Source Localization Accuracy Research Articles

High-Resolution EEG Source Localization in Segmentation-Free Head Models Based on Finite-Difference Method and Matching Pursuit Algorithm.

Electroencephalogram (EEG) is a method to monitor electrophysiological activity on the scalp, which represents the macroscopic activity of the brain. However, it is challenging to identify EEG source regions inside the brain based on data measured by a scalp-attached network of electrodes. The accuracy of EEG source localization significantly depends on the type of head modeling and inverse problem solver. In this study, we adopted different models with a resolution of 0.5 mm to account for thin tissues/fluids, such as the cerebrospinal fluid (CSF) and dura. In particular, a spatially dependent conductivity (segmentation-free) model created using deep learning was developed and used for more realist representation of electrical conductivity. We then adopted a multi-grid-based finite-difference method (FDM) for forward problem analysis and a sparse-based algorithm to solve the inverse problem. This enabled us to perform efficient source localization using high-resolution model with a reasonable computational cost. Results indicated that the abrupt spatial change in conductivity, inherent in conventional segmentation-based head models, may trigger source localization error accumulation. The accurate modeling of the CSF, whose conductivity is the highest in the head, was an important factor affecting localization accuracy. Moreover, computational experiments with different noise levels and electrode setups demonstrate the robustness of the proposed method with segmentation-free head model.

All-phase fast Fourier transform and multiple cross-correlation analysis based on Geiger iteration for acoustic emission sources localization in complex metallic structures

Nowadays, the localization and identification of acoustic emission (AE) source is widely utilized to structural health monitoring (SHM) of complex metallic structures. However, traditional AE source localization methods are generally difficult to localize and characterize AE sources in plate-like structure that has complex geometric features. To alleviate the problem, a novel AE source localization method based on all-phase fast Fourier transform and multiple cross-correlation analysis is proposed in this article. Moreover, least squares and Geiger iteration algorithm are applied to determine the coordinates of AE sources. In addition, an improved Bayesian information criterion (BIC) version named autoregressive BIC (i.e., AR-BIC) is presented to increase the accuracy of source localization. To validate the performance of the proposed approach, the classical pencil lead break tests are carried out on a 316 L stainless steel with 10 laser cladding layers. Experimental waveforms are generated from AE sources near laser cladding layers, the surface of the structure, and on its edges. Additionally, to evaluate the performance of the proposed approach in three-dimensional AE source localization, an industrial storage tank is used to acquire three-dimensional AE sources through manually striking. Finally, to further verify the effectiveness of the proposed approach, comparisons with conventional AE source location methods (i.e., PAC or SAMOS AE acquisition system, Newton’s method, and multiple cross-correlation based on Geiger algorithm) and two representative approaches (i.e., deep learning and Bayesian methodology) for localizing AE sources generated by complex metallic structures are conducted. The comparative results demonstrate the effectiveness and superiority of the proposed method in AE-based SHM of complex metallic structures.

Ensemble multi-modal brain source localization using theory of evidence

The primary aim in pre-surgical evaluations in patients with neurological disorders such as epilepsy is determining the precise location of the cortical region responsible for the malfunctions which is called source localization. Different modalities unravel different views of brain activity. Combining these complementary aspects of the brain yields more accurate source localization.In this paper, a method is proposed for combining localization methods in different modalities based on the theory of evidence, the result of some localization methods in modalities are integrated using weights in accordance to their relative performance and are combined using Dempster's rule of combination and is used for the case of EEG and MEG combinatory source localization.The proposed method is evaluated on simulated realistic MEG and EEG data and in different noise and artifact levels and finds the zone of interest in a more accurate way. The AUC criterion is used as a metric for the evaluation. The proposed method results in better localization accuracy in terms of AUC showing the combination of modalities could lead to superior performance.Combining two modalities needs an exact knowledge of the phenomena happening in each modality, making the combination difficult. Here rather of combining EEG and MEG information at the initial phase, the results of some source localization techniques on both modalities are combined. In spite of the simplicity of use, the experimental results of combination showed improvement in epileptic source localization accuracy even in cases that one method shows poor performance. Using the proposed method any number of modalities can be combined without complex consideration and a better brain source localization could be obtained.

A data complementary method for sound source localization based on four-element microphone array groups

Data loss or distortion has adverse effects on sound source localization (SSL) accuracy and stability. Based on the sound source azimuth estimation algorithm, this paper establishes a model of a single four-element main microphone array, and proposes a data complementary method of SSL. The calculation formula of sound source coordinates is derived from the main array. Then, the effectiveness of the proposed algorithm is verified by the study of array parameters. Besides the sound velocity and elevation angle, the array parameters also include the distance between two array elements. Array groups are established surrounding the main array on the horizontal plane, through which the localization data are collected and complementarily processed, so as to relocate the sound source. The results show that the coordinate error rate against the theoretical data is approximately 5% and the error rate of the angle is approximately 0.5%. The SSL efficiency is well guaranteed.

A novel beamformer-based imaging of phase–amplitude coupling (BIPAC) unveiling the inter-regional connectivity of emotional prosody processing in women with primary dysmenorrhea

Objective. Neural communication or the interactions of brain regions play a key role in the formation of functional neural networks. A type of neural communication can be measured in the form of phase–amplitude coupling (PAC), which is the coupling between the phase of low-frequency oscillations and the amplitude of high-frequency oscillations. This paper presents a beamformer-based imaging method, beamformer-based imaging of PAC (BIPAC), to quantify the strength of PAC between a seed region and other brain regions. Approach. A dipole is used to model the ensemble of neural activity within a group of nearby neurons and represents a mixture of multiple source components of cortical activity. From ensemble activity at each brain location, the source component with the strongest coupling to the seed activity is extracted, while unrelated components are suppressed to enhance the sensitivity of coupled-source estimation. Main results. In evaluations using simulation data sets, BIPAC proved advantageous with regard to estimation accuracy in source localization, orientation, and coupling strength. BIPAC was also applied to the analysis of magnetoencephalographic signals recorded from women with primary dysmenorrhea in an implicit emotional prosody experiment. In response to negative emotional prosody, auditory areas revealed strong PAC with the ventral auditory stream and occipitoparietal areas in the theta–gamma and alpha–gamma bands, which may respectively indicate the recruitment of auditory sensory memory and attention reorientation. Moreover, patients with more severe pain experience appeared to have stronger coupling between auditory areas and temporoparietal regions. Significance. Our findings indicate that the implicit processing of emotional prosody is altered by menstrual pain experience. The proposed BIPAC is feasible and applicable to imaging inter-regional connectivity based on cross-frequency coupling estimates. The experimental results also demonstrate that BIPAC is capable of revealing autonomous brain processing and neurodynamics, which are more subtle than active and attended task-driven processing.

Calibration of a Coil Array Geometry Using an X-Ray Computed Tomography

Sensor layout of biomagnetic measurement systems is measured using a multiple coil array that generates a magnetic signal. However, the results of the sensor array measurement included the error of the coil array because the coil array was not calibrated. In this paper, we proposed a calibration method to obtain the effective geometry and uncertainty of the coil array. The calibration was performed based on the X-ray CT measurements and numerical analysis of the position and shape of the coils. The differences between the designed and calibrated coil array geometries were 0.6 mm, 0.7°, and 0.3 mm with respect to the center position, orientation of the normal vector, and radius of the coils, respectively. The uncertainty of the calibration was 0.3 mm and 1.70 in terms of the dimension and orientation, respectively. We measured the sensor array layout of a magnetoencephalography (MEG) system using a calibrated coil array geometry. The source localization accuracy of the MEG system was improved compared with that of the sensor array layout obtained using the designed coil array geometry. We revealed the necessity of calibrating the coil array, regardless of the precision of the fabrication.

Sky localization of space-based gravitational wave detectors

Localizing the sky position of the gravitational wave source is a key scientific goal for gravitational wave observations. Employing the Fisher information matrix approximation, we compute the angular resolutions of LISA and TianQin, two planned space-based gravitational wave detectors and examine how detectors' configuration properties, such as the orientation change of the detector plane, heliocentric or geocentric motion and the arm length etc. affect the accuracy of source localization. We find that the amplitude modulation due to the annual changing orientation of the detector plane helps LISA get better accuracy in the sky localization and better sky coverage at frequencies below several mHz, and its effect on TianQin is negligible although the orientation of TianQin's detector plane is fixed. At frequencies above roughly 30mHz, TianQin's ability in the sky localization is better than LISA. Further we explore potential space detector networks for fast and accurate localization of the gravitational wave sources. The LISA-TianQin network has better ability in sky localization for sources with frequencies in the range 1-100 mHz and the network has larger sky coverage for the angular resolution than the individual detector.

Localization and characterization of rotating noise sources on axial fans by means of an irregularly shaped microphone array

Aerodynamic noise emitted by low-speed axial fans has been receiving increasing attention in various sectors of high societal impact, such as automotive and HVAC systems. In this framework, turbulence interaction, flow non-uniformities, trailing-edge boundary layer fluctuations and blade-tip leakages are different mechanisms generating aeroacoustic sources on the rotating blades and contributing to the overall emitted sound. An accurate localization of the sound sources on the surface of the blade is instrumental in separating and isolating these contributions and, therefore, in designing novel sound mitigation concepts. The main objective of this paper is to present an inexpensive and efficient way to isolate and quantify the noise generating mechanisms on rotating blades by means of a irregularly shaped microphone array. The technique is based on ROtating Source Identifier (ROSI) and has been implemented and validated at the von Karman Institute for Fluid Dynamics (VKI). Simulated benchmark datasets that refer to rotating point sources emitting white noise have been considered for the validation of the method. The accuracy in the source localization and in the source strength reconstruction has been evaluated for a fixed and a variable angular rate. Moreover, the algorithm implementation has been parallelized with the purpose of reducing its computational time, which represents the main drawback of ROSI. Finally, the developed technique has been applied to measure the noise sources generated by a forward-skewed subsonic axial fan operated at maximum efficiency. In this case, it has been possible to successfully localize and characterize the major noise sources on the blades. Although further investigation will be necessary to gain better insight into the topic, the present work constitutes an important step for a better understanding of the physical phenomena occurring in the noise generation of an axial fan.

Study on the rupture properties and automatic identification model of micro-earthquakes and blasting events in a coal mine

Source location is the key step of microseismic monitoring. The monitored microseismic signals are often mixed with unrecognized blasting interference signals, which affect the results of microseismic monitoring and location. Therefore, it is very important to extract the characteristic parameter information to identify the microseismic signal and blasting signal. The rupture processes during micro-earthquakes and blasting events in a coal mine are complicated and have different characteristics, which seriously affects the safety of coal mine. To quantify the seismic source properties of micro-earthquakes and blasting events in coal mines, and further distinguish between micro-earthquakes and blasting events, the source parameters of micro-earthquakes and blasting events in coal mine were obtained, and the differences between micro-earthquakes and blasting events were investigated by comparing the characteristics of their respective source parameters. Firstly, the corner frequency f0, spectral level Ω0, seismic moment M0, source energy E, source radius R, stress drop △σ, apparent stress σa, and magnitude (Mw and ML) of micro-earthquakes and blasting events in Qianqiu coal mine were calculated using the Brune model and grid-search method; then, the relationship between seismic moment and the other source parameters was analysed, the differences between micro-earthquakes and blasting events were studied based on the above source parameters, and the automatic identification model of micro-seismic and blast signals thus established; finally, the local magnitude was calculated and the relationship between moment magnitude and local magnitude analysed. The magnitudes of micro-earthquakes and blasting events are determined based on the calculated Mw and ML. The above analysis can be used to determine and quantify the seismic source properties and scale of micro-earthquakes and blasting events, and further distinguish micro-earthquakes from blasting events effectively to ensure the accuracy of source location and allow implementation of effective control measures.

Study on the Localization Method of Multi-Aperture Acoustic Array Based on TDOA

When the background noise is large or the sound source is far away from the microphone array, the localization accuracy of target sound sources will decrease dramatically. In order to solve this problem, a localization method of multi-aperture acoustic array based on time difference of arrival(TDOA) is proposed. The multi-aperture acoustic array is constructed by two small sub microphone arrays, which is supposed to surpass the performance of the equivalent large array composed of all microphones. The positions of the target sound source in two local coordinates are separately estimated by the two sub microphone arrays based on the generalized trust-region sub-problem in the modified polar representation (GTRS-MPR) method. Through the space coordinate transformation, the estimated two positions of the target sound source in the two local coordinates can be transferred into one global coordinate. To optimize the final estimated position of the target sound source by the multi-aperture acoustic array, two spatial lines are formed between the reference microphones of the two sub-arrays and the estimated two sources' positions in the global coordinate, and a search algorithm of shortest distance point based on the least-square method is proposed to fuse the localization results of the two sub-arrays. A simulation and an experimental platform are set up to verify the proposed method. The results show that the proposed method has higher localization accuracy compared with the existing methods. Especially, the accuracy of range estimation is greatly improved, which will be more suitable for the far-field sound source localization.

A multi-point crosstalk attack detection and localization scheme based on hierarchical PCE in multi-domain optical networks

With the limited number of detection devices and the uncertainty of crosstalk attack source localization, how to propose an effective detection and localization scheme for multipoint crosstalk attack problem in multi-domain optical networks is an important problem that needs to be solved. A new multipoint crosstalk attack detection and location scheme HP-CADL (Hierarchical PCE-Crosstalk Attack Detection and Location) for multi-domain optical networks based on hierarchical PCE is proposed by using the monitoring point selection strategy of local immune algorithm and distributed localization considering continuous parametric analysis. VPI simulation results show that the scheme not only achieves low-cost monitoring and detection and accurate localization of multiple crosstalk attack sources, but also achieves higher accuracy and better performance than other similar schemes in the same multi-domain environment.

Narrowband multi-source direction-of-arrival estimation in the spherical harmonic domain.

A conventional approach to wideband multi-source (MS) direction-of-arrival (DOA) estimation is to perform single source (SS) DOA estimation in time-frequency (TF) bins for which a SS assumption is valid. Such methods use the W-disjoint orthogonality (WDO) assumption due to the speech sparseness. As the number of sources increases, the chance of violating the WDO assumption increases. As shown in the challenging scenarios with multiple simultaneously active sources over a short period of time masking each other, it is possible for a strongly masked source (due to inconsistency of activity or quietness) to be rarely dominant in a TF bin. SS-based DOA estimators fail in the detection or accurate localization of masked sources in such scenarios. Two analytical approaches are proposed for narrowband DOA estimation based on the MS assumption in a bin in the spherical harmonic domain. In the first approach, eigenvalue decomposition is used to decompose a MS scenario into multiple SS scenarios, and a SS-based analytical DOA estimation is performed on each. The second approach analytically estimates two DOAs per bin assuming the presence of two active sources per bin. The evaluation validates the improvement to double accuracy and robustness to sensor noise compared to the baseline methods.

Bearing estimation of screams using a volumetric microphone array mounted on a UAV

The use of Unmanned Aerial Vehicles (UAVs), also called drones, is increasing for emergency and rescue operations. UAVs can be equipped with state-of-the-art technology to enable surveillance and provide quick situational awareness. Considering that UAVs better reach inaccessible and larger areas than other types of vehicles, such as Unmanned Ground Vehicles (UGVs), they could be used to locate people during catastrophes, and support the rescue team. For this purpose, an automatic and accurate detection, bearing estimation, and source localization system focused on specific audio events, such as persons’ screams, is being developed at Fraunhofer FKIE. The solve those tasks, the system uses a particular volumetric array of MEMS microphones, called “Crow’s Nest Array,” combined with advanced array processing techniques, such as beamforming. The spatial distribution and number of microphones in arrays have a crucial influence on the bearing estimation of audio events; therefore, in this paper, microphone array configurations are described, and their performance in different open field experiments is presented.

First-Arrival Picking for Microseismic Monitoring Based on Deep Learning

In microseismic monitoring, achieving an accurate and efficient first-arrival picking is crucial for improving the accuracy and efficiency of microseismic time-difference source location. In the era of big data, the traditional first-arrival picking method cannot meet the real-time processing requirements of microseismic monitoring process. Using the advanced idea of deep learning-based end-to-end classification and the prominent feature extraction advantages of a fully convolution neural network, this paper proposes a first-arrival picking method of effective signals for microseismic monitoring based on UNet++ network, which can significantly improve the accuracy and efficiency of first-arrival picking. In this paper, we first introduced the methodology of the UNet++-based picking method. And then, the performance of the proposed method is verified by the experiments with finite-difference forward modeling simulated signals and actual microseismic records under different signal-to-noise ratios, and finally, comparative experiments are performed using the U-Net-based first-arrival picking algorithm and the Short-Term Average to Long-Term Average (STA/LTA) algorithm. The results show that compared to the U-Net network, the proposed method can obviously improve the first-arrival picking accuracy of the low signal-to-noise ratio microseismic signals, achieving significantly higher accuracy and efficiency than the STA/LTA algorithm, which is famous for its high efficiency in traditional algorithms.

NMF-weighted SRP for multi-speaker direction of arrival estimation: robustness to spatial aliasing while exploiting sparsity in the atom-time domain

Localization of multiple speakers using microphone arrays remains a challenging problem, especially in the presence of noise and reverberation. State-of-the-art localization algorithms generally exploit the sparsity of speech in some representation for this purpose. Whereas the broadband approaches exploit time-domain sparsity for multi-speaker localization, narrowband approaches can additionally exploit sparsity and disjointness in the time-frequency representation. Broadband approaches are robust to spatial aliasing but do not optimally exploit the frequency domain sparsity, leading to poor localization performance for arrays with short inter-microphone distances. Narrowband approaches, on the other hand, are vulnerable to spatial aliasing, making them unsuitable for arrays with large inter-microphone spacing. Proposed here is an approach that decomposes a signal spectrum into a weighted sum of broadband spectral components (atoms) and then exploits signal sparsity in the time-atom representation for simultaneous multiple source localization. The decomposition into atoms is performed in situ using non-negative matrix factorization (NMF) of the short-term amplitude spectra and the localization estimate is obtained via a broadband steered-response power (SRP) approach for each active atom of a time frame. This SRP-NMF approach thereby combines the advantages of the narrowband and broadband approaches and performs well on the multi-speaker localization task for a broad range of inter-microphone spacings. On tests conducted on real-world data from public challenges such as SiSEC and LOCATA, and on data generated from recorded room impulse responses, the SRP-NMF approach outperforms the commonly used variants of narrowband and broadband localization approaches in terms of source detection capability and localization accuracy.

Local Explosion Detection and Infrasound Localization by Reverse Time Migration Using 3-D Finite-Difference Wave Propagation

Infrasound data are routinely used to detect and locate volcanic and other explosions, using both arrays and single sensor networks. However, at local distances (<15 km) topography often complicates acoustic propagation, resulting in inaccurate acoustic travel times leading to biased source locations when assuming straight-line propagation. Here we present a new method, termed Reverse Time Migration-Finite-Difference Time Domain (RTM-FDTD), that integrates numerical modeling into the standard RTM back-projection process. Travel time information is computed across the entire potential source grid via FDTD modeling to incorporate the effects of topography. The waveforms are then back-projected and stacked at each grid point, with the stack maximum corresponding to the likely source. We apply our method to three volcanoes with different network configurations, source-receiver distances, and topography. At Yasur Volcano, Vanuatu, RTM-FDTD locates explosions within ∼20 m of the source and differentiates between multiple vents. RTM-FDTD produces a more accurate location for the two Yasur subcraters than standard RTM and doubles the number of detected events. At Sakurajima Volcano, Japan, RTM-FDTD locates the source within 50 m of the active vent despite notable topographic blocking. The RTM-FDTD location is similar to that from the Time Reversal Mirror method, but is more computationally efficient. Lastly, at Shishaldin Volcano, Alaska, RTM and RTM-FDTD both produce realistic source locations (<50 m) for ground-coupled airwaves recorded on a four-station seismic network. We show that RTM is an effective method to detect and locate infrasonic sources across a variety of scenarios, and by integrating numerical modeling, RTM-FDTD produces more accurate source locations and increases the detection capability.

Determination of the time-dependent moment tensor using time reverse imaging

We have developed an approach to determine the time-dependent moment tensor and the origin time in addition to commonly derived locations of seismic events using time reverse imaging (TRI). It is crucial to locate and characterize the occurring microseismicity without making a priori assumptions about the sources to fully understand the subsurface processes inducing seismicity. Low signal-to-noise ratios (S/Ns) often force standard methods to make assumptions about sources or only characterize selected larger magnitude events. In TRI, microearthquakes are located by back propagating the full-recorded time-reversed wavefield through a velocity model until it ideally convergences on the source location. Therefore, it is less affected by low S/Ns and potentially locates and characterizes most of the events. After distinguishing artificial convergence locations from source locations, the quality of the source location and the moment tensors are derived by recording the stress at the determined source locations during the back propagation of the time-reversed wavefield. A robust workflow is derived using synthetic test cases in a realistic scenario with velocity models that only approximate the true velocity model and/or noisy displacement traces. The influence of a rudimentary velocity model on the source-location accuracy and characterization is significant. Our workflow handles these less-than-optimal station distributions and velocity models. Finally, the derived workflow is successfully applied to field data recorded at the geothermal field of Los Humeros, Mexico. Although only a 1D velocity model is currently available, source locations and (time-dependent) moment tensors could be determined for selected events.

Geolocation of RFIs by Multiple Snapshot Difference Method for Synthetic Aperture Interferometric Radiometer

The presence of unauthorized radio frequency interference (RFI) sources seriously affects the retrieval of brightness temperature of a synthetic aperture interferometric radiometer (SAIR). Postobservation RFI geolocation is important for improving the RFI situation hereafter and mitigating the impact of the identified RFIs. Previous works have demonstrated the potential of using high-/super-resolution direction-of-arrival (DOA) estimation techniques to achieve accurate localization of RFI sources in SAIR imagery. In this article, a multiple snapshot difference method is proposed to further reduce the RFI source geolocation bias. The covariance matrices of the consecutive snapshots with power changed RFIs are picked out and subtracted to cancel out the background scene. A MUSIC-based DOA algorithm is developed. Numerical simulations validate the theoretical correctness and the practical effectiveness of the proposed method.

Analysis of Hydroacoustic Signals Associated to the Loss of the Argentinian ARA San Juan Submarine

On November 15, 2017, an event related to the disappearance of the Argentine military submarine ARA San Juan was detected by two hydrophone triplet stations of the IMS network, established to enforce the nuclear test ban treaty (CTBT). From the two direct hydroacoustic arrivals recorded at 6000 and 8000 km from the localized wreckage, calculated location based on hydroacoustic data only is poorly constrained, and the associated uncertainties are large. In an attempt to interpret the recorded signals, an air dropped calibration grenade was conducted by the Argentine Navy two weeks later, on December 1, 2017, near the last known position of the submarine. From the comparison of temporal and spectral features of both events, we confirm the impulsive nature of the San Juan event. Array processing was performed with a progressive multi-channel correlation method (PMCC). Fine propagation details of direct arrivals are very well resolved in time-frequency space and thirteen secondary arrivals are revealed for the San Juan event, within the fifteen minutes following direct arrivals. The detections presented in this paper were calculated with DTK-PMCC software embedded in the NDC-In-A-Box virtual machine, and can be reproduced by any CTBTO principal user (Member State user which can access raw waveform data and data bulletins). All the identified late arrivals are associated to reflections or refractions from seamounts, islands and the South American continental Slope. The accurate identification of all the reflectors allows to significantly improve the source location accuracy: 95% confidence ellipse area has been reduced by a factor of 100 compared to location obtained from direct arrivals only, and the estimated location is 3.5 km from the known location of the wreckage. The originality of the relocation method is that it is based on the joint inversion of both San Juan and calibration events unknown parameters, and from the selection of only a well-chosen subset of secondary arrivals. Its calculation did not require either the need of advanced oceanographic specifications, or sophisticated methods requiring heavy computational means. Finally, a detailed cepstral analysis of the direct and secondary arrivals has allowed to detect the existence of a second impulse (doublet) in the signals associated to both San Juan and calibration events. Unlike the calibration event, the anisotropic character of the delays measured from the San Juan cepstra suggests that the 15 November signal was generated by two impulsive acoustic sources closely separated in space and time over scales comparable to the size of the submarine. This study demonstrates the capability of the hydroacoustic component of the IMS network to accomplish its mission of Comprehensive Nuclear-Test-Ban Treaty monitoring.

Square-shaped sensor clusters for acoustic source localization in anisotropic plates by wave front shape-based approach

Various techniques have emerged in the past few years for localizing the acoustic source in an anisotropic plate. The wave front shape-based approach, one of the recent additions to this field of research, has the advantage of circumventing the unrealistic assumption of a straight line wave propagation path through an anisotropic medium. In their most recent versions, the two major wave front shape-based techniques (i.e., the ellipse- and the parametric curve-based techniques) are applicable to the situations with an unknown orientation of the axes of symmetry of an anisotropic plate. However, this approach still relies on estimating the angle of wave-incidence at a given location of the plate via a single L-shaped sensor cluster. The incidence angle so obtained may deviate significantly from the true angle of wave arrival. To improve the estimation accuracy of the incidence angle, in the present study a square-shaped cluster composed of four densely-spaced sensors forming the four vertices of a square is proposed to be installed at the location of interest. Essentially, a square-shaped sensor cluster contains four L-shaped clusters oriented in different directions. A formulation to estimate the angle of incidence from the signal data acquired by a squared-shaped cluster is presented. The wave front shape-based approach can then be applied to estimate the acoustic source location. A numerical study is conducted to illustrate the proposed methodology. Performance comparisons between square- and L-shaped clusters reveal that in general the square-shaped clusters lead to more accurate source location estimates than the L-shaped clusters.