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Advances in GNSS Signal Processing and Navigation—Second Edition

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A special issue of Sensors (ISSN 1424-8220). This special issue belongs to the section "Navigation and Positioning".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 6716

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Special Issue Editors

Prof. Dr. Ming Huang

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Guest Editor

School of Information Science and Engineering, Yunnan University, Kunming 650500, China
Interests: GNSS spoofing and jamming detection; radio monitoring; deep learning
Special Issues, Collections and Topics in MDPI journals

Dr. Jingjing Yang

E-Mail Website
Guest Editor

School of Information Science and Engineering, Yunnan University, Kunming 650091, China
Interests: wireless communication; signal processing; radio monitoring; deep learning
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Dr. Zhe Xiao

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Guest Editor

Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore
Interests: signal processing; deep learning; generative artificial intelligence
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Special Issue Information

Dear Colleagues,

As a fundamental spatiotemporal information service infrastructure, the Global Navigation Satellite System (GNSS) provides precise Positioning, Navigation, and Timing (PNT) services and enables a wide range of innovative applications. However, due to the use of MEO/HEO satellites, the quality of received GNSS signals is highly susceptible to environmental factors, including non-line-of-sight (NLOS) reception, spoofing attacks, and jamming. Globally, more than 10,000 radio frequency interference (RFI) events were reported by the International Telecommunication Union (ITU) in 2021, detected through the in-flight monitoring of aircraft GNSS receivers. With GNSS-denied environments becoming increasingly widespread, there is an urgent need to develop new GNSS architectures, signal processing algorithms, and techniques to improve PNT services. This Special Issue will highlight the latest technological developments in GNSS signal processing, LEO opportunistic Doppler-aided GNSS positioning, GNSS alternatives, and novel applications. We invite researchers and investigators to contribute original research or review articles to this Special Issue, the scope of which will broadly encompass, but will not be limited to, the following topics:

GNSS signal processing for Positioning, Navigation, and Timing;
Cybersecurity frameworks of GNSS for PNT services;
Opportunistic PNT with signals from LEO communication satellites and signal processing;
Opportunistic PNT with signals from terrestrial radio frequency sources and signal processing;
Electromagnetic space radio safety and GNSS signal monitoring frameworks;
GNSS signal processing based on machine learning, deep learning, and generative artificial intelligence;
Artificial intelligence applications for GNSS;
GNSS spoofing detection and signal processing;
GNSS jamming detection and signal processing;
GNSS signal monitoring and signal processing;
Passive radar signal processing based on GNSS signals;
GPS service for geodynamics;
GNSS real-time kinematic (RTK) techniques and signal processing;
Environment classification based on GNSS signal;
Soil moisture retrieval from GNSS observations.

Prof. Dr. Ming Huang
Dr. Jingjing Yang
Dr. Zhe Xiao
Guest Editors

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Keywords

GNSS signal processing
LEO opportunistic doppler-aided GNSS positioning
GNSS alternatives

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Published Papers (8 papers)

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Research

33 pages, 8873 KB

Open AccessArticle

Mathematical Modeling of Atmospheric Effects on Distance Determination Accuracy in the VDES R-Mode System

by Krzysztof Bronk, Patryk Koncicki, Adam Lipka, Rafal Niski and Blazej Wereszko

Sensors 2026, 26(10), 3127; https://doi.org/10.3390/s26103127 - 15 May 2026

Viewed by 190

Abstract

This paper investigates the impact of atmospheric conditions on distance determination accuracy in the VDES R-Mode system, based on system development and long-term analytical work conducted within the ORMOBASS project. A dedicated VDES R-Mode transmitter and monitoring station were developed and deployed in Poland, in the Port of Gdynia and at the boatswain’s office in the port of Jastarnia, respectively. Both stations were synchronized in time and frequency using a fiber-optic link and White Rabbit technology, ensuring high-precision and stable operation during long-term measurements. Based on a one-year stationary measurement campaign, a comprehensive dataset combining ranging results and meteorological observations was collected and analyzed. Statistical evaluation demonstrated that atmospheric conditions—particularly rainfall intensity and water vapor density—have a measurable impact on ranging accuracy. These findings motivated the development of a mathematical model describing the relationship between atmospheric conditions and distance measurement errors. The proposed logarithmic regression-based approach was validated using real measurement data; the authors also demonstrated its ability to reduce error variability during changing weather conditions, indicating its potential for future implementation in VDES R-Mode receivers. Full article

(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)

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20 pages, 3882 KB

Open AccessArticle

Cooperative Design of Ranging and Communication for In-Band Full-Duplex Inter-Satellite Links

by Hao Feng, Zhuo Yang, Hong Ma, Yiwen Jiao, Tao Wu, Yang Cai, Hongbin Ma and Zhiyong Shan

Sensors 2026, 26(10), 3013; https://doi.org/10.3390/s26103013 - 10 May 2026

Viewed by 656

Abstract

To address the limited communication capacity of the traditional time-division half-duplex (TDHD) systems in BDS-3 inter-satellite links (ISLs), this paper proposes a cooperative design of ranging and communication based on an in-band full-duplex (IBFD) architecture. By utilizing BDS broadcast ephemeris to assist signal acquisition and selecting the serial acquisition strategy with the lowest computational complexity, a 100% acquisition success rate can be achieved within milliseconds. This completely releases the 250 ms preamble originally used for acquisition in the traditional time slot. Adopting the IBFD system, the ISL time-slot structure is optimally redesigned: the preamble is used for signal acquisition and tracking to accomplish inter-satellite ranging, while the original measurement period is used for QPSK dual-channel parallel data transmission. This design extends the effective communication duration from 1 s to 2.5 s, expands the communication from single-channel to dual-channel, and theoretically achieves a 5-fold improvement in communication efficiency. Simulation analysis shows that, while the communication efficiency is significantly improved, the ranging accuracy remains essentially unchanged compared with the traditional TDHD system. Without altering the existing 3 s time-slot duration, this method achieves cooperative optimization of ranging and communication, providing a feasible technical solution for enhancing the communication capacity of BDS-3 ISLs. Full article

(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)

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15 pages, 1882 KB

Open AccessArticle

Prediction of BDS-3 Satellite Clock Bias Based on the Mamba-LSTM Model

by Yihao Cai, Hengyi Yue, Tu Yuan and Mengjie Wu

Sensors 2026, 26(9), 2643; https://doi.org/10.3390/s26092643 - 24 Apr 2026

Viewed by 225

Abstract

Since coming into full operation in 2020, the BeiDou-3 Navigation Satellite System (BDS-3) has provided global users with positioning, navigation and time-synchronization services. Satellite clock bias is a key factor that affects real-time precise point positioning (PPP), precise orbit determination and the optimization of navigation message parameters; high-precision prediction of clock bias is therefore critical for improving the accuracy and reliability of BDS-3. To further enhance the prediction accuracy and stability of satellite clock bias, we propose a hybrid model based on Mamba-LSTM. This combined model leverages the strengths of the Multimodal Adaptive Model Building Algorithm (Mamba) and the Long Short-Term Memory neural network (LSTM) to predict satellite clock bias. Using precise BDS-3 satellite clock bias data from the International GNSS Service (IGS), we carried out prediction experiments. First, we compared the proposed model’s predictive performance with that of the Mamba and LSTM models. In short-term (6 h) and long-term (24 h) prediction scenarios, the average prediction RMSE of Mamba-LSTM improved by approximately 41.7% and 48% relative to Mamba, and by approximately 50.4% and 54.7% relative to the LSTM results, respectively. Next, we ran comparison experiments against traditional neural networks—the BP model and the CNN model. In mid-term (12 h) and long-term (24 h) prediction scenarios, the average prediction RMSE of Mamba-LSTM improved by approximately 59.6% and 63.1% compared with BP, and by approximately 52.4% and 56.2% compared with CNN, respectively. The results indicate that the Mamba-LSTM hybrid model can significantly improve the accuracy and stability of satellite clock bias prediction. Full article

(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)

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23 pages, 9568 KB

Open AccessArticle

Characteristics of Ionospheric Responses over China During the November 2023 Geomagnetic Storm and Evaluation of Positioning Performance of CORS in Low-Latitude Regions

by Linghui Li, Youkun Wang, Junhua Zhang, Jun Tang, Fengjiao Yu, Jintao Wang and Zhichao Zhang

Sensors 2026, 26(7), 2198; https://doi.org/10.3390/s26072198 - 2 Apr 2026

Viewed by 433

Abstract

This study used Global Navigation Satellite System (GNSS) observations from the China Crustal Movement Observation Network (CMONOC) and the Kunming Continuously Operating Reference Station (KMCORS) network to investigate ionospheric response characteristics over China during the geomagnetic storm of 4–6 November 2023, and to assess their impacts on CORS-based real-time kinematic (RTK) positioning performance in the low-latitude Kunming region. A quantitative assessment was conducted by integrating regional two-dimensional dTEC (%) maps over China, BeiDou Navigation Satellite System (BDS) Geostationary Earth Orbit (GEO) total electron content (TEC), the rate of TEC index (ROTI), and RTK positioning solutions to evaluate ionospheric disturbances, irregularity activity, and associated degradation in positioning performance. Results indicate that, during geomagnetic storms, ionospheric responses over China exhibit pronounced phase-dependent and latitudinal variations. During the second geomagnetic storm on 5–6 November, positive responses were dominant at mid-to-high latitudes, whereas alternating positive and negative responses were observed at low latitudes. During the recovery phase, the Kunming region successively experienced a positive ionospheric storm lasting approximately 10 h, followed by a negative ionospheric storm lasting about 7 h, with relative TEC variations reaching a maximum of approximately 90%. The GEO TEC time series was consistent with the temporal evolution of the two-dimensional dTEC (%), while ROTI increased markedly during the disturbance enhancement period (21:00 UT on 5 November to 07:00 UT on 6 November 2023). During periods of enhanced ionospheric response and irregularities, RTK positioning performance was observed to deteriorate markedly. The fixed-solution rate at medium-to-long baseline stations decreased from nearly 100% to close to 0%, accompanied by an increase in vertical positioning errors to approximately 20 cm, whereas short-baseline stations were only minimally affected. These results indicate that ionospheric disturbances during geomagnetic storms exert a pronounced impact on CORS-based RTK positioning services in the Kunming region, with the magnitude of this impact being closely related to baseline length. Full article

(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)

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24 pages, 7986 KB

Open AccessArticle

GVMD-NLM: A Hybrid Denoising Method for GNSS Buoy Elevation Time Series Using Optimized VMD and Non-Local Means Filtering

by Huanghuang Zhang, Shengping Wang, Chao Dong, Guangyu Xu and Xiaobo Cai

Sensors 2026, 26(2), 522; https://doi.org/10.3390/s26020522 - 13 Jan 2026

Viewed by 410

Abstract

GNSS buoys are essential for real-time elevation monitoring in coastal waterways, yet the vertical coordinate time series are frequently contaminated by complex non-stationary noise, and existing denoising methods often rely on empirical parameter settings that compromise reliability. This paper proposes GVMD-NLM, a hybrid denoising framework optimized by an improved Grey Wolf Optimizer (GWO). The method introduces an adaptive convergence factor decay function derived from the Sigmoid function to automatically determine the optimal parameters (K and

α

) for Variational Mode Decomposition (VMD). Sample Entropy (SE) is then employed to identify low-frequency effective signals, while the remaining high-frequency noise components are processed via Non-Local Means (NLM) filtering to recover residual information while suppressing stochastic disturbances. Experimental results from two datasets at the Dongguan Waterway Wharf demonstrate that GVMD-NLM consistently outperforms SSA, CEEMDAN, VMD, and GWO-VMD. In Dataset One, GVMD-NLM reduced the RMSE by 26.04% (vs. SSA), 17.87% (vs. CEEMDAN), 24.28% (vs. VMD), and 13.47% (vs. GWO-VMD), with corresponding SNR improvements of 11.13%, 7.00%, 10.18%, and 5.05%. In Dataset Two, the method achieved RMSE reductions of 28.87% (vs. SSA), 17.12% (vs. CEEMDAN), 18.45% (vs. VMD), and 10.26% (vs. GWO-VMD), with SNR improvements of 10.48%, 5.52%, 6.02%, and 3.11%, respectively. The denoised signal maintains high fidelity, with correlation coefficients (R) reaching 0.9798. This approach provides an objective and automated solution for GNSS data denoising, offering a more accurate data foundation for waterway hydrodynamics research and water level monitoring. Full article

(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)

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23 pages, 1593 KB

Open AccessArticle

WAWA: Wavelet Analysis-Based Watermarking Authentication for GNSS Civil Signal with Immediate Symbol-Level Verification

by Xinyu Tang, Xiaomei Tang, Honglei Lin, Yi Wu and Guangfu Sun

Sensors 2025, 25(21), 6615; https://doi.org/10.3390/s25216615 - 28 Oct 2025

Viewed by 878

Abstract

Existing GNSS authentication schemes suffer from critical drawbacks such as high verification latency and prohibitive memory requirements, leaving time-sensitive applications vulnerable to spoofing. The core challenge is the inability to transmit strong, real-time cryptographic credentials through the bandwidth-limited GNSS signal. This paper introduces WAWA, a Wavelet Analysis-based Watermarking Authentication scheme that operates at the physical layer of the GNSS signal. The central innovation of WAWA is its use of the wavelet domain to achieve a high-capacity data channel, allowing a complete public-key digital signature to be embedded directly within the signal structure. This enables receivers to perform immediate, symbol-level authentication using a public key, which fundamentally removes the verification delay and reliance on time synchronization seen in conventional methods. Furthermore, it eliminates the need for large memory buffers, a critical barrier for resource-constrained devices. We present the complete design of the watermark generation, embedding, and extraction process, alongside a novel dual-path verification framework adaptable to both standalone and network-assisted receivers. Performance analysis shows that WAWA achieves immediate authentication while offering superior effective bandwidth and maintaining low memory overhead. Although it introduces a controllable signal correlation loss, validated through both theoretical modeling and simulation, WAWA presents an exceptional balance of security, immediacy, and resource efficiency, offering a promising new paradigm for ensuring trustworthy PNT sensor data in time-critical and resource-sensitive applications, particularly in large-scale sensor networks and autonomous systems. Full article

(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)

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19 pages, 2127 KB

Open AccessArticle

User-Side Long-Baseline Undifferenced Network RTK Positioning Under Geomagnetic Storm Conditions Using a Power Spectral Density-Constrained Ionospheric Delay Model

by Yixi Wang, Huizhong Zhu, Qi Xu, Jun Li, Chuanfeng Song and Bo Li

Sensors 2025, 25(20), 6433; https://doi.org/10.3390/s25206433 - 17 Oct 2025

Viewed by 954

Abstract

To address the problem of the degraded positioning accuracy of the long-baseline undifferenced network RTK (URTK) under extreme space weather conditions, herein, we propose a user-side atmospheric delay estimation strategy based on the undifferenced network RTK concept to enhance positioning performance in geomagnetic storm environments. First, an ambiguity-resolution model that jointly estimates atmospheric error parameters is used to fix the carrier-phase integer ambiguities for long-baseline reference stations. The accurately fixed inter-station ambiguities are then linearly transformed to recover station-specific undifferenced integer ambiguities; undifferenced observation errors at each reference station are computed to generate corresponding undifferenced correction terms. Lastly, recognizing that ionospheric delays vary sharply during geomagnetic storms and can severely compromise the availability of regional undifferenced correction models, we estimate the residual atmospheric parameters on the user side after applying regional corrections. Experimental results show that the server side is not significantly impacted during geomagnetic storms and can continue operating normally. On the user side, augmenting the solution with atmospheric parameter estimation effectively improves positioning availability. Under strong geomagnetic storms, the proposed mode improves user-station positioning accuracy by 63.7%, 60.7%, and 64.4% in the east (E), north (N), and up (U) components, respectively, relative to the conventional user-side solution; under moderate storm conditions, the corresponding improvements are 16.7%, 10.0%, and 11.1%. Full article

(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)

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23 pages, 17632 KB

Open AccessArticle

Multipath Identification and Mitigation for Enhanced GNSS Positioning in Urban Environments

by Qianxia Li, Xue Hou, Yuanbin Ye, Wenfeng Zhang, Qingsong Li and Yuezhen Cai

Sensors 2025, 25(19), 6061; https://doi.org/10.3390/s25196061 - 2 Oct 2025

Cited by 1 | Viewed by 2168

Abstract

Due to the increasing demand for accurate and robust GNSS positioning for location-based services (LBS) in urban regions, the impacts prevalent in metropolitan areas, like multipath reflections and various interferences, have become persistent challenges. Consequently, developing effective strategies to address these sophisticated influences has become both a primary research focus and a shared priority. In this paper, the authors explore an approach to identify and mitigate the drawbacks arising from multipath effects in urban positioning. Unlike conventional ways for building complex models, an adaptive data-driven methodology is proposed to identify the fingerprints of a multipath in GNSS observations. This approach utilizes the Fourier transform (FT) to examine code multipath and other error sources in terms of frequency, as represented by the power spectrum. Wavelet decomposition and signal spectrum methods are subsequently applied to seek traces of code multipath in multilayer decompositions. Based on the exhibited multipath features, the impacts of multipath in GNSS observations are detected and mitigated in the reconstructed observations. The proposed method is validated for both static and dynamic positioning scenarios, demonstrating seamless integration with existing positioning models. The feasibility has been verified through a series of experiments and tests under urban environments using navigation terminals and smartphones. Full article

(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)

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