A Novel Long‐Time Accumulation Method for Double‐Satellite TDOA/FDOA Interference Localization

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 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.

The cross ambiguity function (CAF) has been commonly used to find time difference of arrival (TDOA) and frequency difference of arrival (FDOA). In most cases, direct computation of the CAF by using a conventional method such as fast Fourier transform is too computationally intensive. Thus, a two-stage approach consisting of a coarse mode to find rough TDOA/FDOA estimates and a fine mode for precise estimation was introduced. However, there has been no methodology for selecting an interpolation factor determined by the sampling frequency and target precision which significantly affects the computational complexity. In addition, even if the computational complexity can be reduced by using the optimal interpolation factor, the huge transmission data through the datalink between sensors and the central station still remains to be an obstacle for an electronic warfare (EW) system. In this respect, we derive an optimal interpolation factor and then propose a new two-stage TDOA/FDOA estimation algorithm using a resampling block to reduce the computational complexity and the data size simultaneously in EW systems. In the proposed method, the optimal interpolation factor can be used irrespective of the sampling frequency and the target precision. Simulation results show that the optimal interpolation factor efficiently reduces the computational burden without the loss of estimation performance.

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.

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.

Robust TDOA/FDOA estimation from emitter signals for hybrid localization using UAVs

Uncertainty in sensor (receiver) locations can seriously deteriorate the source localization accuracy. A localization algorithm needs to take the sensor location errors into account in order to improve source location estimate. This paper considers the localization for the position and velocity of a moving source using the time differences of arrival (TDOAs) and frequency differences of arrival (FDOAs) of a signal received at a number of sensors that have random location errors. The proposed method is based on the Taylor-series method that jointly estimates both the source and sensor locations simultaneously. Simulation results show that with a reasonable initial guess close to the true solution to begin with, the proposed method converges to the true solution and achieves the CRLB accuracy for both near-field and far-field sources.

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 this paper, geolocation problem using noisy differences in time of arrival (TDOA) and frequency difference of arrival (FDOA) measurements is considered, and a sub-BLUE solution is proposed, a new TDOA/FDOA based recursive geolocation algorithm is also developed. The efficiency of the new algorithms is illustrated with simulation results.

The location and velocity information gives crucial impacts and supports in many applications. In this paper, we address the the problem of source localization based on time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements. The nonlinear and nonconvex maximum likelihood estimation can be approximated by Monte Carlo importance sampling technique. We derive the importance function analogous to Gaussian distribution based on Fisher information matrix (FIM) where the global convergence can be guaranteed with sufficient samples. Then we consider the source localization under sensor location uncertainties. The localization information of both sensors and source is jointly estimated by importance sampling. The simulation results illustrate that the proposed method is superior than other existing methods and it can attain the Cramer-Rao lower bound at moderate noise levels.

This paper focuses on localizing a moving source with time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements in a wireless sensor network. An improved two-stage weighted least squares closed-form solution is proposed. The weighted spherical-interpolation method and deviation refining method are applied in the first and second stage respectively. It is analytically verified that the performance of proposed solution can attain the Cramer-Rao lower bound under mild Gaussian noise assumption. The proposed solution is shown to be effective and significantly decreases the bias of the estimate in terms of numerical simulations.

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