Time Difference Of Arrival Measurements Research Articles

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.

High-Precision Time Difference of Arrival Estimation Method Based on Phase Measurement

In unmanned aerial vehicle (UAV)-based time difference of arrival (TDOA) positioning technique, baselines are limited due to communication constraints. In this case, the accuracy is highly sensitive to the TDOA measurements’ error. This article primarily addresses the problem of short-baseline high-precision time synchronization and TDOA measurement. We conducted a detailed analysis of error models in TDOA systems, considering both the time and phase measurement. We utilize the frequency division wireless phase synchronization technique in TDOA systems. Building upon this synchronization scheme, we propose a novel time delay estimation method that relies on phase measurements based on the integer least squares method. The performance of this method is demonstrated through Monte Carlo simulations and outdoor experiments. The standard deviations of synchronization and TDOA measurements in experiments are 1.12 ps and 1.66 ps, respectively. Furthermore, the circular error probable (CEP) accuracy is improved from 0.33%R to 0.02%R, offering support for the practical application of distributed short-baseline high-precision passive location techniques.

UTIL: An ultra-wideband time-difference-of-arrival indoor localization dataset

Ultra-wideband (UWB) time-difference-of-arrival (TDOA)-based localization has emerged as a promising, low-cost, and scalable indoor localization solution, which is especially suited for multi-robot applications. However, there is a lack of public datasets to study and benchmark UWB TDOA positioning technology in cluttered indoor environments. We fill in this gap by presenting a comprehensive dataset using Decawave’s DWM1000 UWB modules. To characterize the UWB TDOA measurement performance under various line-of-sight (LOS) and non-line-of-sight (NLOS) conditions, we collected signal-to-noise ratio (SNR), power difference values, and raw UWB TDOA measurements during the identification experiments. We also conducted a cumulative total of around 150 min of real-world flight experiments on a customized quadrotor platform to benchmark the UWB TDOA localization performance for mobile robots. The quadrotor was commanded to fly with an average speed of 0.45 m/s in both obstacle-free and cluttered environments using four different UWB anchor constellations. Raw sensor data including UWB TDOA, inertial measurement unit (IMU), optical flow, time-of-flight (ToF) laser altitude, and millimeter-accurate ground truth robot poses were collected during the flights. The dataset and development kit are available at https://utiasdsl.github.io/util-uwb-dataset/ .

Reverberation-Robust Self-Calibration and Synchronization of Distributed Microphone Arrays by Mitigating Heteroscedasticity and Outlier Occurrence in TDoA Measurements.

The network of distributed microphone arrays is usually established in an ad hoc manner; hence, network parameters such as the mutual positioning and rotation of the arrays, positions of sources, and synchronization of their recording onset times are initially unknown. In this article, we consider the problem of passively jointly self-calibrating and synchronizing distributed arrays in reverberant rooms. We use a typical two-step approach where, initially, the relative geometry of the network is estimated using Direction of Arrival (DoA) measurements. Subsequently, the absolute scale and synchronization parameters are estimated using Time Difference of Arrival (TDoA) measurements. This article presents methods to improve the robustness and accuracy of estimation of the absolute geometric scaling and synchronization parameters in reverberant conditions, in which TDoA measurements do not follow a normal distribution; furthermore, outliers often occur. To remedy these issues, we propose a Weighted Least Squares (WLS) estimator and schema for weighting the TDoA measurements to increase the estimation accuracy from heteroscedastic TDoA measurements. In addition, we propose an iterative reweighing algorithm with a binary weight to detect and reject TDoA outliers, which exploits the residuals of the parametric model in the least absolute value minimization. A numerical evaluation shows significant improvements in the proposed method over the state of the art in terms of the relative scaling error and mean absolute value of the synchronization parameters.

Closed-Form DoA Solution for Co-Centered Orthogonal Microphone Arrays Based on Multilateration Equations

This study proposes a closed-form direction-of-arrival (DoA) solution derived from multilateration equations for microphone arrays of co-centered and orthogonal pairs. The generalized cross-correlation phase transform (GCC-Phat) algorithm is used to obtain the time-difference-of-arrival (TDoA) values. Simulation studies have shown the success of our proposed method compared to existing DoA methods in the literature by varying the sampling frequency of the sound signal, inter-microphone distances, and the source distance. The results from the simulation are validated by the measurements from our experiments. Our proposed solution gives better results than the far-field solution against the angle error, which is more pronounced at incidence angles smaller than 15°. These angle errors, which approach 3° using the far-field method, are reduced to less than 0.5 degrees using our proposed solution. Our solution also gives more stable results against TDoA measurement errors. Our proposed solution achieves a 66% improvement for azimuth angle and 5.88% improvement for elevation angle compared to the simulation results in the absence of TDoA measurement error, outperforming the far-field approach. When normally distributed sampling error is added to TDoA measurements, with a standard deviation of three samples, our proposed solution achieves a 41% improvement for azimuth angle and a 5.44% improvement for elevation angle. In our field measurements, an absolute mean error of 0.94 degrees was observed with our proposed method for azimuth angle. It is shown to be a more stable and faster solution method for real-time applications.

A two‐stage iterative method for short‐wave source localisation

AbstractShort‐wave source localisation has an important role in many fields. A two‐stage iterative algorithm is proposed based on the ionospheric virtual height (IVH) model using the direction of arrival (DOA) and time difference of arrival (TDOA) measurements, which is divided into DOA stage and TDOA stage. The optimisation problem of the TDOA stage can be obtained by using the result of DOA stage and TDOA measurements. During the solution process, the non‐convex quadratic equation constraints are converted to linear constraints, which can lead to the algorithm converges to the global optimal solution and the optimal solution can be analytically solved. The theoretical analysis demonstrates that the localisation accuracy of both stages can reach the corresponding constrained Cramér‐Rao lower bound (CCRLB). And the accuracy of TDOA stage achieves the CCRLB of hybrid localisation. Finally, the performance of the proposed method is demonstrated by simulations.

An Efficient Hybrid Multi-Station TDOA and Single-Station AOA Localization Method

Multi-station passive localization algorithms based on hybrid Time Difference of Arrival (TDOA) and Angle of Arrival (AOA) have been thoroughly studied. But it usually requires each station to obtain the AOA of the source and relies on the precise station position. These conditions are generally not satisfied in practical applications. In addition, the geometry between the source and these stations also affects the localization accuracy. This paper studies the passive source localization problem based on multi-station TDOA and single-station AOA measurements. First, we propose a closed-form solution source localization method based on multi-station TDOA and single-station AOA measurements, which requires only the reference station used to calculate TDOA to be able to observe the AOA measurements of the source. It solves the problem of hybrid localization of different numbers of TDOA and AOA measurements. Theoretical analysis proves that the performance of the proposed method can reach the Cramer-Rao Lower Bound (CRLB) under small noise conditions. Then, we model the relationship between the position of each station relative to the source and the localization accuracy. Through the D-optimality criterion, we obtain the optimal geometry between multiple stations and the source Simulation results confirm the validity of these theories.

Acoustic TDOA Measurement and Accurate Indoor Positioning for Smartphone

The global satellite navigation signal works well in open areas outdoors. However, due to its weakness, it is challenging to position continuously and reliably indoors. In this paper, we developed a hybrid system that combines radio signals and acoustic signals to achieve decimeter-level positioning indoors. Specifically, acoustic transmitters are synchronized with different codes. At the same time, our decoding scheme only requires a simple cross-correlation operation without time-frequency analysis. Secondly, acoustic signals will be reflected by glass, walls and other obstacles in the indoor environment. Time difference of arrival (TDOA) measurement accuracy is seriously affected. We developed a robust first path detection algorithm to obtain reliable TDOA measurement values. Finally, we combine the maximum likelihood (ML) algorithm with the proposed TDOA measurement method to obtain the location of the smartphone. We carried out static positioning experiments for smartphones in two scenes. The experimental results show that the average positioning error of the system is less than 0.5 m. Our system has the following advantages: (1) smartphone access. (2) an unlimited number of users. (3) easily deployed acoustic nodes. (4) decimeter-level positioning accuracy.

3D TDOA Emitter Localization Using Conic Approximation.

This paper develops a new time difference of arrival (TDOA) emitter localization algorithm in the 3D space, employing conic approximations of hyperboloids associated with TDOA measurements. TDOA measurements are first converted to 1D angle of arrival (1D-AOA) measurements that define TDOA cones centred about axes connecting the corresponding TDOA sensor pairs. Then, the emitter location is calculated from the triangulation of 1D-AOAs, which is formulated as a system of nonlinear equations and solved by a low-complexity two-stage estimation algorithm composed of an iterative weighted least squares (IWLS) estimator and a Taylor series estimator aimed at refining the IWLS estimate. Important conclusions are reached about the optimality of sensor-emitter and sensor array geometries. The approximate efficiency of the IWLS estimator is also established under mild conditions. The new two-stage estimator is shown to be capable of outperforming the maximum likelihood estimator while performing very close to the Cramer Rao lower bound in poor sensor-emitter geometries and large noise by way of numerical simulations.

Fundamental Limits of Doppler Shift-Based, ToA-Based, and TDoA-Based Underwater Localization

Dear Editor, This paper is concerned with the underwater localization based on acoustic signals. Specifically, we will focus on the search of an underwater target that can constantly broadcast a beacon signal, such as a black box. Common measurements for localization are Doppler shift [1], time of arrival (ToA) [2]–[4], time difference of arrival (TDoA) [5], [6], angle of arrival (AoA) [7], etc. In this paper we will investigate the fundamental limits of Doppler shift-Based, ToA-Based, TDoA-based underwater localization. Note that AoA is not covered, because Doppler shift can be viewed as one type of AoA. The discussion will focus on short-baseline positioning with a mobile anchor, i.e., an autonomous underwater vehicle (AUV). Due to the large distance and the limited battery life of the AUV, the target is quite likely to lie outside the convex hull of the AUV's trajectory. In such cases, we will show that accurate localization is almost impossible by exclusively dependent on a single type of measurements. However, system performance will be significantly improved by combing Doppler shift with ToA or TDoA measurements. The reason for such improvement will be unveiled theoretically and numerically in this letter.

Robust localization under NLOS environment in the presence of isolated outliers by full-Set TDOA measurements

Different from the traditional approach of using the reduced set of time-difference-of-arrival (TDOA) measurements, localization by the full TDOA set is discussed here. It avoids choosing a specific reference sensor and exploits more measurements, conferring robustness against outliers. Nevertheless, the none-line-of-sight (NLOS) propagation still presents challenges for the existing full-set positioning algorithms. In this work, we develop an iterative scheme that utilizes the full TDOA measurements for localization capable of simultaneously mitigating the influence of outliers and NLOS-path measurements. The proposed scheme consists of the localization and identification modules, and they are designed with low complexity to meet real-time positioning demands. The theoretical optimal TDOA methods using full-set measurements are proposed in the localization module. Besides, to identify the NLOS measurements, the identification module adopts a greedy search-based random sample consensus (GS-RSC) algorithm. It can work cooperatively with the proposed lightweight localization module, returning a set free of outliers, NLOS measurements, and an accurate source location estimate. The theoretical analysis and experiments illustrate the superiority of the proposed scheme over the state-of-the-art TDOA full-set algorithms for handling outliers and NLOS measurements in localization.

An iterative algorithm for the joint estimation of multiple targets and observation stations using direction of arrival and time difference of arrival measurements despite station position errors

AbstractDirection of arrival (DOA) and time difference of arrival (TDOA) hybrid localisation is an effective localisation technique. Station position errors affect localisation performance. Owing to the highly non‐linear nature of the problem, there are few methods of DOA/TDOA hybrid localisation in the presence of station position errors. Hence, an iterative constrained weighted least squares (ICWLS) algorithm is proposed to estimate locations of multiple targets and stations for DOA/TDOA hybrid localisation with station position errors. To ensure convergence to the global optimal solution, non‐convex equality constraints are approximated to linear constraints during each iteration. The weighted averaging strategy using the results of the previous iteration is used to reduce the number of iterations. Theoretical analysis and simulation results show that the ICWLS can reach the Cramér–Rao lower bound. Additionally, the performance of multiple targets is better than that of a single target. The simulation results show that the ICWLS algorithm has higher accuracy than other methods and higher localisation accuracy can be maintained when the observation stations are under an ill‐conditioned geometry.

TDOA-Based Target Tracking Filter While Reducing NLOS Errors in Cluttered Environments.

We consider tracking a moving target in a wireless communication system that is based on the radio signal. Considering a bounded workspace with many unknown obstacles, we handle tracking a non-cooperative transmitter using multiple signal receivers. Here, a non-cooperative transmitter is a transmitter whose signal emission time is not known in advance. We consider a time difference of arrival (TDOA) location problem, which locates the transmitter by processing the signal measurement time at multiple receivers. In tracking a non-cooperative transmitter, non-line-of-sight (NLOS) errors occur if obstacles block the LOS line connecting the receiver and the moving transmitter. Our article addresses how to track a moving transmitter while decreasing the NLOS error in TDOA-only measurements. We propose an algorithm to localize a transmitter while decreasing the NLOS error in TDOA measurements. For tracking a moving transmitter in real time, we integrate the proposed localization algorithm and the interacting multiple model Kalman filter (IMM KF). As far as we know, our article is novel in tracking a moving transmitter based on TDOA-only measurements in an unknown mixed LOS/NLOS workspace. We show that the proposed filter considerably decreases the NLOS errors in TDOA-only measurements while running fast. Therefore, the proposed tracking scheme is suitable for tracking a moving transmitter in real time. Through MATLAB simulations, we show that the proposed filter outperforms other state-of-the-art TDOA filters, considering both time efficiency and tracking accuracy.

Bayesian detection and tracking of odontocetes in 3-D from their echolocation clicks.

Localization and tracking of marine animals can reveal key insights into their behaviors underwater that would otherwise remain unexplored. A promising nonintrusive approach to obtaining location information of marine animals is to process their bioacoustic signals, which are passively recorded using multiple hydrophones. In this paper, a data processing chain that automatically detects and tracks multiple odontocetes (toothed whales) in three dimensions (3-D) from their echolocation clicks recorded with volumetric hydrophone arrays is proposed. First, the time-difference-of-arrival (TDOA) measurements are extracted with a generalized cross-correlation that whitens the received acoustic signals based on the instrument noise statistics. Subsequently, odontocetes are tracked in the TDOA domain using a graph-based multi-target tracking (MTT) method to reject false TDOA measurements and close gaps of missed detections. The resulting TDOA estimates are then used by another graph-based MTT stage that estimates odontocete tracks in 3-D. The tracking capability of the proposed data processing chain is demonstrated on real acoustic data provided by two volumetric hydrophone arrays that recorded echolocation clicks from Cuvier's beaked whales (Ziphius cavirostris). Simulation results show that the presented MTT method using 3-D can outperform an existing approach that relies on manual annotation.

A Practice-Distributed Thunder-Localization System with Crowd-Sourced Smart IoT Devices.

Lightning localization is of great significance to weather forecasting, forest fire prevention, aviation, military, and other aspects. Traditional lightning localization requires the deployment of base stations and expensive measurement equipment. With the development of IoT technology and the continuous expansion of application scenarios, IoT devices can be interconnected through sensors and other technical means to ultimately achieve the goal of automatic intelligent computing. Therefore, this paper proposes a low-cost distributed thunder-localization system based on IoT smart devices, namely ThunderLoc. The main idea of ThunderLoc is to collect dual-microphone data from IoT smart devices, such as smartphones or smart speakers, through crowdsourcing, turning the localization problem into a search problem in Hamming space. We studied the dual microphones integrated with smartphones and used the sign of Time Difference Of Arrival (TDOA) as measurement information. Through a simple generalized cross-correlation method, the TDOA of thunderclaps on the same smartphone can be estimated. After quantifying the TDOA measurement from the smartphone node, thunder localization was performed by minimizing the Hamming distance between the binary sequence and the binary vector measured in a database. The ThunderLoc system was evaluated through extensive simulations and experiments (a testbed with 30 smartphone nodes). The extensive experimental results demonstrate that ThunderLoc outperforms the main existing schemes in terms of effectively locating position and good robustness.

Bayesian detection and tracking of odontocetes in 3D from their echolocation clicks

To study behaviors of marine mammals in a nonintrusive manner, their bio-acoustical signals can be recorded by volumetric hydrophone arrays that provide time difference of arrival (TDOA) measurements for localization and tracking. Multi-target tracking (MTT) in 3-D using TDOA measurements from multiple sensors, however, must cope with non-linear measurement models and high-dimensional states. False alarms, missed detections and unknown data associations impose further challenges, often requiring human operators to annotate the data manually. We propose a data processing chain that automatically detects and tracks odontocetes from their echolocation clicks. The echolocation clicks are detected with a generalized cross-correlation that whitens the instrument noise. Two stages of tracking are performed using a tracking framework based on factor graphs and the sum-product algorithm (SPA). The odontocetes are first tracked in the TDOA domain to remove false alarms and then in the 3-D domain, fusing the tracked TDOAs across all sensors. To efficiently handle the considered non-linear and high-dimensional MTT scenario, particle flow is embedded in the SPA. According to simulation results, the proposed tracking method outperforms the existing approach using manual data annotation. Tracking of Cuvier’s beaked whales (Ziphius cavirostris), whose echolocation clicks are recorded by two volumetric hydrophone arrays, is demonstrated.

An Improved Chaos Driven Hybrid Differential Evolutionand Butterfly Optimization Algorithm for Passive Target Localization Using TDOA Measurements

This paper addresses the problem of time difference of arrival (TDOA) based passive target localizationand proposes an improved chaos-driven hybrid differential evolution (DE) algorithm and butterfly optimization algorithm (BOA), named ICDEBOA, to solve this complex optimization problem. The proposed algorithm consists of a new mutation strategy with the mechanisms of the BOA algorithm incorporated into the DE algorithm. To boost optimization effectiveness, chaos theory is employed to adjust the control parameter values. The considered localization problem is formulated using the maximum likelihood estimator. To perform the accuracy comparison, the convex constrained weighting least squares algorithm is applied to the considered localization problem as the widely used method in literature. The statistical analysis shows that the proposed modifications to the ICDEBOA algorithm improve its optimization performance, as demonstrated by the improved performance on the CEC2014 benchmark problems. The ICDEBOA algorithm is also shown to be more robust than existing algorithms in noisy environments. Numerical simulation results show that the proposed ICDEBOA algorithm meets the CRLB and achieves better performance than the CWLS, DE, and BOA algorithms.

Multistatic Localization by Differential Time Delays and Time Differences of Arrival in the Absence of Transmitter Position

We can only extract the differential time delay (DTD) measurements between the direct and reflected paths in multistatic localization when there is no synchronization in time between the transmitter and receiver and among the receivers. This paper first addresses the problem of multistatic localization of a fixed object when the transmitter position is not available by using the DTD measurements. We propose a two-step optimization method for jointly estimating the object and transmitter positions. In the first step, we formulate a non-convex constrained weighted least squares (CWLS) problem by transforming the DTD measurement model and introducing nuisance variables. Such a non-convex CWLS problem is then relaxed to a tractable convex semidefinite programming (SDP) problem by applying semidefinite relaxation. In the second step, the error coming from relaxation and approximation in the SDP solution is reduced iteratively through solving a generalized trust region subproblem (GTRS) in each iteration. If the receivers are synchronized such that the time difference of arrival (TDOA) measurements can be acquired in addition to DTD, we formulate a different CWLS problem by utilizing both DTD and TDOA measurements, which is solved by convex relaxation as well. The relaxed SDP problem can achieve the optimal solution of the CWLS problem, and further refinement is no longer needed. We conduct the mean square error (MSE) analysis to validate that both proposed methods are able to achieve the Cramer-Rao Lower Bound (CRLB) performance under small Gaussian noise, which is also validated by simulations.

Geolocation and Tracking by TDOA Measurements Based on Space–Air–Ground Integrated Network

Due to the development of manufacturing and launch technologies for satellites, there are now more and more satellite networks. Hence, cooperative reconnaissance is possible to implement among satellite networks, aerial vehicles and ground stations. In this paper, we study the method of geolocation and tracking by time difference of arrival (TDOA) measurements based on space–air–ground integrated (SAGI) network. We first analyze the Cramer Rao lower bound (CRLB) for the source localization accuracy in different coordinate systems. Then, we compare the effects of different system errors, such as clock synchronization error, position bias of the observers, elevation bias of the target and non-horizontal velocity of the target. Further, we also develop a maximum likelihood (ML) estimator for target position and velocity. Finally, the theoretical performance of the proposed estimator is validated via computer simulations.

Emitter Location Using Frequency Difference of Arrival Measurements Only.

It is desirable to enable emitter location using frequency difference of arrival (FDoA) measurements only, since many signals are characterized by coarse range resolution and fine Doppler resolution. For instance, while using the cross-ambiguity function (CAF) to measure the time difference of arrival (TDoA) and the FDoA of a narrowband signal, it is difficult to obtain accurate TDoA measurements because the Doppler resolution is higher than the range resolution. Grid-based and sample-based algorithms are developed to solve the two-dimensional (2D) emitter location problem, where the solution space is approximated, respectively, by generating deterministic and random emitter location candidates. Simulation results corroborate the viability of both non-iterative algorithms to estimate the emitter location using a single-time snapshot of FDoA measurements only, without any prior location information or any knowledge about the distribution of measurement errors. The achieved accuracies are sufficient for early warning purposes, preparing defenses, and cueing more accurate location sensors by directing additional surveillance resources.