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Keywords = time-difference-of-arrival (TDOA)

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37 pages, 7185 KB  
Article
Position Calibration of Shallow-Sea Hydrophone Arrays in Reverberant Environments
by Changjing Xiong, Bo Yang, Wei Wang, Yeyao Liu, Tianli Liu, Dahai Yu and Chuanhe Li
J. Mar. Sci. Eng. 2025, 13(10), 1922; https://doi.org/10.3390/jmse13101922 - 7 Oct 2025
Viewed by 119
Abstract
To address the problem of shallow-sea hydrophone calibration, this paper proposes a shallow-sea hydrophone calibration algorithm for the horizontal and depth directions, respectively. In the horizontal direction, a calibration method combining an improved Particle Swarm Optimization (PSO) algorithm and the Time Difference Of [...] Read more.
To address the problem of shallow-sea hydrophone calibration, this paper proposes a shallow-sea hydrophone calibration algorithm for the horizontal and depth directions, respectively. In the horizontal direction, a calibration method combining an improved Particle Swarm Optimization (PSO) algorithm and the Time Difference Of Arrival (TDOA) algorithm is proposed. In the depth direction, a depth calibration formula using the time delay difference between Non-Line-of-Sight (NLOS) waves and Line-of-Sight (LOS) waves is put forward. By combining this with the proposed PSO algorithm, the PSO NLOS–LOS depth correction algorithm is obtained. The specific position of the hydrophone is determined by combining the algorithms for horizontal direction and depth. The advantages of the proposed algorithms are verified through simulations and experiments. Simulations show that in the horizontal direction, the proposed algorithm can reduce the average calibration error under different hydrophone array radii to 0.8690 m. In the depth direction, the specific propagation delay is unknown. Compared with the traditional depth calculation method, which requires the specific propagation delay to be known, the algorithm proposed in this paper can reduce the impact on depth calculation caused by delay deviation due to sound ray refraction; in addition, it provides stronger robustness and more accurate depth calibration in shallow sea environments. The new method shows significant improvement in the depth calculation process compared with the traditional algorithm, especially in terms of fault tolerance for errors in the horizontal direction. Experiments show that by combining the calibration algorithms proposed in this paper, the positioning accuracy of the hydrophone array is significantly improved and the average positioning error of the hydrophone array is reduced to within 12 m. Full article
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16 pages, 1669 KB  
Article
An Improved Adaptive Kalman Filter Positioning Method Based on OTFS
by Siqi Xia, Aijun Liu and Xiaohu Liang
Sensors 2025, 25(19), 6157; https://doi.org/10.3390/s25196157 - 4 Oct 2025
Viewed by 399
Abstract
To mitigate the degradation of positioning accuracy in sixth-generation mobile communication systems under dynamic line-of-sight (LOS) and non-line-of-sight (NLOS) conditions, this paper proposes an improved adaptive Kalman filter positioning method based on Orthogonal Time Frequency Space (OTFS)-modulated signals. Firstly, the distance can be [...] Read more.
To mitigate the degradation of positioning accuracy in sixth-generation mobile communication systems under dynamic line-of-sight (LOS) and non-line-of-sight (NLOS) conditions, this paper proposes an improved adaptive Kalman filter positioning method based on Orthogonal Time Frequency Space (OTFS)-modulated signals. Firstly, the distance can be measured by using the OTFS-modulated signals transmitted between base stations and nodes. Secondly, the distance information is converted into the distance difference information to establish the time difference of arrival (TDOA) positioning equation, which is preliminarily solved using the Chan algorithm. Thirdly, residuals are calculated based on the preliminary positioning results, dividing the complex environment into distinct regions and adaptively determining corresponding genetic factors for each region. Finally, the selected genetic parameters are substituted into the Sage–Husa adaptive Kalman filter equations to estimate positioning results. The simulation analysis demonstrates that in complex environments featuring both line-of-sight and non-line-of-sight conditions, the vehicle motion trajectories estimated using this method more closely approximate actual trajectories. Additionally, both the accuracy and stability of positioning results show significant improvement compared to traditional methods. Full article
(This article belongs to the Section Communications)
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24 pages, 3995 KB  
Article
Research on Leakage Localization in Gaseous CO2 Pipelines Using the Acoustic Emission Method
by Xinze Li and Yao Ma
Appl. Sci. 2025, 15(19), 10501; https://doi.org/10.3390/app151910501 - 28 Sep 2025
Viewed by 198
Abstract
In the CCUS industrial chain, the pipeline transportation of CO2 is a crucial link that connects the upstream and downstream. However, currently, there is still no reliable, stable, and efficient method for detecting pipeline leaks. Based on the time difference in arrival [...] Read more.
In the CCUS industrial chain, the pipeline transportation of CO2 is a crucial link that connects the upstream and downstream. However, currently, there is still no reliable, stable, and efficient method for detecting pipeline leaks. Based on the time difference in arrival (TDOA) localization method within the acoustic emission technique, this study conducted preliminary experiments on air pipeline leak localization and experiments on gaseous CO2 pipeline leak localization, thereby establishing the applicability of acoustic emission technology for leak detection in gaseous CO2 pipelines. In the preliminary experiment on air pipeline leak location, the SNR (signal-to-noise ratio) of the CEEMDAN denoising algorithm is greater than that of the EEMD denoising algorithm. The larger the SNR, the smaller the signal interference, which proves the superiority of the CEEMDAN denoising algorithm. In the experiment on gaseous CO2 pipeline leak location, the CEEMDAN denoising algorithm was adopted. Five time-delay estimation methods, namely GCC, Roth weighting, PHAT weighting, ML weighting, and SCOT weighting, were used for location calculations. The positioning accuracies were 10.6%, 6.9%, 6.9%, 8.6%, and 8.6% respectively, all meeting the engineering accuracy requirements. Combining the results of the preliminary experiment on air pipeline leak location, the Roth weighting time-delay estimation method is recommended. The results show that: Acoustic emission technology can be used for the leak location of gaseous CO2 pipelines. Full article
(This article belongs to the Topic Oil and Gas Pipeline Network for Industrial Applications)
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21 pages, 5975 KB  
Article
Research on the Localization Method of Outdoor Ground Vibration Signals Based on MEMS Accelerometers
by Runping Liu, Xiuyan Zhao, Bin Zhou and Qi Wei
Sensors 2025, 25(18), 5776; https://doi.org/10.3390/s25185776 - 16 Sep 2025
Viewed by 395
Abstract
Addressing the need for intrusion detection and localization in critical areas, this study develops a method for outdoor ground vibration source localization utilizing subterranean-deployed MEMS accelerometers. First, the Particle Swarm Optimization (PSO) algorithm is employed to minimize the Geometric Dilution of Precision (GDOP), [...] Read more.
Addressing the need for intrusion detection and localization in critical areas, this study develops a method for outdoor ground vibration source localization utilizing subterranean-deployed MEMS accelerometers. First, the Particle Swarm Optimization (PSO) algorithm is employed to minimize the Geometric Dilution of Precision (GDOP), thereby determining the optimal configuration of the sensor array. The acquired signals are then filtered, and a novel time delay estimation algorithm, termed the Sliding Window Derivative (SWD) algorithm, is proposed. This method utilizes a sliding window to compute the sum of squared differences between adjacent sampling points within the window, generating a time-windowed energy change signal. The derivative of this signal yields a rate-of-change curve, highlighting abrupt signal transitions. The SWD algorithm, in conjunction with the STA/LTA–AIC algorithm, precisely identifies the first arrival point of the vibration signal, determining its time of arrival at each of the four sensors. Finally, an improved two-step weighted least squares method based on Time Difference of Arrival (TDOA) is used to calculate the position of the vibration source. Experimental results demonstrate an average positional error of 0.095 m and an average directional error of 0.935 degrees, validating the efficacy of the proposed method in achieving high-precision localization in outdoor environments. Full article
(This article belongs to the Section Navigation and Positioning)
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17 pages, 1743 KB  
Article
Robust Blind Algorithm for DOA Estimation Using TDOA Consensus
by Danilo Greco
Acoustics 2025, 7(3), 52; https://doi.org/10.3390/acoustics7030052 - 26 Aug 2025
Viewed by 613
Abstract
This paper proposes a robust blind algorithm for direction of arrival (DOA) estimation in challenging acoustic environments. The method introduces a novel Time Difference of Arrival (TDOA) consensus framework that effectively identifies and filters outliers using Median and Median Absolute Deviation (MAD) statistics. [...] Read more.
This paper proposes a robust blind algorithm for direction of arrival (DOA) estimation in challenging acoustic environments. The method introduces a novel Time Difference of Arrival (TDOA) consensus framework that effectively identifies and filters outliers using Median and Median Absolute Deviation (MAD) statistics. By combining this consensus approach with whitening transformation and Lawson norm optimization, the algorithm achieves superior performance in noisy and reverberant conditions. Comprehensive simulations demonstrate that the proposed method significantly outperforms traditional approaches and modern alternatives such as SRP-PHAT and robust MUSIC, particularly in environments with high reverberation times and low signal-to-noise ratios. The algorithm’s robustness to impulsive noise and varying microphone array configurations is also evaluated. Results show consistent improvements in DOA estimation accuracy across diverse acoustic scenarios, with root mean square error (RMSE) reductions of up to 30% compared to standard methods. The computational complexity analysis confirms the algorithm’s feasibility for real-time applications with appropriate implementation optimizations, showing significant improvements in estimation accuracy compared to conventional approaches, particularly in highly reverberant conditions and under impulsive noise. The proposed algorithm maintains consistent performance without requiring prior knowledge of the acoustic environment, making it suitable for real-world applications. Full article
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51 pages, 15030 KB  
Review
A Review on Sound Source Localization in Robotics: Focusing on Deep Learning Methods
by Reza Jalayer, Masoud Jalayer and Amirali Baniasadi
Appl. Sci. 2025, 15(17), 9354; https://doi.org/10.3390/app15179354 - 26 Aug 2025
Cited by 1 | Viewed by 1578
Abstract
Sound source localization (SSL) adds a spatial dimension to auditory perception, allowing a system to pinpoint the origin of speech, machinery noise, warning tones, or other acoustic events, capabilities that facilitate robot navigation, human–machine dialogue, and condition monitoring. While existing surveys provide valuable [...] Read more.
Sound source localization (SSL) adds a spatial dimension to auditory perception, allowing a system to pinpoint the origin of speech, machinery noise, warning tones, or other acoustic events, capabilities that facilitate robot navigation, human–machine dialogue, and condition monitoring. While existing surveys provide valuable historical context, they typically address general audio applications and do not fully account for robotic constraints or the latest advancements in deep learning. This review addresses these gaps by offering a robotics-focused synthesis, emphasizing recent progress in deep learning methodologies. We start by reviewing classical methods such as time difference of arrival (TDOA), beamforming, steered-response power (SRP), and subspace analysis. Subsequently, we delve into modern machine learning (ML) and deep learning (DL) approaches, discussing traditional ML and neural networks (NNs), convolutional neural networks (CNNs), convolutional recurrent neural networks (CRNNs), and emerging attention-based architectures. The data and training strategy that are the two cornerstones of DL-based SSL are explored. Studies are further categorized by robot types and application domains to facilitate researchers in identifying relevant work for their specific contexts. Finally, we highlight the current challenges in SSL works in general, regarding environmental robustness, sound source multiplicity, and specific implementation constraints in robotics, as well as data and learning strategies in DL-based SSL. Also, we sketch promising directions to offer an actionable roadmap toward robust, adaptable, efficient, and explainable DL-based SSL for next-generation robots. Full article
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20 pages, 1235 KB  
Article
Variable-Speed UAV Path Optimization Based on the CRLB Criterion for Passive Target Localization
by Lijia Chen, Chengfeng You, Yixin Wang and Xueting Li
Sensors 2025, 25(17), 5297; https://doi.org/10.3390/s25175297 - 26 Aug 2025
Cited by 1 | Viewed by 708
Abstract
The performance of passive target localization is significantly influenced by the positions of unmanned aerial vehicle swarms (UAVs). In this paper, we investigate the problem of UAV path optimization to enhance the localization accuracy. Firstly, a passive target localization signal model based on [...] Read more.
The performance of passive target localization is significantly influenced by the positions of unmanned aerial vehicle swarms (UAVs). In this paper, we investigate the problem of UAV path optimization to enhance the localization accuracy. Firstly, a passive target localization signal model based on the time difference of arrival (TDOA) algorithm, which is then improved by the Chan method and Taylor series expansion, is established. Secondly, the Cramer–Rao lower bound (CRLB) of the modified TDOA algorithm is derived and adopted as the evaluation criterion to optimize the UAVs’ positions at each time step. Different from the existing works, in this paper, we consider the UAVs to have variable speed; therefore, the feasible region of the UAVs’ positions is changed from a circle into an annular region, which will extend the feasible region, enhancing the localization accuracy while increasing the computation complexity. Thirdly, to improve the efficiency of the UAV path optimization algorithm, the particle swarm optimization (PSO) algorithm is applied to search for the optimal positions of the UAVs for the next time step. Finally, numerical simulations are conducted to verify the validity and effectiveness of the proposals in this paper. Full article
(This article belongs to the Special Issue Radar Target Detection, Imaging and Recognition)
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14 pages, 4343 KB  
Article
A Novel Method for Localizing PD Source in Power Transformer: Considering NLOS Propagation of Electromagnetic Waves
by Qingdong Zhu, Mengzhao Zhu, Wenbing Zhu, Chao Gu, Cheng Pan and Zijun Pan
Sensors 2025, 25(16), 5099; https://doi.org/10.3390/s25165099 - 16 Aug 2025
Viewed by 467
Abstract
A novel partial discharge (PD) source localization method was proposed based on the traditional time difference in arrival (TDOA) method. Specifically, the non-line-of-sight (NLOS) propagation phenomenon of the ultra-high-frequency (UHF) signal was considered, and the NLOS propagation error was approximately replaced by a [...] Read more.
A novel partial discharge (PD) source localization method was proposed based on the traditional time difference in arrival (TDOA) method. Specifically, the non-line-of-sight (NLOS) propagation phenomenon of the ultra-high-frequency (UHF) signal was considered, and the NLOS propagation error was approximately replaced by a constant, thereby limiting the effect of NLOS propagation. Moreover, the strategy of utilizing more than four sensors was adopted to reduce the possible effect of overcorrection on NLOS propagation. In this paper, the derivation and implementation process of the proposed method is introduced from the perspectives of mathematical model and geometrical model, and its localization results were compared with the traditional TDOA method through an experimental study. The results showed that the speed of error increase of the traditional method presented faster, and the increment of sensor number helped to improve the localization accuracy, but the reduction in localization error becomes insignificant when the sensors exceed six. Finally, the experimental verifications were conducted based on a 35 kV testing transformer with six sensor installations. The experiments found that the proposed localization method had a better calculated accuracy and stability; the obtained minimum calculated error was 10.88 cm, the calculated accuracy can be improved by 82.04% and 78.94%, respectively, with six sensors than four and five sensors arrangement. Full article
(This article belongs to the Section Electronic Sensors)
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27 pages, 21019 KB  
Article
A UWB-AOA/IMU Integrated Navigation System for 6-DoF Indoor UAV Localization
by Pengyu Zhao, Hengchuan Zhang, Gang Liu, Xiaowei Cui and Mingquan Lu
Drones 2025, 9(8), 546; https://doi.org/10.3390/drones9080546 - 1 Aug 2025
Viewed by 3285
Abstract
With the increasing deployment of unmanned aerial vehicles (UAVs) in indoor environments, the demand for high-precision six-degrees-of-freedom (6-DoF) localization has grown significantly. Ultra-wideband (UWB) technology has emerged as a key enabler for indoor UAV navigation due to its robustness against multipath effects and [...] Read more.
With the increasing deployment of unmanned aerial vehicles (UAVs) in indoor environments, the demand for high-precision six-degrees-of-freedom (6-DoF) localization has grown significantly. Ultra-wideband (UWB) technology has emerged as a key enabler for indoor UAV navigation due to its robustness against multipath effects and high-accuracy ranging capabilities. However, conventional UWB-based systems primarily rely on range measurements, operate at low measurement frequencies, and are incapable of providing attitude information. This paper proposes a tightly coupled error-state extended Kalman filter (TC–ESKF)-based UWB/inertial measurement unit (IMU) fusion framework. To address the challenge of initial state acquisition, a weighted nonlinear least squares (WNLS)-based initialization algorithm is proposed to rapidly estimate the UAV’s initial position and attitude under static conditions. During dynamic navigation, the system integrates time-difference-of-arrival (TDOA) and angle-of-arrival (AOA) measurements obtained from the UWB module to refine the state estimates, thereby enhancing both positioning accuracy and attitude stability. The proposed system is evaluated through simulations and real-world indoor flight experiments. Experimental results show that the proposed algorithm outperforms representative fusion algorithms in 3D positioning and yaw estimation accuracy. Full article
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18 pages, 3278 KB  
Article
A Hybrid 3D Localization Algorithm Based on Meta-Heuristic Weighted Fusion
by Dongfang Mao, Guoping Jiang and Yun Zhao
Mathematics 2025, 13(15), 2423; https://doi.org/10.3390/math13152423 - 28 Jul 2025
Viewed by 415
Abstract
This paper presents a hybrid indoor localization framework combining time difference of arrival (TDoA) measurements with a swarm intelligence optimization technique. To address the nonlinear optimization challenges in three-dimensional (3D) indoor localization via TDoA measurements, we systematically evaluate the artificial bee colony (ABC) [...] Read more.
This paper presents a hybrid indoor localization framework combining time difference of arrival (TDoA) measurements with a swarm intelligence optimization technique. To address the nonlinear optimization challenges in three-dimensional (3D) indoor localization via TDoA measurements, we systematically evaluate the artificial bee colony (ABC) algorithm and chimpanzee optimization algorithm (ChOA). Through comprehensive Monte Carlo simulations in a cubic 3D environment with eight beacons, our comparative analysis reveals that the ChOA achieves superior localization accuracy while maintaining computational efficiency. Building upon the ChOA framework, we introduce a multi-beacon fusion strategy incorporating a local outlier factor-based linear weighting mechanism to enhance robustness against measurement noise and improve localization accuracy. This approach integrates spatial density estimation with geometrically consistent weighting of distributed beacons, effectively filtering measurement outliers through adaptive sensor fusion. The experimental results show that the proposed algorithm exhibits excellent convergence performance under the condition of a low population size. Its anti-interference capability against Gaussian white noise is significantly improved compared with the baseline algorithms, and its anti-interference performance against multipath noise is consistent with that of the baseline algorithms. However, in terms of dealing with UWB device failures, the performance of the algorithm is slightly inferior. Meanwhile, the algorithm has relatively good time-lag performance and target-tracking performance. The study provides theoretical insights and practical guidelines for deploying reliable localization systems in complex indoor environments. Full article
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19 pages, 4251 KB  
Article
A Complete Solution for Ultra-Wideband Based Real-Time Positioning
by Vlad Ratiu, Ovidiu Ratiu, Olivier Raphael Smeyers, Vasile Teodor Dadarlat, Stefan Vos and Ana Rednic
Sensors 2025, 25(15), 4620; https://doi.org/10.3390/s25154620 - 25 Jul 2025
Viewed by 664
Abstract
Real-time positioning is a technological field with a multitude of applications, which expand across many scopes: from positioning within a large area to localization within smaller spaces; from locating people to locating equipment; from large-scale industrial or military applications to commercially available solutions. [...] Read more.
Real-time positioning is a technological field with a multitude of applications, which expand across many scopes: from positioning within a large area to localization within smaller spaces; from locating people to locating equipment; from large-scale industrial or military applications to commercially available solutions. There are at least as many implementations of real-time positioning as there are applications and challenges. Within the domain of Radio Frequency (RF) systems, positioning has been approached from multiple angles. Some of the more common solutions involve using Time of Flight (ToF) and time difference of arrival (TDoA) technologies. Within TDoA-based systems, one common limitation stems from the computational power necessary to run the multi-lateration algorithms at a high enough speed to provide high-frequency refresh rates on the tag positions. The system presented in this study implements a complete hardware and software TDoA-based real-time positioning system, using wireless Ultra-Wideband (UWB) technology. This system demonstrates improvements in the state of the art by addressing the above limitations through the use of a hybrid Machine Learning solution combined with algorithmic fine tuning in order to reduce computational power while achieving the desired positioning accuracy. This study presents the design, implementation, verification and validation of the aforementioned system, as well as an overview of similar solutions. Full article
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24 pages, 538 KB  
Article
Bias-Reduced Localization for Drone Swarm Based on Sensor Selection
by Bo Wu, Bazhong Shen, Yonggan Zhang, Li Yang and Zhiguo Wang
Sensors 2025, 25(13), 4034; https://doi.org/10.3390/s25134034 - 28 Jun 2025
Viewed by 547
Abstract
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, [...] Read more.
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
(This article belongs to the Section Sensor Networks)
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14 pages, 2307 KB  
Article
A Joint Decoherence-Based AOA and TDOA Positioning Approach for Interference Monitoring in Global Navigation Satellite System
by Wenjian Wang, Yinghong Wen and Yongxia Liu
Appl. Sci. 2025, 15(13), 7050; https://doi.org/10.3390/app15137050 - 23 Jun 2025
Viewed by 479
Abstract
Global navigation satellite system (GNSS) has been widely used in many fields due to their low cost and high positioning accuracy. Because of the open frequency of navigation signals, the low power of navigation signals, and the growing reliance of many modern wireless [...] Read more.
Global navigation satellite system (GNSS) has been widely used in many fields due to their low cost and high positioning accuracy. Because of the open frequency of navigation signals, the low power of navigation signals, and the growing reliance of many modern wireless systems on satellite-based navigation, GNSS performance may be easily affected by interference signals. Monitoring and troubleshooting of interference sources are important means to guarantee the normal use of satellite navigation applications and are an important part of GNSS operation in complex electromagnetic environments; however, traditional angle of arrival (AOA) algorithms cannot efficiently operate with coherent signals, so a decoherence-based orientation scheme is proposed to optimize the AOA algorithm. Furthermore, a joint AOA and time difference of arrival (TDOA) interference localization algorithm is proposed for problems such as the lack of accuracy in a single interference source localization algorithm. Numerical simulation results show that decoherence-based AOA localization can be well applied to various interference signals, and the accuracy of the joint AOA and TDOA interference localization algorithm is higher than that of single-method interference localization. In addition, the physical verification further verifies the usability and reliability of the GNSS interference source positioning algorithm proposed in this paper. Full article
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25 pages, 4360 KB  
Article
Positioning-Based Uplink Synchronization Method for NB-IoT in LEO Satellite Networks
by Qiang Qi, Tao Hong and Gengxin Zhang
Symmetry 2025, 17(7), 984; https://doi.org/10.3390/sym17070984 - 21 Jun 2025
Viewed by 1062
Abstract
With the growth of Internet of Things (IoT) business demands, NB-IoT integrating low earth orbit (LEO) satellite communication systems is considered a crucial component for achieving global coverage of IoT networks in the future. However, the long propagation delay and significant Doppler frequency [...] Read more.
With the growth of Internet of Things (IoT) business demands, NB-IoT integrating low earth orbit (LEO) satellite communication systems is considered a crucial component for achieving global coverage of IoT networks in the future. However, the long propagation delay and significant Doppler frequency shift of the satellite-to-ground link pose substantial challenges to the uplink and downlink synchronization in LEO satellite-based NB-IoT networks. To address this challenge, we first propose a Multiple Segment Auto-correlation (MSA) algorithm to detect the downlink Narrow-band Primary Synchronization Signal (NPSS), specifically tailored for the large Doppler frequency shift of LEO satellites. After detection, downlink synchronization can be realized by determining the arrival time and frequency of the NPSS. Then, to complete the uplink synchronization, we propose a position-based scheme to obtain the Timing Advance (TA) values and pre-compensated Doppler shift value. In this scheme, we formulate a time difference of arrival (TDOA) equation using the arrival times of NPSSs from different satellites or at different times as observations. After solving the TDOA equation using the Chan method, the uplink synchronization is completed by obtaining the TA values and pre-compensated Doppler shift value from the terminal position combined with satellite ephemeris. Finally, the feasibility of the proposed scheme is verified in an Iridium satellite constellation. Compared to conventional GNSS-assisted methods, the approach proposed in this paper reduces terminal power consumption by 15–40%. Moreover, it achieves an uplink synchronization success rate of over 98% under negative SNR conditions. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Future Wireless Networks)
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18 pages, 11193 KB  
Article
Uncertainty of Aircraft Localization with Multilateration and Known Altitude
by Rafał Osypiuk and Filip Surma
Electronics 2025, 14(12), 2420; https://doi.org/10.3390/electronics14122420 - 13 Jun 2025
Viewed by 620
Abstract
Manned and unmanned air traffic is experiencing rapid growth. The basis for the safety of flight operations is its reliable surveillance. In addition to primary and secondary radar, modern systems based on satellite positioning play a key role in air traffic control. An [...] Read more.
Manned and unmanned air traffic is experiencing rapid growth. The basis for the safety of flight operations is its reliable surveillance. In addition to primary and secondary radar, modern systems based on satellite positioning play a key role in air traffic control. An important addition to the above systems is multilateration (MLAT). The majority of existing MLAT algorithms operate under the assumption that only the time difference of arrival (TDOA) is available for consideration. However, in scenarios that are more reflective of reality, altitude measurements are also typically included. In this study, we not only extend an existing algorithm to accommodate these additional data points but also derive insights into how the accuracy of measurements is influenced by the incorporation of supplementary information. An important part of this contribution is the software, which, by solving nonlinear optimization problems, allows for the analysis of the distribution of MLAT stations while ensuring the smallest possible measurement uncertainties. Full article
(This article belongs to the Section Systems & Control Engineering)
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