Direct solution for fixed source location using well-posed TDOA and FDOA measurements

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

To weaken the effect of receiver location error on localization accuracy and make the localization model closer to the practical scenario, this paper considers the receiver location errors, usually neglected in prior studies into the measurement model, and proposes an algebraic method for locating a moving source using time difference of arrival (TDOA), frequency difference of arrival (FDOA), and differential Doppler rate measurements. The proposed method is based on the pseudo-linear set of equations and two-step weighted least square estimator. Only noise values of receiver locations and three types of positioning measurements are available for processing. In addition, a new Cramér-Rao lower bound (CRLB) combining TDOA, FDOA, and differential Doppler rate in the presence of receiver location errors is also derived in this paper. Theoretical analysis and simulation results both indicate that the proposed method can attain CRLB at a moderate noise level, avoid the rank deficiency problem efficiently, and achieve a significant improvement over the existing methods.

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.

This paper considers the problem of moving source localization by introducing an additional Doppler frequency shift (DFS) measurement into the previous location system using time differences of arrival (TDOAs) and frequency differences of arrival (FDOAs). Because of the separation of associated data channels and the difference in the estimation techniques, the DFS is independent of TDOA and FDOA measurements. The Cramer-Rao lower bound (CRLB) analysis shows that introducing DFS can improve source localization accuracy comparing with that of the TDOA and FDOA localization system, especially for the velocity location accuracy. An improved two-step weighted least-squares (I-TSWLS) source localization method utilizing DFS as well as TDOA and FDOA is developed. The solution is shown analytically to achieve the CRLB over small noise region, and have a better performance than that of the TSWLS method, especially when the sensor station error noises become large. Simulation results demonstrate the good performance of the proposed method.

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.

In this paper, we propose a cooperative localization method for moving source using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. Research on cooperative localization of moving source is an important topic to solve the passive source localization problem in different fields, such as radar, sonar, navigation, wireless communications and so forth. We investigate the improvement in source estimation accuracy. In the cooperative localization structure, a cooperative localization method based on quasi-Newton (QN) approach and two-step weighted least-squares (TSWLS) method is designed. The research results prove that the source localization accuracy has been improved effectively by using cooperative localization method based on QN-TSWLS method.

We consider the problem of geolocating two unknown co-channel emitters by a cluster of formation-flying satellites using both time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. As the association between the TDOA/FDOA measurements obtained by each pair of satellites and the corresponding emitters is typically not known, the emitter-measurement association and the emitters' locations need to be jointly estimated. In this paper, we first formulate the joint estimation problem as a mixed integer nonlinear optimization problem. Then, we propose a semidefinite relaxation-based approach to tackle the problem and demonstrate its efficacy via simulations.

This paper considers the problem of tracking a moving target using the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements obtained at two unmanned aerial vehicles (UAVs) with varying baseline. Accumulation time is necessary because the emitter position cannot be estimated at each emission when there are only two UAVs as sensors. And the target position and velocity estimation accuracy often suffer from low convergence in conventional formation flight mode no matter what nonlinear filtering algorithm is used. Based on the analysis of the influence of different flight modes on the positioning performance, a moving target tracking system from two UAVs with varying baseline is proposed. The performance of unscented Kalman filter (UKF) under proposed system is analysed and compared with the Cramer-Rao lower bound (CRLB). Simulation results show that the proposed system can speed up the convergence.

In double‐satellite interference localization system, the position of the interference source is computed by estimating the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) between the signals retransmitted by two satellites. The traditional cross ambiguity function (CAF)‐based TDOA/FDOA estimation method requires the constant TDOA/FDOA between the two received signals, which can be satisfied only when the signal length is short. Therefore, the CAF estimation method cannot be applied in long‐time accumulation (LTA). To solve this problem, a novel LTA method is proposed based on signal segmentation. In the proposed method, the two received signals are first divided into several short signal segments. Subsequently, the TDOA, the initial FDOA, and the FDOA change rate of each signal segment are estimated by a modified CAF method. After compensating the FDOA difference between the signal segments, the results are spliced again to form a complete signal without FDOA variation. Consequently, the signal energy can be concentrated and the estimation accuracy of FDOA can be improved. Experimental results of real data demonstrate that greater signal‐to‐noise ratio (SNR) gain is achieved by the proposed method, compared to the traditional CAF‐based method.

The position and velocity estimation of underwater moving targets is an important part of the application of underwater sensor networks. The commonly used fusion of time difference of arrival (TDOA) and angle of arrival (AOA) can only roughly estimate the target position, but also has some limitations for nonlinear problems. So in order to overcome the nonlinear problem and improve the accuracy of underwater target location.Based on TDOA and AOA, this paper adopts a three-step location method which combines frequency difference of arrival (FDOA).At the same time, the whale algorithm is used to optimize the measurement error based on the weighted least square method (Tswls). Finally, the experimental results show that compared with TDOA location method and tdoa/aoa hybrid location algorithm, this method is superior to the above methods in the accuracy and bias of position and velocity estimation.

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 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.

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.

Passive geolocation of communication emitters provides great benefits to military and civilian surveillance and security operations. Measurement combination for stationary emitters based on Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) may be obtained by sensors mounted on mobile platforms, for example, on a pair of Unmanned Aerial Vehicles (UAVs). This paper relies on joint TDOA/FDOA estimation algorithm. Then we put forward a kind of method by adjusting the receiver direction to improve the precision of localization. The results of the simulation show that the method can improve precision of the positioning 2–10 times.KeywordsPassive localizationDouble-star positioning systemTime differences of arrival (TDOA)Frequency differences of arrival (FDOA)Geometric dilution of precision (GDOP)

This paper presents a comprehensive study of methods for detecting and localizing electronic warfare (EW) sources under complex conditions, which include the influence of intensive intentional jamming, multipath signal propagation, time-varying emission parameters, and dynamic movement of the sources. The relevance of the research is driven by the growing role of EW means in modern armed conflicts and the need to ensure timely detection and neutralization of such threats. The classification of EW sources based on spectral, energy, and spatial characteristics is considered, along with an analysis of their impact on communication, radar, and navigation systems. Traditional methods for determining the coordinates of sources—such as amplitude, phase, TDOA (Time Difference of Arrival), and FDOA (Frequency Difference of Arrival)—are examined in detail, as well as modern approaches that rely on adaptive antenna arrays, spectral analysis, and artificial intelligence algorithms for signal identification. Special attention is given to algorithms for improving localization accuracy in noisy and dynamic environments, including adaptive filtering methods, multiposition signal processing (data fusion), optimization of sensor network configurations, and trajectory prediction of moving objects. Results of computer simulations are presented, with error assessments for various application scenarios and different interference levels. The proposed approaches can be applied in advanced electronic intelligence systems and automated EW countermeasure complexes to enhance the efficiency of real-time detection, identification, and localization of emission sources. Keywords: electronic warfare, source localization, TDOA, FDOA, adaptive antennas, artificial intelligence, multisensor processing, intensive jamming, simulation.