Search Results (22)

Distributed passive acoustic tracking is an important technique for detecting and localizing a non-cooperative underwater target, in which the frequency difference of arrival (FDOA) is a widely used measurement. FDOA reflects the differences in the target’s radial velocity relative to spatially distributed receiving nodes through Doppler-induced variations in the instantaneous frequencies of line-spectrum components. However, conventional FDOA-based methods rely heavily on the stable and accurate estimation of instantaneous line-spectrum frequencies, and their performance degrades when the line spectrum is affected by frequency fluctuations caused by target operating variations and external disturbances. To address this issue, this paper proposes a new measurement, the cross-correlation frequency difference of arrival (CFDOA), which exploits the temporal correlation of line-spectrum to characterize inter-node radial-velocity differences and reduces the reliance on accurate instantaneous-frequency estimation. To evaluate the effect of the proposed CFDOA measurement on positioning performance, a unified FDOA/CFDOA measurement equation is established within the same target position estimation framework. In addition, for scenarios with a limited number of receiving nodes, a recursive estimation scheme combining constrained initial-state search and particle filtering is developed. The simulation and sea-trial results demonstrate that, in the presence of line-spectrum frequency fluctuations, the proposed CFDOA measurement yields more accurate position estimates than conventional FDOA. Full article

This paper presents the Gaussian conditional method (GCM) for the problem of frequency difference of arrival (FDOA)-only source localization under correlated noise. GCM identifies the source position through approximating its posterior distribution using a Gaussian mixture model (GMM) and applying successive conditioning to the measurement likelihood. The algorithm development leverages the fact that FDOA measurements follow a multivariate Gaussian distribution with a non-diagonal covariance. Simulation results demonstrate that GCM can achieve the Cramér–Rao lower bound (CRLB) under moderate noise levels, while having lower computational complexity than baseline techniques including the recently developed Gaussian division method (GDM). The proposed algorithm is particularly effective for passively locating narrowband sources, where the time difference of arrival (TDOA) measurements become unreliable, and it can operate without the need for accurate initialization. Full article

To address the problem of accurate localization of high-speed drone swarm intrusions, this paper adopts time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements, aiming to improve the performance of estimating the motion state of drone swarms. To this end, a two-step strategy is proposed in this study. Firstly, a small number of sensor nodes with random locations are selected in the wireless sensor network, and the constraint-weighted least squares (CWLS) method is used to obtain the rough position and speed information of the drone swarm. Based on this rough information, the objective function of node optimization is constructed and solved using the randomized semidefinite program (SDP) algorithm proposed in this paper to screen out the sensor nodes with optimal localization performance. Secondly, the sensor nodes screened in the first step are used to re-localize the drone swarm, and the CWLS problem is constructed by combining the TDOA and FDOA measurements, and a deviation elimination scheme is proposed to further improve the localization accuracy of the drone swarm. Simulation results show that the randomized SDP algorithm proposed in this paper has the optimal localization effect, and moreover, the bias reduction scheme proposed in this paper can make the localization error of the drone swarm reach the Cramér–Rao Lower Bound (CRLB) with a low signal-to-noise ratio (SNR). Full article

For real-time detection scenarios such as battlefield reconnaissance and surveillance, where high positioning accuracy is required and receiving station resources are limited, we propose an innovative distributed aerial target localization method with low degrees of freedom. This method is based on a hybrid measurement approach. First, a measurement model is established using the spatial geometric relationship between the distributed node network configuration and the target, with angle of arrival (AOA) and time difference of arrival (TDOA) measurements employed to estimate partial target parameters. Then, frequency difference of arrival (FDOA) measurements are utilized to enhance the accuracy of parameter estimation. Finally, using inter-node measurements, a pseudo-linear system of equations is constructed to complete the three-node aerial target localization. The method uses satellites as radiation sources to transmit signals, with unmanned aerial vehicles (UAVs) acting as receiving station nodes to capture the signals. It effectively utilizes hybrid measurement information, enabling aerial target localization with only three receiving stations. Simulation results validate the significant advantages of the proposed algorithm in enhancing localization accuracy, reducing system costs, and optimizing resource allocation. This technology not only provides an efficient and practical localization solution for battlefield reconnaissance and surveillance systems but also offers robust technical support and broad application prospects for the future development of unmanned systems, intelligent surveillance, and emergency rescue. Full article

In this paper, the problem of source localization using only frequency difference of arrival (FDOA) measurements is considered. A new FDOA-only localization technique is developed to determine the position of a narrow-band source. In this scenario, time difference of arrival (TDOA) measurements are not normally useful because they may have large errors due to the received signal having a small bandwidth. Conventional localization algorithms such as the two-stage weighted least squares (TSWLS) method, which jointly exploits TDOA and FDOA measurements for positioning, are thus no longer applicable since they will suffer from the thresholding effect and yield meaningless localization results. FDOA-only localization is non-trivial, mainly due to the high nonlinearity inherent in FDOA equations. Even with two FDOA measurements being available, FDOA-only localization still requires finding the roots of a high-order polynomial. For practical scenarios with more sensors, a divide-and-conquer (DAC) approach may be applied, but the positioning solution is suboptimal due to ignoring the correlation between FDOA measurements. To address these challenges, in this work, we propose a Bayesian approach for FDOA-only source positioning. The developed method, referred to as the Gaussian division method (GDM), first converts one FDOA measurement into a Gaussian mixture model (GMM) that specifies the prior distribution of the source position. Next, the GDM assumes uncorrelated FDOA measurements and fuses the remaining FDOAs sequentially by invoking nonlinear filtering techniques to obtain an initial positioning result. The GDM refines the solution by taking into account and compensating for the information loss caused by ignoring that the FDOAs are in fact correlated. Extensive simulations demonstrate that the proposed algorithm provides improved performance over existing methods and that it can attain the Cramér–Rao lower bound (CRLB) accuracy under moderate noise levels. Full article

In the context of the Jammertest 2023, a collaborative experiment was carried out by the European Commission Joint Research Centre (JRC), the European Space Operations Centre of ESA (ESOC), the Norwegian Communication Authority, and the Norwegian Defense Research Establishment (FFI) to explore potential RF interference monitoring in the navigation GNSS band from LEO. The experiment utilizes the ESA OPS-SAT satellite and the possibility of transmitting a custom jamming signal pattern during the Jammertest event. The objective is to validate the feasibility of detecting and locating ground-generated jamming signals using SDR technology on-board LEO. The insight into the signal structure and location provides a unique chance to assess the performance and limitations of this approach in a real-world scenario. This paper presents the processing of raw RF data collected during the in-flight experiment, including the generation of frequency difference of arrival (FDOA) observables and emitter geolocation. Despite the constraints posed by onboard resources and mission limitations, this work offers a persuasive proof of concept and suggests new guidelines for implementing this technology on future LEO missions. Full article

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