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Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition)

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A special issue of Remote Sensing (ISSN 2072-4292). This special issue belongs to the section "Satellite Missions for Earth and Planetary Exploration".

Deadline for manuscript submissions: closed (30 April 2025) | Viewed by 13139

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Prof. Dr. Baocheng Zhang

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Guest Editor

Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China
Interests: GNSS; precise point positioning; PPP-RTK
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Dr. Robert Odolinski

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National School of Surveying, University of Otago, 310 Castle Street, Dunedin 9016, New Zealand
Interests: multi-GNSS precise positioning; integer ambiguity resolution; low-cost GNSS receiver
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Dear Colleagues,

As an effective tool for providing precise navigation and positioning, the multi-frequency and multi-constellation GNSS plays an important role in various fields such as geological monitoring, urban services, and global meteorology. In addition, the Beidou Satellite Navigation System (BDS) is a global navigation satellite system developed by China, and the third generation achieved global coverage of timing and navigation by 2020. All of these services rely on fundamental theories, models, and algorithms to pinpoint the position and speed of each spacecraft. Beidou/GNSS will inevitably participate in more applications in the future, so the reliability and timeliness of data processing in particular parameter estimations, as well as quality control and other aspects, still need to be improved and perfected.

It is our pleasure to announce the launch of a new Special Issue in Remote Sensing whose goal is to collect papers on BDS/GNSS positioning algorithms, integrated navigation, and data processing for Earth science applications. Research topics include but are not limited to (a} satellite orbit dynamics (solar radiation pressure, attitude); (b) ground-based and space-borne GNSS receivers monitoring global ionospheric climate and weather and low-orbit GNSS retrieving environmental parameters on land and at sea; and (c) Earth observations that integrate GNSS with geodesy and geophysics, such as the Global Geodesy Observation System—GGOS.

Prof. Dr. Baocheng Zhang
Dr. Robert Odolinski
Guest Editors

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Keywords

multi-frequency and multi-constellation GNSS
BDS
POD/LEO
navigation and timing
geodesy and geophysics
advance of high-precision product

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Published Papers (11 papers)

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16 pages, 10018 KiB

Open AccessCommunication

Impact of the May 2024 Extreme Geomagnetic Storm on the Ionosphere and GNSS Positioning

by Ekaterina Danilchuk, Yury Yasyukevich, Artem Vesnin, Aleksandr Klyusilov and Baocheng Zhang

Remote Sens. 2025, 17(9), 1492; https://doi.org/10.3390/rs17091492 - 23 Apr 2025

Viewed by 549

Abstract

Global navigation satellite systems provide important data sets that can be used to study the influence of various space weather factors. We analyzed the effects of the main phase of the May 2024 extreme geomagnetic storm on the ionosphere and GPS kinematic precise point positioning (PPP). ROTI and global ionospheric maps showed the ionospheric dynamics. The auroral oval expanded up to low latitudes: up to 30°N in the American sector and up to 45°N in the European–Asian sector during the main phase of the geomagnetic storm. The ROTI peaked at 2 TECU/min, which is four times as much against the background. The equatorial anomaly crest intensified considerably (up to 200 TECU) and shifted poleward in the American sector. The counter-propagation finally caused the equatorial anomaly to cross the auroral oval boundary. The ROTI correlated with errors in the kinematic PPP. Positioning errors increased 1.5–5 times at the boundary of the auroral oval. Increased positioning errors propagated according to the shift of the auroral oval boundary. The geomagnetic storm significantly affected the positioning and the ionosphere, threatening various applications based on navigation and communication. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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21 pages, 5359 KiB

Open AccessArticle

Deep Learning-Based Feature Matching Algorithm for Multi-Beam and Side-Scan Images

by Yu Fu, Xiaowen Luo, Xiaoming Qin, Hongyang Wan, Jiaxin Cui and Zepeng Huang

Remote Sens. 2025, 17(4), 675; https://doi.org/10.3390/rs17040675 - 16 Feb 2025

Viewed by 899

Abstract

Side-scan sonar and multi-beam echo sounder (MBES) are the most widely used underwater surveying tools in marine mapping today. The MBES offers high accuracy in depth measurement but is limited by low imaging resolution due to beam density constraints. Conversely, side-scan sonar provides high-resolution backscatter intensity images but lacks precise positional information and often suffers from distortions. Thus, MBES and side-scan images complement each other in depth accuracy and imaging resolution. To obtain high-quality seafloor topography images in practice, matching between MBES and side-scan images is necessary. However, due to the significant differences in content and resolution between MBES depth images and side-scan backscatter images, they represent a typical example of heterogeneous images, making feature matching difficult with traditional image matching methods. To address this issue, this paper proposes a feature matching network based on the LoFTR algorithm, utilizing the intermediate layers of the ResNet-50 network to extract shared features between the two types of images. By leveraging self-attention and cross-attention mechanisms, the features of the MBES and side-scan images are combined, and a similarity matrix of the two modalities is calculated to achieve mutual matching. Experimental results show that, compared to traditional methods, the proposed model exhibits greater robustness to noise interference and effectively reduces noise. It also overcomes challenges, such as large nonlinear differences, significant geometric distortions, and high matching difficulty between the MBES and side-scan images, significantly improving the optimized image matching results. The matching error RMSE has been reduced to within six pixels, enabling the accurate matching of multi-beam and side-scan images. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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20 pages, 4377 KiB

Open AccessArticle

Improving BeiDou Global Navigation Satellite System (BDS-3)-Derived Station Coordinates Using Calibrated Satellite Antennas and Station Inter-System Translation Parameters

by Tao Zhang, Shiwei Guo, Lei Fan and Chuang Shi

Remote Sens. 2025, 17(3), 510; https://doi.org/10.3390/rs17030510 - 31 Jan 2025

Viewed by 689

Abstract

The BeiDou global navigation satellite system (BDS-3) has been widely applied in various geodetic applications since its full operation. However, the estimated station coordinates using BDS-3 are less precise compared to GPS results. It contains systematic errors caused by scale bias with respect to International GNSS Service (IGS) 2020 frame and Inter-System Translation Parameters (ISTPs). In order to improve the consistency of BDS-3-derived station coordinates with respect to IGS20 products, we firstly estimated the satellite antenna Phase Center Offsets (PCOs) for BDS-3 Medium Earth Orbit (MEO) constellation, and then estimated station-specific ISTPs from GPS to BDS-3 systems. The results indicate that the PCO-Z estimates show large differences among satellites from different manufacturers and orbit planes. The estimated BDS-3 satellite PCOs exhibit a systematic bias of −9.3 cm in the Z-direction compared to ground calibrations. The maximum mean station-specific ISTPs can reach up to 3 mm, highlighting significant variability and the need for refinement in positioning. When using the estimated PCOs instead of igs20.atx values, the estimated scale bias with respect to the IGS20 frame is reduced from 0.38 ppb to −0.12 ppb, indicating that the refined BDS-3 satellite PCOs are well compatible with IGS20. Regarding the Up component that is correlated with the scale factor, the station coordinate differences with respect to the IGS20 frame is reduced from 7.0 mm to 6.2 mm in terms of the root mean square (RMS), which is improved by 11.4%. Considering the additional ISTP corrections, a further improvement of 17% was obtained in station coordinates. The RMS of station coordinate differences with respect to the IGS20 frame is 2.3 mm, 2.7 mm, and 5.2 mm for the North, East, and Up components, respectively. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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20 pages, 7765 KiB

Open AccessArticle

Rapid High-Precision Ranging Technique for Multi-Frequency BDS Signals

by Jie Sun, Jiaolong Wei, Zuping Tang and Yuze Duan

Remote Sens. 2024, 16(23), 4352; https://doi.org/10.3390/rs16234352 - 21 Nov 2024

Viewed by 764

Abstract

The rapid expansion of BeiDou satellite navigation applications has led to a growing demand for real-time high-precision positioning services. Currently, high-precision positioning services face challenges such as a long initialization time and heavy reliance on reference station networks, thereby failing to fulfill the requirements for real-time, wide-area, and centimeter-level positioning. In this study, we consider the multi-frequency signals that are broadcast by a satellite to share a common reference clock and possess identical RF channels and propagation paths with strict temporal, spectral, and spatial coupling between signal components, resulting in strongly coherent propagation delays. Firstly, we accurately establish a multi-frequency signal model that fully exploits those coherent characteristics among the multi-frequency BDS signals. Subsequently, we propose a rapid high-precision ranging technique using the code and carrier phases of multi-frequency signals. The proposed method unitizes multi-frequency signals via a coherent joint processing unit consisting of a joint tracking state estimator and a coherent signal generator. The joint tracking state estimator simultaneously estimates the biased pseudorange and its change rate, ionospheric delay and its change rate, and ambiguities. The coherent signal generator updates the numerically controlled oscillator (NCO) to adjust the local reference signal’s code and carrier replicas of different frequencies, changing them according to the state estimated by the joint tracking state estimator. Finally, the simulation results indicate that the proposed method efficiently diminishes the estimated biased pseudorange and ionospheric delay errors to below 0.1 m. Furthermore, this method reduces the carrier phase errors by more than 60% compared with conventional single-frequency-independent tracking methods. Consequently, the proposed method can achieve rapid centimeter-level results ranging for up to 1 min without using precise atmosphere corrections and provide enhanced tracking sensitivity and robustness. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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18 pages, 7119 KiB

Open AccessArticle

Multi-GNSS Precise Point Positioning with Ambiguity Resolution Based on the Decoupled Clock Model

by Shuai Liu, Yunbin Yuan, Xiaosong Guo, Kezhi Wang and Gongwei Xiao

Remote Sens. 2024, 16(16), 2999; https://doi.org/10.3390/rs16162999 - 15 Aug 2024

Cited by 1 | Viewed by 1495

Abstract

Ambiguity resolution (AR) can markedly enhance the precision of precise point positioning (PPP) and accelerate the convergence process. The decoupled clock model represents a pivotal approach for ambiguity resolution, yet current research on this topic is largely confined to GPS. Consequently, in this study, we extend the investigation of the decoupled clock model to multi-GNSS. Firstly, based on the conventional model, we derive the multi-GNSS decoupled clock estimation model and the precise point positioning with ambiguity resolution (PPP-AR) model. Secondly, we provide a detailed explanation of the estimation process for the multi-GNSS decoupled clock estimation. To validate the efficacy of the proposed model, we conduct multi-GNSS decoupled clock estimation and PPP-AR experiments using six days of observation data. The results demonstrate that the decoupled clocks of GPS, Galileo, and BDS-3 can all achieve high accuracy, thus fully meeting the requirement of ambiguity resolution. In terms of positioning performance, the joint three systems have higher positioning accuracy, reaching 3.10 cm and 6.13 cm in horizontal and vertical directions, respectively. Furthermore, the convergence time (CT) and time to first fix (TTFF) are shortened, to 23.13 min and 13.65 min, respectively. The experimental findings indicate that the proposed multi-GNSS decoupled clock model exhibits high precision and rapid positioning service capabilities. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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10 pages, 2726 KiB

Open AccessCommunication

Performance of Ground-Based Global Navigation Satellite System Precipitable Water Vapor Retrieval in Beijing with the BeiDou B2b Service

by Yunchang Cao, Zhenhua Cheng, Jingshu Liang, Panpan Zhao, Yucan Cao and Yizhu Wang

Remote Sens. 2024, 16(16), 2902; https://doi.org/10.3390/rs16162902 - 8 Aug 2024

Viewed by 1073

Abstract

The accurate measurement of water vapor is essential for research about and the applications of meteorology, climatology, and hydrology. Based on the BeiDou PPP-B2b service, real-time precipitable water vapor (PWV) can be retrieved with the precise point positioning (PPP) software (XTW-PPP version 0.0). The experiment was conducted in Beijing in January 2023. Three solutions were designed with PPP using the BeiDou system only, the GPS system only, and the BeiDou-GPS combined solution. Real-time PWVs for the three solutions were validated with the ERA5 reanalysis data. Between the PWV values from the single BeiDou and ERA5, there was a bias of 0.7 mm and an RMSE of 1.8 mm. For the GPS case, the bias was 0.73 mm and the RMSE was 1.97 mm. The biases were less than 1 mm and RMSEs were less than 2 mm. Both the BeiDou and the GPS processing performed very well. But little improvement was found for the BeiDou-GPS combined solution, compared with the BeiDou system-only and the GPS system-only solution. This may be due to the poor handling of two different kinds of errors for the GPS and the BeiDou systems in our PPP software. A better PWV estimation with the two systems is to estimate PWV with a single system at the first step and then obtain the optimization by Bayesian model averaging. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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30 pages, 1493 KiB

Open AccessArticle

Meta-Signal Processing with Data/Pilot Combining for Beidou B2 Signals

by Daniele Borio

Remote Sens. 2024, 16(14), 2537; https://doi.org/10.3390/rs16142537 - 10 Jul 2024

Cited by 2 | Viewed by 1510

Abstract

Beidou Navigation Satellite System (BDS) third generation satellites currently broadcast Open Service (OS) signals into two closely spaced Radio Frequencies (RFs) in the B2 band. These are the B2a and B2b signal components, which form the current implementation of the Asymmetric Constant-Envelope Binary Offset Carrier (ACE-BOC) modulation. The B2a signal features both a data and a pilot channel, whereas the B2b component is data only with data symbols of 1 ms duration. The absence of a pilot channel and the fast data rate make the processing of the B2b component challenging. Tracking performance can, however, be improved by jointly processing the B2a and B2b components. In this respect, meta-signal approaches are investigated for jointly processing the B2a and B2b signals. Two meta-signal tracking architectures are proposed: the first considers the pilot channel of the B2a component and the data channel of the B2b signal. The second exploits all the power available and also implements data/pilot combining on the B2a channel. Both architectures allow the extension of the integration time beyond the data symbol duration using non-coherent approaches. Theoretical results are supported by simulations and real data analysis performed using a custom Software Defined Radio (SDR) receiver. Simulation and experimental results clearly show the benefits of the meta-signal approach, which can be effectively adopted for the processing of asymmetric modulations such as the current implementation of the ACE-BOC, which lacks a pilot channel on the B2b component. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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21 pages, 7014 KiB

Open AccessArticle

A GRNN-Based Model for ERA5 PWV Adjustment with GNSS Observations Considering Seasonal and Geographic Variations

by Haoyun Pang, Lulu Zhang, Wen Liu, Xin Wang, Yuefeng Wang and Liangke Huang

Remote Sens. 2024, 16(13), 2424; https://doi.org/10.3390/rs16132424 - 1 Jul 2024

Cited by 2 | Viewed by 1371

Abstract

Precipitation water vapor (PWV) is an important parameter in numerical weather forecasting and climate research. However, existing PWV adjustment models lack comprehensive consideration of seasonal and geographic factors. This study utilized the General Regression Neural Network (GRNN) algorithm and Global Navigation Satellite System (GNSS) PWV in China to construct and evaluate European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Reanalysis (ERA5) PWV adjustment models for various seasons and subregions based on meteorological parameters (GMPW model) and non-meteorological parameters (GFPW model). A linear model (GLPW model) was established for model accuracy comparison. The results show that: (1) taking GNSS PWV as a reference, the Bias and root mean square error (RMSE) of the GLPW, GFPW, and GMPW models are about 0/1 mm, which better weakens the systematic error of ERA5 PWV. The overall Bias of the GLPW, GFPW, and GMPW models in the Northwest (NWC), North China (NC), Tibetan Plateau (TP), and South China (SC) subregions is approximately 0 mm after adjustment. The adjusted overall RMSE of the GLPW, GFPW, and GMPW models of the four subregions are 0.81/0.71/0.62 mm, 1.15/0.95/0.77 mm, 1.66/1.26/1.05 mm, and 2.11/1.35/0.96 mm, respectively. (2) The accuracy of the three models is tested using GNSS PWV, which is not involved in the modeling. The adjusted overall RMSE of the GLPW, GFPW, and GMPW models in the four subregions are 0.89/0.85/0.83 mm, 1.61/1.58/1.27 mm, 2.11/1.75/1.68 mm and 3.65/2.48/1.79 mm, respectively. As a result, the GFPW and GMPW models have better accuracy in adjusting ERA5 PWV than the linear model GLPW. Therefore, the GFPW and GMPW models can effectively contribute to water vapor monitoring and the integration of multiple PWV datasets. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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21 pages, 18584 KiB

Open AccessArticle

A New Grid Zenith Tropospheric Delay Model Considering Time-Varying Vertical Adjustment and Diurnal Variation over China

by Jihong Zhang, Xiaoqing Zuo, Shipeng Guo, Shaofeng Xie, Xu Yang, Yongning Li and Xuefu Yue

Remote Sens. 2024, 16(11), 2023; https://doi.org/10.3390/rs16112023 - 4 Jun 2024

Cited by 3 | Viewed by 1138

Abstract

Improving the accuracy of zenith tropospheric delay (ZTD) models is an important task. However, the existing ZTD models still have limitations, such as a lack of appropriate vertical adjustment function and being unsuitable for China, which has a complex climate and great undulating terrain. A new approach that considers the time-varying vertical adjustment and delicate diurnal variations of ZTD was introduced to develop a new grid ZTD model (NGZTD). The NGZTD model employed the Gaussian function and considered the seasonal variations of Gaussian coefficients to express the vertical variations of ZTD. The effectiveness of vertical interpolation for the vertical adjustment model (NGZTD-H) was validated. The root mean squared errors (RMSE) of the NGZTD-H model improved by 58% and 22% compared to the global pressure and temperature 3 (GPT3) model using ERA5 and radiosonde data, respectively. The NGZTD model’s effectiveness for directly estimating the ZTD was validated. The NGZTD model improved by 22% and 31% compared to the GPT3 model using GNSS-derived ZTD and layered ZTD at radiosonde stations, respectively. Seasonal variations in Gaussian coefficients need to be considered. Using constant Gaussian coefficients will generate large errors. The NGZTD model exhibited outstanding advantages in capturing diurnal variations and adapting to undulating terrain. We analyzed and discussed the main error sources of the NGZTD model using validation of spatial interpolation accuracy. This new ZTD model has potential applications in enhancing the reliability of navigation, positioning, and interferometric synthetic aperture radar (InSAR) measurements and is recommended to promote the development of space geodesy techniques. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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13 pages, 4096 KiB

Open AccessTechnical Note

Cube: An Open-Source Software for Clock Offset Estimation and Precise Point Positioning with Ambiguity Resolution

by Shuai Liu, Yunbin Yuan, Xiaosong Guo, Kezhi Wang and Gongwei Xiao

Remote Sens. 2024, 16(15), 2739; https://doi.org/10.3390/rs16152739 - 26 Jul 2024

Viewed by 1241

Abstract

Precise point positioning (PPP) is a prevalent, high-precision spatial absolution positioning method, and its performance can be enhanced by ambiguity resolution (AR). To fulfill the growing need for high-precision positioning, we developed an open-source GNSS data processing package based on the decoupled clock model called Cube, which integrates decoupled clock offset estimation and precise point positioning with ambiguity resolution (PPP-AR). Cube is a secondary development based on RTKLIB. Besides the decoupled clock model, Cube can also estimate legacy clocks for the International GNSS Service (IGS), as well as clocks with satellite code bias extraction, and perform PPP-AR using the integer-recovered clock model. In this work, we designed satellite clock estimation and PPP-AR experiments with one week of GPS data to validate Cube’s performance. Results show that the software can produce high-precision satellite clock products and positioning results that are adequate for daily scientific study. With Cube, researchers do not need to rely on public PPP-AR products, and they can estimate decoupled clock products and implement PPP-AR anytime. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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12 pages, 2620 KiB

Open AccessTechnical Note

Telescopic Network of Zhulong for Orbit Determination and Prediction of Space Objects

by Xiangxu Lei, Zhendi Lao, Lei Liu, Junyu Chen, Luyuan Wang, Shuai Jiang and Min Li

Remote Sens. 2024, 16(13), 2282; https://doi.org/10.3390/rs16132282 - 22 Jun 2024

Cited by 2 | Viewed by 1067

Abstract

The increasing proliferation of space debris, intermittent space incidents, and the rapid emergence of massive LEO satellite constellations pose significant threats to satellites in orbit. Ground-based optical observations play a crucial role in space surveillance and space situational awareness (SSA). The Zhulong telescopic observation network stands as a pivotal resource in the realm of space object tracking and prediction. This publicly available network plays a critical role in furnishing essential data for accurately delineating and forecasting the orbit of space objects in Earth orbit. Comprising a sophisticated array of hardware components including precise telescopes, optical sensors, and image sensors, the Zhulong network synergistically collaborates to achieve unparalleled levels of precision in tracking and observing space objects. Central to the network’s efficacy is its ability to extract positional information, referred to as angular data, from consecutive images. These angular data serve as the cornerstone for precise orbit determination and prediction. In this study, the CPF (Consolidated Prediction Format) orbit serves as the reference standard against which the accuracy of the angular data is evaluated. The findings reveal that the angular data error of the Zhulong network remains consistently below 3 arcseconds, attesting to its remarkable precision. Moreover, through the accumulation of angular data over time, coupled with the utilization of numerical integration and least squares methods, the Zhulong network facilitates highly accurate orbit determination and prediction for space objects. These methodologies leverage the wealth of data collected by the network to extrapolate trajectories with unprecedented accuracy, offering invaluable insights into the behavior and movement of celestial bodies. The results presented herein underscore the immense potential of electric optic telescopes in the realm of space surveillance. By harnessing the capabilities of the Zhulong network, researchers and astronomers can gain deeper insights into the dynamics of space objects, thereby advancing our understanding of the cosmos. Ultimately, the Zhulong telescopic observation network emerges as a pioneering tool in the quest to unravel the mysteries of the universe. Full article

(This article belongs to the Special Issue Beidou/GNSS Positioning, Navigation and Timing: Methods and Technology (Second Edition))

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