Source Localization Problem Research Articles

A triangular acoustic emission source location method considering its anisotropic propagation behavior on the surface of finger-joint-laminated board

ABSTRACT To understand the anisotropic propagation characteristics of acoustic emission (AE) signals in finger-joint-laminated boards, an improved planar localization method for AE sources is proposed. Initially, the AE source was generated by the pencil-lead break (PLB) at a fixed position on the surface of the glued wood specimen, and two AE sensors were arranged in different directions at a fixed distance of 60 mm, and the AE propagation velocity was calculated according to the time difference of arrival (TDOA). For clarity, the grain parallel direction was defined as 0 degrees, with velocities measured every 10 degrees through a counterclockwise rotation. Using these measurements, two angular anisotropic wave velocity models were developed. Subsequently, three AE sensors arranged linearly on the specimen surface pinpointed the AE source’s location. This source location problem was formulated as a multi-parameter optimization model, constrained by the geometric relationships between the AE source and the sensors. A particle swarm optimization (PSO) algorithm was utilized to estimate the AE source’s angles relative to each sensor. The findings indicate that the located AE sources deviated by 6.0–19.0 mm from the predetermined PLB positions, with inaccuracies largely attributed to the anisotropic AE wave velocity models’ precision.

Gaussian process-based online sensor selection for source localization

This paper addresses the sensor selection problem for source localization within cyber–physical systems (CPSs). While recent machine learning and reinforcement learning approaches aim to optimize sensor selection and placement within the Area of Interest (AoI), their need for intensive data collection and training precludes online operation. Furthermore, these methods often require prior knowledge of the unknown source’s characteristics and lack adaptability to the dynamic nature of CPSs, leading to inefficiencies in unseen environments. This paper addresses these shortcomings using Gaussian process Optimization coupled with an active sensor selection mechanism to locate the unknown source within the AoI. The proposed approach first builds a probabilistic model of the environment, which is discretized into a grid, without prior training using a Gaussian Process surrogate model. Next, the model iteratively and systematically learns the underlying spatial phenomenon using Gaussian Process optimization. Concurrently, the approach selects a subset of sensors by optimizing a fitness function that advocates selecting informative and energy-efficient sensors. Next, the probabilistic model, having accurately learned the environment, directs the algorithm to the unknown source by identifying the cell with the highest likelihood of containing it. Finally, a peak refinement step is performed, which computes the exact location of the source within the designated cell. The proposed method’s efficacy is validated through experiments in radioactive source localization, validation studies, and adaptability assessments across various environments. In terms of quality of localization (QoL), it outperforms recent localization benchmarks, such as a reinforcement learning-based approach and DANS, by around 18% and 100%, respectively.

Systematic analysis of acoustic source localization maps for performance assessment

Noise pollution is a raising problematic mainly associated to the development of industry, cities, and transportation. In that context, the characterization of noise sources is key point to help the understanding of noise generation mechanisms and to be able to develop effective noise reduction strategies. Microphones phased array measurements can be used as input to solve the inverse problem of source localization allowing to obtain source maps for each frequency of interest. Conventional beamforming (CBF) is the most famous source localization algorithm which uses the interpretation of the propagation delays measured between each array microphones. However, the analysis of output source maps can be made difficult by the low spatial resolution in the low-frequency range and the presence of side-lobes associated with microphones distribution that can lead to additional wrong sources. This paper presents a systematic analysis of source maps to identify potential noise sources by using different methods (local maxima, Metropolis-Hastings). The set of potential noise sources can then be compared to the set of real sources to assess the CBF performances. This methodology is successfully applied to measurements performed in anechoic room for various source configurations highlighting CBF limitations (spatial resolution, correlated sources, reflective environment).

High-resolution acoustic imaging method based on block sparsity constraint

Acoustic imaging method is a critical task in various applications since it can locate the sound sources. However, the resolution of the method becomes low at low frequencies. This paper proposes a novel method to realize high-resolution acoustic imaging based on block sparsity constraint. By dividing the focusing area into blocks, the block sparse property of sound sources can be utilized to improve the resolution of the result. In this study, a block orthogonal matching pursuit method is introduced to deal with source localization problem with block sparsity constraint. To evaluate the performance of the proposed method, it is tested through numerical simulations and an experiment. The results of simulations prove that the proposed acoustic imaging method based on block sparsity constraint can localize sound sources accurately and performs better than that based on sparsity constraint. The results of the experiment further validate these findings.

Development and simulation of two novel indoor odor source localization methods using a modified shark smell optimization algorithm

Aiming to solve the problem of odor source localization (OSL) in the presence of interference sources, this paper presents two methods based on swarm intelligence algorithms. We initially introduced the shark smell optimization (SSO) algorithm and modified it for OSL tasks. Subsequently, mechanisms for collective information sharing and preventing falling into local minima were incorporated, leading to the development of the Improved Shark Smell Optimization (I-SSO) algorithm. We tested both algorithms in a computational fluid dynamics (CFD) simulated environment with a single interference source and compared them to the particle swarm optimization (PSO) algorithm and whale optimization algorithm (WOA). In scenarios with one and two interference sources. The results showed that the I-SSO algorithm outperformed the other three algorithms in both environment settings, demonstrating a higher success rate and superior search distance efficiency.

Hybrid deconvolution method based on mode composition beamforming for separating sound sources with different motion modes

The presence of sound sources that rotate can cause interference with stationary acoustic imaging, especially if the intensity of the rotating sound source is strong. Vice versa, stationary sound sources can also interfere with rotational acoustic imaging. Current algorithms for separating and locating rotating and stationary sound sources have problems such as weak separation capabilities, complex calculations, and limited array layouts. To address these challenges more effectively, a frequency-domain hybrid deconvolution method based on modal composition beamforming is proposed to separate and localize rotating and stationary sound sources. This algorithm operates within the frequency domain and is not restricted by array layout or the tonal single-frequency nature of sound sources. First, the point spread function and cross-point spread function matrices of the array are derived based on the modal transfer function. Then, a system of linear equations is constructed to separate rotating and stationary sound sources. Finally, the sound source separation and localization problems are solved through Gaussian Seidel and sparse-constrained deconvolution, respectively. Compared with the virtual rotating array method combined with matrix completion, simulation and experimental results demonstrate that this method can accurately locate and separate rotating and stationary sound sources, even when there is a substantial difference in intensity between rotating and stationary sound sources.

On bias and its reduction via standardization in discretized electromagnetic source localization problems

In electromagnetic source localization problems stemming from linearized Poisson-type equation, the aim is to locate the sources within a domain that produce given measurements on the boundary. In this type of problem, biasing of the solution is one of the main causes of mislocalization. A technique called standardization was developed to reduce biasing. However, the lack of a mathematical foundation for this method can cause difficulties in its application and confusion regarding the reliability of solutions. Here, we give a rigorous and generalized treatment for the technique using the Bayesian framework to shed light on the technique’s abilities and limitations. In addition, we take a look at the noise robustness of the method that is widely reported in numerical studies. The paper starts by giving a gentle introduction to the problem and its bias and works its way toward standardization.

Phase space representation of sound field excited by a noise source in underwater acoustic waveguide.

The analysis of the field excited in a waveguide by a point noise source is performed using the phase space representation of this field given by the distribution of its amplitude in the depth-angle-time space. The transition from the traditional description of the field amplitude as a function of depth and time to phase space representation is performed using the coherent state expansion developed in quantum mechanics. In this paper, the correlation function of noise signals arriving at different points of the phase plane depth-angle is investigated. Numerical simulation data show that measurements of signal correlations in phase space, performed with the help of a receiving vertical antenna, can be used as input data in solving the problem of source localization and reconstruction of unknown parameters of the sound speed profile. It is shown that in phase space there is an analog of the classical interference pattern observed in the distribution of sound intensity in the distance-frequency plane. The slopes of striations in this interference pattern, as in the conventional one, are given by the Chuprov waveguide invariant.

Three-Dimensional Signal Source Localization with Angle-Only Measurements in Passive Sensor Networks

Some passive sensors can provide only relative angles of a signal source. To obtain the signal source location, multiple passive sensors can be constructed into a passive sensor network through communication links. This paper investigates the source localization problem with angle-only measurements in three-dimensional space. First, we present an intersection localization method, which estimates the target position by minimizing the sum of distances between lines formed by angle-only measurements. It has the same target position estimate as the widely used least-squares (LS) method, but with a lower computational cost. Furthermore, considering the differences in measurement accuracy of sensors, the weighted least-squares (WLS) algorithm can achieve better localization performance than the LS method. Unfortunately, since the coefficient matrix and the noise vector are correlated, the WLS method is biased. The bias-compensation WLS (BCWLS) method is also presented in this paper to reduce the bias by estimating the correlation between the coefficient matrix and the pseudolinear noise vector. To evaluate the performance of the presented algorithms, numerical simulations are conducted, indicating that the superiority of the intersection localization method in computational cost and the superiority of the BCWLS method in localization accuracy.

HMSL: Source localization based on higher-order Markov propagation

The widespread use of the Internet and social media has brought us great convenience, but it has also exposed us to a lot of false information and malicious attacks. It is vital to accurately locate the source of the harmful spread to prevent it from spreading further. Most previous studies have assumed that the propagation path is memoryless and always the shortest path. This assumption implies the first-order Markov property of propagation paths. This paper takes into account the higher-order Markov property of propagation paths in the source localization problem. Firstly, the problem of source localization based on observers is formulated. Then, we introduce the higher-order Markov property of propagation paths into the problem and propose a reaction–synchronization–diffusion model to model the propagation process on the higher-order network. On this basis, we build a framework named source localization based on higher-order Markov propagation (HMSL), which is compatible with traditional algorithms for source localization. After that, we conducted experiments on a real dataset and found that the HMSL has significant improvement in the source localization compared to the first-order network. Sensitivity analysis indicates that the degree of improvement is significantly influenced by the probability of infection and the proportion of higher-order nodes. Furthermore, we investigated the reason behind the improvement and found that the first-order network creates paths that do not exist within the raw data. When these fake paths are shorter than actual propagation paths, the length of propagation paths and estimated activation time of observers will be underestimated, thus decreasing the accuracy of source localization. The HMSL framework can solve this problem effectively.

Mine seismic source location via forward modeling of spherical waves in a multilayered horizontal or inclined medium

Seismic source location is a classic inverse problem in seismology. In mathematical physics, inverse problems have multiple natural solutions. The objective of this study was to develop a generic theory and method of seeking the true solution from multiple solutions for the location of a coal mine seismic source in an idealized velocity structure model of a coal mine with a small scale and complex geological environment. Starting from the simplest velocity structure model, the complexity of the model gradually increased, until it approached the real velocity structure model, i.e., the multilayered horizontal and inclined velocity structure model, in order to find a generic method for solving the multi-solution inverse problem of coal mine seismic source location. Specifically, the wavefront distribution equation in a two-layer horizontal medium was derived and then expanded to any multi-layer horizontal medium. Based on this equation, a positive definite nonlinear equation system was established from the perspective of any observation system. The equation system contained four unknown variables of the spatiotemporal position of the seismic source. To determine the spatiotemporal parameters of the seismic source, nonlinear equations for four stations were required. To solve the nonlinear equation system, an initial iteration value was determined. In order to reduce the difficulty of determining the initial iteration value, the variable substitution method was used to reduce the number of location parameters. By rotating the original geodetic coordinate system of the station to be parallel and orthogonal to the medium interface, the wavefront method was extended to inclined medium. In conclusion, in this study, the problem of coal mine seismic source location in a multi-layer horizontal or inclined medium was effectively solved. The method proposed in this study provides a reference for solving the true solution from multiple solutions for the location of a coal mine seismic source in small-scale coal mines with complex geological environments.

Source localization in deep ocean based on complex convolutional neural network

To solve the problem that phase information cannot be used effectively in underwater acoustic localization, a deep learning network based on complex convolutional neural network is proposed in this paper. The complex convolution layer is used to effectively utilize the phase features favorable to the source localization problem, and the phase information is used to improve the feature extraction performance. Through simulation, the performance of the network for source localization in deep-sea direct arrival region under different SNR conditions is analyzed. The results show that the complex convolutional network proposed in this paper can locate the sound source with less computation and has better performance under the condition of low SNR.

A fast algorithm for diffusion source localization in large-scale complex networks

Abstract The identification of the origin of diffusion processes in complex networks is a subject of significant interest across numerous interdisciplinary fields. One approach to solving this issue involves the placement of a few observer nodes within the network and the estimation of the unknown source through the utilization of information gathered by these observer nodes. However, this approach presents certain drawbacks, particularly with regard to computational complexity. To address this limitation, this study introduces an innovative Hill-Climbing algorithm designed to efficiently identify diffusion sources within large-scale complex networks. Our approach, the Local Search Hill Climbing (LSHC) method, transforms the source localization problem into an optimization task, utilizing strategically deployed observer nodes. Experiments conducted on both random and scale-free network models demonstrate that our method significantly reduces computational time while maintaining high accuracy in pinpointing the diffusion source. This approach offers a substantial improvement over traditional methods and holds considerable promise for practical applications in network science.

Robust time-of-arrival localization via ADMM

This article considers the problem of source localization (SL) using possibly unreliable time-of-arrival (TOA) based range measurements. Adopting the strategy of statistical robustification, we formulate TOA SL as minimization of a versatile loss that possesses resistance against the occurrence of outliers. We then present an alternating direction method of multipliers (ADMM) to tackle the nonconvex optimization problem in a computationally attractive iterative manner. Moreover, we prove that the solution obtained by the proposed ADMM will correspond to a Karush–Kuhn–Tucker point of the formulation when the algorithm converges, and discuss reasonable assumptions about the robust loss function under which the approach can be theoretically guaranteed to be convergent. Numerical investigations demonstrate the superiority of our method over many existing TOA SL schemes in terms of positioning accuracy and computational simplicity. In particular, the proposed ADMM achieves estimation results with mean square error performance closer to the Cramér–Rao lower bound than its competitors in our simulations of impulsive noise environments.

Weighted Centroids in Adaptive Nelder–Mead Simplex: With heat source locator and multiple myeloma predictor applications

This paper introduces a novel approach for enhancing the Nelder–Mead Simplex method by utilizing the weighted mean of simplex vertices to efficiently determine the search direction towards optima. The Nelder–Mead algorithm is commonly used for solving unconstrained optimization problems through iterative direct search. While the Nelder–Mead algorithm excels in low-dimensional scenarios, its challenges in higher dimensions are addressed in our study.We reveal that the Nelder–Mead Simplex algorithm’s operations rely not only on the problem dimension but also on adaptive descending parameters for calculating the weighted centroid of vertices. The adaptive weights are determined based on the concept that generating a descending sequence depends on the fitness values of vertices. Consequently, the search direction tends to prioritize vertices with superior fitness values over others.Through extensive testing on renowned high-dimensional benchmark functions, the proposed algorithm outperforms both the standard and adaptive Nelder–Mead simplex algorithms in terms of performance demonstrating superior consistency and reliability. Furthermore, it is applied to an inverse heat source location problem formulated as a linear elliptic partial differential equation, serving as a large-scale real-world application. Additionally, the algorithm successfully addresses a neural network model solving a classification problem concerning the prediction of multiple myeloma, a type of bone marrow cancer, in patients, achieving an average accuracy of 92.3% with a minimal standard deviation of 0.13%. When the results obtained from eight different methods used in the study are compared in terms of performance in general, the proposed method is among the top three optimization algorithms. These real-world applications showcase the method’s versatility.

Global strong convexity and characterization of critical points of time-of-arrival-based source localization

In this work, we study a least-squares formulation of the source localization problem given time-of-arrival measurements. We show that the formulation, albeit non-convex in general, is globally strongly convex under certain condition on the geometric configuration of the anchors and the source and on the measurement noise. Next, we derive a characterization of the critical points of the least-squares formulation, leading to a bound on the maximum number of critical points under a very mild assumption on the measurement noise. In particular, the result provides a sufficient condition for the critical points of the least-squares formulation to be isolated. Prior to our work, the isolation of the critical points is treated as an assumption without any justification in the localization literature. The said characterization also leads to an algorithm that can find a global optimum of the least-squares formulation by searching through all critical points. We then establish an upper bound of the estimation error of the least-squares estimator. Finally, our numerical results corroborate the theoretical findings and show that our proposed algorithm can obtain a global solution regardless of the geometric configuration of the anchors and the source.

Antenna Pattern Calibration Method for Phased Array of High-Frequency Surface Wave Radar Based on First-Order Sea Clutter

The problem of accurate source localization has been an area of focus in high-frequency surface wave radar (HFSWR) applications. However, antenna pattern distortion (APD) decreases the direction-of-arrival (DOA) estimation performance of the multiple signal classification (MUSIC) algorithm. Up to now, limited studies have been conducted on the calibration of antenna pattern distortion for phased arrays in HFSWR. In this paper, we first analyze the effect of APD on the performance of the MUSIC algorithm through estimation of accuracy and angular resolution. We demonstrate that using the actual pattern (or say APD) can improve DOA estimation performance. Based on this proposition, we propose a novel iterative calibration method that employs the first-order sea clutter data and can jointly estimate DOA and APD in an iterative way. To obtain available calibration points, we introduce the extraction methods of the first-order sea clutter spectrum and single-DOA spectrum points. Meanwhile, in each iteration, the Beamspace MUSIC algorithm and artificial hummingbird algorithm (AHA) are utilized to estimate the DOA and APD, respectively. Numerical results reveal a good coincidence between the actual pattern and the estimated APD. We also apply this method to process the experimental data of HFSWR. We obtain the APD vector of the real phased array and improve the direction-finding performance of several real ship targets using this vector. Both numerical and experimental results prove the correctness of our proposed calibration method.

A novel efficient estimator for three‐dimensional bearings‐only source localisation with unknown sensor altitude and systematic measurement errors

AbstractA novel two‐stage profile maximum likelihood estimator is proposed to estimate the source location and the systematic errors jointly, with the aim of addressing the problem of source localisation using angle‐only measurements from a single sensor with unknown sensor altitude and systematic measurement errors. The proposed two‐stage profile maximum likelihood estimator algorithm is capable of decoupling the azimuth and elevation angle measurements while transforming the original maximum likelihood optimisation problem into two sub‐problems, that is, two‐dimensional‐projected maximum likelihood estimator and relative altitude maximum likelihood estimator. In terms of the two‐dimensional‐projected maximum likelihood estimator, an algorithm combining pseudo‐linear estimating and Kalman filtering is proposed to generate an initial estimate. Subsequently, a Gauss–Newton iterative method is developed to estimate the two‐dimensional‐projected target location and the azimuth systematic error jointly. The relative height maximum likelihood estimator is initialised using a pseudo‐linear estimator. Next, a Gauss–Newton iterative algorithm is adopted to estimate the elevation systematic error and the relative height. As indicated by the result of the simulation studies, the proposed algorithm exhibits an estimation performance close to the Cramér–Rao lower bound with unknown sensor altitude and systematic measurement errors.

Decentralized fault tolerant source localization without sensor parameters in wireless sensor networks

In this paper, we study the source (event) localization problem in decentralized wireless sensor networks (WSNs) under faulty sensor nodes without knowledge of the sensor parameters. Source localization has many applications, such as localizing WiFi hotspots and mobile users. Some works in the literature localize the source by utilizing the knowledge or estimates of the fault probability of each sensor node or the region of influence of the source. However, this paper proposes two approaches: the hitting set and feature selection for estimating the source location without any knowledge of the sensor parameters under faulty sensor nodes in WSN. The proposed approaches provide better or comparable source localization performances. For the hitting set approach, we also derive a lower bound on the required number of samples. In addition, we extend the proposed methods for localizing multiple sources. Finally, we provide extensive simulations to illustrate the performances of the proposed methods against the centroid, maximum likelihood (ML), fault-tolerant ML (FTML), and subtract on negative add on positive (SNAP) estimators. The proposed approaches significantly outperform the centroid and maximum likelihood estimators for faulty sensor nodes while providing comparable or better performance to FTML or SNAP algorithm. In addition, we use real-world WiFi data set to localize the source in comparison to the support vector machine based estimator in the literature, where the proposed methods outperformed the estimator.

A novel visual representation method for multi-dimensional sound scene analysis in source localization problem

A visual representation method, DoAgram, for multi-dimensional sound scene analysis is suggested. The visual representation of the sound source localization result gives intuitive information about the estimated one to the end user. Also, image-based deep learning is popularly used in the acoustic field nowadays, so such a visualized one can be used for data augmentation. To analyze the spatial sound scene for the moving source, the method displays the estimated azimuth angle and elevation angle of the source, and its corresponding time stamp and frequencies as RGB color channels and metadata by mapping the spatial coordinate to color space. Even though the suggested method is human-interpretable, decoding is needed for the quantitative analysis. Therefore, the time and frequency scanning method, and a histogram to estimate the DoA of the source are proposed. An experiment is conducted in an anechoic chamber to localize two quadcopter drones that have a mean angular velocity of 8°/s ± 9°/s (95 % CI) and 25°/s ± 31°/s (95 % CI), respectively, and the spatial sound scene analysis is implemented using the proposed methods. The test result shows that the trajectories with respect to the time of each source are well separated. Also, an additional test is conducted using an open-access audio dataset for machine learning. The cumulative source mapping method is adopted for the spatial sound scene analysis, and the decoded result shows that the DoAgram is feasible to adopt for machine learning applications.