Source Localization Problem Research Articles

Experimental study on multi-robot 3D source localization in indoor environments with weak airflow

The purpose of this paper is to provide a new method for solving the problem of the 3D source localization in indoor environments with weak airflow by the experimental study on the multi-robot method. For this purpose, we developed a 3D MRO (mobile robot olfaction) system consisting of three mobile robots. The gas sensor carried with each robot has a moving range of 0.5 m to 1.5 m on the Z-axis. A total of 60 experiments were conducted to validate and compare the standard whale optimization algorithm (SWOA) and the standard particle swarm optimization (SPSO) methods in a 7.65 m×4.1 m experimental area with two source heights (0.75 m and 1.05 m). For two source heights, the success rate and localization step of the SPSO method are 56.7% (17/30) and 31.4 steps, respectively. In addition, the success rate and localization step of the SWOA method are 80% (24/30) and 32.9 steps, respectively. These results show that the SWOA method has strong application potential in indoor environments with weak airflow.

Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements

In this paper, we consider a time-varying optimization approach to the problem of tracking a moving target using noisy time-of-arrival (TOA) measurements. Specifically, we formulate the problem as that of sequential TOA-based source localization and apply online gradient descent (OGD) to it to generate the position estimates of the target. To analyze the tracking performance of OGD, we first revisit the classic least-squares formulation of the (static) TOA-based source localization problem and elucidate its estimation and geometric properties. In particular, under standard assumptions on the TOA measurement model, we establish a bound on the distance between an optimal solution to the least-squares formulation and the true target position. Using this bound, we show that the loss function in the formulation, albeit non-convex in general, is locally strongly convex at its global minima. To the best of our knowledge, these results are new and can be of independent interest. By combining them with existing techniques from online strongly convex optimization, we then establish the first non-trivial bound on the cumulative target tracking error of OGD. Our numerical results corroborate the theoretical findings and show that OGD can effectively track the target at different noise levels.

RFI Source Localization Based on Joint Sparse Recovery in Microwave Interferometric Radiometry

Recently, the radio frequency interference (RFI) poses a growing threat to the Microwave Interference Radiometer with Aperture Synthesis (MIRAS) led by the European Space Agency, whose scientific goal is to monitor the soil moisture and ocean salinity of the Earth. RFI localization is a critical step to mitigate the impact of RFI sources on the brightness temperature (BT) maps. In this paper, we propose an effective and robust RFI source localization approach combined with the joint sparse recovery (JSR) theory by using multi-snapshot data. The JSR method utilizes the joint sparsity property of RFI sources in the spatial domain to improve the robustness and accuracy for RFI source localization problem. First, we propose a JSR model by exploiting the joint sparsity of multi-snapshot visibility data with RFI contained from MIRAS after conducting the field of view (FOV) registration. Then, we present a greedy algorithm using the orthogonal matching pursuit on multi-snapshot data (MSOMP) to localize RFI sources. Results on synthetic data and real satellite data both show that, compared with the previous existing approaches, the proposed method has a better performance on the mitigation of the localization accuracy bias, especially for a low BT value range case and a mixed BT value range case with multiple RFI sources.

Source space reduction for eLORETA

Objective. We introduce Sparse exact low resolution electromagnetic tomography (eLORETA), a novel method for estimating a nonparametric solution to the source localization problem. Its goal is to generate a sparser solution compared to other source localization methods including eLORETA while benefitting from the latter’s superior source localization accuracy. Approach. Sparse eLORETA starts by reducing the source space of the Lead Field Matrix using structured sparse Bayesian learning from which a Reduced Lead Field Matrix is constructed, which is used as input to eLORETA. Main results. With Sparse eLORETA, source sparsity can be traded against signal fidelity; the proposed optimum is shown to yield a much sparser solution than eLORETA’s with only a slight loss in signal fidelity. Significance. When pursuing a data-driven approach, for cases where it is difficult to choose specific regions of interest, or when subsequently a connectivity analysis is performed, source space reduction could prove beneficial.

Two-dimensional detection based LRSS point recognition for multi-source DOA estimation

This paper aims to tackle the multiple source localization problem using the signals recorded by a B-format microphone in reverberant environments. The proposed approach analyses the energy and phase information of recorded signals in the time–frequency (T-F) domain to present a two-dimensional detection of low-reverberant-single-source (LRSS) points, where the pressure–velocity energy difference and pressure–velocity phase difference are exploited. The direction of arrival (DOA) estimation of actual sources by utilizing the designed weight kernel density estimation are conducted base on the direction cues derived from the LRSS points. Evaluation on simulated data and data recorded in an actual acoustic chamber demonstrates that a better performance can be obtained through the proposed algorithm in highly reverberant environments.

Closed-Form Pseudolinear Estimators for DRSS-AOA Localization.

This paper investigates the hybrid source localization problem using differential received signal strength (DRSS) and angle of arrival (AOA) measurements. The main advantage of hybrid measurements is to improve the localization accuracy with respect to a single sensor modality. For sufficiently short wavelengths, AOA sensors can be constructed with size, weight, power and cost (SWAP-C) requirements in mind, making the proposed hybrid DRSS-AOA sensing feasible at a low cost. Firstly the maximum likelihood estimation solution is derived, which is computationally expensive and likely to become unstable for large noise levels. Then a novel closed-form pseudolinear estimation method is developed by incorporating the AOA measurements into a linearized form of DRSS equations. This method eliminates the nuisance parameter associated with linearized DRSS equations, hence improving the estimation performance. The estimation bias arising from the injection of measurement noise into the pseudolinear data matrix is examined. The method of instrumental variables is employed to reduce this bias. As the performance of the resulting weighted instrumental variable (WIV) estimator depends on the correlation between the IV matrix and data matrix, a selected-hybrid-measurement WIV (SHM-WIV) estimator is proposed to maintain a strong correlation. The superior bias and mean-squared error performance of the new SHM-WIV estimator is illustrated with simulation examples.

Computation of the Double Metric Dimension in Convex Polytopes

A source detection problem in complex networks has been studied widely. Source localization has much importance in order to model many real-world phenomena, for instance, spreading of a virus in a computer network, epidemics in human beings, and rumor spreading on the internet. A source localization problem is to identify a node in the network that gives the best description of the observed diffusion. For this purpose, we select a subset of nodes with least size such that the source can be uniquely located. This is equivalent to find the minimal doubly resolving set of a network. In this article, we have computed the double metric dimension of convex polytopes R n and Q n by describing their minimal doubly resolving sets.

Single-Sensor EMI Source Localization Using Time Reversal: An Experimental Validation

The localization of electromagnetic interference (EMI) sources is of high importance in electromagnetic compatibility applications. Recently, a novel localization technique based on the time-reversal cavity (TRC) concept was proposed using only one sensor, and its application to localize EMI sources was validated numerically. In this paper, we present a validation of the proposed time-reversal process in which the forward step of the time-reversal process is performed experimentally and the backward step is carried out via numerical simulations, a realistic scenario which is applicable to practical source localization problems. To the best of the authors’ knowledge, this is the first implementation of a three-dimensional electromagnetic time-reversal process in which the forward signal is provided experimentally while the backward propagation step is carried out numerically. The considered experimental setup is formed by a partially open cavity and two monopole antennas to emulate the EMI source and the sensor (receiving antenna), respectively. Assuming that the location of the source is the feed point of the monopole antenna, the resulting three-dimensional location error in the experimental validation was only 1.49 cm, which is about one-third the length of the monopole antenna, corresponding to about λmin/2 (diffraction limit).

A novel method for asynchronous source localisation based on time of arrival measurements

Source localisation is an important component in the application of wireless sensor networks, and plays a key role in environmental monitoring, healthcare and battlefield surveillance and so on. In this article, the source localisation problem based on time-of-arrival measurements in asynchronous sensor networks is studied. Because of imperfect time synchronisation between the anchor nodes and the signal source node, the unknown parameter of start transmission time of signal source makes the localisation problem further sophisticated. The derived maximum-likelihood estimator cost function with multiple local minimum is non-linear and non-convex. A novel two-step method which can solve the global minimum is proposed. First, by leveraging dimensionality reduction, the maximum (minimum) distance maximum (minimum) time-of-arrival matching-based second-order Monte Carlo method is applied to find a rough initial position of the signal source with low computational complexity. Then, the rough initial position value is refined using trust region method to obtain the final positioning result. Comparative analysis with state-of-the-art semidefinite programming and min–max criterion-based algorithms are conducted. Simulations show that the proposed method is superior in terms of localisation accuracy and computational complexity, and can reach the optimality benchmark of Cramér–Rao Lower Bound even in high signal-to-noise ratio environments.

A Total Lp-Norm Optimization for Bearing-Only Source Localization in Impulsive Noise with SαS Distribution

This paper considers the problem of robust bearing-only source localization in impulsive noise with symmetric -stable distribution based on the Lp-norm minimization criterion. The existing Iteratively Reweighted Pseudolinear Least-Squares (IRPLS) method can be used to solve the least LP-norm optimization problem. However, the IRPLS algorithm cannot reduce the bias attributed to the correlation between system matrices and noise vectors. To reduce this kind of bias, a Total Lp-norm Optimization (TLPO) method is proposed by minimizing the errors in all elements of system matrix and data vector based on the minimum dispersion criterion. Subsequently, an equivalent form of TLPO is obtained, and two algorithms are developed to solve the TLPO problem by using Iterative Generalized Eigenvalue Decomposition (IGED) and Generalized Lagrange Multiplier (GLM), respectively. Numerical examples demonstrate the performance advantage of the IGED and GLM algorithms over the IRPLS algorithm.

Uniqueness and nonuniqueness for the [formula omitted] minimization source localization problem with three measurements

The source localization problem has been studied by many researchers and applied to a wide range of areas including Global Positioning System (GPS) localization. Although there have been studies examining closed form solutions for cases with not so large noise, only the existence of local solution in L2 minimization settings is known. In this paper, L1 minimization with three measurements is studied, and nonuniqueness examples for the minimization are provided. Futher, the uniqueness of the solution in certain conditions is stated and proven. The proof is based on the analysis for the extreme points of the objective function. The singular points are the three source points and the three measurement circles. The critical points are the Fermat point and some points located inside of one measurement circle and outside two other circles. The numbers of the latter critical points are infinite for the equilateral measurement triangle and one for nonequilateral measurement triangle. The analysis for these critical points is also provided. Finally, a few numerical implementations are provided to clarify the uniqueness and nonuniqueness of the problem.

A novel bearing-only localization for generalized Gaussian noise

A maximum likelihood estimator for bearing only source localization problem is addressed. Bearing measurements are assumed to be corrupted by additive generalized Gaussian noise, making the proposed estimator capable of keeping its performance high for a range of noise densities, i.e., from highly impulsive to uniform noises. Most previous works rely on small noise approximation and adopt recursive methods; therefore they need a good initial guess and high computational load. The novelty of this paper is to propose a non-iterative importance sampling based method to find a solution to the unconstrained lp-norm minimization problem for highly non-linear cost functions not known before. Our estimator is simple, does not need derivation or matrix multiplication operations, and requires generating a fair number of random particles.

Sparse Representation for Cardiac Electrical Activity Imaging in Magnetocardiography

Signal sparsity has been widely discussed in communication system, cloud computing, multimedia processing and computational biology. Reconstructing the sparsely distributed current sources of the heart by means of non-invasive magnetocardiography (MCG) measurement and various optimization methods provides a new way to solve the inverse problem of the cardiac magnetic field. The problem of sparse source location of MCG is in the time series of MCG measurement caused by active sparse current source, can the spatiotemporal source be reconstructed accurately and effectively? For the above problem, the scientific contributions of the paper include: (1) A modified focal underdetermined system solver algorithm is proposed for a sparse solution, by combing with dynamic regularization factor and smoothed sparse constraint; (2) Lead field matrix is reduced by prior information of cardiac magnetic field map to reduce under-determination; (3) Spatiotemporal sources are reconstructed for non-invasive cardiac electrical activity imaging. The results of real MCG data demonstrate the effectiveness of this method for cardiac electrical activity imaging. The temporal and spatial changes of the current sources are similar to the depolarization and repolarization process of the ventricle.

A Deep Q-Network for robotic odor/gas source localization: Modeling, measurement and comparative study

Robotic odor/gas source localization is a widely studied field, but most of the existing works are about rule-based algorithms. In this paper, the Deep Q-Network algorithm is applied to solve the odor source localization problem. An odor hits distribution model is proposed to model the odor concentration distribution in indoor environments, taking the dispersion by airflow, the odor molecular random walk, and the obstacles into account. The Deep Q-Network takes the stacked historic measurement data as the input and outputs the expected cumulative future reward of actions of the robots. The network is trained through 35,000 repeated episodes of random odor source localization tasks. The Deep Q-Network method is evaluated under four different environment settings in a simplified simulator and compared with two widely used odor source localization algorithms. The evaluation results demonstrate the advantages of the proposed algorithm. The algorithm is also validated in more complex indoor environments.

ECG Localization Method Based on Volume Conductor Model and Kalman Filtering.

The 12-lead electrocardiogram was invented more than 100 years ago and is still used as an essential tool in the early detection of heart disease. By estimating the time-varying source of the electrical activity from the potential changes, several types of heart disease can be noninvasively identified. However, most previous studies are based on signal processing, and thus an approach that includes physics modeling would be helpful for source localization problems. This study proposes a localization method for cardiac sources by combining an electrical analysis with a volume conductor model of the human body as a forward problem and a sparse reconstruction method as an inverse problem. Our formulation estimates not only the current source location but also the current direction. For a 12-lead electrocardiogram system, a sensitivity analysis of the localization to cardiac volume, tilted angle, and model inhomogeneity was evaluated. Finally, the estimated source location is corrected by Kalman filter, considering the estimated electrocardiogram source as time-sequence data. For a high signal-to-noise ratio (greater than 20 dB), the dominant error sources were the model inhomogeneity, which is mainly attributable to the high conductivity of the blood in the heart. The average localization error of the electric dipole sources in the heart was 12.6 mm, which is comparable to that in previous studies, where a less detailed anatomical structure was considered. A time-series source localization with Kalman filtering indicated that source mislocalization could be compensated, suggesting the effectiveness of the source estimation using the current direction and location simultaneously. For the electrocardiogram R-wave, the mean distance error was reduced to less than 7.3 mm using the proposed method. Considering the physical properties of the human body with Kalman filtering enables highly accurate estimation of the cardiac electric signal source location and direction. This proposal is also applicable to electrode configuration, such as ECG sensing systems.

Iterative Diagonal Unloading Beamforming for Multiple Acoustic Sources Localization Using Compact Sensor Arrays

Compact acoustic sensor arrays are nowadays popular devices for audio sensing due to minimum size and lightness characteristics that make it attractive for numerous applications such as human-computer interaction, acoustic scene analysis, teleconferencing systems, hearing aid, robotics, and bioacoustics. A compact array has a small inter-microphone distance that allows to reduce the spatial aliasing effect in the acoustic source localization problem, degrading however the spatial resolution. Thus, as a consequence, the capability of this class of sensors in the localization of multiple acoustic sources is rather limited. In this paper, we present an iterative diagonal unloading (IDU) beamforming suitable for the direction of arrivals (DOAs) estimation of concurrent multiple sources using compact microphone arrays. The method is based on the identification of the dominant signal, which corresponds to the largest peak in the pseudo-spectrum (i.e., the acoustic response map) computed by the DU beamformer, and on an iterative cancellation of the dominant signal from the covariance matrix to compute a new spatial pseudo-spectrum. All the pseudo-spectrum responses computed with the iterative procedure are summed to obtain a high resolution map of the acoustic scene. We analyze the DOAs estimation performance using compact uniform linear arrays (ULAs) and spherical microphone arrays (SMAs) with simulations and real acoustic data. The results show that the proposed IDU beamforming increases the spatial resolution allowing an effective localization of concurrent multiple sources.

A Feed-Forward Neural Network Approach for Energy-Based Acoustic Source Localization

The localization of an acoustic source has attracted much attention in the scientific community, having been applied in several different real-life applications. At the same time, the use of neural networks in the acoustic source localization problem is not common; hence, this work aims to show their potential use for this field of application. As such, the present work proposes a deep feed-forward neural network for solving the acoustic source localization problem based on energy measurements. Several network typologies are trained with ideal noise-free conditions, which simplifies the usual heavy training process where a low mean squared error is obtained. The networks are implemented, simulated, and compared with conventional algorithms, namely, deterministic and metaheuristic methods, and our results indicate improved performance when noise is added to the measurements. Therefore, the current developed scheme opens up a new horizon for energy-based acoustic localization, a field where machine learning algorithms have not been applied in the past.

Moving source localization using TOA and FOA measurements with imperfect synchronization

The clock bias and drift caused by imperfect time synchronization is a practical issue in localization problems. In this paper, we address the moving source localization problem using time-of-arrival and frequency-of-arrival measurements, where imperfect time synchronization is present. We transform the measurement models and formulate a nonlinear and non-convex weighted least squares (WLS) problem to jointly estimate the unknown source position, velocity, clock bias and drift. We then apply semidefinite relaxation (SDR) to the non-convex WLS problem to obtain a convex semidefinite program, which can be solved efficiently. We show through theoretical mean square error analysis that the WLS solution is able to attain the Cramer–Rao lower bound (CRLB) under small Gaussian noise condition. Simulation results show that the proposed SDR method has comparable performance with the maximum likelihood estimation method, and thus achieves the CRLB accuracy, when the noise is not too large.

Robust RSS-Based Source Localization With Unknown Model Parameters in Mixed LOS/NLOS Environments

In this paper, we address the received-signal-strength (RSS) based source localization problem in mixed line-of-sight/non-line-of-sight (LOS/NLOS) environments, where the model parameters are unknown. To accommodate the additional path losses incurred by NLOS signal propagations, we introduce a random variable to the outdoor RSS measurement model to represent the additional path loss. Based on this modified model, we propose a robust localization method for the case of unknown model parameters. Specifically, we introduce a balancing parameter and express the additional path loss term as the sum of the balancing parameter and an error term, and then formulate a robust weighted least squares (RWLS) problem to jointly estimate the source location, the unknown model parameters, and the balancing parameter. The RWLS problem is solved in an iterative manner, where the S-Lemma and the semidefinite relaxation technique are used. Both simulated and real experimental data verify that the proposed method works well in both dense and sparse NLOS environments.

Optimal Geometry Analysis for TDOA-Based Localization Under Communication Constraints

The sensor-source geometry has a significant effect on accuracy of source localization problems. In a sensor placement problem, one attempts to optimally place the sensors in the surveillance area so as to optimize a performance criterion. Sensor placement methods mainly solve the associated problems without taking any specific constraint on permissible location of sensors into account. In practical applications, however, possible location for deployment of the sensors are subject to such limitations as environmental, industrial, and communication constraints, which affects the optimal sensor-source geometry. In this article, we consider the problem of optimal sensor placement, based on time difference of arrival measurement, under some communication constraints. It is assumed that the sensors can communicate with the reference sensor only when the associated sensor-reference interdistance is lower than a given constant value (due to a limited communication budget). The analysis conducted in this article is based on the D-optimality criterion, i.e., maximizing the determinant of associated Fisher information matrix. We theoretically analyze the optimal sensor-source geometry with an arbitrary number of sensors in two cases of the source being inside and outside of the permissible sensor placement area. Numerical simulations are included to verify the theoretical results.