Time Difference Of Arrival Research Articles

Distributed extended Kalman filtering for acoustic simultaneous localization and environment mapping

The localization accuracy of Acoustic Simultaneous Localization and Mapping (ASLAM) often suffers from environmental noise and room reverberation. To solve this problem, an ASLAM method based on distributed extended Kalman filter is proposed. Specifically, the distance between the sound source and the robot is effectively estimated by the gating mechanism method in the case of unknown location of the sound source. Then, the Time Difference of Arrival (TDOA) between robots, the Direction of Arrival (DOA) and the distance between the sound source and the robot are presented as observation. Next, the robots' trajectories and the sound source's position are tracked by multiple extended Kalman filters. Finally, the ASLAM localization is completed by fusing the sound source and the robots' positioning information through average consensus algorithm, respectively. The proposed method can efficiently promote the ASLAM localization accuracy in complex acoustic environments. The experimental results verify the effectiveness of the proposed method.

Research on acoustic localization method for multiple leakage sources of water-cooling wall in furnace

Abstract The water-cooling wall of the furnace often leaks under harsh conditions such as high temperature and pressure, which affects the safety and economic operation of the boiler. To achieve the localization of multiple leakage sources in water-cooling wall, an acoustic positioning method based on improved differential evolution and density-based spatial clustering of application with noise (IDE-DBSCAN) is proposed. The nonlinear equation system is constructed using time delay of arrival (TDOA) obtained by the generalized second cross-correlation algorithm, and the IDE algorithm is used to solve nonlinear equation system and obtain multiple spatial positions corresponding to multiple TDOA sequences. To eliminate false leakage sources, the paper presents IDE-DBSCAN to cluster the multiple estimated positions. The number of clusters obtained is the number of leakage sources, and the cluster centers are the location coordinates of the leakage sources. The numerical simulation results show that compared to traditional acoustic positioning methods, IDE-DBSCAN has higher positioning accuracy and better anti-noise ability. In addition, experiments are implemented on multiple leakage sound sources within a measurement area of 1m×1m×1.06m, and the positioning errors remain within 5cm. The proposed method provides a theoretical basis and experimental verification for further research on multiple leakages localization of water-cooling wall in furnace.

PET detectors with depth-of-interaction and time-of-flight capabilities.

In positron emission tomography (PET), measurements of depth-of-interaction (DOI) information and time-of-flight (TOF) information are important. DOI information reduces the parallax error, and TOF information reduces noise by measuring the arrival time difference of the annihilation photons. Historically, these have been studied independently, and there has been less implementation of both DOI and TOF capabilities because previous DOI detectors did not have good TOF resolution. However, recent improvements in PET detector performance have resulted in commercial PET scanners achieving a coincidence resolving time of around 200ps, which result in an effect even for small objects. This means that TOF information can now be utilized even for a brain PET scanner, which also requires DOI information. Therefore, various methods have been proposed to obtain better DOI and TOF information. In addition, the cost of PET detectors is also an important factor to consider, since several hundred detectors are used per PET scanner. In this paper, we review the latest DOI-TOF detectors including the history of detector development. When put into practical use, these DOI-TOF detectors are expected to contribute to the improvement of imaging performance in brain PET scanners.

Research on features and localization of AE signals from the mechanical body of industrial robots based on WD-EMD

Abstract In order to reveal the propagation characteristics of acoustic emission (AE) signals in the body of industrial machinery, the characteristic frequencies and wave speeds of AE signals propagated on the interior and exterior surfaces (IS and ES) of the body were extracted. Subsequently, an algorithm utilizing characteristic frequency and time difference of arrival (TDOA) is proposed for the identification and localization of AE sources. Initially, an AE source is induced on the IS and ES of the body using the pencil-lead break method in accordance to ASTM standards, and the AE signal is captured by two piezoelectric sensors at a sampling frequency of 3 MHz. Then, to avoid the limitations of wavelet decomposition using self-selected wavelet scale and the problem that a single indicator cannot properly evaluate the correlation between independent mode functions (IMFs) with the original signal, this paper will conduct 4-layer wavelet decomposition of the original signal according to the response frequency range of the sensor, and select the wavelet details within the stable range of the response frequency of the sensor for preliminary reconstruction,and then the empirical mode decomposition (EMD) method is used to decompose the de-noised AE signal into 7 IMFs, and the AE waveform is reconstructed by the combined information of correlation coefficient and variance accounted for. Secondly, the reconstruction method combined with EMD analysis and a single index is compared with the proposed method in this paper to verify the reliability of the proposed method. In addition, the frequency domain characteristics of AE signal propagation process on the IS and ES of the body are extracted. Finally, based on the TDOA principle, the propagation speed of AE signal on the IS and ES of the body is calculated. Based on the geometric relationship between the AE source and two sensors, an algorithm for the location of the AE source is proposed. The results show that the proposed signal reconstruction method can effectively extract the features of AE signals, and the average positioning accuracy of the localization algorithm based on characteristic frequency and TDOA reaches 0.86%.

Single channel sound source localization by using combinations of multiple tubes

A method for localizing the direction arrival of the sound source with a single channel is proposed with the configuration of system consists of a single channel acoustic sensor and multiple inlets with specific path length of tubes or pipes. The time delay of arrival at each inlet can be estimated from the autocorrelation function measured at the sensor and the positions of peak in autocorrelation function are changed according to the incidence angle. By using this concept, the basic configurations are considered and the related investigations are conducted as solutions to several problems that need to be solved. The proposed concept is validated experimentally in anechoic chamber and outdoor conditions. As a method to expand the range of observation angle, the configuration with difference length is investigated and it is confirmed that the unique solution for the whole direction can be obtained by a combination of tubes and inlets.

Localization for surface microseismic monitoring based on arrival time correction and VFOM

Abstract Unconventional resources have emerged as the primary source to meet the escalating demand for energy consumption, with hydraulic fracturing standing out as an effective means of boosting production. The utilization of microseismic monitoring is crucial for acquiring real-time or semi-real-time extension information of the fracture network to guide the fracturing process. The precise positioning of microseismic events is a fundamental aspect of microseismic monitoring. Traditional methods relying on (relative) arrival time significantly impact positioning accuracy due to picking errors. While waveform-based methods offer high accuracy, they require precise velocity models and are time-consuming. To overcome challenges associated with arrival time pickup and velocity accuracy, we introduce a virtual field optimization method (VFOM) based on arrival time correction. Initially, an equivalent velocity model is established, and the arrival time difference resulting from the model transformation of the master event is calculated to correct the observed arrival time of the target event. Subsequently, we match detector pairs, establish hyperboloids based on the corrected arrival time difference, and employ the intersection point of all hyperboloids as the positioning result. After that, we use the location results of the master event to enhance the accuracy of the target event. Finally, we apply the proposed method to both synthetic test and field datasets, demonstrating a significant improvement in the positioning accuracy and stability provided by the novel method. The robustness against arrival time error renders it a suitable choice for surface monitoring applications where signal quality is compromised. Furthermore, the simplified velocity model significantly diminishes the computational requirements in the positioning process, enhancing its efficiency, and consequently holds vast potential for application in real-time monitoring.

Space‐Time Monitoring of Seafloor Velocity Changes Using Seismic Ambient Noise

AbstractWe use seismic ambient noise recorded by dense ocean bottom nodes (OBNs) in the Gorgon gas field, Western Australia, to compute time‐lapse seafloor models of shear‐wave velocity. The extracted hourly cross‐correlation (CC) functions in the frequency band 0.1–1 Hz contain mainly Scholte waves with very high signal‐to‐noise ratio. We observe temporal velocity variations (dv/v) at the order of 0.1% with a peak velocity change of 0.8% averaged from all station pairs, from the conventional time‐lapse analysis with the assumption of a spatially homogeneous dv/v. With a high‐resolution reference (baseline) model from full waveform inversion of Scholte waves, we present an elastic wave equation based double‐difference inversion (EW‐DD) method, using arrival time differences between the reference and time‐lapsed Scholte waves, for mapping temporally varying dv/v in the heterogeneous subsurface. The time‐lapse velocity models reveal increasing/decreasing patterns of shear‐wave velocity in agreement with those from the conventional analysis. The velocity variation exhibits a ∼24‐hr cycling pattern, which appears to be inversely correlated with the diurnal variations in sea level height, possibly associated with dilatant effects for porous, low‐velocity shallow seafloor and rising pore pressure with higher sea level. This study demonstrates the feasibility of using dense passive seismic surveys and wave‐equation time‐lapse inversion for quantitative monitoring of subsurface property changes in the horizontal and depth domain.

Quantity properties of variate and coefficient in errors-in-variables model under Gaussian noise

Total least-squares (TLS) aims to estimate the unknown parameters of an errors-in-variables (EIV) model from noisy observations when the coefficients are also perturbed by errors. It is helpful to know whether more variates and coefficients lead to more accurate estimation for TLS. In this study, our motivation was to reveal the relationship between the estimation performance and the number of variates or coefficients. The challenge was how to observe a performance change when using additional variates/coefficients. First, the Cramér–Rao bound (CRB) and the hybrid Bhattacharyya–Barankin (HBB) bound were derived for the multivariate EIV model under Gaussian noise typical to most systems. Second, we theoretically affirmed the properties by validating the analytical CRB that additional variates/coefficients were favorable. Third, the quantity properties were verified by simulation about CRB and HBB, considering the source direction estimation using time difference of arrival as an example. We conclude that the estimation performance can be improved if additional variates/coefficients are available. The multivariate TLS should be superior to the univariate one. The conclusions have significance for guiding practical system development.

Spatial acoustic emission localization method for damage to prestressed steel strands of girders using special-shaped waveguide rods

As an essential load-bearing member of post-tensioned prestressed girders, prestressed steel strands will inevitably reduce the safety and durability of the bridge if damaged. However, traditional damage localization methods for the steel strand require numerous acoustic emission (AE) sensors with a complex arrangement in the prestressed girder. This study proposes a spatial AE localization method using a dual-sensor array with the assistance of special-shaped waveguide rods. The spatial damage localization is achieved by combining the time difference of arrival (TDOA) of the AE wave with the propagation attenuation law. Transverse and longitudinal damage localization for prestressed steel strands are verified on a simplified platform containing different special-shaped waveguide rods. For transverse damage localization, the TDOA of the maximum AE amplitudes is superior to that of the first waves. For longitudinal damage localization, the relative localization accuracy reaches 94%. With this method, only two AE sensors are required to localize the three-dimensional damage to the prestressed steel strands in a girder.

Novel Response Surface Technique for Composite Structure Localization Using Variable Acoustic Emission Velocity.

The time difference of arrival (TDOA) method has traditionally proven effective for locating acoustic emission (AE) sources and detecting structural defects. Nevertheless, its applicability is constrained when applied to anisotropic materials, particularly in the context of fiber-reinforced composite structures. In response, this paper introduces a novel COmposite LOcalization using Response Surface (COLORS) algorithm based on a two-step approach for precise AE source localization suitable for laminated composite structures. Leveraging a response surface developed from critical parameters, including AE velocity profiles, attenuation rates, distances, and orientations, the proposed method offers precise AE source predictions. The incorporation of updated velocity data into the algorithm yields superior localization accuracy compared to the conventional TDOA approach relying on the theoretical AE propagation velocity. The mean absolute error (MAE) for COLORS and TDOA were found to be 6.97 mm and 8.69 mm, respectively. Similarly, the root mean square error (RMSE) for COLORS and TODA methods were found to be 9.24 mm and 12.06 mm, respectively, indicating better performance of the COLORS algorithm in the context of source location accuracy. The finding underscores the significance of AE signal attenuation in minimizing AE wave velocity discrepancies and enhancing AE localization precision. The outcome of this investigation represents a substantial advancement in AE localization within laminated composite structures, holding potential implications for improved damage detection and structural health monitoring of composite structures.

Where's Whaledo: A software toolkit for array localization of animal vocalizations.

Where's Whaledo is a software toolkit that uses a combination of automated processes and user interfaces to greatly accelerate the process of reconstructing animal tracks from arrays of passive acoustic recording devices. Passive acoustic localization is a non-invasive yet powerful way to contribute to species conservation. By tracking animals through their acoustic signals, important information on diving patterns, movement behavior, habitat use, and feeding dynamics can be obtained. This method is useful for helping to understand habitat use, observe behavioral responses to noise, and develop potential mitigation strategies. Animal tracking using passive acoustic localization requires an acoustic array to detect signals of interest, associate detections on various receivers, and estimate the most likely source location by using the time difference of arrival (TDOA) of sounds on multiple receivers. Where's Whaledo combines data from two small-aperture volumetric arrays and a variable number of individual receivers. In a case study conducted in the Tanner Basin off Southern California, we demonstrate the effectiveness of Where's Whaledo in localizing groups of Ziphius cavirostris. We reconstruct the tracks of six individual animals vocalizing concurrently and identify Ziphius cavirostris tracks despite being obscured by a large pod of vocalizing dolphins.

Research on pipeline leakage localization method based on CZIM algorithm

The time difference of arrival is a common method to find the leakage point of water pipeline. The leakage point localization is achieved by calculating the time delay between the signals reaching different sensors. Mainstream time delay estimation algorithms based on signal correlation analysis are susceptible to the introduction of noise signals, low sampling rates, and signal clipping, resulting in inaccurate localization results. The article analyzed the impact of different interference factors and proposed a new time delay estimation algorithm based on signal cross-zero information modulation (CZIM) to address these problems. By normalizing the amplitude of the two signals at the detection points on both sides of the pipeline leakage position, two sets of sparse signal sequences with only two eigenvalues of 0 and 1 are obtained. The error coefficient function is calculated by a similar traversal method to finally index the time delay. In this paper, the principle and characteristics of the algorithm are analyzed and compared with the most commonly used GCC method. In both numerical simulations and actual pipe leakage localization experiments, the CZIM algorithm has shown its wide applicability, low impact by low sampling rate, and adaptability to low signal-to-noise ratios, etc. At the same time, the algorithm is simple in design and has a small amount of calculation and can meet the demand for real-time data processing, providing a new idea for the development of acoustic localization technology.

A Co-Localization Algorithm for Underwater Moving Targets with an Unknown Constant Signal Propagation Speed and Platform Errors.

Underwater mobile acoustic source target localization encounters several challenges, including the unknown propagation speed of the source signal, uncertainty in the observation platform's position and velocity (i.e., platform systematic errors), and economic costs. This paper proposes a new two-step closed-form localization algorithm that jointly estimates the angle of arrival (AOA), time difference of arrival (TDOA), and frequency difference of arrival (FDOA) to address these challenges. The algorithm initially introduces auxiliary variables to construct pseudo-linear equations to obtain the initial solution. It then exploits the relationship between the unknown and auxiliary variables to derive the exact solution comprising solely the unknown variables. Both theoretical analyses and simulation experiments demonstrate that the proposed method accurately estimates the position, velocity, and speed of the sound source even with an unknown sound speed and platform systematic errors. It achieves asymptotic optimality within a reasonable error range to approach the Cramér-Rao lower bound (CRLB). Furthermore, the algorithm exhibits low complexity, reduces the number of required localization platforms, and decreases the economic costs. Additionally, the simulation experiments validate the effectiveness of the proposed localization method across various scenarios, outperforming other comparative algorithms.

An efficient estimator for source localization in WSNs using RSSD and TDOA measurements

Range-based localization has received considerable attention in wireless sensor networks due to its ability to efficiently locate the unknown source of a signal. However, the localization accuracy with a single set of measurements may be inadequate, especially in dynamic and noisy environments. To mitigate this problem, received signal strength difference (RSSD) and time difference of arrival (TDOA) measurements are used to develop an efficient estimator to reduce the bias and improve localization accuracy. First, the RSSD/TDOA-based maximum likelihood (ML) localization problem is transformed into a hybrid information nonnegative constrained least squares (HI-NCLS) framework. Then, this framework is used to develop an effective bias-reduction localization approach (BRLA) with a two-step linearization process. The first step employs a linear solving method (LSM) which exploits an active set method to obtain a sub-optimal estimator. The second step uses a bias reduction method (BRM) to mitigate the correlation from linearization and a weighted instrumental variables matrix (IVM) which is weakly correlated with the noise but strongly correlated with the data matrix (DM) is used in place of the DM. Performance results are presented which demonstrate that the proposed BRLA provides better localization performance than state-of-the-art methods in the literature.

Collaborative positioning for emergency rescuers based on INS, GPS and ZigBee

Multi-person cooperative positioning is one of the main techniques to improve the success rate of search and rescue. Nevertheless, current integrated positioning solutions for ZigBee and inertial navigation system (INS) are insufficiently versatile and commonly necessitate pre-existing infrastructure within the area. In this study, it is not necessary to install ZigBee positioning anchors in the environment in advance, and all positioning devices were mounted on rescuers, in contrast to previous positioning methods. First, an improved time difference of arrival (TDOA) method is proposed, which weights the position coordinates to minimize positioning errors. Then, the position data of the commander and the rescuers are substituted into the hyperbolic equations of the improved TDOA method, and the initial position of the rescuers is solved by Taylor method. Finally, based on the initial position, an improved Extended Kalman filter (EKF) position update technology is proposed, which uses ZigBee positioning system to monitor the east and north position of rescuers, and uses barometers to measure the altitude of rescuers. The magnetometers are used to limit the heading angle of the rescuers, so as to realize the high-precision 3D positioning of the emergency rescuers in the harsh environment. In this paper, three different scenarios are used to verify the effectiveness of the proposed method. The experimental results demonstrate that, when compared to the inertial positioning method, the traditional TDOA method, and the cooperative positioning method based on the relative ranging constraints of UWB and INS, respectively, the average positioning accuracy of the proposed method is 68.58%, 48.71%, and 13.59% higher.

TDOA-based UWB indoor 1D localization via weighted sliding window filtering

Accurate localization of a person or object is a significant aspect in the field of industrial internet of things (IoT). Ultra-wideband (UWB) localization system, a promising technology, has been widely studied due to its high accuracy in 2D and 3D scenarios. Moreover, in narrow corridors and deep-well environments, the 1D localization is also an important application with the advantage of resource saving, however which attracts less attention. In this paper, we focus on the problem of 1D localization and propose a practical localization model with time difference of arrivals (TDOA). To solve the nonlinear 1D localization problem, we design an algorithm that integrates the dichotomous method and Newton's iterative method, which realizes an efficient solution. Meanwhile, in order to cope with the random errors in the real scenes, we introduce a sliding window algorithm to filter out the undesirable solutions. By observing the localization error map, we design a weighted sliding window algorithm to achieve further improvement of the localization accuracy. In addition, we derive the Cramér-Rao lower bound (CRLB) for 1D localization of TDOA. Simulations and practical experiments show that our proposed algorithm greatly benefits the localization accuracy of 1D TDOA and provides strong support for its practical application.

Enhanced Moving Source Localization with Time and Frequency Difference of Arrival: Motion-Assisted Method for Sub-Dimensional Sensor Networks

Localizing a moving source by Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) commonly requires at least N+1 sensors in N-dimensional space to obtain more than N pairs of TDOAs and FDOAs, thereby establishing more than 2N equations to solve for 2N unknowns. However, if there are insufficient sensors, the localization problem will become underdetermined, leading to non-unique solutions or inaccuracies in the minimum norm solution. This paper proposes a localization method using TDOAs and FDOAs while incorporating the motion model. The motion between the source and sensors increases the equivalent length of the baseline, thereby improving observability even when using the minimum number of sensors. The problem is formulated as a Maximum Likelihood Estimation (MLE) and solved through Gauss–Newton (GN) iteration. Since GN requires an initialization close to the true value, the MLE is transformed into a semidefinite programming problem using Semidefinite Relaxation (SDR) technology, while SDR results in a suboptimal estimate, it is sufficient as an initialization to guarantee the convergence of GN iteration. The proposed method is analytically shown to reach the Cramér–Rao Lower Bound (CRLB) accuracy under mild noise conditions. Simulation results confirm that it achieves CRLB-level performance when the number of sensors is lower than N+1, thereby corroborating the theoretical analysis.

Fast iterative shooter localization in urban terrain using ray casting.

This study presents a method for real-time capable localization of impulsive acoustic events in urban terrain, omitting the need for precomputation phases, such as in time matching or impulse response matching. Using ray casting, solutions of the wave equation are computed using a boundary discretization of intersected objects, forming a weighted graph using line of sight checks, and deploying an A* search graph traversal algorithm for the calculation of the propagation time. Subsequently, the wave amplitude along the identified eigenrays is computed. The study discusses the properties and suitability of cost functions based on time differences of arrival, amplitude differences of arrival, and a combined cost function for iterative ray-based localization. The method is validated using pressure data of the muzzle blasts of various firearms collected via unattended ground sensors during an experimental campaign at the military urban combat facility in Walenstadt, Switzerland.

Fast and Fault-Tolerant Passive Hyperbolic Localization Using Sensor Consensus

The accuracy of passive hyperbolic localization applications using Time Difference of Arrival (TDOA) measurements can be severely compromised in non-line-of-sight (NLOS) situations. Consensus functions have been successfully used to provide robust and accurate location estimates in such challenging situations. In this paper, a fast branch-and-bound computational method for finding the global maximum of consensus functions is proposed and the global convergence property of the algorithm is mathematically proven. The performance of the method is illustrated by simulation experiments and real measurements.

Two-Dimensional Target Localization Approach via a Closed-Form Solution Using Range Difference Measurements Based on Pentagram Array

This paper presents a simple and fast closed-form solution approach for two-dimensional (2D) target localization using range difference (RD) measurements. The formulation of the localization problem is derived using a pentagram array. The target position is determined using passive radar measurements (RDs) between the target and the (N+1=10) receivers’ locations. The method facilitates the problem of target position and can be used as a counter-parallel method for spherical interpolation (SI) and spherical intersection (SX) methods in time difference of arrival (TDOA) and radar systems. The performance of the method is examined in 2D target localization using numerical analysis under the distribution of receivers in the pentagram array. The simulations are conducted using four different far-distance targets and comparatively large-area distributed receivers. The RD measurements were distorted by two different values of Gaussian errors based on ionosphedriec time delays of 20 and 50 nsec owing to the different receivers’ positions. The findings highly verified the validity of the method for addressing the problem of target localization. Additionally, a theoretical accuracy study of the method is given, which solely relies on the RD measurements.