Frequency Difference Of Arrival Research Articles

Closed-Form Method for Unified Far-Field and Near-Field Localization Based on TDOA and FDOA Measurements

When the near-field and far-field information of a target is uncertain, it is necessary to choose a suitable localization method. The modified polar representation (MPR) method integrates the two scenarios and achieves a unified localization with direction of arrival (DOA) estimation in the far field and position estimation in the near field. Previous studies have only proposed solutions for stationary environments and have not considered the motion factor. Therefore, this paper proposes a new unified positioning algorithm using multi-sensor time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements without prior target source information. The method represents the position of the target source using MPR and describes the localization problem as a weighted least squares (WLS) problem with two constraints. We first obtain the initial estimates by WLS without considering the constraints and then investigate a two-step error correction method based on the constraints. The first step corrects the initial estimate using the Taylor series expansion technique, and the second step corrects the DOA estimate in the previous step using the direct error compensation technique based on the properties of the second constraint. Simulation experiments show that the method is effective for the unified positioning of moving targets and can achieve the Cramer–Rao lower bound (CRLB).

A Co-Localization Algorithm for Underwater Moving Targets with an Unknown Constant Signal Propagation Speed and Platform Errors.

Underwater mobile acoustic source target localization encounters several challenges, including the unknown propagation speed of the source signal, uncertainty in the observation platform's position and velocity (i.e., platform systematic errors), and economic costs. This paper proposes a new two-step closed-form localization algorithm that jointly estimates the angle of arrival (AOA), time difference of arrival (TDOA), and frequency difference of arrival (FDOA) to address these challenges. The algorithm initially introduces auxiliary variables to construct pseudo-linear equations to obtain the initial solution. It then exploits the relationship between the unknown and auxiliary variables to derive the exact solution comprising solely the unknown variables. Both theoretical analyses and simulation experiments demonstrate that the proposed method accurately estimates the position, velocity, and speed of the sound source even with an unknown sound speed and platform systematic errors. It achieves asymptotic optimality within a reasonable error range to approach the Cramér-Rao lower bound (CRLB). Furthermore, the algorithm exhibits low complexity, reduces the number of required localization platforms, and decreases the economic costs. Additionally, the simulation experiments validate the effectiveness of the proposed localization method across various scenarios, outperforming other comparative algorithms.

Enhanced Moving Source Localization with Time and Frequency Difference of Arrival: Motion-Assisted Method for Sub-Dimensional Sensor Networks

Localizing a moving source by Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) commonly requires at least N+1 sensors in N-dimensional space to obtain more than N pairs of TDOAs and FDOAs, thereby establishing more than 2N equations to solve for 2N unknowns. However, if there are insufficient sensors, the localization problem will become underdetermined, leading to non-unique solutions or inaccuracies in the minimum norm solution. This paper proposes a localization method using TDOAs and FDOAs while incorporating the motion model. The motion between the source and sensors increases the equivalent length of the baseline, thereby improving observability even when using the minimum number of sensors. The problem is formulated as a Maximum Likelihood Estimation (MLE) and solved through Gauss–Newton (GN) iteration. Since GN requires an initialization close to the true value, the MLE is transformed into a semidefinite programming problem using Semidefinite Relaxation (SDR) technology, while SDR results in a suboptimal estimate, it is sufficient as an initialization to guarantee the convergence of GN iteration. The proposed method is analytically shown to reach the Cramér–Rao Lower Bound (CRLB) accuracy under mild noise conditions. Simulation results confirm that it achieves CRLB-level performance when the number of sensors is lower than N+1, thereby corroborating the theoretical analysis.

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.

Underwater Transmitter Localization Based on TDOA and FDOA Considering the Unknown Time-Varying Emission Frequency

This article considers locating a noncooperative underwater transmitter utilizing multiple receivers, such that each receiver can measure the frequency difference of arrival (FDOA) as well as the time difference of arrival (TDOA) of the transmitter’s sound. This article considers the case where the unknown emission frequency of the transmitter changes as time goes. This article addresses hybrid TDOA-FDOA localization, under the assumption that the transmitter’s maximum speed is known in advance. To the best of our knowledge, this article is unique in tackling hybrid TDOA-FDOA localization, considering the case where the unknown emission frequency changes as time goes on. Under MATLAB simulations, this article shows that the proposed hybrid localization method is comparable to the ideal case, where the time-varying emission frequency is known in advance. Furthermore, we show that the proposed localization approach outperforms the case where the emission frequency is estimated as a wrong value.

Multiple Signal TDOA/FDOA Joint Estimation with Coherent Integration

Passive localization relies significantly on the estimation of the Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) to accurately determine the location of a target. The precision of TDOA and FDOA estimation is affected by signal parameters of time and frequency distribution. In case of multiple signals arising at different frequency bands and intercepted simultaneously by spatially separate sensors covering a wide frequency band, the traditional method is first to separate the signals from the mixed wideband signal through digital down conversion (DDC), which brings multiple narrowband signals, and then the estimation of TDOA and FDOA of each narrowband signal can be performed using cross ambiguity function (CAF). The paper introduces a novel approach for estimating TDOA and FDOA of multiple signals simultaneously, which employs a coherent integration method. First, the cross ambiguity function for each signal is realized with the narrowband signal as the same as the traditional method. Next, the phase relation of each CAF is analyzed, then the joint CAF can be obtained with phase compensation, from which multiple signal TDOA and FDOA estimations will be implemented simultaneously. Numerical simulations are performed to compare the two methods, and the results demonstrate the superiority of the proposed algorithm.

Joint Direct Estimation of Emitter Location and Antenna Beam Direction Based on Baseband Reconstruction

This paper addresses the problem of locating a stationary noncooperative emitter using multiple moving receivers. A signal baseband reconstruction based algorithm is proposed to locate the emitter directly from the received signals, without assuming static delay and Doppler shift in any observing interval. Besides the information of time-differences-of arrival (TDOA) and frequency-differences-of-arrival (FDOA), the received signal strength (RSS) information is further utilized when the source emits signals in free space with an omni antenna. In a more complex scenario where the emitter adopts a directional antenna, an iterative algorithm is proposed to jointly estimate the emitter location and its antenna beam direction, where a traditional direct position determination (DPD) method is used to initiate the iteration. The Cramér-Rao lower bounds (CRLBs) of the emitter position and the beam direction are derived. Three numerical cases are included to investigate the performance of the proposed algorithms. The signal baseband reconstruction based DPD algorithm shows improved applicability when the assumption of static time delay and Doppler shift is inappropriate and performs similarly with the classical DPD methods when the assumption holds. In case of free space propagation, it shows that the localization accuracy can be improved when RSS is further utilized. When the transmitting beam is directional, however, simply ignoring the directivity characteristics would lead to nonnegligible localization biases. By jointly estimating the emitter location and antenna beam direction, the RSS information can be effectively utilized to improve the localization accuracy, and a much more accurate estimation of beam direction can be obtained simultaneously.

Neighborhood Selection Synchronization Mechanism-Based Moving Source Localization Using UAV Swarm

To obtain the accurate time difference of arrival (TDOA) and frequency difference of arrival (FDOA) for passive localization in an unmanned aerial vehicle (UAV) swarm, UAV swarm network synchronization is necessary. However, most of the traditional distributed time synchronization protocols are based on iteration, which hinders efficiency improvement. High communication costs and long convergence times are often required in large-scale UAV swarm networks. This paper presents a neighborhood selection-all selection (NS-AS) synchronization mechanism-based moving source localization method for UAV swarms. First, the NS-AS synchronization mechanism is introduced, to model the UAV swarm network synchronization process. Specifically, the UAV neighbors are first grouped by sector, and the most representative neighbors are selected from each sector for the state update calculation. When the UAV swarm network reaches a fully connected state, the synchronization mechanism is switched to select all neighbors, to improve the convergence speed. Then, the TDOA-FDOA joint localization algorithm is employed to locate the moving radiation source. Through simulation, the effectiveness of the proposed method is verified by the system convergence and localization performance under different parameters. Experimental results show that the synchronization mechanism based on NS-AS effectively improves the convergence speed of the system while ensuring the accuracy of moving radiation source localization.

A survey of GNSS interference monitoring technologies

With the increasing economic and strategic significance of the global navigation satellite systems (GNSS), interference events also occur frequently. Interference monitoring technologies aim to monitor the interference that may affect the regular operation of the GNSS. Interference monitoring technologies can be divided into three parts: interference detection and recognition, interference source direction finding, and interference source location and tracking. Interference detection aims to determine whether interference exists. This paper introduces the classification of interference and the corresponding detection methods. The purpose of interference recognition is to recognize and classify interference. It is often combined with pattern recognition and machine learning algorithms. Interference source direction finding aims to estimate the direction of the interference signal. There are three kinds of methods: amplitude, phase, and spatial spectrum estimation. Interference source location aims to estimate the position of the interference signal. It is usually based on the received signal strength (RSS), time difference of arrival (TDOA), frequency difference of arrival (FDOA), angle of arrival (AOA) or direction of arrival (DOA). Interference source tracking aims to track moving interference sources, and it is generally based on Kalman filter theory. This paper summarizes the interference monitoring technologies and their latest progress. Finally, prospects for interference monitoring technologies are offered.

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.

Hybrid TDOA/FDOA and track optimization of UAV swarm based on A-optimality

The source location based on the hybrid time difference of arrival (TDOA)/frequency difference of arrival (FDOA) is a basic problem in wireless sensor networks, and the layout of sensors in the hybrid TDOA/FDOA positioning will greatly affect the accuracy of positioning. Using unmanned aerial vehicle (UAV) as base stations, by optimizing the trajectory of the UAV swarm, an optimal positioning configuration is formed to improve the accuracy of the target position and velocity estimation. In this paper, a hybrid TDOA/FDOA positioning model is first established, and the positioning accuracy of the hybrid TDOA/FDOA under different positioning configurations and different measurement errors is simulated by the geometric dilution of precision (GDOP) factor. Second, the Cramer-Rao lower bound (CRLB) matrix of hybrid TDOA/FDOA location under different moving states of the target is derived theoretically, the objective function of the track optimization is obtained, and the track of the UAV swarm is optimized in real time. The simulation results show that the track optimization effectively improves the accuracy of the target position and velocity estimation.

Willow Catkin Optimization Algorithm Applied in the TDOA-FDOA Joint Location Problem

The heuristic optimization algorithm is a popular optimization method for solving optimization problems. A novel meta-heuristic algorithm was proposed in this paper, which is called the Willow Catkin Optimization (WCO) algorithm. It mainly consists of two processes: spreading seeds and aggregating seeds. In the first process, WCO tries to make the seeds explore the solution space to find the local optimal solutions. In the second process, it works to develop each optimal local solution and find the optimal global solution. In the experimental section, the performance of WCO is tested with 30 test functions from CEC 2017. WCO was applied in the Time Difference of Arrival and Frequency Difference of Arrival (TDOA-FDOA) co-localization problem of moving nodes in Wireless Sensor Networks (WSNs). Experimental results show the performance and applicability of the WCO algorithm.

TDOA –FDOA method for tracking of a moving target in a distributed sensor scenario

Tracking of an underwater target in ocean environment is very important in both military and civilian applications. This paper focuses on the localization and tracking of a moving target by a passive multi-static sonar system using TOA, Time Difference and Frequency Difference of Arrival measurements. An algorithm is developed for an acoustic sensor distributed network of five sensors and an acoustic moving source. TDOAFDOA method is used to track a moving source usingTime Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) measurements, as a closed form solution. The highly nonlinear measurement equations of TDOA and FDOA are first converted into pseudo linear equations. This is achieved by introducing extra parameters. These equations are solved using a weighted least squares (WLS) method. Five distributed stationary receivers are used to track a moving acoustic target. The moving target parameters estimated from the above WLS method are improved by an Unscented Kalman Filter. The mean square errors of these estimates are compared and the results are analyzed.

A Closed-Form Solution for Source Localization Using FDOA Measurements Only

This letter focuses on source localization using frequency difference of arrival (FDOA) measurements only. An efficient two-step weighted least square (TSWLS) method is proposed to estimate the unknown source position in closed form. In its first step, intermediate variables are introduced to pseudo-linearize FDOA equations. In the second step, the source position estimate is updated from solution equations established by using the first-order perturbation analysis. Theoretical analysis and numerical results have demonstrated the efficiency of the proposed method.

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.

Geolocation of a known-altitude moving source using TDOA and FDOA in the presence of altitude error

Using precise source altitude prior information can significantly improve the source geolocation accuracy. However, in practice, the available source altitude may contain certain errors due to the movement of the source, which can affect the geolocation accuracy. This paper considers geolocating a moving source using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements in the presence of altitude error. The geolocation performance when the known altitude is assumed accurate but in fact has errors is investigated analytically. An efficient closed-form estimator is then developed for localization. The analysis results validate that the proposed closed-form estimator can attain the constrained Cramér-Rao lower bound (CCRLB) over small noise regions. Simulations show good agreement with the theoretical developments and demonstrate the good performance of the proposed geolocation method.

Fast TDOA and FDOA Estimation for Coherent Pulse Signals

Time difference of arrival (TDOA) and frequency difference of arrival (FDOA) have been widely used for localizing temporally continuous signals passively. Temporal sparsity of pulse signals makes their TDOA and FDOA estimation processes much different, and computational complexity is a major concern in this area. This paper addresses the problem of fast TDOA and FDOA estimation of pulse signals and focuses mainly on narrowband coherent pulses. By decoupling the effects of TDOA and FDOA in the cost function of localization approximately, we propose a fast coarse TDOA and FDOA estimation method. The estimates are then refined with the cross-ambiguity function (CAF) algorithm within a small TDOA and FDOA neighborhood. In the simulations, the proposed method is demonstrated to have satisfying TDOA and FDOA estimation precisions, and it exceeds existing counterparts largely in computational efficiency.

A Multi-Pulse Cross Ambiguity Function for the Wideband TDOA and FDOA to Locate an Emitter Passively

The time difference of arrival (TDOA) and frequency difference of arrival (FDOA) between two receivers are widely used to locate an emitter. Algorithms based on cross ambiguity functions can simultaneously estimate the TDOA and FDOA accurately. However, the algorithms, including the joint processing of received data, require transferring a large volume of data to a central computing unit. It can be a heavy load for the data link, especially for a wideband signal obtained at a high sampling rate. Thus, we proposed a multi-pulse cross ambiguity function (MPCAF) to compress the data before transmitting and then estimate the TDOA and FDOA with the compressed data. The MPCAF consists of two components. First, the raw data are compressed with a proposed two-dimensional compression function. Two methods to construct a reference pulse used in the two-dimensional compression function are considered: a raw data-based method constructs the pulse directly from the received signal, and a signal parameter-based method constructs it through the parameters of the received signal. Second, a wideband cross-correlation function is studied to refine the TDOA and FDOA estimates with the compressed data. The simulation and Cramer–Rao lower bound (CRLB) analyses show that the proposed method dramatically reduces the data transmission load but estimate the TDOA and FDOA well. The hardware-in-the-loop simulation confirms the method’s effectiveness.

The Joint Phantom Track Deception and TDOA/FDOA Localization Using UAV Swarm without Prior Knowledge of Radars’ Precise Locations

This paper develops the model of the joint phantom track deception and the joint techniques of time-difference of arrival (TDOA) and frequency-difference of arrival (FDOA) localization to deceive air defense radar networks under the condition that an unmanned aerial vehicle (UAV) swarm has no prior knowledge of the radars’ precise locations, and related performance experiment and analysis are presented to demonstrate the effectiveness of the proposed method and to clarify the influence factors of phantom track deception. The main contributions of this paper are as follows. Firstly, the model of phantom track deception against a radar network by UAV swarm without prior knowledge of the radars’ positions are established. Secondly, TDOA/FDOA are adapted to locate networked enemy radars using UAV swarm, where the Fisher information matrix (FIM) is derived to evaluate the estimation accuracy. Thirdly, the uncertainty analysis consisting of radar location error and UAV position error is deduced. With these efforts, the integrated capability of sensing and jamming is realized. Moreover, the same source testing using space resolution cell (SRC) from the perspective of a radar network is executed to provide guidance for phantom track design. Finally, performance experiment and analysis are given to verify the theoretical analysis with simulation results.

Location Parameter Estimation of Moving Aerial Target in Space–Air–Ground-Integrated Networks-Based IoV

Estimating the location parameters of moving target is an important part of intelligent surveillance for the Internet of Vehicles (IoV). Satellite has the potential to play a key role in many applications of space–air–ground-integrated networks (SAGINs). In this article, a novel passive location parameter estimator using multiple satellites for the moving aerial target is proposed. In this estimator, the direct wave signals in reference channels are first filtered by a band-pass filter, followed by a sequence cancelation algorithm to suppress the direct-path interference and multipath interference. Then, the fourth-order cyclic cumulant cross ambiguity function (FOCCCAF) of the signals in the reference channels and the four-weighted fractional Fourier transform FOCCCAF (FWFRFT-FOCCCAF) of signals in the surveillance channels are derived. Using them, the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) are estimated and the distance between the target and the receiver and the velocity of the moving aerial target are estimated by using multiple satellites. Finally, the Cramer–Rao lower bounds of the proposed location parameter estimators are derived to benchmark the estimator. The simulation results show that the proposed method can effectively and precisely estimate the location parameters of the moving aerial target.