Three-dimensional Source Localization Research Articles

Formulas for three-dimensional source localization using multipath time delays measured by asynchronous distributed sensors in deep water

In this study, three-dimensional source localization is investigated based on time delays between the direct (D) and surface-reflected (SR) paths measured using asynchronous distributed sensors in the deep-water reliable-acoustic-path environment. Instead of matching replicas, we develop computationally efficient formulas to locate the source. The formulas are derived by first pseudolinearizing the measurement model of the D–SR time delay and then solving the obtained pseudolinear system of equations using the instrumental variable technique. Furthermore, the Cramér–Rao lower bound of the investigated problem is derived theoretically. Monte Carlo simulations are performed to demonstrate the performance of the proposed formulas. The results show that the formulas can provide a localization accuracy comparable to that of the matching algorithm when the measurement noise level is low, while exhibiting an acceptable inferiority at high noise levels. Finally, the feasibility of the proposed formulas is verified using experimental data acquired in the western Pacific. In all experimental test groups, the localization biases of the proposed formulas do not exceed 250 m in the horizontal plane and are less than 5% for depth estimation.

Three-Dimensional Source Localization Based on 1-D AOA Measurements: Low-Complexity and Effective Estimator

Three-Dimensional Source Localization Based on 1-D AOA Measurements: Low-Complexity and Effective Estimator

Three-Dimensional Source Localization with Sparse Symmetric Cross Array.

Three-dimensional (3-D) localization information, including elevation angle, azimuth angle, and range, is important for locating a single source with spherical wave-fronts. Aiming to reduce the high computational complexity of the classical 3-D multiple signal classification (3D-MUSIC) localization method, a novel low-complexity reduced-dimension MUSIC (RD-MUSIC) algorithm based on the sparse symmetric cross array (SSCA) is proposed in this article. The RD-MUSIC converts the 3-D exhaustive search into three one-dimensional (1-D) searches, where two of them are obtained by a two-stage reduced-dimension method to find the angles, and the remaining one is utilized to obtain the range. In addition, a detailed complexity analysis is provided. Simulation results demonstrate that the performance of the proposed algorithm is extremely close to that of the existing rank-reduced MUSIC (RARE-MUSIC) and 3D-MUSIC algorithms, whereas the complexity of the proposed method is significantly lower than that of the others, which is a big advantage in practice.

Three-dimensional source localization using sparse Bayesian learning on a spherical microphone array.

The identification of acoustic sources in a three-dimensional (3D) domain based on measurements with an array of microphones is a challenging problem: it entails the estimation of the angular position of the sources (direction of arrival), distance relative to the array (range), and the quantification of the source amplitudes. A 3D source localization model using a rigid spherical microphone array with spherical wave propagation is proposed. In this study, sparse Bayesian learning is used to perform localization in 3D space and examine the use of principal component analysis to denoise the measurement data. The performance of the proposed method is examined numerically and experimentally, which is tested both in a free-field and in a reverberant environment. The numerical and experimental investigations demonstrate that the approach offers accurate localization in a 3D domain, resolving closely spaced sources and making it possible to identify sources located at different ranges.

Efficient source positioning method based on two stations using GROA and AOA measurements

By utilising the gain ratio of arrival (GROA) and angles of arrival (AOAs), three-dimensional source localisation with only two stations is studied. The weighted least squares (WLS) algorithm yields the typical closed-form solution, which is obtained by first establishing a set of linear equations and then determining the source position. However, the WLS solution exhibits poor performance at high noise levels. Hence, an efficient parameter augmented constraint method is proposed by extending the parameter space. The proposed method minimises the cost function by imposing a quadratic constraint such that the expectation of the cost function will attain its minimum value at the true solution. In addition, the proposed method yields an explicit algebraic solution and does not depend on a good initial guess; thus, there is no convergence problem. Theoretical analysis and simulation results verify the effectiveness of the proposed method.

Z-Score EEG Biofeedback: Past, Present, and Future

Human electroencephalogram (EEG) biofeedback (neurofeedback) started in the 1940s using one EEG recording channel, then four channels in the 1990s, and in 2004, expanded to 19 channels using Low Resolution Electromagnetic Tomography (LORETA) of the microampere three-dimensional current sources of the EEG. In 2004–2006 the concept of a real-time comparison of the EEG to a healthy reference database was developed and tested using surface EEG z score neurofeedback based on a statistical bell curve called real-time z scores. The real-time or live normative reference database comparison was developed to help reduce the uncertainty of what threshold to select to activate a feedback signal and to unify all EEG measures to a single value (i.e., the distance from the mean of an age-matched reference sample). In 2009 LORETA z score neurofeedback further increased specificity by targeting brain network hubs referred to as Brodmann areas. A symptom checklist program to help link symptoms to dysregulation of brain networks based on fMRI and positron emission tomography (PET) and neurology was created in 2009. The symptom checklist and National Institutes of Health–based networks linking symptoms to brain networks grew out of the human brain mapping program started in 1990 that continues today. A goal is to increase specificity of EEG biofeedback by targeting brain network hubs and connections between hubs likely linked to the patient's symptoms. Developments first introduced in 2017 provide increased resolution of three-dimensional source localization with 12,700 voxels using swLORETA with the capacity to conduct cerebellar neurofeedback and neurofeedback of subcortical brain hubs such as the thalamus, amygdala, and habenula. Future applications of swLORETA z score neurofeedback represent another example of the transfer of knowledge gained by the human brain mapping initiatives to further aid in helping people with cognition problems as well as balance problems and parkinsonism. A brief review of the past, present, and future predictions of z score neurofeedback are discussed with special emphasis on new developments that point toward a bright and enlightened future in the field of EEG biofeedback.

New approaches for automatic threedimensional source localization of acoustic emissions – Applications to concrete specimens

The task of locating a source in space by measuring travel time differences of elastic or electromagnetic waves from the source to several sensors is evident in varying fields. The new concepts of automatic acoustic emission localization presented in this article are based on developments from geodesy and seismology. A detailed description of source location determination in space is given with the focus on acoustic emission data from concrete specimens. Direct and iterative solvers are compared. A concept based on direct solvers from geodesy extended by a statistical approach is described which allows a stable source location determination even for partly erroneous onset times. The developed approach is validated with acoustic emission data from a large specimen leading to travel paths up to 1m and therefore to noisy data with errors in the determined onsets. The adaption of the algorithms from geodesy to the localization procedure of sources of elastic waves offers new possibilities concerning stability, automation and performance of localization results. Fracture processes can be assessed more accurately.

Recursive source localisation by time difference of arrival sensor networks with sensor position uncertainty

In a passive sensor network, time difference of arrival (TDOA) measurements are often exploited for source localisation. The extended Kalman filter (EKF) is usually used for source localisation in a mobile sensor network; however, its performance is limited because of the non-linearity of the TDOA in relation to the source position. Especially when the available sensor positions include uncertainties, accurate localisation becomes much more challenging. To improve the localisation performance, this study develops two linear recursive three-dimensional source localisation algorithms by taking into consideration the random sensor position noises. An illustrative example is given to demonstrate that the proposed linear recursive localisation algorithms outperform the EKF localisation algorithm. Performance comparison between the two proposed algorithms is also provided.

Mismatch of Near-Field Bearing-Range Spatial Geometry in Source-Localization by a Uniform Linear Array

Many near-field source-localization algorithms intentionally simplifies the exact spatial geometry among the emitter and the sensors, in order to speed up the signal-processing involved. For example, the Fresnel approximation is a second order Taylor-series approximation. Such intentional approximation introduces a systemic error in the algorithm's modeling of the actual objective reality from which the measured data arise. A mismatch thus exists between the algorithm's presumptions versus the data it processes. This modeling-mismatch will introduce a systematic bias in the bearing-range estimates of the near-field source-localization algorithm. This bias is non-random, and adds towards the random estimation-errors due to the additive and/or multiplicative noises. The open literature currently offers no rigorous mathematical analysis on this issue. This proposed project aims to fill this literature gap, by deriving explicit formulas of the degrading effects in three-dimensional source-localization, due to approximating the source/sensor geometry by any order of the Taylor's series expansion.

Toward a better understanding of the pathophysiology of OCD SSRI responders: QEEG source localization

To demonstrate the utility of three-dimensional source localization of the scalp-recorded electroencephalogram (EEG) for the identification of the most probable underlying brain dysfunction in patients with obsessive-compulsive disorder (OCD). Eyes-closed resting EEG data was recorded from the scalp locations of the International 10/20 System. Variable resolution electromagnetic tomography (VARETA) was applied to artifact-free EEG data. This mathematical algorithm estimates the source generators of EEG recorded from the scalp. An excess in the alpha range was found with sources in the corpus striatum, in the orbito-frontal and temporo-frontal regions in untreated OCD patients. This abnormality was seen to decrease following successful treatment with paroxetine. The VARETA findings of an activation/deactivation pattern in cortical and subcortical structures in paroxetine-responsive patients are in good accordance with data obtained in previously published positron emission tomography studies related to current hypotheses of a thalamo-striatal-frontal feedback loop being relevant for understanding the pathophysiology of OCD.

Fetal magnetocardiographic mapping using independent component analysis

Fetal magnetocardiography (fMCG) is the only noninvasive technique allowing effective assessment of fetal cardiac electrical activity during the prenatal period. The reconstruction of reliable magnetic field mapping associated with fetal heart activity would allow three-dimensional source localization. The efficiency of independent component analysis (ICA) in restoring reliable fetal traces from multichannel fMCG has already been demonstrated. In this paper, we describe a method of reconstructing a complete set of fetal signals hidden in multichannel fMCG preserving their correct spatial distribution, waveform, polarity and amplitude. Fetal independent components, retrieved with an ICA algorithm (FastICA), were interpolated (fICI method) using information gathered during FastICA iterations. The restored fetal signals were used to reconstruct accurate magnetic mapping for every millisecond during the average beat. The procedure was validated on fMCG recorded from the 22nd gestational week onward with a multichannel MCG system working in a shielded room. The interpolated traces were compared with those obtained with a standard technique, and the consistency of fetal mapping was checked evaluating source localizations relative to fetal echocardiographic information. Good magnetic field distributions during the P-QRS-T waves were attained with fICI for all gestational periods; their reliability was confirmed by three-dimensional source localizations.

Electrophysiological measurements of anterior cingulate function.

Based on recent findings from various areas of brain research the anterior cingulate cortex (ACC) within the prefrontal cortex is increasingly considered as a brain region activated during tasks requiring conflict-monitoring and allocation of attention. In the present study with event-related potentials (ERPs) the question has been addressed, whether the NoGo-condition of the Continuous Performance Test is associated with enough conflict-monitoring and allocation of attention in order to activate the ACC in healthy controls. Low Resolution Electromagnetic Tomography (LORETA), a new three-dimensional source localization method, revealed significantly increased brain electrical activity during the NoGo-ERP as compared to the Go-ERP with its maximum located exactly within the ACC in four independent samples of healthy subjects. These results relate the conflict-monitoring requirements associated with inhibition of a prepared motor response (NoGo-condition) to a powerful brain electrical ACC-activity. This non-invasive, easy to perform and inexpensive electrophysiological measurement, therefore, provides a new method for the assessment of ACC-function in healthy subjects.

Three-dimensional source localization in a waveguide

This paper deals with three-dimensional (3-D) passive localization of a narrowband point source in a 2 1/2 -dimensional waveguide using an array of sensors. Two different maximum likelihood (ML) procedures for estimating the source range, depth, and direction-of-arrival (DOA) based on the normal mode representation of the received data are studied. In the first procedure, ML estimation of range and depth is applied on the data collected by a vertical array, and DOA is estimated using the ML algorithm on the data received by a separate, horizontal array. In the second procedure, the ML algorithm is applied on the data received by a two-dimensional (2-D), hybrid array for simultaneously estimating of all three source location parameters. Our study shows that although a horizontal array is sufficient for 3-D localization, to reduce sensitivity of the localization algorithm, a 2-D array should be used. The presented performance analysis of the two algorithms enables one to determine the performance losses in using the stage-wise, suboptimal algorithm relative to the optimal one in any given scenario. Numerical examples with channel parameters, which are typical to shallow water source localization, show performance losses of 0-3 dB. Simulation results of the two ML algorithms and their comparison with the Cramer-Rao bound (CRB) support the theory.

Three-dimensional source localization in a range-dependent environment: Comparison of matched-mode and matched-field processing.

Matched-mode localization of a simulated acoustic source in range, depth, and bearing is demonstrated for multiple vertical arrays. Specific examples shown use twin vertical arrays in a sloping bottom environment, with sound speed increasing with depth. The environment is modeled with adiabatic normal modes. Results of matched-mode source localization are compared with matched-field localization results. It is found for the cases studied that matched-mode processing is an order of magnitude faster than matched-field processing. Matched-mode processing consistently gives equal or lower sidelobe levels than matched-field processing. Comparison of several array configurations (differing in number of phones, vertical aperture, and location) indicates better performance for the arrays that resolve more normal modes.

Neuromagnetic functional localization: principles, state of the art, and perspectives.

The neuromagnetic method has been providing impressive results in the understanding of the functions and of some pathologies of the human brain. The possibility of achieving three-dimensional source localization represents a fundamental step forward in the study of the organization of cortical areas, in that of focal disorders and, in general, in the investigation of brain information processing. The development of large multichannel systems to achieve real time functional localization is being carried on in several countries and the first prototypes are already operating for a full assessment of the benefits of the technique. The use of time-varying magnetic pulses provides the opportunity for non-invasive stimulation of the central nervous system toward the achievement of functional imaging of the motor cortices.