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Editorial

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4 pages, 175 KiB

Open AccessEditorial

An Overview of a Special Issue on Upcoming Positioning, Navigation, and Timing: GPS, GLONASS, Galileo and BeiDou

by Chang-Ki Hong, Tae-Suk Bae and Jay Hyoun Kwon

Remote Sens. 2022, 14(9), 1982; https://doi.org/10.3390/rs14091982 - 20 Apr 2022

Cited by 3 | Viewed by 3890

Abstract

In recent decades, global navigation satellite systems (GNSSs) have experienced significant changes [...] Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

Research

Jump to: Editorial

16 pages, 8785 KiB

Open AccessArticle

Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products

by Tao Geng, Rui Jiang, Yifei Lv and Xin Xie

Remote Sens. 2022, 14(6), 1389; https://doi.org/10.3390/rs14061389 - 13 Mar 2022

Cited by 14 | Viewed by 2556

Abstract

The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China’s BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still [...] Read more.

The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China’s BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still a lack of comprehensive research on the onboard clocks of the entire BDS-3 constellation. In this study, the precise clock products of GeoForschungsZentrum (GFZ) from day-of-year (DOY) 1, 2021 to DOY 300, 2021 were used to analyze the characteristics and performance of BDS-3 onboard clocks from the following aspects: clock bias, frequency, drift rate, fitting residuals, periodicity, and frequency stability. Compared with BDS-2, the clock quality of BDS-3 satellites has been greatly improved, but there are still jumps in the clock offsets and frequency series of BDS-3 clocks. The drift rate of BDS-3 clocks varies within the range between

- {2 \times 10}^{- 18} {and 2 \times 10}^{- 18} {s / s}^{2}

. The daily model fitting residuals of passive hydrogen masers (PHM) on BDS-3 medium Earth orbit (MEO), inclined geosynchronous orbit (IGSO), and geostationary (GEO) satellites are 0.15, 0.28, and 0.46 ns, respectively. The overlapping Allan deviation (OADEV) of BDS-3 MEO clocks is

4 {. 0 \times 10}^{- 14} s / s

at a time interval of 1000 s. The PHMs on BDS-3 MEO satellites exhibit fewer periodic signals than those of Rb clocks. In addition, the precise clock offsets of the BDS-3 PHMs carried on the MEO, IGSO, and GEO satellites show different periodicities, which are similar to those of the corresponding types of BDS-2 satellites. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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27 pages, 8066 KiB

Open AccessArticle

Intersystem Bias in GPS, GLONASS, Galileo, BDS-3, and BDS-2 Integrated SPP: Characteristics and Performance Enhancement as a Priori Constraints

by Lin Pan, Zhehao Zhang, Wenkun Yu and Wujiao Dai

Remote Sens. 2021, 13(22), 4650; https://doi.org/10.3390/rs13224650 - 18 Nov 2021

Cited by 11 | Viewed by 3298

Abstract

Global navigation satellite systems (GNSSs) have been booming in recent years, and the space segment of all four of the GNSSs, including BDS (BDS-3/BDS-2), Galileo, GPS, and GLONASS, has almost been fully deployed at present. The single point positioning (SPP) technology, which is [...] Read more.

Global navigation satellite systems (GNSSs) have been booming in recent years, and the space segment of all four of the GNSSs, including BDS (BDS-3/BDS-2), Galileo, GPS, and GLONASS, has almost been fully deployed at present. The single point positioning (SPP) technology, which is widely used in satellite navigation and low-accuracy positioning, can benefit from the multi-GNSS integration, but the additional intersystem bias (ISB) parameters should be introduced to ensure the compatibility among different GNSSs. In this study, the ISB estimates derived from four-system integrated SPP are carefully characterized, and the performance enhancement attributed to a priori ISB constraints by prediction for position solutions under open sky and constrained visibility environments is rigorously evaluated. The results indicate that the ISB between BDS-3 and BDS-2 cannot be ignored. The daily ISBs show step changes when encountering the replacement of receiver types, while it is not the case for the receiver firmware versions. The daily ISBs are roughly consistent for the stations equipped with the same type of receivers. The short-term stability of epochwise ISBs for GLONASS, Galileo, BDS-2, and BDS-3 with respect to GPS can be 2.335, 1.262, 1.741, and 1.532 ns, respectively, whereas the corresponding long-term stability for daily ISBs can be 1.258, 1.288, 2.713, and 2.566 ns, respectively. The single-day prediction accuracy of daily ISBs for GLONASS, Galileo, BDS-2, and BDS-3 with respect to GPS can be 1.055, 0.640, 1.242, and 0.849 ns, respectively. The improvements on positioning accuracy after introducing a priori ISB constraints can be over 20% at an elevation mask of 40° and 50° with a time span of ISB prediction of a day. As to the availability, it is only 64.0% for traditional four-system SPP under a cutoff elevation of 50°, while the corresponding availability is increased to approximately 90.0% after considering a priori ISB constraints. For completeness, the characteristics of ISBs estimated with the low-cost u-blox M8T receiver and the Xiaomi Mi8 smartphone as well as the contribution of a priori ISB constraints to the multisystem SPP solutions with these devices are also investigated. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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20 pages, 3864 KiB

Open AccessArticle

High-Accuracy Attitude Determination Using Single-Difference Observables Based on Multi-Antenna GNSS Receiver with a Common Clock

by Chenglong Zhang, Danan Dong, Wen Chen, Miaomiao Cai, Yu Peng, Chao Yu and Jianping Wu

Remote Sens. 2021, 13(19), 3977; https://doi.org/10.3390/rs13193977 - 5 Oct 2021

Cited by 13 | Viewed by 2857

Abstract

A global navigation satellite system (GNSS) receiver with multi-antenna using clock synchronization technology is a powerful piece of equipment for precise attitude determination and reducing costs. The single-difference (SD) can eliminate both the satellites and receiver clock errors with the common clock between [...] Read more.

A global navigation satellite system (GNSS) receiver with multi-antenna using clock synchronization technology is a powerful piece of equipment for precise attitude determination and reducing costs. The single-difference (SD) can eliminate both the satellites and receiver clock errors with the common clock between antennas, which benefits the GNSS short-baseline attitude determination due to its lower noise, higher redundancy and stronger function model strength. However, the existence of uncalibrated phase delay (UPD) makes it difficult to obtain fixed SD attitude solutions. Therefore, the key problem for the fixed SD attitude solutions is to separate the SD UPD and fix the SD ambiguities into integers between antennas. This article introduces the one-step ambiguity substitution approach to separate the SD UPD, through which we merge the SD UPD parameter with the SD ambiguity of the reference satellite ambiguity as the new SD UPD parameter. Reconstructing the other SD ambiguities, the rank deficiency can be remedied by nature, and the new SD ambiguities can have a natural integer feature. Finally, the fixed SD baseline and attitude solutions are obtained by combining the ambiguity substitution approach with integer ambiguity resolution (IAR). To verify the effect of the ambiguity substitution approach and the advantages of the SD observables with a common clock in practical applications, we conducted static, kinematic, and vehicle experiments. In static experiments, the root mean squared errors (RMSEs) of the yaw and pitch angles obtained by the SD observables with a common clock were improved by approximately 80% and 93%, respectively, compared to double-difference (DD) observables with a common clock in multi-day attitude solutions. The kinematic results show that the dispersion of the SD-Fix in the pitch angle is two times less that of the DD-Fix, and the standard deviations (STDs) of the pitch angle for SD-Fix can reach 0.02°. Based on the feasibility, five bridges with low pitch angles in the vehicle experiment environment, which the DD observables cannot detect, were detected by the SD observables with a common clock. The attitude angles obtained by the SD observables were also consistent with the fiber optic gyroscope (FOG) inertial navigation system (INS). This research on the SD observables with a common clock provides higher accuracy. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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32 pages, 33008 KiB

Open AccessArticle

Precise Point Positioning with Almost Fully Deployed BDS-3, BDS-2, GPS, GLONASS, Galileo and QZSS Using Precise Products from Different Analysis Centers

by Xuanping Li and Lin Pan

Remote Sens. 2021, 13(19), 3905; https://doi.org/10.3390/rs13193905 - 29 Sep 2021

Cited by 7 | Viewed by 3111

Abstract

The space segment of all the five satellite systems capable of providing precise position services, namely BeiDou Navigation Satellite System (BDS) (including BDS-3 and BDS-2), Global Positioning System (GPS), GLObal NAvigation Satellite System (GLONASS), Galileo and Quasi-Zenith Satellite System (QZSS), has almost been [...] Read more.

The space segment of all the five satellite systems capable of providing precise position services, namely BeiDou Navigation Satellite System (BDS) (including BDS-3 and BDS-2), Global Positioning System (GPS), GLObal NAvigation Satellite System (GLONASS), Galileo and Quasi-Zenith Satellite System (QZSS), has almost been fully deployed at present, and the number of available satellites is approximately 136. Currently, the precise satellite orbit and clock products from the analysis centers European Space Agency (ESA), GeoForschungsZentrum Potsdam (GFZ) and Wuhan University (WHU) can support all five satellite systems. Thus, it is necessary to investigate the positioning performance of a five-system integrated precise point positioning (PPP) (i.e., GRECJ-PPP) using the precise products from different analysis centers under the current constellation status. It should be noted that this study only focuses on the long-term performance of PPP based on daily observations. The static GRECJ-PPP can provide a convergence time of 5.9–6.9/2.6–3.1/6.3–7.1 min and a positioning accuracy of 0.2–0.3/0.2–0.3/1.0–1.1 cm in east/north/up directions, respectively, while the corresponding kinematic statistics are 6.8–8.6/3.3–4.0/7.8–8.1 min and 1.0–1.1/0.8/2.5–2.6 cm in three directions, respectively. For completeness, although the real-time precise products from the analysis center Centre National d’Etudes Spatiales (CNES) do not incorporate QZSS satellites, the performance of real-time PPP with the other four satellite systems (i.e., GREC-PPP) is also analyzed. The real-time GREC-PPP can achieve a static convergence time of 8.7/5.2/11.2 min, a static positioning accuracy of 0.6/0.8/1.3 cm, a kinematic convergence time of 11.5/6.9/13.0 min, and a kinematic positioning accuracy of 1.7/1.6/3.6 cm in the three directions, respectively. For comparison, the results of single-system and dual-system PPP are also provided. In addition, the consistency of the precise products from different analysis centers is characterized. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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14 pages, 1867 KiB

Open AccessArticle

Real-Time Estimation of GPS-BDS Inter-System Biases: An Improved Particle Swarm Optimization Algorithm

by Wenhao Zhao, Genyou Liu, Shengliang Wang, Ming Gao and Dong Lv

Remote Sens. 2021, 13(16), 3214; https://doi.org/10.3390/rs13163214 - 13 Aug 2021

Cited by 8 | Viewed by 2121

Abstract

The restart of the receiver will lead to the change in the non-overlapping frequency inter-system biases (ISB), which will make it difficult to apply the tightly combined RTK method of pre-calibrating ISB to the actual scene. Particle swarm optimization (PSO) algorithm can be [...] Read more.

The restart of the receiver will lead to the change in the non-overlapping frequency inter-system biases (ISB), which will make it difficult to apply the tightly combined RTK method of pre-calibrating ISB to the actual scene. Particle swarm optimization (PSO) algorithm can be used to estimate the fractional part of the inter-system phase bias (F-ISPB) in real time, which is not affected by the receiver restart. However, the standard PSO can easily fall into local optimum and cannot accurately estimate the value of F-ISPB. In this contribution, based on the characteristics of F-ISPB, we propose an improved PSO with adaptive search space and elite reservation strategy to estimate the F-ISPB in real time. When the value of F-ISPB is close to the boundary of the search space, the improved PSO will transform the search space so that F-ISPB will be located near the central region of the new search space, which will greatly reduce the situation of the standard PSO easily falling into local optimum. Since F-ISPB is very stable, an elite retention strategy will help us to estimate F-ISPB faster and more accurately. Three sets of short baseline static data were selected for testing. The results show that the inter-system differenced model based on the improved PSO has a higher ambiguity fixed rate and positioning accuracy than the inter-system differenced model based on the standard PSO and the classical intra-system differenced model, and the fewer the number of satellites, the more obvious the effect. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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Figure 1
Relationship between ratio and F-ISPB for first epoch. (a,c) The baseline CUTB–CUTC. (b,d) The baseline CUTB–CUT0. Full article ">Figure 2
Relationship between ratio and F-ISPB for all epochs. (a,c) CUTB–CUTC. (b,d) CUTB–CUT0. Full article ">Figure 3
Number of GPS and BDS satellites at different cut-off elevation angles. (a) 15 degrees. (b) 25 degrees. (c) 35 degrees. (d) 45 degrees. Full article ">Figure 4
F-ISPB estimation results of CUTB–CUT0 baseline. (a) Standard PSO. (b) PSO for adaptive search space. (c) PSO for elite retention strategy. (d) Improved PSO with both functions. Full article ">Figure 5
The distribution of ratio values at different cut-off elevation angles. (a) 15 degrees. (b) 25 degrees. (c) 35 degrees. (d) 45 degrees. Full article ">Figure 6
Ambiguity success rate and average of ratio at different cut-off elevation angles. (a) Ambiguity success rate. (b) Average of ratio. Full article ">Figure 7
F-ISPB estimation results of IGG01–IGG02 baseline. Full article ">

22 pages, 7502 KiB

Open AccessArticle

Modeling and Performance Evaluation of Precise Positioning and Time-Frequency Transfer with Galileo Five-Frequency Observations

by Wei Xu, Wen-Bin Shen, Cheng-Hui Cai, Li-Hong Li, Lei Wang and Zi-Yu Shen

Remote Sens. 2021, 13(15), 2972; https://doi.org/10.3390/rs13152972 - 28 Jul 2021

Cited by 10 | Viewed by 2433

Abstract

The present Global Navigation Satellite System (GNSS) can provide at least double-frequency observations, and especially the Galileo Navigation Satellite System (Galileo) can provide five-frequency observations for all constellation satellites. In this contribution, precision point positioning (PPP) models with Galileo E1, E5a, E5b, E5 [...] Read more.

The present Global Navigation Satellite System (GNSS) can provide at least double-frequency observations, and especially the Galileo Navigation Satellite System (Galileo) can provide five-frequency observations for all constellation satellites. In this contribution, precision point positioning (PPP) models with Galileo E1, E5a, E5b, E5 and E6 frequency observations are established, including a dual-frequency (DF) ionospheric-free (IF) combination model, triple-frequency (TF) IF combination model, quad-frequency (QF) IF combination model, four five-frequency (FF) IF com-bination models and an FF uncombined (UC) model. The observation data of five stations for seven days are selected from the multi-GNSS experiment (MGEX) network, forming four time-frequency links ranging from 454.6 km to 5991.2 km. The positioning and time-frequency transfer performances of Galileo multi-frequency PPP are compared and evaluated using GBM (which denotes precise satellite orbit and clock bias products provided by Geo Forschung Zentrum (GFZ)), WUM (which denotes precise satellite orbit and clock bias products provided by Wuhan University (WHU)) and GRG (which denotes precise satellite orbit and clock bias products provided by the Centre National d’Etudes Spatiales (CNES)) precise products. The results show that the performances of the DF, TF, QF and FF PPP models are basically the same, the frequency stabilities of most links can reach sub10^?16 level at 120,000 s, and the average three-dimensional (3D) root mean square (RMS) of position and average frequency stability (120,000 s) can reach 1.82 cm and 1.18 × 10^?15, respectively. The differences of 3D RMS among all models are within 0.17 cm, and the differences in frequency stabilities (in 120,000 s) among all models are within 0.08 × 10^?15. Using the GRG precise product, the solution performance is slightly better than that of the GBM or WUM precise product, the average 3D RMS values obtained using the WUM and GRG precise products are 1.85 cm and 1.77 cm, respectively, and the average frequency stabilities at 120,000 s can reach 1.13 × 10^?15 and 1.06 × 10^?15, respectively. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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20 pages, 16409 KiB

Open AccessArticle

Research on Tightly Coupled Multi-Antenna GNSS/MEMS Single-Frequency Single-Epoch Attitude Determination in Urban Environment

by Ming Gao, Genyou Liu, Shengliang Wang, Gongwei Xiao, Wenhao Zhao and Dong Lv

Remote Sens. 2021, 13(14), 2710; https://doi.org/10.3390/rs13142710 - 9 Jul 2021

Cited by 7 | Viewed by 2477

Abstract

GNSS-only attitude determination is difficult to perform well in poor-satellite-tracking environments such as urban areas with high and dense buildings or trees. In addition, it is harder to resolve integer ambiguity in the case of single-frequency single-epoch process mode. In this contribution, a [...] Read more.

GNSS-only attitude determination is difficult to perform well in poor-satellite-tracking environments such as urban areas with high and dense buildings or trees. In addition, it is harder to resolve integer ambiguity in the case of single-frequency single-epoch process mode. In this contribution, a low-cost MEMS gyroscope is integrated with multi-antenna GNSS to improve the performance of the attitude determination. A new tightly coupled (TC) model is proposed, which uses a single filter to achieve the optimal estimation of attitude drift, gyro biases and ambiguities. In addition, a MEMS-Attitude-aided Quality-Control method (MAQC) for GNSS observations is designed to eliminate both the carrier multipath errors and half-cycle slips disturbing ambiguity resolution. Vehicle experiments show that in GNSS-friendly scenarios, the Ambiguity Resolution (AR) success rate of the proposed model with MAQC can reach 100%, and the accuracy of attitudes are (0.12, 0.2, 0.2) degrees for heading, pitch and roll angles, respectively. Even in harsh scenarios, the AR success rate increases from about 67% for the GNSS only case to above 90% after coupling GNSS tightly with MEMS, and it is further improved to about 98% with MAQC. Meanwhile, the accuracy and continuity of attitude determination are effectively guaranteed. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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28 pages, 12232 KiB

Open AccessArticle

Characterization of Carrier Phase-Based Positioning in Real-World Jamming Conditions

by Søren Skaarup Larsen, Anna B. O. Jensen and Daniel H. Olesen

Remote Sens. 2021, 13(14), 2680; https://doi.org/10.3390/rs13142680 - 7 Jul 2021

Cited by 5 | Viewed by 2409

Abstract

GNSS signals arriving at receivers at the surface of the Earth are weak and easily susceptible to interference and jamming. In this paper, the impact of jamming on the reference station in carrier phase-based relative baseline solutions is examined. Several scenarios are investigated [...] Read more.

GNSS signals arriving at receivers at the surface of the Earth are weak and easily susceptible to interference and jamming. In this paper, the impact of jamming on the reference station in carrier phase-based relative baseline solutions is examined. Several scenarios are investigated in order to assess the robustness of carrier phase-based positioning towards jamming. Among others, these scenarios include a varying baseline length, the use of single- versus dual-frequency observations, and the inclusion of the Galileo and GLONASS constellations to a GPS only solution. The investigations are based on observations recorded at physical reference stations in the Danish TAPAS network during actual jamming incidents, in order to realistically evaluate the impact of real-world jamming on carrier phase-based positioning accuracy. The analyses performed show that, while there are benefits of using observations from several frequencies and constellations in positioning solutions, special care must be taken in solution processing. The selection of which GNSS constellations and observations to include, as well as when they are included, is essential, as blindly adding more jamming-affected observations may lead to worse positioning accuracy. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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15 pages, 3078 KiB

Open AccessArticle

Analysis of BDS/GPS Signals’ Characteristics and Navigation Accuracy for a Geostationary Satellite

by Meng Wang, Tao Shan, Wanwei Zhang and Hao Huan

Remote Sens. 2021, 13(10), 1967; https://doi.org/10.3390/rs13101967 - 18 May 2021

Cited by 14 | Viewed by 4330

Abstract

The utilization of Global Navigation Satellite System (GNSS) is becoming an attractive navigation approach for geostationary orbit (GEO) satellites. A high-sensitivity receiver compatible with Global Position System (GPS) developed by the United States and BeiDou Navigation Satellite System (BDS) developed by China has [...] Read more.

The utilization of Global Navigation Satellite System (GNSS) is becoming an attractive navigation approach for geostationary orbit (GEO) satellites. A high-sensitivity receiver compatible with Global Position System (GPS) developed by the United States and BeiDou Navigation Satellite System (BDS) developed by China has been used in a GEO satellite named TJS-5 to demonstrate feasibility of real-time navigation. According to inflight data, the GNSS signal characteristics including availability, position dilution of precision (PDOP), carrier-to-noise ratio (C/N₀), observations quantity and accuracy are analyzed. The mean number of GPS and GPS + BDS satellites tracked are 7.4 and 11.7 and the mean PDOP of GPS and GPS + BDS are 10.24 and 3.91, respectively. The use of BDS significantly increases the number of available navigation satellites and improves the PDOP. The number of observations with respect to C/N₀ is illustrated in detail. The standard deviation of the pseudorange noises are less than 4 m, and the corresponding carrier phase noises are mostly less than 8 mm. We present the navigation performance using only GPS observations and GPS + BDS observations combination at different weights through comparisons with the precision reference orbits. When GPS combined with BDS observations, the root mean square (RMS) of the single-epoch least square position accuracy can improve from 32.1 m to 16.5 m and the corresponding velocity accuracy can improve from 0.238 m/s to 0.165 m/s. The RMS of real-time orbit determination position accuracy is 5.55 m and the corresponding velocity accuracy is 0.697 mm/s when using GPS and BDS combinations. Especially, the position accuracy in x-axis direction reduced from 7.24 m to 4.09 m when combined GPS with BDS observations. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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18 pages, 2839 KiB

Open AccessArticle

Accuracy Analysis of GNSS Hourly Ultra-Rapid Orbit and Clock Products from SHAO AC of iGMAS

by Qinming Chen, Shuli Song and Weili Zhou

Remote Sens. 2021, 13(5), 1022; https://doi.org/10.3390/rs13051022 - 8 Mar 2021

Cited by 19 | Viewed by 3071

Abstract

With the development of the global navigation satellite system(GNSS), the hourly ultra-rapid products of GNSS are attracting more attention due to their low latency and high accuracy. A new strategy and method was applied by the Shanghai Astronomical Observatory (SHAO) Analysis Center (AC) [...] Read more.

With the development of the global navigation satellite system(GNSS), the hourly ultra-rapid products of GNSS are attracting more attention due to their low latency and high accuracy. A new strategy and method was applied by the Shanghai Astronomical Observatory (SHAO) Analysis Center (AC) of the international GNSS Monitoring and Assessment Service (iGMAS) for generating 6-hourly and 1-hourly GNSS products, which mainly include the American Global Positioning System (GPS), the Russian Global’naya Navigatsionnaya Sputnikova Sistema (GLONASS), the European Union’s Galileo, and the Chinese BeiDou navigation satellite system (BDS). The 6-hourly and 1-hourly GNSS orbit and clock ultra-rapid products included a 24-h observation session which is determined by 24-h observation data from global tracking stations, and a 24-h prediction session which is predicted from the observation session. The accuracy of the 1-hourly orbit product improved about 1%, 31%, 13%, 11%, 23%, and 9% for the observation session and 18%, 43%, 45%, 34%, 53%, and 15% for the prediction session of GPS, GLONASS, Galileo, BDS Medium Earth Orbit (MEO), Inclined Geosynchronous Orbit (IGSO), and GEO orbit, when compared with reference products with high accuracy from the International GNSS service (IGS).The precision of the 1-hourly clock products can also be seen better than the 6-hourly clock products. The accuracy and precision of the 6-hourly and 1-hourly orbit and clock verify the availability and reliability of the hourly ultra-rapid products, which can be used for real-time or near-real-time applications, and show encouraging prospects. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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23 pages, 9771 KiB

Open AccessArticle

Modeling and Analysis of BDS-2 and BDS-3 Combined Precise Time and Frequency Transfer Considering Stochastic Models of Inter-System Bias

by Guoqiang Jiao, Shuli Song, Qinming Chen, Chao Huang, Ke Su, Zhitao Wang and Na Cheng

Remote Sens. 2021, 13(4), 793; https://doi.org/10.3390/rs13040793 - 21 Feb 2021

Cited by 15 | Viewed by 2612

Abstract

BeiDou global navigation satellite system (BDS) began to provide positioning, navigation, and timing (PNT) services to global users officially on 31 July, 2020. BDS constellations consist of regional (BDS-2) and global navigation satellites (BDS-3). Due to the difference of modulations and characteristics for [...] Read more.

BeiDou global navigation satellite system (BDS) began to provide positioning, navigation, and timing (PNT) services to global users officially on 31 July, 2020. BDS constellations consist of regional (BDS-2) and global navigation satellites (BDS-3). Due to the difference of modulations and characteristics for the BDS-2 and BDS-3 default civil service signals (B1I/B3I) and the increase of new signals (B1C/B2a) for BDS-3, a systemically bias exists in the receiver-end when receiving and processing BDS-2 and BDS-3 signals, which leads to the inter-system bias (ISB) between BDS-2 and BDS-3 on the receiver side. To fully utilize BDS, the BDS-2 and BDS-3 combined precise time and frequency transfer are investigated considering the effect of the ISB. Four kinds of ISB stochastic models are presented, which are ignoring ISB (ISB_NO), estimating ISB as random constant (ISB_CV), random walk process (ISB_RW), and white noise process (ISB_WN). The results demonstrate that the datum of receiver clock offsets can be unified and the ISB deduced datum confusion can be avoided by estimating the ISB. The ISB_CV and ISB_RW models are superior to ISB_WN. For the BDS-2 and BDS-3 combined precise time and frequency transfer using ISB_NO, ISB_CV, ISB_RW, and ISB_WN, the stability of clock differences of old signals can be enhanced by 20.18%, 23.89%, 23.96%, and 11.46% over BDS-2-only, respectively. For new signals, the enhancements are ?50.77%, 20.22%, 17.53%, and ?3.69%, respectively. Moreover, ISB_CV and ISB_RW models have the better frequency transfer stability. Consequently, we recommended the optimal ISB_CV or suboptimal ISB_RW model for BDS-2 and BDS-3 combined precise time and frequency transfer when processing the old as well as the new signals. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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23 pages, 8894 KiB

Open AccessArticle

An In-Depth Assessment of the New BDS-3 B1C and B2a Signals

by Qinghua Zhang, Yongxing Zhu and Zhengsheng Chen

Remote Sens. 2021, 13(4), 788; https://doi.org/10.3390/rs13040788 - 21 Feb 2021

Cited by 22 | Viewed by 3952

Abstract

An in-depth and comprehensive assessment of new observations from BDS-3 satellites is presented, with the main focus on the Carrier-to-Noise density ratio (C/N₀), the quality of code and carrier phase observations for B1C and B2a signal. The signal characteristics of geosynchronous [...] Read more.

An in-depth and comprehensive assessment of new observations from BDS-3 satellites is presented, with the main focus on the Carrier-to-Noise density ratio (C/N₀), the quality of code and carrier phase observations for B1C and B2a signal. The signal characteristics of geosynchronous earth orbit (GEO), inclined geosynchronous satellite orbit (IGSO) and medium earth orbit (MEO) satellites of BDS-3 were grouped and compared, respectively. The evaluation results of the new B1C and B2a signals of BDS-3 were compared with the previously B1I/B2I/B3I signals and the interoperable signals of GPS, Galileo and quasi-zenith satellite system (QZSS) were compared simultaneously. As expected, the results clearly show that B1C and B2a have better signal strength and higher accuracy, including code and carrier phase observations. The C/N₀ of the B2a signal is about 3 dB higher than other signals. One exception is the code observation accuracy of B3I, which value is less than 0.15 m. The carrier precision of B1C and B2a is better than that of B1I/B2I/B3I. Despite difference-in-difference (DD) observation quantity or zero-base line evaluation is adopted, while B1C is about 0.3 mm higher carrier precision than B2a. The BDS-3 MEO satellite and GPS, Galileo, and QZSS satellites have the same level of signal strength, code and phase observation accuracy at the interoperable frequency, namely 1575.42 MHz and 1176.45 MHz which are very suitable for the co-position application. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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14 pages, 27296 KiB

Open AccessArticle

A Single-Difference Multipath Hemispherical Map for Multipath Mitigation in BDS-2/BDS-3 Short Baseline Positioning

by Chao Liu, Yuan Tao, Haiqiang Xin, Xingwang Zhao, Chunyang Liu, Haojie Hu and Tengfei Zhou

Remote Sens. 2021, 13(2), 304; https://doi.org/10.3390/rs13020304 - 17 Jan 2021

Cited by 18 | Viewed by 3237

Abstract

The BeiDou Navigation Satellite System (BDS) features a heterogeneous constellation so that it is difficult to mitigate the multipath in the coordinate-domain. Therefore, mitigating the multipath in the observation-domain becomes more important. Sidereal filtering is commonly used for multipath mitigation, which needs to [...] Read more.

The BeiDou Navigation Satellite System (BDS) features a heterogeneous constellation so that it is difficult to mitigate the multipath in the coordinate-domain. Therefore, mitigating the multipath in the observation-domain becomes more important. Sidereal filtering is commonly used for multipath mitigation, which needs to calculate the orbit repeat time of each satellite. However, that poses a computational challenge and damages the integrity at the end of the multipath model. Therefore, this paper proposes a single-difference model based on the multipath hemispherical map (SD-MHM) to mitigate the BDS-2/BDS-3 multipath in a short baseline. The proposed method is converted from double-difference residuals to single-difference residuals, which is not restricted by the pivot satellite transformation. Moreover, it takes the elevation and the azimuth angles of the satellite as the independent variables of the multipath model. The SD-MHM overcomes the unequal observation time of some satellites and does not require specific hardware. The experimental results show that the SD-MHM reduces the root mean square of the positioning errors by 56.4%, 63.9%, and 67.4% in the east, north, and vertical directions; moreover, it contributes to an increase in the baseline accuracy from 1.97 to 0.84 mm. The proposed SD-MHM has significant advantages in multipath mitigation compared with the advanced sidereal filtering method. Besides, the SD-MHM also features an excellent multipath correction capability for observation data with a period of more than seven days. Therefore, the SD-MHM provides a universal strategy for BDS multipath mitigation. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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17 pages, 26774 KiB

Open AccessArticle

Clustering Code Biases between BDS-2 and BDS-3 Satellites and Effects on Joint Solution

by Liang Chen, Min Li, Ying Zhao, Fu Zheng, Xuejun Zhang and Chuang Shi

Remote Sens. 2021, 13(1), 15; https://doi.org/10.3390/rs13010015 - 22 Dec 2020

Cited by 15 | Viewed by 2492

Abstract

China’s BeiDou navigation satellite system (BDS) has finished global constellation construction and can achieve joint solution, simultaneously relying on the B1I + B3I signals of the BDS-2 and BDS-3 satellites. For reasons mostly related to chip shape distortions, navigation satellite observations are corrupted [...] Read more.

China’s BeiDou navigation satellite system (BDS) has finished global constellation construction and can achieve joint solution, simultaneously relying on the B1I + B3I signals of the BDS-2 and BDS-3 satellites. For reasons mostly related to chip shape distortions, navigation satellite observations are corrupted by receiver-dependent code biases. Those biases are brought into observation residuals and degrade the pseudorange correction accuracy. Herein, we present a code bias estimation algorithm, using what we found to be an obvious clustering code bias phenomenon between the BDS-2 and BDS-3 satellites, leading to the systematic biases existing in the BDS-2+3 joint solution. Therefore, we propose a BDS-2+3 joint solution with code bias self-calibration, which can accurately strip off clustering code biases between the BDS-2 and BDS-3 satellites, and can greatly improve precise point positioning (PPP) convergence speed and accuracy. The statistics showed that the residual biases and root mean square (RMS) improved by 36% and 15% and the convergence time improved by approximately 35%. In the convergence stage, the positioning accuracy improved by approximately 38% and 21% in the horizontal and vertical directions, respectively. Meanwhile, in the post-convergence stage, the accuracy improved by approximately 10%. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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19 pages, 4345 KiB

Open AccessArticle

LEO Onboard Real-Time Orbit Determination Using GPS/BDS Data with an Optimal Stochastic Model

by Xuewen Gong, Jizhang Sang, Fuhong Wang and Xingxing Li

Remote Sens. 2020, 12(20), 3458; https://doi.org/10.3390/rs12203458 - 21 Oct 2020

Cited by 17 | Viewed by 4181

Abstract

The advancements of Earth observations, remote sensing, communications and navigation augmentation based on low Earth orbit (LEO) platforms present strong requirements for accurate, real-time and autonomous navigation of LEO satellites. Precise onboard real-time orbit determination (RTOD) using the space-borne data of multiple global [...] Read more.

The advancements of Earth observations, remote sensing, communications and navigation augmentation based on low Earth orbit (LEO) platforms present strong requirements for accurate, real-time and autonomous navigation of LEO satellites. Precise onboard real-time orbit determination (RTOD) using the space-borne data of multiple global navigation satellite systems (multi-GNSS) becomes practicable along with the availability of multi-GNSS. We study the onboard RTOD algorithm and experiments by using America’s Global Positioning System (GPS) and China’s regional BeiDou Navigation Satellite System (BDS-2) space-borne data of the FengYun-3C satellite. A new pseudo-ambiguity parameter, which combines the constant phase ambiguity, the orbit and clock offset error of the GPS/BDS broadcast ephemeris in the line-of-sight (LOS), is defined and estimated in order to reduce the negative effect of the LOS error on onboard RTOD. The analyses on the variation of the LOS error in the GPS/BDS broadcast ephemeris indicate that the pseudo-ambiguity parameter could be modeled as a random walk, and the setting of the power spectral density in the random walk model decides whether the pseudo-ambiguity can be estimated reasonably and the LOS error could be reduced or not. For different types of GPS/BDS satellites, the LOS errors show different variation characteristics, so the power spectral density should be set separately and differently. A numerical search approach is presented in this paper to find the optimal setting of the power spectral density for each type of GPS/BDS satellite by a series of tests. Based on the optimal stochastic model, a 3-dimensional (3D) real-time orbit accuracy of 0.7–2.0 m for position and 0.7–1.7 mm/s for velocity could be achieved only with dual-frequency BDS measurements and the broadcast ephemeris, while a notably superior orbit accuracy of 0.3–0.5 m for position and 0.3–0.5 mm/s for velocity is achievable using dual-frequency GPS/BDS measurements, due to the absorption effect of the estimated pseudo-ambiguity on the LOS error of the GPS/BDS broadcast ephemeris. Compared to using GPS-alone data, the GPS/BDS fusion only marginally improves the onboard RTOD orbit accuracy by about 1–3 cm, but the inclusion of BDS satellites increases the number of the tracked GNSS satellites and thus speeds up the convergence of the filter. Furthermore, the GPS/BDS fusion could help suppress the local orbit errors, ensure the orbit accuracy and improve the reliability and availability of the onboard RTOD when fewer GPS satellites are tracked in some anomalous arcs. Full article

(This article belongs to the Special Issue Upcoming Positioning, Navigation and Timing: GPS, GLONASS, Galileo and BeiDou)

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