Search Results (16)

Based on the generalized cross-correlation method (GCC), the period peaks in the cross-correlation function (CCF) of frequency shift keying (FSK) signals will degrade the estimation performance of time difference of arrival (TDOA), as well as the estimation performance of frequency difference of arrival (FDOA), through the cross ambiguity function (CAF), in the case of a low signal-to-noise ratio (SNR). An improved TDOA/FDOA estimation algorithm made using period peaks is proposed in this paper to better understand the performance of TDOA/FDOA estimation for FSK signals. First, the cross ambiguity function of FSK signals is computed, and the peak position of the CAF is found to obtain coarse TDOA/FDOA estimation results, as per the usual method. Next, the mainlobe and period sidelobes are found according to the peak position and period interval; then, the peaks of each sidelobe around the mainlobe are found, and the period TDOA estimations are obtained. Then, the improved TDOA estimation can be used to calculate the average value of period TDOA estimations. Last, the period sidelobes accumulate to the mainlobe, and the improved FDOA estimation result are obtained by finding the peak position of the accumulated mainlobe. Simulations are performed to demonstrate that the proposed algorithm provides a better performance. Full article

The Doppler effect caused by the rapid movement of high-speed rail services has a great impact on the accuracy of train positioning and speed measurement. Existing train positioning algorithms require a large number of trackside equipment and sensors, resulting in high construction and maintenance costs. Aiming to solve the above two problems, this article proposes a train positioning algorithm based on orthogonal time–frequency space (OTFS) modulation and integrated sensing and communication (ISAC). Firstly, based on the OTFS, the positioning and speed measurement architecture of communication awareness integration is constructed. Secondly, a two-stage estimation (TSE) algorithm is proposed to estimate the delay Doppler parameters of HST. In the first stage, a low-complexity coarse grid search is used, and in the second stage, a refined off-grid search is used to obtain the delay Doppler parameters. Then, the time difference of arrival/frequency difference of arrival (TDOA/FDOA) algorithm based on multiple base stations is used to locate the target, the weighted least square method is used to calculate the location, and the Cramér–Rao lower bound (CRLB) for positioning and speed measurement is derived. The simulation results demonstrate that, compared to GNSS/INS and OFDM radars, the algorithm exhibits enhanced positioning and speed measurement accuracy. Full article

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). Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

Due to the large measurement error in the practical non-cooperative scene, the passive localization algorithms based on traditional numerical calculation using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) often have no solution, i.e., the estimated result cannot meet the localization background knowledge. In this context, this paper intends to introduce interval analysis theory into joint FDOA/TDOA-based localization algorithm. The proposed algorithm uses the dichotomy algorithm to fuse the interval measurement of TDOA and FDOA for estimating the velocity and position of a moving target. The estimation results are given in the form of an interval. The estimated interval must contain the true values of the position and velocity of the radiation target, and the size of the interval reflects the confidence of the estimation. The point estimation of the position and the velocity of the target is given by the midpoint of the estimation interval. Simulation analysis shows the efficacy of the algorithm. Full article