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GNSS Signals and Precise Point Positioning

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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: 1 October 2024 | Viewed by 13407

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Prof. Dr. Thomas Pany

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Institute of Space Technology and Space Applications, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Interests: navigation; GNSS; signal processing; inertial navigation
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Special Issue Information

Dear Colleagues,

Since global navigation satellite systems (GNSSs) became available to the public, GNSSs have become a well-established tool in a broad area of research. They have provided unprecedented precision and reliability to navigation systems, especially when fused with other sensing modalities. Ushered in by an increasing demand for availability, accuracy, and reliability, the mitigation of these challenges has steered intense research on advanced receiver design. These requirements are imposed by critical applications such as autonomous driving, power grid, classical aviation, and terrestrial navigation, as well as unmanned aerial and ground vehicles.

The precise point positioning (PPP) technique is receiving increasing interest due to its cost-effectiveness, global coverage and high accuracy. PPP is the key technology to realize global, precise, real-time, dynamic positioning and navigation, and is also the frontier research direction of GNSSs. However, the emergence of multiple satellite navigation systems, including BDS, Galileo, modernized GPS, and GLONASS, brings great opportunities and challenges for PPP. These solutions are shaping the future of GNSS receivers through advanced signal processing and machine learning tools.

This Special Issue considers varied solutions and applications to improve GNSS navigation quality, as well as new applications and improvements in precise point positioning navigation. Special attention is devoted to smartphones and low-cost receivers, data analysis for GNSS, different types of navigation, data demodulation as for the Galileo High Accuracy Service, and combining different sensors with GNSS.

Prof. Dr. Thomas Pany
Guest Editor

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Keywords

GNSS positioning
GNSS navigation
signal processing
advances in precise point positioning (PPP)
advances in real-time kinematic (RTK) positioning
baseband signal processing for high-precision GNSS receivers
performance bounds in high-precision navigation
high-sensitivity receivers
GNSS applications to position, navigation, and timing-based devices and services

Published Papers (14 papers)

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Research

16 pages, 4115 KiB

Open AccessArticle

A Machine Learning-Based Tropospheric Prediction Approach for High-Precision Real-Time GNSS Positioning

by Jianping Chen and Yang Gao

Sensors 2024, 24(10), 2957; https://doi.org/10.3390/s24102957 - 7 May 2024

Viewed by 459

Abstract

For high-precision positioning applications, various GNSS errors need to be mitigated, including the tropospheric error, which remains a significant error source as it can reach up to a few meters. Although some commercial GNSS correction data providers, such as the Quasi-Zenith Satellite System (QZSS) Centimeter Level Augmentation Service (CLAS), have developed real-time precise regional troposphere products, the service is available only in limited regional areas. The International GNSS Service (IGS) has provided precise troposphere correction data in TRO format post-mission, but its long latency of 1 to 2 weeks makes it unable to support real-time applications. In this work, a real-time troposphere prediction method based on the IGS post-processing products was developed using machine learning techniques to eliminate the long latency problem. The test results from tropospheric predictions over a year using the proposed method indicate that the new method can achieve a prediction accuracy (RMSE) of 2 cm, making it suitable for real-time applications. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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20 pages, 7000 KiB

Open AccessArticle

An Improved Initial Alignment Method Based on SE₂(3)/EKF for SINS/GNSS Integrated Navigation System with Large Misalignment Angles

by Jin Sun, Yuxin Chen and Bingbo Cui

Sensors 2024, 24(9), 2945; https://doi.org/10.3390/s24092945 - 6 May 2024

Viewed by 365

Abstract

This paper proposes an improved initial alignment method for a strap-down inertial navigation system/global navigation satellite system (SINS/GNSS) integrated navigation system with large misalignment angles. Its methodology is based on the three-dimensional special Euclidean group and extended Kalman filter (SE₂(3)/EKF) and aims to overcome the challenges of achieving fast alignment under large misalignment angles using traditional methods. To accurately characterize the state errors of attitude, velocity, and position, these elements are constructed as elements of a Lie group. The nonlinear error on the Lie group can then be well quantified. Additionally, a group vector mixed error model is developed, taking into account the zero bias errors of gyroscopes and accelerometers. Using this new error definition, a GNSS-assisted SINS dynamic initial alignment algorithm is derived, which is based on the invariance of velocity and position measurements. Simulation experiments demonstrate that the alignment method based on SE₂(3)/EKF can achieve a higher accuracy in various scenarios with large misalignment angles, while the attitude error can be rapidly reduced to a lower level. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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22 pages, 23751 KiB

Open AccessArticle

Modified RTK-GNSS for Challenging Environments

by Ellarizza Fredeluces, Tomohiro Ozeki, Nobuaki Kubo and Ahmed El-Mowafy

Sensors 2024, 24(9), 2712; https://doi.org/10.3390/s24092712 - 24 Apr 2024

Viewed by 439

Abstract

Real-Time Kinematic Global Navigation Satellite System (RTK-GNSS) is currently the premier technique for achieving centimeter-level accuracy quickly and easily. However, the robustness of RTK-GNSS diminishes in challenging environments due to severe multipath effects and a limited number of available GNSS signals. This is a pressing issue, especially for GNSS users in the navigation industry. This paper proposes and evaluates several methodologies designed to overcome these issues by enhancing the availability and reliability of RTK-GNSS solutions in urban environments. Our novel approach involves the integration of conventional methods with a new technique that leverages surplus satellites—those not initially used for positioning—to more reliably detect incorrect fix solutions. We conducted three tests in densely built-up areas within the Tokyo region. The results demonstrate that our approach not only surpasses the fix rate of the latest commercial receivers and a popular open-source RTK-GNSS program but also improves positional reliability to levels comparable to or exceeding those of the aforementioned commercial technology. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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12 pages, 1181 KiB

Open AccessArticle

Global Navigation Satellite System Receiver Positioning in Harsh Environments via Clock Bias Prediction by Empirical Mode Decomposition and Back Propagation Neural Network Method

by Libin Du, Hao Chen, Yibo Yuan, Longjiang Song and Xiangqian Meng

Sensors 2024, 24(7), 2342; https://doi.org/10.3390/s24072342 - 7 Apr 2024

Viewed by 421

Abstract

This paper proposes a novel method to improve the clock bias short-term prediction accuracy of navigation receivers then solve the problem of low positioning accuracy when the satellite signal quality deteriorates. Considering that the clock bias of a navigation receiver is equivalent to a virtual satellite, the predicted value of clock bias is used to assist navigation receivers in positioning. Consequently, a combined prediction method for navigation receiver clock bias based on Empirical Mode Decomposition (EMD) and Back Propagation Neural Network (BPNN) analysis theory is demonstrated. In view of systematic errors and random errors in the clock bias data from navigation receivers, the EMD method is used to decompose the clock bias data; then, the BPNN prediction method is used to establish a high-precision clock bias prediction model; finally, based on the clock bias prediction value, the three-dimensional positioning of the navigation receiver is realized by expanding the observation equation. The experimental results show that the proposed model is suitable for clock bias time series prediction and providing three-dimensional positioning information meets the requirements of navigation application in the harsh environment of only three satellites. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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15 pages, 6296 KiB

Open AccessArticle

A Two-Step Regional Ionospheric Modeling Approach for PPP-RTK

by Zhenyu Xu, Changsheng Cai, Lin Pan, Wujiao Dai and Bei He

Sensors 2024, 24(7), 2307; https://doi.org/10.3390/s24072307 - 5 Apr 2024

Viewed by 455

Abstract

In the precise point positioning/real-time kinematic (PPP-RTK) technique, high-precision ionospheric delay correction information is an important prerequisite for rapid PPP convergence. The commonly used ionospheric modeling approaches in the PPP-RTKs only take the trend term of the ionospheric total electron content (TEC) variations into account. As a result, the residual ionospheric delay still affects the positioning solutions. In this study, we propose a two-step regional ionospheric modeling approach that involves combining a polynomial fitting model (PFM) and a Kriging interpolation (KI) model. In the first step, a polynomial fitting method is used to model the trend term of the ionospheric TEC variations. In the second step, a KI method is used to compensate for the residual term of the ionospheric TEC variations. Datasets collected from continuously operating reference stations (CORSs) in Hunan Province, China, are used to validate the PFM/KI method by comparing with a single PFM method and a combined PFM and inverse distance weighting interpolation (IDWI) method. The experimental results show that the two-step PFM/KI modeled ionospheric delay achieves an average root mean square (RMS) error of 1.8 cm, which is improved by about 48% and 23% when compared with the PFM and PFM/IDWI methods, respectively. Regarding the positioning performance, the PPP-RTK with the PFM/KI method takes an average of 1.8 min or 4.0 min to converge to a positioning accuracy of 1.3 cm or 2.5 cm in the horizontal and vertical directions, respectively. The convergence times are decreased by about 18% and 14% in the horizontal direction and 9% and 5% in the vertical direction over the PFM and the PFM/IDWI methods, respectively. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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19 pages, 10690 KiB

Open AccessArticle

Designing and Testing an IoT Low-Cost PPP-RTK Augmented GNSS Location Device

by Domenico Amalfitano, Matteo Cutugno, Umberto Robustelli and Giovanni Pugliano

Sensors 2024, 24(2), 646; https://doi.org/10.3390/s24020646 - 19 Jan 2024

Viewed by 963

Abstract

Nowadays, the availability of affordable multi-constellation multi-frequency receivers has broadened access to accurate positioning. The abundance of satellite signals coupled with the implementation of ground- and satellite-based correction services has unlocked the potential for achieving real-time centimetre-level positioning with low-cost instrumentation. Most of the current and future applications cannot exploit well-consolidated satellite positioning techniques such as Network Real Time Kinematic (RTK) and Precise Point Positioning (PPP); the former is inapplicable for large user bases due to the necessity of a two-way communication link between the user and the NRTK service provider, while the latter necessitates long convergence times that are not in keeping with kinematic application. In this context, the hybrid PPP-RTK technique has emerged as a potential solution to meet the demand for real-time, low-cost, accurate, and precise positioning. This paper presents an Internet of Things (IoT) GNSS device developed with low-cost hardware; it leverages a commercial PPP-RTK correction service which delivers corrections via IP. The main target is to obtain both horizontal and vertical decimetre-level accuracies in urban kinematic tests, along with other requisites such as solution availability and the provision of connection ports for interfacing an IoT network. A vehicle-borne kinematic test has been conducted to evaluate the device performance. The results show that (i) the IoT device can deliver horizontal and vertical positioning solutions at decimetre-level accuracy with the targeted solution availability, and (ii) the provided IoT ports are feasible for gathering the position solutions over an internet connection. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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17 pages, 5610 KiB

Open AccessArticle

RTK+OSNMA Positioning for Road Applications: An Experimental Performance Analysis in Finland

by José M. Vallet García and M. Zahidul H. Bhuiyan

Sensors 2024, 24(2), 621; https://doi.org/10.3390/s24020621 - 18 Jan 2024

Viewed by 796

Abstract

We compare the performance of dual-band (GPS L1/L2 and Galileo E1/E5a) real-time kinematic (RTK) positioning in an open sky and urban scenarios in southern Finland using two different authentication schemes: one using only satellites authenticated by Galileo’s open service navigation message authentication (OSNMA) service (which at the moment of our tests led to using only authenticated Galileo satellites) and the other with no authentication. The results show the actual trade-off between accuracy and availability vs. authenticity associated with using only OSNMA-authenticated satellites, while the authentication of only Galileo satellites is possible (e.g., a drop of RTK positioning availability from 96.67 to 86.01% in our open sky and from 73.55 to 18.65% in our urban scenarios, respectively), and an upper bound of the potential performance that could be reached in similar experimental conditions had the authentication of GPS satellites been supported (e.g., an overall 14 cm and

10.20

m

95% horizontal accuracy in our open sky and urban scenarios, with below 30, 20 and 10

c

m

during 97.39, 96.03 and 92.43% of the time in the open sky and 49.12, 45.96 and 39.63% in the urban scenarios, respectively). Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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16 pages, 6676 KiB

Open AccessArticle

A Multi-Scale Anti-Multipath Algorithm for GNSS-RTK Monitoring Application

by Shouhua Wang, Shuaihu Wang and Xiyan Sun

Sensors 2023, 23(20), 8396; https://doi.org/10.3390/s23208396 - 11 Oct 2023

Cited by 1 | Viewed by 786

Abstract

During short baseline measurements in the Real-Time Kinematic Global Navigation Satellite System (GNSS-RTK), multipath error has a significant impact on the quality of observed data. Aiming at the characteristics of multipath error in GNSS-RTK measurements, a novel method that combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and adaptive wavelet packet threshold denoising (AWPTD) is proposed to reduce the effects of multipath error in GNSS-RTK measurements through modal function decomposition, effective coefficient sieving, and adaptive thresholding denoising. It first utilizes the ICEEMDAN algorithm to decompose the observed data into a series of intrinsic mode functions (IMFs). Then, a novel IMF selection method is designed based on information entropy to accurately locate the IMFs containing multipath error information. Finally, an optimized adaptive denoising method is applied to the selected IMFs to preserve the original signal characteristics to the maximum possible extent and improve the accuracy of the multipath error correction model. This study shows that the ICEEMDAN-AWPTD algorithm provides a multipath error correction model with higher accuracy compared to singular filtering algorithms based on the results of simulation data and GNSS-RTK data. After the multipath correction, the accuracy of the E, N, and U coordinates increased by 49.2%, 65.1%, and 56.6%, respectively. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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24 pages, 5983 KiB

Open AccessArticle

Theoretical Upper and Lower Limits for Normalized Bandwidth of Digital Phase-Locked Loop in GNSS Receivers

by Young-Jin Song, Thomas Pany and Jong-Hoon Won

Sensors 2023, 23(13), 5887; https://doi.org/10.3390/s23135887 - 25 Jun 2023

Cited by 1 | Viewed by 1116

Abstract

Determining the loop noise bandwidth and the coherent integration time is essential and important for the design of a reliable digital phase-locked loop (DPLL) in global navigation satellite system (GNSS) receivers. In general, designers set such parameters approximately by utilizing the well-known fact that the DPLL is stable if the normalized bandwidth, which is the product of the integration time and the noise bandwidth, is much less than one. However, actual limit points are not fixed at exactly one, and they vary with the loop filter order and implementation method. Furthermore, a lower limit on the normalized bandwidth may exist. This paper presents theoretical upper and lower limits for the normalized bandwidth of DPLL in GNSS receivers. The upper limit was obtained by examining the stability of DPLL with a special emphasis on the digital integration methods. The stability was investigated in terms of z-plane root loci with and without the consideration of the computational delay, which is a delay induced by the calculation of the discriminator and the loop filter. The lower limit was analyzed using the DPLL measurement error composed of the thermal noise, oscillator phase noise, and dynamic stress error. By utilizing the carrier-to-noise density ratio threshold which indicates the crossing point between the measurement error and the corresponding threshold, the lower limit of the normalized bandwidth is obtained. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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16 pages, 900 KiB

Open AccessArticle

Characterizing Periodic Variations of Atomic Frequency Standards via Their Frequency Stability Estimates

by Weiwei Cheng, Guigen Nie and Jian Zhu

Sensors 2023, 23(11), 5356; https://doi.org/10.3390/s23115356 - 5 Jun 2023

Viewed by 920

Abstract

The onboard atomic frequency standard (AFS) is a crucial element of Global Navigation Satellite System (GNSS) satellites. However, it is widely accepted that periodic variations can influence the onboard AFS. The presence of non-stationary random processes in AFS signals can lead to inaccurate separation of the periodic and stochastic components of satellite AFS clock data when using least squares and Fourier transform methods. In this paper, we characterize the periodic variations of AFS using Allan and Hadamard variances and demonstrate that the Allan and Hadamard variances of the periodics are independent of the variances of the stochastic component. The proposed model is tested against simulated and real clock data, revealing that our approach provides more precise characterization of periodic variations compared to the least squares method. Additionally, we observe that overfitting periodic variations can improve the precision of GPS clock bias prediction, as indicated by a comparison of fitting and prediction errors of satellite clock bias. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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12 pages, 1231 KiB

Open AccessCommunication

Software Correction of Speed Measurement Determined by Phone GNSS Modules in Applications for Runners

by Pawel Biernacki

Sensors 2023, 23(5), 2678; https://doi.org/10.3390/s23052678 - 1 Mar 2023

Viewed by 1204

Abstract

This paper presents the results of a study on software correction of speed measurements taken by GNSS receivers installed in cell phones and sports watches. Digital low-pass filters were used to compensate for fluctuations in measured speed and distance. Real data obtained from popular running applications for cell phones and smartwatches were used for simulations. Various measurement situations were analyzed, such as running at a constant speed or interval running. Taking a very high accuracy GNSS receiver as the reference equipment, the solution proposed in the article reduces the measurement error of the traveled distance by 70%. In the case of measuring speed in interval running, the error could be reduced by up to 80%. The low-cost implementation allows simple GNSS receivers to approach the quality of distance and speed estimation of very precise and expensive solutions. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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29 pages, 26529 KiB

Open AccessArticle

Performance Analysis of Real-Time GPS/Galileo Precise Point Positioning Integrated with Inertial Navigation System

by Lei Zhao, Paul Blunt, Lei Yang and Sean Ince

Sensors 2023, 23(5), 2396; https://doi.org/10.3390/s23052396 - 21 Feb 2023

Cited by 3 | Viewed by 1476

Abstract

The integration of global navigation satellite system (GNSS) precise point positioning (PPP) and inertial navigation system (INS) is widely used in navigation for its robustness and resilience, especially in case of GNSS signal blockage. With GNSS modernization, a variety of PPP models have been developed and studied, which has also led to various PPP/INS integration methods. In this study, we investigated the performance of a real-time GPS/Galileo zero-difference ionosphere-free (IF) PPP/INS integration with the application of uncombined bias products. This uncombined bias correction was independent of PPP modeling on the user side and also enabled carrier phase ambiguity resolution (AR). CNES (Centre National d’Etudes Spatiales) real-time orbit, clock, and uncombined bias products were used. Six positioning modes were evaluated, including PPP, PPP/INS loosely coupled integration (LCI), PPP/INS tightly coupled integration (TCI), and three of these with uncombined bias correction through a train positioning test in an open sky environment and two van positioning tests at a complex road and city center. All of the tests used a tactical-grade inertial measurement unit (IMU). In the train test, we found that ambiguity-float PPP had almost identical performance with LCI and TCI, which reached an accuracy of 8.5, 5.7, and 4.9 cm in the north (N), east (E) and up (U) direction, respectively. After AR, significant improvements on the east error component were achieved, which were 47%, 40%, and 38% for PPP-AR, PPP-AR/INS LCI, and PPP-AR/INS TCI, respectively. In the van tests, frequent signal interruptions due to bridges, vegetation, and city canyons make the IF AR difficult. TCI achieved the highest accuracies, which were 32, 29, and 41 cm for the N/E/U component, respectively, and also effectively eliminated the solution re-convergence in PPP. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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20 pages, 7847 KiB

Open AccessArticle

Table-Based Adaptive Digital Phase-Locked Loop for GNSS Receivers Operating in Moon Exploration Missions

by Young-Jin Song and Jong-Hoon Won

Sensors 2022, 22(24), 10001; https://doi.org/10.3390/s222410001 - 19 Dec 2022

Cited by 2 | Viewed by 1624

Abstract

An adaptive digital phase-locked loop (DPLL) continually adjusts the noise bandwidth of the loop filter in global navigation satellite system (GNSS) receivers to track signals by measuring the signal-to-noise ratio and/or dynamic stress. Such DPLLs have a relatively large amount of computational complexity compared with the conventional DPLL. A table-based adaptive DPLL is proposed that adjusts the noise bandwidth value by extracting it from the pre-generated table without additional calculations. The values of the noise bandwidth table are computed in an optimal manner in consideration of the thermal noise, oscillator phase noise, and dynamic stress error. The calculation method of the proper integration time to maintain the stability of the loop filter is presented. Additionally, the simulation is configured using the trajectory analysis results from the Moon exploration mission and shows that the proposed algorithm operates stably in harsh environments, while a conventional fixed bandwidth loop cannot. The proposed algorithm has a similar phase jitter performance to the existing adaptive DPLL algorithms and has an execution time that is approximately 2.4–5.4 times faster. It is verified that the proposed algorithm is computationally efficient while maintaining jitter performance. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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13 pages, 3349 KiB

Open AccessArticle

Prediction of IGS RTS Orbit Correction Using LSTM Network at the Time of IOD Change

by Beomsoo Kim and Jeongrae Kim

Sensors 2022, 22(23), 9421; https://doi.org/10.3390/s22239421 - 2 Dec 2022

Cited by 1 | Viewed by 1106

Abstract

The international GNSS service (IGS) real-time service (RTS) provides orbit and clock corrections for the global navigation satellite system (GNSS) via the internet. RTS is widely used for real-time, precise positioning and its data is transmitted via the internet. Intermittent data loss can occur and cause positioning accuracy degradation. RTS data has a discontinuity when the issue of data (IOD) changes every two hours. If the signal loss occurs immediately after the IOD change, then the performance of the RTS prediction degrades significantly. We propose an adjustment method to make the RTS data across the IOD change, which makes it possible to use long RTS data for building a prediction model. The proposed adjustment method is combined with a long-short-term memory (LSTM) network to improve long-period prediction accuracy. Experiments with GPS and RTS were performed to evaluate the RTS orbit prediction accuracy. The LSTM with the IOD adjustment outperforms other polynomial prediction methods, and the positioning accuracy with the predicted RTS orbit correction shows a significant improvement. Full article

(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)

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