Source Localization Problem Research Articles

An improved underwater TDOA/AOA joint localisation algorithm

To solve the problem of sound source localisation in underwater sensor networks, this paper constructs a pseudo-linear equation system of time difference of arrival and angle of arrival (TDOA/AOA) and then uses the weighted least squares algorithm to estimate the target position. This paper proposes a two-stage weighted least squares algorithm that uses target position error. First, the adapted TDOA equation and the existing AOA equation are combined into the first-stage weighted least squares algorithm, which improves the estimation accuracy of the first stage compared with the traditional algorithm. Second, this paper uses the target position error in the second stage to derive a new TDOA/AOA equation. Finally, the target position calculated in the previous stage is adjusted by the solved target position error. The performance of the proposed algorithm is verified by comparison with the Cramer–Rao lower bound. Simulation results show that the proposed algorithm still has good localisation performance even under high-angle noise.

An Efficient Constrained Weighted Least Squares Method With Bias Reduction for TDOA-Based Localization

This paper addresses the source location problem by using time-difference-of-arrival (TDOA) measurements. The two-stage weighted least squares (TWLS) algorithm has been widely used in the TDOA location. However, the estimation accuracy of the source location is poor and the bias is significant when the measurement noise is large. Owing to the nonlinear nature of the system model, we reformulate the localization problem as a constrained weighted least squares problem and derive the theoretical bias of the source location estimate from the maximum-likelihood (ML) estimation. To reduce the location bias and improve location accuracy, a novel bias-reduced method is developed based on an iterative constrained weighted least squares algorithm. The new method imposes a set of linear equality constraints instead of the quadratic constraints to suppress the bias. Numerical simulations demonstrate the significant performance improvement of the proposed method over the traditional methods. The bias is reduced significantly and the Cramer–Rao lower bound accuracy can also be achieved.

Adaptive Imaging of Sound Source Based on Total Variation Prior and a Subspace Iteration Integrated Variational Bayesian Method

Sound source visualization has been widely used in many scenarios such as aerospace, industrial production, and urban management. Sound source localization technology plays an essential role in the realization of sound source visualization. The imaging results and calculation cost are the primary considerations in the problem of sound source localization. This article proposes a subspace iteration integrated variational Bayesian (SVB) method to realize adaptive imaging of different sound sources. First, the proposed variational Bayesian (VB) method is based on total variation (TV) prior to balance the sparsity and smoothness of the imaging results. Second, the subspace optimization method in the probability measure space is integrated into the proposed SVB method to solve the involved ill-posed inverse problem. The proposed SVB method can significantly improve the calculation speed, especially for large-scale inverse problems. Finally, the speed and robustness of the proposed SVB method can be demonstrated according to the extensive results of simulation and experimental validation.

Inverse Solution of Steady-State Responses Based on Sparse Bayesian Learning

Steady-state responses (SSRs), evoked by various patterns of periodic stimuli, comprise an important category of evoked potentials. To explore the neural generators of SSRs, a unified framework solving the inverse problem for a single subject or integrating multiple subjects is indispensable. Inspired by the phenomenon that the oscillation frequency of an SSR follows that of the periodic stimulus, we consider the problem of source localization for SSRs using the Fourier components at the stimulation frequency instead of directly using the waveform in this paper. The multi-channel electroencephalogram (EEG) Fourier components at the stimulation frequency is shown to equal multiplying the lead field matrix (LFM) by a complex-valued vector that contains the amplitudes and phases of sources in the cortex, contaminated by spontaneous EEG and electrical noise. This complex-valued inverse problem is further solved in the framework of sparse Bayesian learning, where the non-stationarity of spontaneous EEG among epochs is considered, and the joint sparsity of complex-valued source component vectors is modeled and utilized to improve the source localization performance. Expectation-maximization (EM) is employed to give the ultimate SSR source localization algorithm. By the proposed method, not only a single subject's SSR source localization can be achieved, but also the common locations of a certain type of SSR integrating multiple subjects can be given, even when the electrode layout or number of electrodes varies among subjects. The validity and superior performance of the proposed method was verified by simulations compared with other methods. Real SSR stimulation/recording experiments were also performed, where the electric generators of 40-Hz auditory steady-state responses (ASSRs) by various stimulation patterns were investigated.

Multiple Acoustic Source Localization in Microphone Array Networks

The problem of multiple acoustic source localization using observations from a microphone array network is investigated in this article. Multiple source signals are assumed to be window-disjoint-orthogonal (WDO) on the time-frequency (TF) domain and time delay of arrival (TDOA) measurements are extracted at each TF bin. A Bayesian network model is then proposed to jointly assign the measurements to different sources and estimate the acoustic source locations. Considering that the WDO assumption is usually violated under reverberant and noisy environments, we construct a relational network by coding the distance information between the distributed microphone arrays such that adjacent arrays have higher probabilities of observing the same acoustic source, which is able to mitigate the miss detection issues in adverse environments. A Laplace approximate variational inference method is introduced to estimate the hidden variables in the proposed Bayesian network model. Both simulations and real data experiments are performed. The results show that our proposed method is able to achieve better source localization accuracy than existing methods.

Efficient Underwater Acoustical Localization Method Based On Time Difference and Bearing Measurements

This article addresses the underwater acoustical localization problem by using the time-difference-of-arrival (TDOA) and bearing-angle-of-arrival (BAOA) measurements. For the underwater acoustic equipment, such as the ultrashort baseline system (USBL), whose bearing measurements are different from the traditional angle-of-arrival (AOA) model, a closed-form solution for the hybrid TDOA/BAOA-based source localization problem is developed. However, the solution suffers from the measurement noise and cannot achieve the Cramer–Rao lower bound (CRLB) performance in the case of large measurement noise. Thus, an iterative constrained weighted least-squares method is presented to further minimize the error in the case of large noise. The CRLB for hybrid TDOA/BAOA source localization is analyzed, and the solution is proved to achieve the CRLB performance. Numerical simulations and field tests demonstrate that the proposed method outperforms the traditional methods in terms of estimation bias and accuracy. It can achieve the CRLB performance better.

Source localization in large-scale asynchronous sensor networks

The problem of uncooperative source localization and synchronization in asynchronous sensor networks has been considered previously in a centralized manner, where all the raw measurements are delivered to a processing center. However, for large-scale sensor networks the transmission of raw measurements over the networks requires considerable communication overhead, besides being vulnerable to transmission failure and interference, and the computational load at the processing center is rather heavy. A more suitable candidate to this problem is the distributed estimation considered in this paper, where each sensor node communicates with its neighboring nodes only, and the parameters are estimated at each sensor via information cooperation. In order to decouple the unknown source positions and sensor clock offsets, we propose to update them iteratively based on the belief propagation (BP) framework. To reduce the complexity of parameter update at each sensor, the sigma point based estimation method is adopted. Theoretical analyses concerning the computational complexity and communication overhead are carried out. Simulation results demonstrate that the proposed method could estimate the source positions distributively with much lower complexity and communication overhead compared with the centralized methods at the cost of acceptable performance degradation.

Robust NLOS Bias Mitigation for Hybrid RSS-TOA Based Source Localization Under Unknown Transmission Parameters

This letter addresses the problem of source localization in non-line of sight (NLOS) environment using received signal strength (RSS) and time of arrival (TOA) measurements when both transmission time and power are unknown. To mitigate the NLOS bias, a robust weighted least square (RWLS) problem is formulated from original non-convex maximum-likelihood (ML) estimation problem using a set of tight approximations. The RWLS problem is further tightened by a novel convex-hull constraint and is ultimately solved using second-order cone programming (SOCP). Simulation results confirm the optimal performance of the proposed robust method in various network scenarios and also validate its excellence over state-of-art methods.

Directional source localization based on RSS-AOA combined measurements

Source localization plays an indispensable role in many applications. This paper addresses the directional source localization problem in a three-dimensional (3D) wireless sensor network using hybrid received-signal-strength (RSS) and angle-of-arrival (AOA) measurements. Both the position and transmission orientation of the source are to be estimated. In the considered positioning scenario, the angle and range measurements are respectively corresponding to the AOA model and RSS model that integrates the Gaussian-shaped radiation pattern. Given that the localization problem is non-convex and the unknown parameters therein are coupled together, this paper adopts the second-order cone relaxation and alternating optimization techniques in the proposed estimation algorithm. Moreover, to provide a performance benchmark for any localization method, the corresponding Cramer-Rao lower bounds (CRLB) of estimating the unknown position and transmission orientation of the source are derived. Numerical and simulation results demonstrate that the presented algorithm effectively resolves the problem, and its estimation performance is close to the CRLB for the localization with the hybrid measurements.

DOA and Range Estimation Using a Uniform Linear Antenna Array Without A Priori Knowledge of the Source Number

A new efficient root-propagator method based on a uniform linear antenna array is proposed to estimate the directions of arrival (DOAs) and ranges of near-field sources without a priori knowledge of the source number. A non-Hermitian matrix is first designed, which allows the applications of rooting methods. Then, by constructing two propagators, the parameter estimation for near-field sources can be achieved through rooting methods in a decoupled way without eigenvalue decomposition (EVD) and spectrum searches. Finally, the importance of a priori source number to source localization problems is studied, and especially, an improvement is proposed to get rid of this dependence. Numerical examples are carried out to show the effectiveness and validate the theoretical analysis of the proposed root-propagator method. The results show that the proposed method provides more superior performance for near-field source localization than other existing similar methods. Even in the case without a priori knowledge of the source number, the performance of the proposed method is still satisfactory.

Locating multiple information sources in social networks based on the naming game

Identifying the source of information in a network plays a key role in controlling the impact of information. Herein, we study the problem of multiple source localization in the context of information propagation in social networks. We use the theory of the naming game to conduct observations. Moreover, we divide the observations into different sets based on the information provided by them and then estimate the source of each set. Finally, we combine the source of each observation set to obtain all the estimated information sources. The proposed method can locate sources without knowing the number of information sources. Simulations on four real data sets are provided to verify the performance of our method.

A Synchrophasor Data-Driven Method for Forced Oscillation Localization Under Resonance Conditions

This paper proposes a data-driven algorithm for locating the source of forced oscillations and suggests a physical interpretation for the method. By leveraging the sparsity of forced oscillations along with the low-rank nature of synchrophasor data, the problem of source localization under resonance conditions is cast as computing the sparse and low-rank components using Robust Principal Component Analysis (RPCA), which can be efficiently solved by the exact Augmented Lagrange Multiplier method. Based on this problem formulation, an efficient and practically implementable algorithm is proposed to pinpoint the forced oscillation source during real-time operation. Furthermore, theoretical insights are provided for the efficacy of the proposed approach, by use of physical model-based analysis, specifically by highlighting the low-rank nature of the resonance component matrix. Without the availability of system topology information, the proposed method can achieve high localization accuracy in synthetic cases based on benchmark systems and real-world forced oscillations in the power grid of Texas.

A Direct Position Determination Approach for Underwater Acoustic Sensor Networks

In this paper, we consider the source localization problem with an underwater acoustic sensor network (UASN) consisting of a number of platforms each equipped with an array, such as an autonomous underwater vehicle (AUV). Direct position determination (DPD) has been a promising topic in recent years. Existing DPD methods can be divided into two categories: global coherent processing and non-coherent processing. The former is easy to implement in practical tasks but the coherence between the received signals at different nodes are not exploited, while the requirements for coherent processing may not be fulfilled in real environments. A multi-cluster array model is constructed considering the deployment of the nodes with the intention to exploit the available coherence in the UASN and avoiding the side effects of imperfect spatial coherence. A weighted MUSIC direct source localization approach is proposed based on this model. The arrays within a cluster work coherently as a large array and contribute a MUSIC spectrum. The final source position estimate is obtained from a weighted combination of these spectra, and the weights are dependent on the eigenstucture and noise variance of each cluster. We first investigate the theoretical gain of inter-array coherence exploitation on localization accuracy by means of Cramer-Rao bound analysis. Then the model for imperfect spatial coherence is generalized to the multi-cluster system to examine the performance of the proposed approach when the inherent constraints for intra-cluster coherent processing can not be guaranteed. Numerical results demonstrate the superior resolution capability of the proposed approach and its robustness to imperfect spatial coherence.

Adaptive Beamforming Method for MIMO Antenna Array with Constrained Mean Square Error

The Adaptive beam forming with Multikernel based Bayesian learning method beam forming on Uniform Linear Array (ULA) antennas for better localization. Undetermined source localization problem is solved using the Multikernel Sparse Bayesian Learning framework. Beam forming problem is considered the undetermined source localization problem and solved using the adaptive method. The Degree of Freedom (DOF) is increased using the adaptive nature of the manifold matrix while maintaining the same number of antennas. The response model that adaptively adjusts the manifold matrix in the Sparse Bayesian problem uses the Multikernel framework. MATLAB based implementation thus carried out on the ULA clearly exhibits better results over the single kernel model. The Mean Square Error (MSE) and Root Mean Square Error (RMSE) with Signal to Noise Ratio (SNR) variation is obtained to evaluate the performance of the proposed implementation. The performance obtained is found to be satisfactory and is at par with the recent previous implementation.

Experimental design for fully nonlinear source location problems: which method should I choose?

SUMMARYStatistical experimental design (SED) is the field of statistics concerned with designing experiments to obtain as much information as possible about a target of interest. SED algorithms can be divided into two categories: those that assume a linear or linearized relationship between measured data and parameters, and those that account for a fully nonlinear relationship. We compare the most commonly used linear method, Bayesian D-optimization, to two nonlinear methods, maximum entropy design and DN-optimization, in a synthetic seismological source location problem where we define a region of the subsurface in which earthquake sources are likely to occur. Example random sources in this region are sampled with a uniform distribution and their arrival time data across the ground surface are forward modelled; the goal of SED is to define a surface monitoring network that optimally constrains this set of source locations given the data that would be observed. Receiver networks so designed are evaluated on performance—the percentage of earthquake pairs whose arrival time differences are above a threshold of measurement uncertainty at each receiver, the number of prior samples (earthquakes) required to evaluate the statistical performance of each design and the SED compute time for different subsurface velocity models. We find that DN-optimization provides the best results both in terms of performance and compute time. Linear design is more computationally expensive and designs poorer performing networks. Maximum entropy design is shown to be effectively impractical due to the large number of samples and long compute times required.

Decision and Event-Based Fixed-Time Consensus Control for Electromagnetic Source Localization.

This article deals with the problem of electromagnetic source localization (ESL). An evolutionary particle filter, which is first used to make a decision on the positions of electromagnetic sources, has two characteristics. One characteristic is that the number of particles can be significantly reduced while the other characteristic is that the particle diversity can be well improved. On the basis of the estimated positions of electromagnetic sources, the position and velocity of the virtual leader can be determined. Then, an event-based fixed-time consensus control approach is proposed such that the positions and velocities of robots reach consensus with the virtual leader over a fixed-time interval while saving resource consumption by reducing the communication frequencies and updating times of control inputs. Finally, simulation and experimental results show the effectiveness of the proposed decision and event-based fixed-time consensus control approach for ESL.

A Novel Method for Asynchronous Time-of-Arrival-Based Source Localization: Algorithms, Performance and Complexity.

In time-of-arrival (TOA)-based source localization, accurate positioning can be achieved only when the correct signal propagation time between the source and the sensors is obtained. In practice, a clock error usually exists between the nodes causing the source and sensors to often be in an asynchronous state. This leads to the asynchronous source localization problem which is then formulated to a least square problem with nonconvex and nonsmooth objective function. The state-of-the-art algorithms need to relax the original problem to convex programming, such as semidefinite programming (SDP), which results in performance loss. In this paper, unlike the existing approaches, we propose a proximal alternating minimization positioning (PAMP) method, which minimizes the original function without relaxation. Utilizing the biconvex property of original asynchronous problem, the method divides it into two subproblems: the clock offset subproblem and the synchronous source localization subproblem. For the former we derive a global solution, whereas the later is solved by a proposed efficient subgradient algorithm extended from the simulated annealing-based Barzilai–Borwein algorithm. The proposed method obtains preferable localization performance with lower computational complexity. The convergence of our method in Lyapunov framework is also established. Simulation results demonstrate that the performance of PAMP method can be close to the optimality benchmark of Cramér–Rao Lower Bound.

A Lagrangian Multiplier Method for TDOA and FDOA Positioning of Multiple Disjoint Sources with Distance and Velocity Correlation Constraints

This paper considers the source localization problem using time differences of arrival (TDOA) and frequency differences of arrival (FDOA) for multiple disjoint sources moving together with constraints on their distances and velocity correlation. To make full use of the synergistic improvement of multiple source localization, the constraints on all sources are combined together to obtain the optimal result. Unlike the existing methods that can achieve the normal Cramér-Rao lower bound (CRLB), our object is to further improve the accuracy of the estimation with constraints. On the basis of maximum likelihood criteria, a Lagrangian estimator is developed to solve the constrained optimization problem by iterative algorithm. Specifically, by transforming the inequality constraints into exponential functions, Lagrangian multipliers can be used to determine the source locations via Newton’s method. In addition, the constrained CRLB for source localization with distance and velocity correlation constraints is also derived. The estimated accuracy of the source positions and velocities is shown to achieve the constrained CRLB. Simulations are included to confirm the advantages of the proposed method over the existing methods.

Photoacoustic imaging through a cortical bone replica with anisotropic elasticity

Photoacoustic (PA) imaging is an emerging modality, which combines the high optical absorption contrast of biological chromophores with centimeter imaging depths and sub-millimeter resolution of ultrasonic (US) waves. However, PA imaging through cortical bone remains an unmet challenge. Cortical bone is an anisotropic medium, which is not accurately modeled using existing PA image reconstruction methods. In this Letter, we address the PA source localization problem for imaging through a cortical bone-mimicking layer. Our approach accounts for both refraction and elastic anisotropy to accurately reconstruct US and PA images in the presence of a cortical bone replica. We demonstrate our technique using a PA and US experiment, where we image a 700 μm diameter target beneath a cortical bone-mimicking plate. Pulse-echo US experiment is used to estimate the wavespeed in each layer and create an anatomical image of the bone replica, and the PA source is reconstructed using the wavespeed model defined with US. We compute the thickness of the plate with less than 1% error, whereas isotropic assumptions overestimate the thickness by 20% or more. Incorporating both refraction and anisotropy accurately localizes the target with PA and US at the true depth, whereas isotropic assumptions blur the lateral dimension and mislocate the target depth by 1.5–4 mm.

Optimal sensor placement for source localization based on RSSD

Source localization based on the received signal strength (RSS) has received great interest due to its low cost and simple implementation. In this paper we consider the source localization problem based on the received signal strength difference (RSSD) with unknown transmitted power of the source using spatially separated sensors. It is well- known that the relative sensor-source geometry (SSG) plays a significant role in localization performance. For this issue, the fisher information matrix (FIM) which inherently is a function of relative SSG is derived. Then for different scenarios the SSG based on the maximization of determinant of FIM is investigated to obtain the optimal sensor placement. Finally, computer simulations are used to study the performance of various sensor placements. Both theoretical analysis and simulation results reveal the ability of the proposed sensor- source geometries.