DeepTAL: Deep Learning for TDOA-Based Asynchronous Localization Security With Measurement Error and Missing Data

Efficient closed-form solution for target localization using TDOA measurements in the presence of sensor position errors

In this paper, we introduce an integration method of Global Positioning System (GPS) pseudorange and time difference of arrival (TDOA) measurements from a pilot signal of a wireless communication network to solve the navigation problem in the case that the number of visible GPS satellites is not sufficient. TDOA measurements are known to have poor accuracy due to technical limitations of a communication system and propagation environments. The major error source of TDOA is the non-line-of-sight (NLOS). To estimate the TDOA error in a cellular network, we propose a method using a Kalman filter for each TDOA channel. In addition, a method to measure TDOA errors is proposed. Some simulations and real tests are conducted to evaluate the performance of the proposed methods. Real experiments are conducted near the city center of Seoul. Using a commercial cellular phone and a GPS receiver, pseudorange of GPS and TDOAs are measured. Test results show that the proposed methods continuously provide subscribers a reasonably accurate location in the case that GPS data are occasionally insufficient.

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.

This paper proposes an improved two-step weighted least squares (TSWLS) algorithm for target location using time difference of arrival (TDOA) with sensor position errors. The performance of the TSWLS method is improved in a simple way through re-selecting reference sensor and rotating co-ordinate system, and the improved TSWLS(I-TSWLS) algorithm remains to be closed-form and approximately efficient as the TSWLS method. Simulation results show that the I-TSWLS algorithm can achieve the CRLB easily before higher noise threshold, and it exhibits lower estimation bias and better robustness with increasing sensor position errors.

In this paper, we focus on the localization of a passive source from time difference of arrival (TDOA) measurements. TDOA values are computed with respect to pairs of fixed sensors that are required to be accurately time-synchronized. This constitutes a weakness as all synchronization techniques are vulnerable to delay injections. Attackers are able either to spoof the signal or to inject asymmetric delays in the communication channel. By nature, TDOA measurements are highly sensitive to time-synchronization offsets between sensors. Our first contribution is to show that timing attacks can severely affect the localization process. With a delay of a few microseconds injected on one sensor, the resulting estimate might be several kilometers away from the true location of the unknown source. We also show that residual analysis does not enable the detection and identification of timing attacks. Our second contribution is to propose a two-step TDOA-localization technique that is robust against timing attacks. It uses a known source to define a weight for each pair of sensors, reflecting the confidence in their time synchronization. Our solution then uses the weighted least-squares estimator with the newly created weights and the TDOA measurements received from the unknown source. As a result, our method either identifies the network as being too corrupt to localize, or gives a corrected estimate of the unknown position along with a confidence metric. Numerical results illustrate the performance of our technique.

This paper focuses on underwater target tracking based on a multi-static sonar network composed of passive sonobuoys and an active ping. In the multi-static sonar network, the location of the target can be estimated using TDOA (Time Difference of Arrival) measurements. However, since the sensor network may obtain insufficient and inaccurate TDOA measurements due to ambient noise and other harsh underwater conditions, target tracking performance can be significantly degraded. We propose a robust target tracking algorithm designed to operate in such a scenario. First, track management with track splitting is applied to reduce performance degradation caused by insufficient measurements. Second, a target location is estimated by a fusion of multiple TDOA measurements using a Gaussian Mixture Model (GMM). In addition, the target trajectory is refined by conducting a stack-based data association method based on multiple-frames measurements in order to more accurately estimate target trajectory. The effectiveness of the proposed method is verified through simulations.

A multilateration system estimates the position of emitter using time difference of arrival (TDOA) measurements with a lateration algorithm. It involves solving a set of hyperbolic plane equations to determine the position of the emitter given the TDOA measurements that corresponds to the path difference (PD) measurement in distance. A performance model is developed using the relative maximum error bound (RMEB) which relates the plane equation condition number, the relative ground receiving station (GRS) geometry and the PD measurement error to estimate the position estimation (PE) error. By using air traffic monitoring for civil aviation as an application, Monte Carlo simulation verifies the PE error of the performance model for a square GRS configuration. The coverage assumed a 3600 bearing, a range of up to 200 km and a maximum altitude of 15 km. Simulation results also show that the performance model estimates the horizontal position error with a maximum absolute error of 0.1 km up to a range of 200 km at an altitude of 15 km and a minimum absolute error of 0.2 km at an altitude of 15 km.

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.

This paper focuses on the three-dimensional (3-D) source localization problem using one-dimensional (1-D) angle of arrival (AOA) and time difference of arrival (TDOA) measurements. A weighted least square (WLS) estimate is proposed by exploiting the pseudo-linearization technique for this novel scheme. This method provides a closed-form solution of the source position. Then, the Gauss-Newton method is applied to improve the accuracy further. The Cramer-Rao lower bound (CRLB) is derived to evaluate the performance. Simulation results show that the performance of the proposed localization algorithm is close to the CRLB in small measurement noise region.

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.

3-D acoustic homing using 2-D asymptotes

Ultra-Wideband (UWB) communication system provides high accurate localization due to the high multi-path resolution capacity and large bandwidth of a UWB signal. Time Difference of Arrival(TDOA) technique provides very good accuracy, which is suitable for applying to UWB communication and localization systems. Estimating the target location from TDOA measurements is not an easy task since it is dealing with a set of nonlinear equations relating to the target location and the TDOA measurements. All kinds of method is by exhaustive search, which is computationally Intensive and suffers from the initialization and convergence problems. The paper develops an linear solution that estimate the target location, which does have convergence problems. Simulation results indicate that the proposed solution calculates the position of the target precisely.

This paper addresses the problem of localizing an unknown number of static sources emitting unknown signals from time-difference of arrival (TDOA) measurements. Based on the framework of random finite sets and finite set statistics, we formulate the Bayesian estimation problem and develop a particle-based localization algorithm that overcomes the challenges related to the highly non-linear TDOA measurement model, the data associations uncertainty, and the uncertainty in the number of sources to be localized. Simulation results confirm that the number of sources can be determined correctly and accurate location estimates can be obtained when the number of false alarms is low and the probability of detection is high.

Localization has emerged as an attractive solution to enable new business models that rely on location-based services in wireless networks for communication, sensing, and control. In particular, time difference-of-arrival (TDOA) is one of the widely used localization models. However, the conventional TDOA requires precise time synchronization between a target node and anchor nodes for measuring the time difference, which leads to a large number of packets for communication. To reduce packet transmission, we propose a model for measuring the time difference without time synchronization called ASync-TDOA. Different from the conventional model, ASync-TDOA can measure the time difference in a one-way-based ranging by introducing the reference node. Specifically, the time difference between the target node and anchor nodes can be directly measured by the server based on the timestamps from the reference node. After that, the target node is accurately located using least squares and brute force for the time difference. We implement the ASync-TDOA model on a localization system with ultra-wideband signals to estimate the localization of the target node, which is easy to operate in practical engineering. The experiments show that the proposed ASync-TDOA is efficient in reducing the packet transmissions and improving the TDOA measurement and localization precision.

Accurate localization remains a critical challenge in complex environments characterized by multipath propagation, Non-Line-of-Sight (NLOS) conditions, and environmental noise. This paper presents a comprehensive study on enhancing Time Difference of Arrival (TDOA) localization systems utilizing Ultra-Wideband (UWB) signals. The contributions include the development of a robust simulation framework incorporating real-world environmental factors, a comparative analysis of deterministic and statistical approaches, and geometric optimization strategies for anchor placement. The results highlight the capability of TDOA-UWB systems for dependable implementation in industrial sectors, such as logistics, precision agriculture, and mining.