Time Difference Of Arrival Localization Research Articles

High-Precision Joint TDOA and FDOA Location System

Passive location based on TDOA (time difference of arrival) and FDOA (frequency difference of arrival) is the mainstream method for target localization. This paper proposes a fast time–frequency difference positioning method to address issues such as low accuracy, large computational resource utilization, and limited suitability for real-time signal processing in the conventional CAF (cross-ambiguity function)-based approach, aiming to complete the processing of the target radiation source to obtain the target parameters within a short timeframe. In the mixing product operation step of the CAF, a frequency-domain approach replaces the time-domain convolution operation in PW-ZFFT (pre-weighted Zoom-FFT) to reduce the computational load of the CAF. Additionally, a quadratic surface fitting method is used to enhance the accuracy of TDOA and FDOA. The localization solution is obtained using Newton’s method, which can provide more accurate results compared to analytical methods. Next, a signal processing platform is designed with FPGA (field-programmable gate array) and multi-core DSP (digital signal processor), and works by dividing and mapping the algorithm functional modules according to the hardware’s characteristics. We analyze the architectural advantages of multi-core DSP and design methods to improve program performance, such as EDMA transfer optimization, inline function optimization, and cache optimization. Finally, this paper constructs simulation tests in typical positioning scenarios and compares them to hardware measurement results, thus confirming the correctness and real-time capability of the program.

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/ .

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.

Direct, fast and convergent solvers for the non-convex and non-smooth TDoA localization problem

Time-Difference-of-Arrival (TDoA) Source Localization (SL) consists of determining the position of a target given differences of time measurements of several sensors. The TDoA SL problem is formulated as minimizing a non-convex and non-smooth least squares (LS) optimization problem, which is tackled in the existing literature mostly by solving convex relaxations or by taking the square of the measurements. In this work, we tackle the LS problem directly, by first showing that a standard fixed-point (FP) method can be derived. Due to numerical instability and lack of theoretical convergence guarantees of FP, we develop the T-NAM method. This easy-to-implement and novel method uses the Nested Alternating Minimization scheme together with the fast FISTA algorithm. We show that T-NAM converges to critical points of the original LS function – a result that, to the best of our knowledge, is unknown for the TDoA SL problem. Last, we show numerically the advantages of FP and T-NAM relatively to existing works.

Detection and localization of Goliath grouper using their low-frequency pulse sounds

The goal of this paper is to implement and deploy an automated detector and localization model to locate underwater marine organisms using their low-frequency pulse sounds. This model is based on time difference of arrival (TDOA) and uses a two-stage approach, first, to identify the sound and, second, to localize it. In the first stage, an adaptive matched filter (MF) is designed and implemented to detect and determine the timing of the sound pulses recorded by the hydrophones. The adaptive MF measures the signal and noise levels to determine an adaptive threshold for the pulse detection. In the second stage, the detected sound pulses are fed to a TDOA localization algorithm to compute the locations of the sound source. Despite the uncertainties stemming from various factors that might cause errors in position estimates, it is shown that the errors in source locations are within the dimensions of the array. Further, our method was applied to the localization of Goliath grouper pulse-like calls from a six-hydrophone array. It was revealed that the intrinsic error of the model was about 2 m for an array spanned over 50 m. This method can be used to automatically process large amount of acoustic data and provide a precise description of small scale movements of marine organisms that produce low-frequency sound pulses.

Joint TDOA, FDOA and PDOA Localization Approaches and Performance Analysis

Multi-station joint localization has important practical significance. In this paper, phase difference of arrival (PDOA) information is introduced into the joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) localization method to improve the target localization accuracy. First, the Cramer–Rao lower bound (CRLB) of the joint TDOA, FDOA and PDOA localization approach with multi-station precise phase synchronization is derived. Then, the CRLB of the joint TDOA, FDOA and differential PDOA (dPDOA) localization method for the case of phase asynchronization between observation stations is also presented. Furthermore, the authors analyze the influence of the phase wrapping problem on localization accuracy and propose solutions to solve the phase wrapping problem based on cost functions of grid search. Finally, iterative localization algorithms based on maximum likelihood (ML) are proposed for both TDOA/FDOA/PDOA and TDOA/FDOA/dPDOA scenarios, respectively. Simulation results demonstrate the localization performance of the proposed approaches.

Modeling and performance analysis of blockchain-aided secure TDOA localization under random internet-of-vehicle networks

The recent fast growth of the internet-of-vehicle (IoV) market has sparked interest in accurate positioning using time-difference-of-arrival (TDOA) schemes. However, the rapid development of the IoV networks has been challenged by a significant increase in malicious attacks that can drastically degrade the localization performance. In this paper, we propose a blockchain-aided vehicular localization scheme as protection against malicious attacks. Specifically, a lightweight and robust trust evaluation process is developed to identify malicious nodes by using target location estimates and node energy consumption behaviors. We provide a theoretical framework to characterize the impact of blockchain and computational delays on TDOA-based localization. Furthermore, a tractable Crame´r-Rao lower bound (CRLB) is derived using stochastic geometry to quantify the localization performance with random network configurations. Simulation results demonstrate that the proposed scheme efficiently protects the localization system against various malicious attacks and accurately estimates the target position even under a high proportion of malicious nodes. The devised benchmark precisely measures the blockchain-aided TDOA-based localization performance in IoV networks and provides insights into localization optimization without lengthy and complicated simulations.

TDOA positioning in the presence of atmospheric refraction and observer uncertainty influence analysis and correction

Due to the inhomogeneity of the atmosphere, radio waves are subjected to refraction during the propagation process, which reduces its propagation speed and bends the propagation path. If the influence is not considered, a large error will be caused by using time difference of arrival (TDOA). The influence of atmospheric refraction on the TDOA localization under the known elevation constraint is analyzed, a subsection iterative method is proposed to correct the localization error caused by atmospheric refraction, the Cramer-Rao lower bound (CRLB) for location estimation under atmospheric refraction is deduced. The effectiveness of the proposed method is validated through simulation results and analysis.

Robust TDOA localization based on maximum correntropy criterion with variable center

In this paper, we propose a new robust method for the time-difference-of-arrival (TDOA) localization of a source under non-line-of-sight (NLOS) conditions. According to the maximum correntropy criterion with variable center (MCC-VC), the method jointly estimates the source position together with the kernel center and bandwidth using the TDOA measurements. In particular, we formulate two optimization problems based on MCC-VC, one estimating the kernel center and bandwidth, and the other the source position. The first problem is solved by dividing it into two subproblems, which are further approximated by convex problems that can be easily solved by a convex optimization package. The second problem is also divided into two subproblems by invoking the property of the convex conjugate function, which is then solved iteratively by solving the two subproblems in an alternating manner for each iteration. The proposed method does not require any prior information on the NLOS errors, making it easy to apply. Both simulation and real experimental results show that the proposed method performs well in both sparse and dense NLOS environments.

A Novel Airspace Planning Algorithm for Cooperative Target Localization

With the development of modern electromagnetic stealth technology and ARM, traditional active radar detection cannot accomplish its detection mission, limited by its ability. Relying on such superior advantages such as imperceptibility, anti-electromagnetic interference and electromagnetic stealth, passive transducers are playing an indispensable and significant role in situation awareness. While, in addition to different passive transducer localization modes and solutions of target’s location, the reasonable planning and optimal layout of passive transducers’ location are other major factors affecting the precision of localization. Planning an optimal airspace for passive transducers is the key problem to improve the monitoring efficiency. This paper proposes the optimal layout algorithm for the cooperative platform in the space based on the geometrical relationship of cooperative localization. For example, the principle of direction location in traditional methods is simple: only two passive sensors can work, but the location accuracy of long-distance targets is low. At the same time, TDOA (Time Difference Of Arrival) location has high accuracy and good stability, but it needs at least three passive sensors to work together, which requires the most resources. In this paper, a platform optimization layout algorithm based on direction and TDOA hybrid positioning is proposed. Compared with direction positioning, it improves the long-distance positioning accuracy, reduces the number of sensors required for TDOA positioning, and reduces the resource occupancy rate. However, the TDOA positioning data mixed with direction positioning data inevitably leads to the decline of overall accuracy. In order to solve these difficulties, the weighted least square method is used to optimize the accuracy. The simulation shows that, within the designated target airspace, the optimal action airspace can be generated automatically based on the platforms’ cooperation mode. If there is no resource limitation, the airspace planning based on TDOA positioning has the highest accuracy for the target. However, in practical application, considering the resource limitation, the hybrid positioning of direction and TDOA can also meet the requirements of high accuracy and high stability. The average error is reduced by more than 45% compared with direction positioning, and the airspace occupancy is reduced by more than 30% compared with TDOA positioning. The goal of minimizing the scope of platform airspace planning is realized.

Finding the Right Place: Sensor Placement for UWB Time Difference of Arrival Localization in Cluttered Indoor Environments

Ultra-wideband (UWB) time difference of arrival (TDOA)-based localization has recently emerged as a promising indoor positioning solution. However, in cluttered environments, both the UWB radio positions and the obstacle-induced non-line-of-sight (NLOS) measurement biases significantly impact the quality of the position estimate. Consequently, the placement of the UWB radios must be carefully designed to provide satisfactory localization accuracy for a region of interest. In this work, we propose a novel algorithm that optimizes the UWB radio positions for a pre-defined region of interest in the presence of obstacles. The mean-squared error (MSE) metric is used to formulate an optimization problem that balances the influence of the geometry of the radio positions and the NLOS effects. We further apply the proposed algorithm to compute a minimal number of UWB radios required for a desired localization accuracy and their corresponding positions. In a real-world cluttered environment, we show that the designed UWB radio placements provide 47% and 76% localization root-mean-squared error (RMSE) reduction in 2D and 3D experiments, respectively, when compared against trivial placements.

A Hybrid Bald Eagle Search Algorithm for Time Difference of Arrival Localization

The technology of wireless sensor networks (WSNs) is developing rapidly, and it has been applied in diverse fields, such as medicine, environmental control, climate prediction, monitoring, etc. Location is one of the critical fields in WSNs. Time difference of arrival (TDOA) has been widely used to locate targets because it has a simple model, and it is easy to implement. Aiming at the problems of large deviation and low accuracy of the nonlinear equation solution for TDOA, many metaheuristic algorithms have been proposed to address the problems. By analyzing the available literature, it can be seen that the swarm intelligence metaheuristic has achieved remarkable results in this domain. The aim of this paper is to achieve further improvements in solving the localization problem by TDOA. To achieve this goal, we proposed a hybrid bald eagle search (HBES) algorithm, which can improve the performance of the bald eagle search (BES) algorithm by using strategies such as chaotic mapping, Lévy flight, and opposition-based learning. To evaluate the performance of HBES, we compared HBES with particle swarm algorithm, butterfly optimization algorithm, COOT algorithm, Grey Wolf algorithm, and sine cosine algorithm based on 23 test functions. The comparison results show that the proposed algorithm has better search performance than other reputable metaheuristic algorithms. Additionally, the HBES algorithm was used to solve the TDOA location problem by simulating the deployment of different quantities of base stations in a noise situation. The results show that the proposed method can obtain more consistent and precise locations of unknown target nodes in the TDOA localization than that of others.

The Complete Analytical Solution of the TDOA Localization Method

This article is focused on the analytical solution of a TDOA (Time Difference of Arrival) localization method, including analysis of accuracy and unambiguity of a target position estimation in 2D space. The method is processed under two conditions - sufficiently determined localization system and an overdetermined localization system. It is assumed that the TDOA localization system operates in a LOS (Line of Sight) situation and several time-synchronized sensors are placed arbitrarily across the area. The main contribution of the article is the complete description of the TDOA localization method in analytical form only. It means, this paper shows a geometric representation and an analytical solution of the TDOA localization technique model. In addition, analyses of unambiguity and solvability of the method algorithm are presented, together with accuracy analysis of this TDOA technique in analytical form. Finally, the description of this TDOA method is extended to an overdetermined TDOA system. This makes it possible to determine and subsequently optimize its computational complexity, for example increase its computational speed. It seems that such a description of the TDOA localization technique creates a simple and effective tool for technological implementation of this method into military localization systems.

The Geometry of Far-Field Passive Source Localization With TDOA and FDOA

Passive localization of acoustic or radio-frequency sources is often performed using time-difference-of-arrival (TDOA) measurements and/or frequency-difference-of-arrival (FDOA) measurements. TDOA localization has been thoroughly studied, but FDOA less so. This is largely because the TDOA level surfaces are hyperboloids, which are well understood, whereas the FDOA level curves and surfaces are much more complicated. This article addresses the case of known sensor positions and velocities and a stationary source. This article shows examples of the FDOA level curves and surfaces, and shows that they simplify dramatically in the far field, i.e., when the source is much farther from the origin than the sensors. The far-field behavior is of two types, depending on whether the sensor velocities are equal or unequal. The far-field behavior gives insight into conditions needed for far-field TDOA–FDOA localization and FDOA-only localization. This article includes a characterization of feasible far-field TDOA and unequal-velocity FDOA data.

A TDOA localization method for complex environment localization

Time Difference of Arrival (TDOA) algorithm is a widely used wireless network-based localization algorithm. However, with the increasing complexity of real-life localization environments, the disturbances of noise, perturbations and multi-path effect have limited the performance of the classical TDOA algorithm. In view of these, we design an Interaction-derived Sequence Selection (IDSS) method and an Interaction-derived Sequence Adjustment (IDSA) method to reduce localization error caused by Non Line of Sight (NLOS) environments. Furthermore, an Interacting Multiple Model (IMM) framework is proposed to deal with the localization problem in complex mixed environments. Experimental results demonstrate that the IDSS and IDSA methods can enhance TDOA localization performance in NLOS environments, and the IMM framework can maintain strong adaptability in complex mixed environments.

A noise robust automatic radiolocation animal tracking system

Agriculture is becoming increasingly reliant upon accurate data from sensor arrays, with localization an emerging application in the livestock industry. Ground-based time difference of arrival (TDoA) radio location methods have the advantage of being lightweight and exhibit higher energy efficiency than methods reliant upon Global Navigation Satellite Systems (GNSS). Such methods can employ small primary battery cells, rather than rechargeable cells, and still deliver a multi-year deployment. In this paper, we present a novel deep learning algorithm adapted from a one-dimensional U-Net implementing a convolutional neural network (CNN) model, originally developed for the task of semantic segmentation. The presented model (ResUnet-1d) both converts TDoA sequences directly to positions and reduces positional errors introduced by sources such as multipathing. We have evaluated the model using simulated animal movements in the form of TDoA position sequences in combination with real-world distributions of TDoA error. These animal tracks were simulated at various step intervals to mimic potential TDoA transmission intervals. We compare ResUnet-1d to a Kalman filter to evaluate the performance of our algorithm to a more traditional noise reduction approach. On average, for simulated tracks having added noise with a standard deviation of 50 m, the described approach was able to reduce localization error by between 66.3% and 73.6%. The Kalman filter only achieved a reduction of between 8.0% and 22.5%. For a scenario with larger added noise having a standard deviation of 100 m, the described approach was able to reduce average localization error by between 76.2% and 81.9%. The Kalman filter only achieved a reduction of between 31.0% and 39.1%. Results indicate that this novel 1D CNN U-Net like encoder/decoder for TDoA location error correction outperforms the Kalman filter. It is able to reduce average localization errors to between 16 and 34 m across all simulated experimental treatments while the uncorrected average TDoA error ranged from 55 to 188 m.

Multi-link channel simulation based on propagation graph theory and application in performance evaluation of TDOA positioning system

In order to solve the problems of high measurement cost and many uncontrollable interference factors in the accuracy evaluation of time difference of arrival (TDOA) localization method by measurement, a method of evaluating the accuracy of a TDOA localization system based on multi-link channel propagation graph theory is proposed. In this paper, we use the propagation graph theory to generate different channel impulse responses, and ultilize software-defined radio devices to generate channel-distorted radio frequency signals as inputs to multiple TDOA sensors and construct a novel TDOA localization evaluation method. In order to verify the accuracy of the TDOA technology effectively, we simulate the method in 4 typical scenarios. It is the first time that a complex scenario is simulated using multi-channel radio frequency signal to test the localization accuracy of the TDOA system. The simulation result shows that when the signal bandwidth is not smaller than 200 kHz, the multi-link localization system based on graph modeling shows good and stable performance. Moreover, graph modeling method with diffraction model embedded enhances the accuracy of performance simulation for the TDOA system, particularly in the non-line-of-sight scenarios.

Learning-Based Bias Correction for Time Difference of Arrival Ultra-Wideband Localization of Resource-Constrained Mobile Robots

Accurate indoor localization is a crucial enabling technology for many robotics applications, from warehouse management to monitoring tasks. Ultra-wideband (UWB) time difference of arrival (TDOA)-based localization is a promising lightweight, low-cost solution that can scale to a large number of devices-making it especially suited for resource-constrained multi-robot applications. However, the localization accuracy of standard, commercially available UWB radios is often insufficient due to significant measurement bias and outliers. In this letter, we address these issues by proposing a robust UWB TDOA localization framework comprising of (i) learning-based bias correction and (ii) M-estimation-based robust filtering to handle outliers. The key properties of our approach are that (i) the learned biases generalize to different UWB anchor setups and (ii) the approach is computationally efficient enough to run on resource-constrained hardware. We demonstrate our approach on a Crazyflie nano-quadcopter. Experimental results show that the proposed localization framework, relying only on the onboard IMU and UWB, provides an average of 42.08% localization error reduction (in three different anchor setups) compared to the baseline approach without bias compensation. We also show autonomous trajectory tracking on a quadcopter using our UWB TDOA localization approach.

A Novel Method for Location Ambiguity Mitigation of High Pulse Repetition Frequency Radar Signal in Low Earth Orbit Dual-satellite Geolocation System

In order to mitigate the location ambiguity of radar signal in Low Earth Orbit (LEO) dual-satellite Time Difference Of Arrival (TDOA) location system, the ambiguous characteristics of high PRF signal are analyzed, the process of ghost location generating by ambiguous TDOA is introduced, and a method for location ambiguity mitigation by Variation Trendline Matching of TDOA (VTMT) is proposed. If the condition that the residuals between the measured TDOA series and the theoretical TDOA series corresponding to the positioning results approximately obey normal distribution is satisfied, the location where the measured TDOA line is closest to the theoretical TDOA line can be selected as the real position of radar emitter with the Euclidean distance being used to measure the similarity between the two series. Test signal of calibration station validates the effectiveness of the proposed method. Numerical simulations demonstrate that the proposed method can increase the probability of unambiguous location significantly, reduce the requirements of TDOA measurement accuracy and observation time. The proposed method has good prospect for applications to TDOA location of radar signal in long base line location systems.

A 1-D Search Approach for Single Sensor Passive Localization Based on Signal Periodicity

An efficient one-dimensional search solution is proposed for single-sensor emitter localization based on signal periodicity. By introducing an intermediate variable, this single-sensor localization problem can be solved by solving a set of equations for classic multi-sensor time difference of arrival localization, whose algebraic solutions can be obtained by the well-known two-stage weighted least squares (TSWLS) algorithm. In this manner, the two-dimensional or three-dimensional search for the emitter location can be replaced by a one-dimensional search for the intermediate variable. Simulations indicate that, at the expense of a small loss of localization accuracy, the proposed method achieves a significant advantage in computation time, compared with the conventional maximum likelihood technique.