver significantly better performance than simply plugging the incoming signals into MUSIC, but surprisingly, the performance is also better than directly using an actual large antenna array with MUSIC for high angle ranges and low test SNR values. We further analyze the best choice for the training SNR as a function of the test SNR, and observe dramatic changes in …
In this paper, direction-of-arrival estimation using nested array is studied in the framework of sparse signal representation. With the vectorization operator, a new real-valued nonnegative sparse signal recovery model which has a wider virtual array aperture is built. To leverage celebrated compressive sensing algorithms, the continuous parameter space has to be discretized to a number of fixed grid points, which inevitably incurs modeling error caused by off-grid gap. To remedy this issue, a block alternating optimization method is put forth that jointly estimates the sparse signal and refin…
İstanbul Technical University（伊斯坦布尔理工大学）；Queen’s University（女王大学）；Polytechnique Montréal（蒙特利尔理工学院）
In this paper, we present a single-pixel compressive direction of arrival (DoA) estimation technique leveraging a graph attention network (GAT)-based deep-learning framework. The physical layer compression is achieved using a coded-aperture technique, probing the spectrum of far-field sources that are incident on the aperture using a set of spatio-temporally incoherent modes. This information is then encoded and compressed into the channel of the coded-aperture. The coded-aperture is based on a metasurface antenna design and it works as a receiver, exhibiting a single-channel and replacing the…
This paper presents an efficient optimization technique for super-resolution two-dimensional (2D) direction of arrival (DOA) estimation by introducing a new formulation of atomic norm minimization (ANM). ANM allows gridless angle estimation for correlated sources even when the number of snapshots is far less than the antenna size, yet it incurs huge computational cost in 2D processing. This paper introduces a novel formulation of ANM via semi-definite programming, which expresses the original high-dimensional problem by two decoupled Toeplitz matrices in one dimension, followed by 1D angle est…
An attitude of satellite is not always static, sometimes it moves randomly and the antenna pointing of satellite is harder to achieve line of sight communication to other satellite when it is outage by tumbling effect. In order to determine an appropriate direction of satellite antenna in inter-satellite link, this paper analyze estimation performance of the direction of arrival (DoA) using MUSIC algorithm from connected satellite signal source. It differs from optical measurement, magnetic field measurement, inertial measurement, and global positioning system (GPS) attitude determination. The…
Estimating the directions of arrival (DOAs) of multiple sources from a single snapshot obtained by a coherent antenna array is a well-known problem, which can be addressed by sparse signal reconstruction methods, where the DOAs are estimated from the peaks of the recovered high-dimensional signal. In this paper, we consider a more challenging DOA estimation task where the array is composed of non-coherent sub-arrays (i.e., sub-arrays that observe different unknown phase shifts due to using low-cost unsynchronized local oscillators). We formulate this problem as the reconstruction of a joint sp…
Optimal Maximum Likelihood (ML), narrow-band direction finding cannot be easily initialized in coherent and low signal to noise ratio environments. Sparse under-determined solvers are considered as viable solutions to this problem, since they drastically reduce the dimensionality of the search space by exploiting the array model sparseness. However, because of quantized locations, conventional sparse solvers present some ambiguity problems. In this work, we propose a novel boosting scheme for ML-type estimators, referred to as Parallel BOOSTer (P-BOOST), where a set of generalized MUSIC soluti…
