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To address the issue of integrity monitoring for a multi-source information fusion navigation system, a theoretical framework of two-level integrity monitoring is proposed. Firstly, at the system level, a system-integrity-monitoring method based on the Kalman filter weighted least-squares form is established to detect and isolate faulty navigation sources. Secondly, at the sensor level, considering the redundancy of the faulty navigation sources, this paper presents the design of a multi-mode comprehensive fault-detection method for non-redundant navigation sources. Additionally, an extended-dimension matrix optimized sensor-fault detection and verification method for redundant navigation sources is proposed. Finally, integrity risk allocation criteria are established based on the effectiveness of navigation sources to calculate the system protection level and trigger integrity alarms. The two-level integrity-monitoring method was tested on a multi-source information fusion navigation system integrated with an inertial navigation system (INS), global positioning system (GPS), BeiDou satellite navigation system (BDS), Doppler velocity log (DVL), barometric altimeter (BA), and terrain-aided navigation (TAN). Test results demonstrate that the proposed method can effectively isolate the faulty navigation source within 10 s. Furthermore, it can detect the faulty sensors within the faulty navigation sources, thereby enhancing the reliability and robustness of the multi-source information fusion navigation system. [ABSTRACT FROM AUTHOR]

In the indoor and outdoor transition area, due to its poor availability in a complex positioning environment, the BDS/GPS SPP (single-point positioning by combining BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS)) is unable to provide an effective positioning service. In view of the poor positioning accuracy and low sampling rate of the BDS/GPS SPP and the gross error, such as the non-line-of-sight error of UWB (Ultra-Wide-Band), making the accuracy of positioning results poor, a BDS/GPS/UWB tightly coupled navigation model considering pedestrian motion characteristics is proposed to make positioning results more reliable and accurate in the transition area. The core content of this paper is divided into the following three parts: (1) Firstly, the dynamic model and positioning theories of BDS/GPS SPP and UWB are introduced, respectively. (2) Secondly, the BDS/GPS/UWB tightly coupled navigation model is proposed. An environment discrimination factor is introduced to adaptively adjust the variance factor of the system state. At the same time, the gross error detection factor is constructed by using the a posteriori residuals to make the variance factor of the measurement information of the combined positioning system able to be adjusted intelligently for the purpose of eliminating the interference of gross error observations on positioning results. On the other hand, pedestrian motion characteristics are introduced to establish the constraint equation to improve the consistency of positioning accuracy. (3) Thirdly, the actual measured data are used to demonstrate and analyze the reliability of the positioning model proposed by this paper. The experimental results show that the BDS/GPS/UWB tightly coupled navigation model can effectively improve the accuracy and availability of positioning. Compared with BDS/GPS SPP, the accuracy of this model is improved by 57.8%, 76.0% and 56.5% in the E, N and U directions, respectively. [ABSTRACT FROM AUTHOR]

For the past 20 years, Global Navigation Satellite System reflectometry (GNSS-R) technology has successfully shown its potential for remote sensing of the Earth's surface, including ocean and land surfaces. It is a multistatic radar that uses the GNSS signals reflected from the Earth's surface to extract land and ocean characteristics. Because of its numerous advantages such as low cost, multiple signal sources, and all-day/weather and high-spatiotemporal-resolution observations, this new technology has attracted the attention of many researchers. One of its most promising applications is GNSS-R ocean altimetry, which can complement existing techniques such as tide gauging and radar satellite altimetry. Since this technology for ocean altimetry was first proposed in 1993, increasing progress has been made including diverse methods for processing reflected signals (such as GNSS interferometric reflectometry, conventional GNSS-R, and interferometric GNSS-R), different instruments (such as an RHCP antenna with one geodetic receiver, a linearly polarized antenna, and a system of simultaneously used RHCP and LHCP antennas with a dedicated receiver), and different platform applications (such as ground-based, air-borne, or space-borne). The development of multi-mode and multi-frequency GNSS, especially for constructing the Chinese BeiDou Global Navigation Satellite System (BDS-3), has enabled more free signals to be used to further promote GNSS-R applications. The GNSS has evolved from its initial use of GPS L1 and L2 signals to include other GNSS bands and multi-GNSS signals. Using more advanced, multi-frequency, and multi-mode signals will bring new opportunities to develop GNSS-R technology. In this paper, studies of GNSS-R altimetry are reviewed from four perspectives: (1) classifications according to different data processing methods, (2) different platforms, (3) development of different receivers, and (4) our work. We overview the current status of GNSS-R altimetry and describe its fundamental principles, experiments, recent applications to ocean altimetry, and future directions. [ABSTRACT FROM AUTHOR]

The BeiDou Navigation Satellite System (BDS) has developed rapidly, and the combination of BDS Phase II (BDS-2) and BDS Phase III (BDS-3) has attracted wide attention. It is found that there are code ISBs between BDS-2 and BDS-3, which may have a certain impact on the BDS-2 and BDS-3 combined positioning. This paper focuses on the performance of BDS-2/BDS-3 combined B1I single-frequency pseudorange positioning and investigates the positioning performance with and without code ISBs correction for different types of receivers, include geodetic GNSS receivers and low-cost receivers. The results show the following: (1) For geodetic GNSS receivers, the code ISBs of each receiver is about −0.3 m to −0.8 m, and the position deviation is reduced by 7% after correcting code ISBs. The code ISBs in the baseline with homogeneous receivers has a little influence on the positioning result, which can be ignored. The code ISBs in the baseline with heterogeneous receivers is about −0.5 m, and the position deviation is reduced by 4% after correcting code ISBs. (2) The code ISBs in the low-cost receivers are significantly larger than those in the geodetic GNSS receivers, and the impact on the positioning performance of the low-cost receivers is significantly greater than that on the geodetic GNSS receivers. After correcting the code ISBs, the position deviation of low-cost receivers can be reduced by around 12% for both undifferenced and differenced modes. (3) For low-cost receivers, correcting the code ISBs can increase the number of epochs successfully solved, which effectively improves the low-cost navigation and positioning performance. (4) The carrier-phase-smoothing method can effectively reduce the distribution dispersion of code ISBs and make the estimation of ISBs more accurate. The STD values of estimated code ISBs in geodetic GNSS receivers are reduced by about 40% after carrier-phase smoothing, while the corresponding values are reduced by about 7% in low-cost receivers due to their poor carrier-phase observation quality. [ABSTRACT FROM AUTHOR]

In recent years, the multi-GNSS positioning application is becoming more and more popular, same to the low Earth orbit (LEO) satellite precise orbit determination (POD) based on the onboard multi-GNSS measurements. The third-generation Beidou navigation satellite system (BDS-3) provides a new option to obtain the LEO satellite orbit solutions. However, the receiver intersystem bias (ISB) of different GNSS is unavoidable in multi-GNSS data processing. This paper's main goal is absorption of the impact of the ISB between BDS-3 and BDS-2 on the LEO satellite POD. Taking GPS-based POD solutions for the reference orbit, this paper evaluates the orbit accuracy of BDS-2-based POD, BDS-3-based POD, BDS-2 and BDS-3 combined PODs with/without ISB. The BDS-3-based POD accuracy is 6.57 cm in the 3D direction, a 56% improvement over BDS-2-based POD. When the ISB between BDS-3 and BDS-2 is estimated, the BDS-2/3 combined POD accuracy of 5.37 cm in the 3D direction is better than that without ISB, which is a 64% improvement over BDS-2-based POD and 18% improvement over BDS-3-based POD. For GPS and BDS-2/3 combined POD, the GPS and BDS-3 joint POD solutions have the smallest RMS differences in overlapping consistency and smallest RMS differences compared to GPS-based POD. This study indicates that estimating the BDS-2/3 receiver ISB in BDS-2/3 joint POD could improve the orbit accuracy, and the GPS and BDS-3 joint POD solution is better than another combined POD. This paper will provide meaningful references for the LEO satellite multi-GNSS-based POD. [ABSTRACT FROM AUTHOR]

With the global service of the BeiDou Navigation Satellite System (BDS), the Galileo Navigation Satellite System (Galileo), and the modernization of the Global Positioning System (GPS), achieving high-precision positioning through triple-frequency-only observations in medium baseline real-time kinematics (RTK) is anticipated. This study investigates the impacts of double-difference (DD) troposphere delay and ionosphere delay on ambiguity resolution (AR) based on six medium baselines at a latitude of 30°. Additionally, it evaluates positioning accuracy, fixing rate, convergence time, and computational time using triple-frequency-only (B1I/B2a/B3I, E1/E5a/E5b, L1/L2/L5) data, comparing these results to those obtained from dual-frequency (B1I/B2a, E1/E5a, L1/L2) and combined dual-frequency and triple-frequency data. The experimental findings suggest that, for geometry-based wide-lane (WL) AR, the DD troposphere delay and ionosphere delay can be disregarded. However, they cannot be overlooked when aiming to resolve the raw ambiguity. Triple-frequency-only RTK exhibits comparable positioning accuracy to dual-frequency RTK, with its primary advantage lying in faster convergence. The probability of achieving convergence within 180 s is approximately 8.0% higher for triple-frequency-only RTK compared to dual-frequency RTK. In terms of computational time, the use of triple-frequency-only data reduces the required time by 8.26 s compared to the approach that simultaneously employs both dual-frequency and triple-frequency data, resulting in a computational time reduction of approximately 20%. Therefore, when conducting medium baseline RTK positioning, it is recommended to adopt the ambiguity resolution method proposed in this paper based on triple-frequency-only observations. [ABSTRACT FROM AUTHOR]

In 2020, the BeiDou-3 global navigation satellite system (BDS-3) was officially completed and put into service. Currently, network real-time kinematic (RTK) technology is considered the main means through which to improve the positioning accuracy of the BeiDou navigation satellite system (BDS). This paper proposes a long-range undifferenced network RTK (URTK) algorithm, based on multi-frequency observation data of the BDS. First, the multi-frequency phase integer ambiguity resolution (AR) model considering atmospheric error parameters is designed, and the multi-frequency phase integer ambiguity of the long-range BDS reference station is determined. Then, the undifferenced integer ambiguity of each reference station is obtained, using linear variation based on the accurately determined phase integer ambiguity between reference stations, and the undifferenced observation error of each reference station is calculated. Considering the weakening spatial correlation of the observation errors between long-range stations, undifferenced classification error corrections of a reference station network are separated, according to different error characteristics. Finally, the inverse distance weighting method is employed to calculate the classification undifferenced error correction of the rover station. The rover station corrects the observation error through applying the undifferenced error correction to achieve high-precision positioning. The measured data of a long-range continuous operation reference station (CORS) network are selected for an experiment. The results show that the proposed algorithm can quickly and accurately realize the resolution of the BDS integer ambiguity of a reference station network and establish an undifferenced area error correction model in order to achieve accurate classification of undifferenced error correction values for a rover station. In China, the BDS-3 is superior to the global positioning system (GPS) in terms of the satellite number, position dilution of precision (PDOP) value, AR success rate, stability, and convergence time. The results show that the AR success rate, stability, and convergence time increase with the operational frequency, and the BDS-3 can achieve centimeter-level positioning of single-system rover stations without relying on the GPS. [ABSTRACT FROM AUTHOR]

The official launch of the Chinese BeiDou Navigation Satellite System with global coverage (BDS-3) presents significant opportunities for various applications, including precision agriculture and autonomous driving, among others. With its global spatial coverage and hybrid space constellation comprising geosynchronous Earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO) satellites, BDS can significantly contribute to various GNSS remote sensing applications that require real-time, precise water surface height measurements with high temporal and spatial resolution, such as in tidal monitoring. In this paper, we propose a carrier-phase-based method for BDS Reflectometry (BDS-R) to precisely retrieve real-time water surface height. Firstly, the BDS-R altimetry method is introduced, along with a detailed explanation of the data processing procedures. Secondly, a quality control method tailored to the characteristics of low-cost BDS devices is developed. Thirdly, a land altimetry experiment is conducted to evaluate the precision of BDS-R and analyze the specific contribution of the BDS hybrid constellation. Finally, a water surface altimetry experiment validates the real-time monitoring capabilities for low-cost BDS-R. The results indicate that low-cost BDS-R can achieve real-time centimeter-level water level monitoring with a temporal resolution of 1 s in lakefront environments. The performance of BDS-R can be significantly improved by the BDS hybrid constellation, particularly IGSOs. It is concluded that low-cost BDS-R has great potential for promoting ground-based GNSS remote sensing applications. [ABSTRACT FROM AUTHOR]

The design of a modern Global Navigation Satellite System (GNSS) has been exceptionally valued by the military and civilians of various countries. The inclusion of the pilot channel in addition to the navigation data channel is considered one of the major changes in GNSS modernization. Schemes of an equal weight combination (1:1 combination) and power ratio combination for data and pilot are primarily adopted by traditional receivers. With the emergence of the new data and pilot modulation signals with unequal power, such as L1C at Global Positioning System (GPS) L1 frequency and B1C at BeiDou Navigation Satellite System (BDS) B1 frequency, the traditional combination coefficient cannot achieve optimal reception performance. Considering the influence of the combination coefficient on the reception performance, the optimal coefficient of the correlator joint is estimated in this paper. The entire architecture of the data/pilot correlator joint tracking and positioning with unequal power is given. Based on the equivalence principle of the correlator joint and the discriminator joint, the optimal coefficient of the carrier loop is determined. A mathematical model of joint code tracking accuracy is established, and the optimal coefficient of the code loop is determined. The real-life satellite signal and simulation results show that the amplitude–ratio combined scheme is the best for receiving of correlator joints, followed by the power–ratio combination scheme and, finally, the 1:1 combination scheme. It is worth mentioning that the positioning accuracy of the amplitude–ratio combination is improved by 2% compared to the 1:1 combination, and by 1.3% compared to the power–ratio combination for B1C signal. The positioning accuracy of the amplitude–ratio combination is improved by 2.37% compared to the 1:1 combination, and by 1.6% compared to the power–ratio combination for L1C signal. The conclusions of this paper are validated for the traditional data/pilot with an equal power allocation. The techniques and test results provide technical support for GNSS high-precision-user receivers. [ABSTRACT FROM AUTHOR]

Many studies have focused on the smartphone-based global navigation satellite system (GNSS) for its portability. However, complex urban environments, such as urban canyons and tunnels, can easily interfere with GNSS signal qualities. Current smartphone-based positioning technologies using the GNSS signal still pose great challenges. Since the last satellite of the BeiDou navigation system (BDS) was successfully launched on 23 June 2020, it is possible to use a low-cost Android device to realize the localization based on the BDS signals worldwide. This research focuses on smartphone-based outdoor pedestrian navigation utilizing the GPS/BDS multi-constellation system. To improve the localization accuracy, we proposed the Weighted Factor Graph Optimization localization model (W-FGO). In this paper, firstly, we evaluate the signal qualities of the BDS via the data collected by the static experiment. Then, we structure the cost function based on the pseudo-range and the time series data for the traditional Factor Graph Optimization (FGO). Finally, we design the weight model based on the signal quality of each satellite and the time fading factor to further improve the localization accuracy of the conventional FGO method. An Android smartphone is utilized to collect the GNSS data for the evaluation and the localization. The experiment results demonstrate the superior performance of the proposed method. [ABSTRACT FROM AUTHOR]

BeiDou Global Navigation Satellite System (BDS-3) broadcasts multifrequency signals that offer more choices of frequencies and more signal combinations for positioning. This paper analyzes the effect of timing group delay (TGD) and differential code bias (DCB) of BDS-3 on the corresponding triple-frequency positioning. The triple-frequency observation models of BDS-3 are summarized and the DCB correction models are derived for the four different frequency combinations of triple-frequency ionospheric-free (IF) combination (IF123), two dual-frequency IF combinations (IF1213) and triple-frequency uncombined (UC123) positioning modes. Standard point positioning (SPP) and precise point positioning (PPP) experiments were conducted using 30 days of observations from 25 multi-GNSS experiment (MGEX) stations. The results show that the TGD/DCB correction has a significant impact on the accuracy of SPP. The positioning accuracy using IF123 and IF1213 models improved by about 73~90% after TGD correction, in comparison to a 27~30% improvement achieved using the UC123 model. In addition, the correction effect of DCB is slightly better than TGD. The DCB correction significantly improves accuracy in the initial epoch of the PPP, which helps the convergence of the filtering and reduces the convergence time. The average convergence times of IF123, IF1213 and UC123 are 26.1, 26.9 and 38.3 min, respectively, which are reduced by 6.79, 2.54 and 8.59% with DCB correction. The pseudorange residuals are closer to zero-mean random noise after DCB correction. Furthermore, the DCB affects the evaluation of the inter-frequency bias (IFB), ionospheric delay and floating ambiguity parameters. However, the tropospheric delay is almost unaffected by DCB. [ABSTRACT FROM AUTHOR]

As the Global Navigation Satellite System (GNSS) is widely used in all walks of life, the signal structure of satellite navigation is open, and the vulnerability to spoofing attacks is also becoming increasingly prominent, which will seriously affect the credibility of navigation, positioning, and timing (PNT) services. Satellite navigation signal authentication technology is an emerging technical means of improving civil signal anti-spoofing on the satellite navigation system side, and it is also an important development direction and research focus of the GNSS. China plans to carry out the design and development of the next-generation Beidou navigation satellite system (BDS), and one of its core goals is to provide more secure and credible PNT services. This paper first expounds on the principles and technical architecture of satellite navigation signal authentication, then clarifies the development history of satellite navigation signal authentication, and finally proposes the BDS authentication service system architecture. It will provide technical support for the construction and development of the follow-up Beidou authentication service. [ABSTRACT FROM AUTHOR]

Precise Point Positioning (PPP) is an official service of the BeiDou Global Navigation Satellite System (BDS-3) through the PPP-B2b signal. In this paper, we mainly focus on the long-term performance evaluation of BDS-3 PPP-B2b products and their application in time service. Since the PPP-B2b product is only available in and around China area, the arcs of PPP-B2b products are about several hours. We propose to evaluate the time datum stability by using all available satellites. Then, 557 day PPP-B2b products are collected for this experiment. The results show that there are large jumps in the GPS satellite clock time datum series. However, the BDS-3 satellite clock datum stability is almost at the same level with current Space State Representation (SSR) corrections from the International Global navigation satellite system Service (IGS). The difference between PPP-B2b GPS and BDS-3 satellite clock time datum will be absorbed into the Inter System Bias (ISB) parameter. Thus, it should be specially noted that the ISB parameter cannot be estimated as constant values if users use PPP-B2b products. In addition, the accuracy of the BDS-3 satellite clock is significantly better than that of the GPS for both the Root Mean Square Error (RMSE) and standard deviation (STD). The average Signal in Space Range Errors (SISREs) is 0.22 ns and 0.13 ns for GPS and BDS-3, respectively. The one-way timing experiment shows BDS-3 timing stability is 2.9 × 10−14@104 s. In addition, 10 baselines from 13 km to 4494 km are formed for time synchronization evaluation by using PPP-B2b products. The average RMSEs of time synchronization is from 0.46 ns to 1.58 ns and from 0.66 ns to 1.19 ns for GPS and BDS-3, respectively. As for STD, the average values are from 0.27 ns to 0.74 ns and from 0.27 ns to 0.47 ns for GPS and BDS-3, respectively. Overall, the results show that the time datum stability, accuracy, and service performance of BDS-3 PPP-B2b products has been stable over the past two years. [ABSTRACT FROM AUTHOR]

To guarantee the integrity of a global navigation satellite system (GNSS) for safety-critical users, a satellite-based augmentation system (SBAS) makes use of the integrity monitoring architecture, of which the signal quality monitor (SQM) is an important component to address the potential risks caused by satellite-induced signal anomalies. Due to the introduction of dual-frequency multi-constellation (DFMC) techniques in 2025, the ranging uncertainty will be reduced by the elimination of first-order ionospheric delay, but the biases measured in each individual signal will be inflated by the ionosphere-free combinations. Moreover, multiple modulations of DFMC signals might introduce applicability uncertainty of a traditional SQM method that has been protecting GPS L1C/A signal only. Thus, higher requirements are put forward for future SQM methods in detection sensitivity and modulation independence. This paper first proposes a design methodology for the SQM algorithm for BDS B1C/B2a signals, which could be easily extended to the DF combinations of other GNSS core constellations. Then, by comparing the performances of SQM baseline algorithms based on traditional multi-correlator and emerging chip domain observables (CDOs), respectively, the superiority of CDO-based SQM is declared. Detailed design iterations are further discussed, including the algorithm practicalization with optimizing code-phase bin length and lowering sampling frequency, as well as the metric simplification, to promote the overall performance while preserving a lower implementation complexity. Ultimately, a CDO-based SQM algorithm for BDS B1C/B2a signals is reached, which would be considered as an effective candidate in new generation DFMC SBASs. [ABSTRACT FROM AUTHOR]

The BeiDou Global Navigation Satellite System (BDS), including the second generation (BDS-2) and the third generation (BDS-3), has been widely used in areas of positioning, navigation, and timing (PNT). One of the essential prerequisites for accurate PNT service is the precise satellite orbits of multi-frequency and multi-constellation BDS-2 and BDS-3 satellites. As usual, the precise orbit products can be obtained from analysis centers (ACs) of the international GNSS Service (IGS). The precise orbits can also be downloaded from the international GNSS Monitoring and Assessment System (iGMAS). Compared with the IGS ACs, the iGMAS can provide featured services such as satellite orbits based on the new B1C/B2a BDS signals. Considering the indispensability of the new signals, the performance of all BDS precise orbits from iGMAS needs to be known. However, there is no comprehensive assessment of BDS-2 and BDS-3 precise orbits based on B1I/B3II and B1C/B2a frequencies from iGMAS, especially for the period after the BDS entered the stable operation stage. In this paper, BDS-2/BDS-3 final (ISC), rapid (ISR), and ultra-rapid (ISU) products based on B1I/B3I and B1C/B2a frequencies from iGMAS are all assessed comprehensively. Specifically, at first, the precise orbits from iGMAS are compared with the ones from the IGS ACs. Based on this, the satellite laser ranging inspects the precise orbits from iGMAS. Finally, the orbit errors are discussed systematically by considering the beta and elongation angles. Using one year of data, the orbit accuracy of geostationary orbit, inclined geosynchronous orbit, and medium earth orbit (MEO) satellites can almost reach meter to decimeter level, decimeter to sub-decimeter level, and centimeter level, respectively, where the ISC products are the best. The ISC, ISR, and ISU products based on B1I/B3I frequencies are generally better than the ones based on B1C/B2a frequencies. Additionally, according to the SLR data, the results show that the accuracy of precise orbits of BDS-3 is better than that of BDS-2. The mean values of orbit biases of BDS-3 MEO satellites are approximately 2.88 cm. In addition, the orbit errors are related to the beta angle and elongation angle to some extent, and the manufacturers may also have an influence on the orbit errors. [ABSTRACT FROM AUTHOR]

The BeiDou Global Navigation Satellite System (BDS-3) can provide PPP-B2b satellite-based Precise Point Positioning (PPP) real-time service to the Asia–Pacific region via PPP-B2b signal transmitted from the three Geostationary Earth Orbit (GEO) satellites. This paper provides a comprehensive evaluation of the accuracies of the satellite's precise real-time orbit and clock products, including BDS-3 PPP-B2b precise products and the precise real-time products provided by four IGS centers (CAS, DLR, GFZ, and WHU). In addition, the influences of these real-time precise satellite products on the PPP positioning accuracy with single-frequency and dual-frequencies are also studied. Furthermore, the accuracies of broadcast ephemeris and IGS ultra-rapid products are studied, as well as their impact on PPP accuracies. Results illustrate that the orbits accuracies of PPP-B2b orbits are 9.42 cm, 21.26 cm, and 28.65 cm in the radial, along-track, and cross-track components, which are slightly lower than those of real-time orbits provided by the four IGS centers. However, the accuracy of PPP-B2b clock biases is 0.18 ns, which is higher than those provided by IGS Real-Time Service (RTS). In the static positioning test, the 3D positioning accuracy of B1I+B3I dual-frequencies PPP and B1C single-frequency PPP are centimeter-level while using PPP-B2b service, which is slightly lower in horizontal components compared to those obtained based on IGS RTS products. The results of the dynamic vehicle test indicate that the positioning accuracies of B1I+B2b dual-frequency PPP are about 50 cm and 120 cm in horizontal and vertical components, which are close to those of B2b single-frequency PPP using PPP-B2b service. Generally, the PPP-B2b orbit and clock accuracies on real-time PPP present similar performance to that based on IGS RTS. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) signal quality, type of receiver equipment, and external environment can cause GNSS observations to be anomalous, and these anomalies are sometimes reflected in GNSS pseudorange observations rather than phase observations. To better detect blunders in pseudorange observations, this paper proposes three pseudorange blunder detection methods under the same frequency and different code types (case1), and the same code type and different frequencies (case2), of pseudorange observations, which are the Code Observation Difference Method (CODM), the Inter-satellite Code Observation Difference Method (ICODM), and the Inter-epoch and Inter-satellite Code Observation Difference Method (IICODM). The corresponding thresholds for the constructed test statistics of the three detection methods were derived based on the Bessel formula. Performance analysis of the three detection methods was performed under case1 based on C2 and P2 code observation data of Global Positioning System (GPS) at 137 Multi-GNSS Experiment (MGEX) stations, and case2 based on BDS B1I and B3I frequency observation data of BeiDou Navigation Satellite System (BDS) at 232 MGEX stations, on 29 July 2022. The results show that the statistical information value of the three methods in case1 was significantly smaller than that in case2. In the first case, the maximum values of test statistics, RMSE and threshold mean values were 0.526, 0.752 and 2.243 m, respectively, while the corresponding values in case2 were 7.066, 4.490 and 13.480 m respectively. The reason for this is that the data quality of global GPS is higher than that of BDS and the differential observation equation eliminates or weakens more errors with the same frequency and different types of code pseudorange observations. Under the same conditions, compared with ICODM and IICODM, CODM has high computational efficiency and a simple mathematical model. It is recommended to use CODM first for pseudorange blunder detection in the GNSS observation domain. According to the RMSE of 3 times as the limit, it is recommended that the threshold be set to 5 m under case1 for GPS and 15 m under case2 for BDS, which is half the existing reference value. Finally, the blunder detection methods proposed can improve positioning performance through actual data verification. [ABSTRACT FROM AUTHOR]

The tropospheric model is the key model in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI). In this paper, we established the site-wise empirical Wuhan University Tropospheric Model (WTM) by using 10-year (2011–2020) monthly mean and 5-year (2016–2020) hourly ERA5 reanalysis data, where the Zenith Path Delay (ZPD), mapping function, and horizontal gradient as well as meteorological parameters are provided at 1583 specific space geodetic stations with additionally considering the diurnal and semi-diurnal variations. The mapping function and horizontal gradient from the WTM model were evaluated at 524 globally distributed GNSS stations during the year 2020 and compared with the latest grid-wise (1° × 1°) Global Pressure and Temperature 3 (GPT3) model. The significant improvements of the WTM model to the GPT3 model were found at the stations with terrain relief, and the maximal mapping function and horizontal gradient accuracy improvements reached 12.8 and 14.71 mm. The ZPD and mapping functions from the two models were also validated at 31 Multi-GNSS Experiment (MGEX) stations spanning the year 2020 by BeiDou Navigation Satellite System (BDS) Precise Point Positioning (PPP). The significant vertical coordinate and ZTD difference biases between the PPP schemes adopted by the two models were also found, and the largest biases reached −1.78 and 0.87 mm. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) has drawn the attention of scientists and users all over the world for its wide-ranging Earth observations and applications. Since the end of May 2022, more than 130 satellites are available for fully global operational satellite navigation systems, such as BeiDou Navigation Satellite System (BDS), Galileo, GLONASS and GPS, which have been widely used in positioning, navigation, and timing (PNT), e.g., precise orbit determination and location-based services. Recently, the refracted, reflected, and scattered signals from GNSS can remotely sense the Earth's surface and atmosphere with potential applications in environmental remote sensing. In this paper, a review of multi-GNSS for Earth Observation and emerging application progress is presented, including GNSS positioning and orbiting, GNSS meteorology, GNSS ionosphere and space weather, GNSS-Reflectometry and GNSS earthquake monitoring, as well as GNSS integrated techniques for land and structural health monitoring. One of the most significant findings from this review is that, nowadays, GNSS is one of the best techniques in the field of Earth observation, not only for traditional positioning applications, but also for integrated remote sensing applications. With continuous improvements and developments in terms of performance, availability, modernization, and hybridizing, multi-GNSS will become a milestone for Earth observations and future applications. [ABSTRACT FROM AUTHOR]

Since BeiDou Navigation Satellite System (BDS) and Japan's Quasi-Zenith Satellite System (QZSS) have more visible satellites in the Asia-Pacific region, and navigation satellites of Global Positioning System (GPS), Galileo satellite navigation system (Galileo), and GLONASS satellite navigation system (GLONASS) are uniformly distributed globally, the service level of multi-mode Global Navigation Satellite System (GNSS) in the Asia-Pacific region should represent the best service capability. Based on the observation data of 10 Multi-GNSS Experiment (MGEX) stations, broadcast ephemeris and precision ephemeris from 13 to 19 October 2021, this paper comprehensively evaluated the service capability of multi-GNSS in the Asia-Pacific region from three aspects of observation data quality, broadcast ephemeris performance, and precision positioning level. The results show that: (1) the carrier-to-noise-density ratio (C/N0) quality of the GPS and Galileo is the best, followed by BDS and GLONASS, and QZSS is the worst. GPS, BDS-2, GLONASS, and QZSS pseudorange multipath values range from 0 to 0.6 m, while Galileo system and BDS-3 pseudorange multipath values range from 0 to 0.8 m. (2) In terms of broadcast ephemeris accuracy, BDS-3 broadcast ephemeris has the best orbit, and the three-dimensional (3D) Root Mean Square (RMS) is 0.21 m; BDS-2 was the worst, with a 3D RMS of 1.99 m. The broadcast ephemeris orbits of GPS, Galileo, QZSS, and GLONASS have 3D RMS of 0.60 m, 0.62 m, 0.83 m, and 1.27 m, respectively. For broadcast ephemeris clock offset: Galileo has the best performance, 0.61 ns, GLONASS is the worst, standard deviation (STD) is 3.10 ns, GPS, QZSS, BDS-3 and BDS-2 are 0.65 ns, 0.75 ns, and 1.72 ns, respectively. For signal-in-space ranging errors (SISRE), the SISRE results of GPS and Galileo systems are the best, fluctuating in the range of 0 m–2 m, followed by QZSS, BDS-3, Galileo, and BDS-2. (3) GPS, BDS, GLONASS, Galileo, GPS/QZSS, and BDS/QZSS were used for positioning experiments. In static PPP, the convergence time and positioning accuracy of GPS show the best performance. The positioning accuracy of GPS/QZSS and BDS/QZSS is improved compared with that of GPS and BDS. In terms of kinematic PPP, the convergence time and positioning accuracy of GPS/QZSS and BDS/QZSS are improved compared with that of GPS and BDS. In addition to GLONASS and Galileo systems, the other combinations outperformed 3 cm, 3 cm, and 5 cm in the east, north, and up directions. [ABSTRACT FROM AUTHOR]

Low Earth orbit (LEO) satellites benefit future ground-based positioning with their high number, strong signal strength and high speed. The rapid geometry change with the LEO augmentation offers acceleration of the convergence of the precision point positioning (PPP) solution. This contribution discusses the influences of the LEO augmentation on the precise point positioning—real-time kinematic (PPP-RTK) positioning and its integrity monitoring. Using 1 Hz simulated data around Beijing for global positioning system (GPS)/Galileo/Beidou navigation satellite system (BDS)-3 and the tested LEO constellation with 150 satellites on L1/L5, it was found that the convergence of the formal horizontal precision can be significantly shortened in the ambiguity-float case, especially for the single-constellation scenarios with low precision of the interpolated ionospheric delays. The LEO augmentation also improves the efficiency of the user ambiguity resolution and the formal horizontal precision with the ambiguities fixed. Using the integrity monitoring (IM) procedure introduced in the first part of this series of papers, the ambiguity-float horizontal protection levels (HPLs) are sharply reduced in various tested scenarios, with an improvement of more than 60% from 5 to 30 min after the processing start. The ambiguity-fixed HPLs can generally be improved by 10% to 60% with the LEO augmentation, depending on the global navigation satellite system (GNSS) constellations used and the precision of the ionospheric interpolation. [ABSTRACT FROM AUTHOR]

The BeiDou Global Navigation Satellite System (BDS-3) provides real-time precise point positioning (PPP) service via B2b signals, offering real-time decimeter-level positioning for users in China and surrounding areas. However, common interruptions and outliers in PPP-B2b services arise due to factors such as the Geostationary Orbit (GEO) satellite "south wall effect", Issue of Data (IOD) matching errors, and PPP-B2b signal broadcast priorities, posing challenges to continuous high-precision positioning. This study meticulously examines the completeness, continuity, and jumps in PPP-B2b orbit and clock correction using extensive observational data. Based on this analysis, a two-step method for detecting outliers in PPP-B2b orbit and clock corrections is devised, leveraging epoch differences and median absolute deviation. Subsequently, distinct prediction methods are developed for BDS-3 and GPS orbit and clock corrections. Results from simulated and real-time dynamic positioning experiments indicate that predicted corrections can maintain the same accuracy as normal correction values for up to 10 min and sustain decimeter-level positioning accuracy within 30 min. The adoption of predicted correction values significantly enhances the duration of sustaining real-time PPP during signal interruptions. [ABSTRACT FROM AUTHOR]

With the modernization of global navigation satellite systems (GNSS), especially the rapid development of the BeiDou Navigation Satellite System (BDS), more observations of satellites and signals have become available. Using data of the globally distributed MGEX stations, a systematic and comprehensive evaluation of signal characteristics for BDS-3, BDS-2, GPS, and Galileo is conducted in terms of carrier-to-noise ratio (C/N0), code noise, and multipath in the contribution. First, a comprehensive signal quality assessment method for BDS/Galileo/GPS satellites and signals is proposed, including C/N0 modeling and MP modeling. For BDS, the BDS-3 satellites apparently have higher signal power than the BDS-2 satellites at the same frequency such as B1I and B3I, and the signal B2a of BDS-3 is superior to other signals in regard to signal power, which is comparable with the superior Galileo E5 signals and GPS L5. Among all the signals, the observation accuracy of E5 is the highest regardless of receiver types, and next highest are BDS-3 B2a and GPS L5. Due to not being affected by the systematic code errors of BDS-2, the observations of BDS-3 satellites contain smaller multipath errors than that of BDS-2 satellites. As for the multipath suppression performance, the BDS-3 signal B2a, GPS L5, and Galileo E5 and E5b perform better than the other signals, which may be related to their wide signal bandwidths. [ABSTRACT FROM AUTHOR]

The Earth rotation parameters (ERP) play a crucial role in defining the global reference frame and the Global Navigation Satellite System (GNSS) is one of the important tools used to obtain ERP, including polar motion (PM), its rates, and length of day (LOD). The latest IGS Repro3 ERP products, which provided the IGS contribution to the latest ITRF2020, were generated without consideration of the Beidou Navigation Satellite System (BDS) observations. The global BDS, namely the BDS-3 constellation, has been completely constructed from July 2020 and the observing stations are evenly distributed globally now. Two couple dual-frequency combinations, including the B1I/B3I and B1C/B2a combinations, are commonly used for BDS-3 ionosphere-free combination usage. With the goal of identifying the optimal dual-frequency combination for BDS-3 ERP estimates for the future ITRF definition with a consideration of BDS-3, this research evaluated the performance of ERP estimation using B1I/B3I and B1C/B2a combinations. Firstly, we conducted a comparison of the ambiguity resolutions. The mean percentage of successfully resolved ambiguities for the BDS-3 B1C/B2a combination is 86.5%, surpassing that of B1I/B3I. The GNSS satellite orbits and ERP were estimated simultaneously, thus the accuracy of orbits could also reflect the performance of the ERP estimates. Subsequently, we validated the orbits of 22 BDS-3 Medium Earth Orbit (MEO) satellites using Satellite Laser Ranging (SLR), and the root mean square error (RMS) of the SLR residuals for the 3-day arc orbit with B1C/B2a signals was 5.72 cm, indicating superior accuracy compared with the B1I/B3I combination. Finally, we compared the performance of ERP estimation, considering both internal and external accuracy. For the internal accuracy, B1C/B2a-based solutions demonstrated a reduction in mean formal errors of approximately 17% for PM, 22% for LOD, and 21% for PM rates compared with B1I/B3I-based solutions. In terms of external accuracy, we compared BDS-3-derived ERP estimates with the IERS 20C04 products. The B1C/B2a combination exhibited a slightly better standard deviation performance and a significant reduction in mean bias by 56%, 54%, 39%, 64%, and 23% for X, Y polar motion, X, Y polar motion rates, and LOD, respectively, compared with B1I/B3I solutions. In conclusion, the results highlight the excellent signal quality for BDS-3 B1C/B2a and its superiority in ERP estimation when compared with the B1I/B3I combination. [ABSTRACT FROM AUTHOR]

Compared to the traditional ionospheric-free (IF) precise point positioning (PPP) model, the undifferenced and uncombined (UU) PPP has the advantages of lower observation noise and the ability to obtain ionospheric information. Thanks to the IGS (International GNSS Service), real-time service (RTS) can provide RT vertical total electron content (VTEC) products, and an enhanced RT UU-PPP based on the RT-VTEC constraints can be achieved. The global performance of the BeiDou Navigation Satellite System-2 (BDS-2) and BDS-3 joint RT UU-PPP using different RTS products was investigated. There is not much difference in the RTS orbit accuracy of medium earth orbit (MEO) satellites among all analysis centers (ACs), and the optimal orbit accuracy is better than 5, 9, and 7 cm in the radial, along-track, and cross-track directions, respectively. The orbit accuracy of inclined geosynchronous orbit (IGSO) satellites is worse than that of MEO satellites. Except for CAS of 0.46 ns, the RTS clock accuracy of MEO satellites for other ACs achieves 0.2–0.27 ns, and the corresponding accuracy is about 0.4 ns for IGSO satellites. In static positioning, due to the limited accuracy of RT-VTEC, the convergence time of the enhanced RT UU-PPP is longer than that of RT IF-PPP for most ACs and can be better than 25 and 20 min in the horizontal and vertical components, respectively. After convergence, the 3D positioning accuracy of the static RT UU-PPP is improved by no more than 8.7%, and the optimal horizontal and vertical positioning accuracy reaches 3.5 and 7.0 cm, respectively. As for the kinematic mode with poor convergence performance, with the introduction of RT-VTEC constraints, the convergence time of RT UU-PPP can be slightly shorter and reaches about 55 and 60 min in the horizontal and vertical components, respectively. Both the horizontal and vertical positioning accuracies of the kinematic RT UU-PPP can be improved and achieve around 7.5 and 10 cm, respectively. [ABSTRACT FROM AUTHOR]

The signal-in-space range error (SISRE) has a direct impact on the performance of global navigation satellite systems (GNSSs). It is an important indicator of navigation satellite space server performance. The new B-CNAV navigation messages (B-CNAV1 and B-CNAV2) are broadcast on the satellites of the Beidou Global Navigation Satellite System (BDS-3), and they are different from D1 navigation messages in satellite orbit parameters. The orbit accuracy of B-CNAV navigation messages lacks analyses and comparisons with D1. The accuracy and stability of the new hydrogen and rubidium clocks on BDS-3 satellites need annual analyses of long time series, which will affect the service quality of this system. Based on precise ephemeris products from the Center for Orbit Determination in Europe (COD), the orbit error, clock error, and SISRE of 24 medium Earth orbit (MEO) satellite D1 and B-CNAV navigation messages of BDS-3 were computed, analyzed, and compared. Their annual evolution processes for the entire year of 2022 were studied. Thanks to the use of inter-satellite links (ISLs) adopted by BDS-3 MEO satellites, the ages of the ephemeris are accurate and the percent of ages of data, ephemerides (AODEs), and ages of data and clocks (AODCs) shorter than 12 h were 99.95% and 99.96%, respectively. In addition, the broadcast orbit performance was also improved by ISLs. The root mean square (RMS) values of the BDS-3 MEO broadcast ephemeris orbit error were 0.067 m, 0.273 m, and 0.297 m in the radial, cross, and along directions, respectively. Moreover, the 3D RMS value was 0.450 m. Thanks to the use of new orbit parameters in the B-CNAV navigation messages of BDS-3 MEO, its satellite orbit accuracy was obviously better than that of D1 in the radial direction. Its improved accuracy can reach up to about 1.2 cm, and the percentage of its accuracy improvement was about 19.06%. With respect to clock errors, the timescale differences between the two clock products were eliminated to assess the accuracy of broadcasting ephemeris clock errors. A standard deviation value of 0.256 m shows good performances as a result of the use of the two new types of atomic clocks, although the RMS value was 0.541 m due to a nonzero mean bias. Overall, the accuracy of atomic clocks was good. For the new hydrogen and rubidium atomic clocks, their RMS and standard deviation were 0.563 m and 0.231 m and 0.519 m and 0.281 m, respectively. The stability of the former was better than that of the latter. However, due to the nonzero mean bias the latter was better than the former in accuracy. The RMS value of the SISRE of BDS-3 MEO's broadcast ephemeris was 0.556 m, and the value was 0.920 m when it had a 95% confidence level. In contrast, after deducting the influence of the clock error, the value of SISRE_ORB was 0.092 m. Since the satellite clock error was substantially larger than the orbit radial error, the SISRE was mainly affected by the clock error, and their annual evolutions were consistent. Because of the improvement to the B-CNAV's navigation message with respect to orbit radial accuracy, SISRE_ORB has improved in accuracy. Compared to D1, it had a significant effect on improving the accuracy of SISRE_ORB, and the percentage of the accuracy improvement was 8.40%. [ABSTRACT FROM AUTHOR]

The inter-system-like bias between the regional (BDS-2) and global (BDS-3) constellation of the BeiDou Navigation Satellite System (BDS) has been identified on common B1I pseudo-range observations. In this study, its characteristics are investigated with tracking data from the International GNSS Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS) network. Firstly, the satellite-specific inter-system-like bias is calculated and the dependency on satellite is observed. Clearly noticeable discrepancies on BDS-2 and BDS-3 can be identified. Hence, the constellation-specific inter-system-like bias is estimated. Biases for all receivers are quite stable, with standard derivation (STDev) less than 0.2 m in average. The bias shows clear dependence on the receiver, while the firmware and antenna have limited but not negligible impacts, particularly for Trimble NetR9 and Alloy receivers. The Trimble NetR9 with TRM59800.00 antenna shows noticeable discrepancy up to about 1.5 m with different antenna, and the bias of the Trimble Alloy 5.37 jumps about 2.4 m with respect to later firmware. In addition, clear annual variations are observed for stations ABPO and MIZU with Septentrio POLARX5 5.3.2 and ASTERX4 4.4.2 receivers, respectively. Furthermore, the impacts of the biases on the BDS orbit and clock solutions are analyzed. Once BDS-2 and BDS-3 are treated as two independent systems, the root mean square (RMS) of code and carrier phase residuals can be reduced by around 9.3 cm and 0.23 mm, respectively, while the three-dimensional orbit consistency is improved by 6.8%, mainly in the tracking direction. Satellite laser ranging (SLR) shows marginal impacts on IGSO and MEO satellites. However, the SLR residual of C01 shifts −13.2 cm, resulting in a smaller RMS value. In addition, the RMS of linear clock fitting is reduced from 0.050 ns to 0.038 ns for BDS-3 MEO satellites in average. [ABSTRACT FROM AUTHOR]

As an important part of the BeiDou global navigation satellite system (BDS-3), the BeiDou satellite-based augmentation system (BDSBAS) aims to provide a high-integrity navigation service for users in China and its surrounding areas. At present, BDSBAS has completed the preliminary construction of the system and formed the single frequency (SF) augmentation service. The paper introduces the composition and working process of BDSBAS, and expounds the solution and performance evaluation methods of the BDSBAS SF service. Tests based on a general aviation aircraft were carried out at Caihu Airport in Shenyang, China, which simulated the aircraft's take-off and landing operation during the approach phase and the transition flight operation during the en-route phase. On this basis, the BDSBAS SF service performance was analyzed and evaluated. The horizontal positioning errors of the three flight tests are 1.62, 1.27, and 1.49 m, respectively, and the vertical positioning errors are 4.38, 4.30, and 4.04 m, respectively. In the first two tests, the APV-I availability and continuity of the service reach 100%. In the last test, a receiver false alarm event occurred, resulting in an APV-I availability and continuity of 99.993% and 99.989%, respectively. The event was confirmed to be caused by some aviation environmental factors and was not related to the system service. No integrity events occurred during the tests. The test results show that the positioning accuracy, availability, and integrity of the BDSBAS SF service meet the APV-I level requirements of the ICAO standards, which preliminarily illustrates the ability of BDSBAS to be used in the field of civil aviation. [ABSTRACT FROM AUTHOR]

Global navigation satellite system reflectometry technology (GNSS-R) is rarely used for river flow velocity inversion, and in particular, there is currently no research using the BeiDou Navigation Satellite System reflectometry technology (BDS-R) for river flow velocity inversion. In this paper, a carrier phase observation of river flow velocity inversion model is proposed. The interference phase is the integral of the Doppler frequency. The raw intermediate frequency (IF) data sets are processed through an open-loop method to obtain the Doppler frequency observation generated by river flow and then realize velocity inversion. The shore-based river current measurement was conducted on the south bank of Dashengguan Yangtze River in Nanjing city, Jiangsu Province, for nearly two hours on 22 April 2021. After realizing the inversion of river flow velocity in GPS L1, the combined inversion of BDS B1I GEO satellite and IGSO satellite is realized for the first time, which demonstrates the feasibility of river flow velocity inversion using BDS reflected signals. Compared with the real river flow velocity, the GPS L1 PRN 4 (1st period) inversion precision reaches up to 0.028 m/s (mean absolute error, MAE) and 0.036 m/s (root mean square error, RMSE). In parallel, BDS GEO 2 inversion precision can reach 0.048 m/s (MAE) and 0.063 m/s (RMSE), and BDS IGSO 10 inversion precision is 0.061 m/s (MAE) and 0.073 m/s (RMSE). These results illustrate that satellite elevation change rate and distance between specular points and current meter may have a negative effect on the accuracy of river flow velocity inversion. Specular points obstructed by obstacles or too far from the velocity meter may introduce uncertain error in both MAE and RMSE. Neither the satellite elevation nor the signal strength has an obvious correlation with inversion precision, which is consistent with the theoretical principle. [ABSTRACT FROM AUTHOR]

The Fengyun-3E (FY-3E) satellite carrying the advanced Global Navigation Satellite System (GNSS) Radio Occultation Sounder-II (GNOS-II) is already in operation for radio occultation (RO) observation, with the BeiDou Navigation Satellite System (BDS-2 and BDS-3) and Global Positioning System (GPS) signals tracking capability. FY-3E BDS and GPS RO signals tracking capability were first evaluated by comparing their penetration depths, and then the quality of the refractivity, temperature, and specific humidity profiles was analyzed with the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5) data. Results show the mean penetration depth of BDS occultations was 1.65 km compared to 1.09 km of GPS occultations. Between 5 and 25 km, the mean refractivity bias of the BDS (GPS) was −0.14% (0.01%) with the mean standard deviation (SD) being 1.11% (1.52%); the mean temperature biases of both were within ±0.1 K, and the mean SD of BDS was 1.1 K compared to 1.2 K for the GPS; BDS/GPS specific humidity bias was within ±0.3 g/kg with corresponding SD being less than 1.3 g/kg. Seasonal deviations of specific humidities were largest in summer and smallest in winter. Latitudinal deviations over the tropics were generally higher than in other areas. Enriched quantity and high accuracy and precision after careful calibration will promote the FY-3E RO profiles as a reliable data source for the RO community. [ABSTRACT FROM AUTHOR]

Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as Satellite-induced Code Bias (SICB). SICB has been identified in the BDS-2 and the bias will reduce the accuracy or reliability of the CSC. To confront bias, an improved CSC algorithm is proposed by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. The correction model of SICB for IGSO/MEO satellites is established by using a 0.1-degree interval piecewise weighted least squares Third-order Curve Fitting Method (TOCFM). The Variational Mode Decomposition combined with Wavelet Transform (VMD-WT) is proposed to establish the correction model of SICB for the GEO satellite. To verify the proposed method, the SICB model was established by collecting 30 Multi-GNSS Experiment (MGEX) BDS stations in different seasons of a year, in which the BDS data of ALIC, KRGG, KOUR, GCGO, GAMG, and SGOC stations were selected for 11 consecutive days to verify the effectiveness of the algorithm. The results show that there is obvious SICB in the BDS-2 Multipath (MP) combination, but the SICB in the BDS-3 MP is smaller and can be ignored. Compared with the modeling in the references, TOCFM is more suitable for IGSO/MEO SICB modeling, especially for the SICB correction at low elevation angles. After the VMD-WT correction, the Root Mean Square Error (RMSE) of SICB of B1I, B2I, and B3I in GEO satellites is reduced by 53.35%, 63.50%, and 64.71% respectively. Moreover, we carried out ionosphere-free Single Point Positioning (IF SPP), Ionosphere-free CSC SPP (IF CSC SPP), CSC single point positioning with the IGSO/MEO SICB Correction based on the TOCFA Method (IGSO/MEO SICB CSC), and CSC single point positioning with the IGSO/MEO/GEO SICB correction based on VMD-WT and TOCFA (IGSO/MEO/GEO SICB CSC), respectively. Compared to IF SPP, the average improvement of the IGSO/MEO/GEO SICB CSC algorithm in the north, east, and up directions was 24.42%, 27.94%, and 24.98%, respectively, and the average reduction in 3D RMSE is 24.54%. Compared with IF CSC SPP, the average improvement of IGSO/MEO/GEO SICB CSC is 7.03%, 6.50%, and 10.48% in the north, east, and up directions, respectively, while the average reduction in 3D RMSE was 9.86%. IGSO/MEO SICB mainly improves the U direction positioning accuracy, and GEO SICB mainly improves the E and U direction positioning accuracy. After the IGSO/MEO/GEO SICB correction, the overall improvement was about 10% and positioning improved to a certain extent. [ABSTRACT FROM AUTHOR]

The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time. [ABSTRACT FROM AUTHOR]

Positioning of spacecraft (e.g., geostationary orbit (GEO), high elliptical orbit (HEO), and lunar trajectory) is crucial for mission completion. Instead of using ground control systems, global navigation satellite system (GNSS) can be an effective approach to provide positioning, navigation and timing service for spacecraft. In 2020, China finished the construction of the third generation of BeiDou navigation satellite system (BDS-3); this global coverage system will contribute better sidelobe signal visibility for spacecraft. Meanwhile, with more than 100 GNSS satellites, multi-GNSS navigation performance on the spacecraft is worth studying. In this paper, instead of using signal-in-space ranging errors, we simulate pseudorange observations with measurement noises varying with received signal powers. Navigation performances of BDS-3 and its combinations with other systems were conducted. Results showed that, owing to GEO and inclined geosynchronous orbit (IGSO) satellites, all three types (GEO, HEO, and lunar trajectory) of spacecraft received more signals from BDS-3 than from other navigation systems. Single point positioning (SPP) accuracy of the GEO and HEO spacecraft was 17.7 and 23.1 m, respectively, with BDS-3 data alone. Including the other three systems, i.e., GPS, Galileo, and GLONASS, improved the SPP accuracy by 36.2% and 19.9% for GEO and HEO, respectively. Navigation performance of the lunar probe was significantly improved when receiver sensitivity increased from 20 dB-Hz to 15 dB-Hz. Only dual- (BDS-3/GPS) or multi-GNSS (BDS-3, GPS, Galileo, GLONASS) could provide continuous navigation solutions with a receiver threshold of 15 dB-Hz. [ABSTRACT FROM AUTHOR]

Nowadays, integrity monitoring (IM) is required for diverse safety-related applications using intelligent transport systems (ITS). To ensure high availability for road transport users for in-lane positioning, a sub-meter horizontal protection level (HPL) is expected, which normally requires a much higher horizontal positioning precision of, e.g., a few centimeters. Precise point positioning-real-time kinematic (PPP-RTK) is a positioning method that could achieve high accuracy without long convergence time and strong dependency on nearby infrastructure. As the first part of a series of papers, this contribution proposes an IM strategy for multi-constellation PPP-RTK positioning based on global navigation satellite system (GNSS) signals. It analytically studies the form of the variance-covariance (V-C) matrix of ionosphere interpolation errors for both accuracy and integrity purposes, which considers the processing noise, the ionosphere activities and the network scale. In addition, this contribution analyzes the impacts of diverse factors on the size and convergence of the HPLs, including the user multipath environment, the ionosphere activity, the network scale and the horizontal probability of misleading information (PMI). It is found that the user multipath environment generally has the largest influence on the size of the converged HPLs, while the ionosphere interpolation and the multipath environments have joint impacts on the convergence of the HPL. Making use of 1 Hz data of Global Positioning System (GPS)/Galileo/Beidou Navigation Satellite System (BDS) signals on L1 and L5 frequencies, for small- to mid-scaled networks, under nominal multipath environments and for a horizontal PMI down to 2 × 10 − 6 , the ambiguity-float HPLs can converge to 1.5 m within or around 50 epochs under quiet to medium ionosphere activities. Under nominal multipath conditions for small- to mid-scaled networks, with the partial ambiguity resolution enabled, the HPLs can converge to 0.3 m within 10 epochs even under active ionosphere activities. [ABSTRACT FROM AUTHOR]

The BeiDou navigation satellite system (BDS-3) has been deployed and provides positioning, navigation, and timing (PNT) services for users all over the world. On the basis of BDS-2 system signals, BDS-3 adds B1C, B2a, B2b, and other signals to realize compatibility and interoperability with other global navigation satellite systems (GNSS). Network real-time kinematic (RTK) technology is an important real-time regional high-precision GNSS positioning technology. Combined with the network RTK high-precision service platform software developed by the author's research group and the measured data of a provincial continuously operating reference station (CORS) in Hubei, this paper preliminarily evaluates the network RTK service performance under the new signal system of BDS-3. The results show that single BDS-3 adopts the new signal combination (B1C+B2a) and transition signal combination (B1I+B3I) when providing virtual reference station (VRS) services, the RTK fixation rate of the terminal is above 95%, and the horizontal and elevation accuracies are within 1cm and 2 cm, respectively, which meets the requirements of providing high-precision network RTK services by a single BDS-3 system. In addition, the positioning accuracy of BDS-2 is relatively poor, while the accuracy of BDS-3 is better than global positioning systems (GPS) and BDS-2. The combined processing effect of the B1I+B3I transition signal of BDS-2/3 is optimal, the accuracy of E and N directions is better than 0.5 cm, and the accuracy of U direction is better than 1.5 cm. It can be seen from the atmosphere correction accuracy, regional error modeling accuracy, and network RTK terminal positioning accuracy that the service effect of the B1C+B2a combination is slightly better than that of the B1I+B3I combination. When a single BDS-3 constellation provides network RTK services, it is recommended to use the B1C+B2a combination as the main frequency solution, and when the BDS-2/3 constellation provides service, it is recommended to use the B1I+B3I combination as the main frequency solution. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) enables the estimation the ionospheric vertical total electron content (VTEC) as well as the by-product of the satellite Pseudorange observable-specific signal bias (OSB). The single-frequency PPP models, with the ionosphere-float and ionosphere-free approaches in ionospheric studies, have recently been discussed by the authors. However, the multi-frequency observations can improve the performances of the ionospheric research compared with the single-frequency approaches. This paper presents three dual-frequency PPP approaches using the BeiDou Navigation Satellite System (BDS) B1I/B3I observations to investigate ionospheric activities. Datasets collected from the globally distributed stations are used to evaluate the performance of the ionospheric modeling with the ionospheric single- and multi-layer mapping functions (MFs), respectively. The characteristics of the estimated ionospheric VTEC and BDS satellite pseudorange OSB are both analyzed. The results indicated that the three dual-frequency PPP models could all be applied to the ionospheric studies, among which the dual-frequency ionosphere-float PPP model exhibits the best performance. The three dual-frequency PPP models all possess the capacity for ionospheric applications in the GNSS community. [ABSTRACT FROM AUTHOR]

With the realization of global navigation satellite system (GNSS) completion, GNSS reflectometry (GNSS-R) has become increasingly popular due to the advantages of global coverage and the availability of multiple sources in terms of earth remote sensing. This paper analyzes the Beidou navigation satellite system (BDS) signal reflection detection of multiple satellites and multiple moving targets under multiple-input and multiple-output (MIMO) radar systems and proposes a series of methods to suppress multiple Doppler phase influences and improve the range detection property. The simulation results show the restored target peaks, which match the RCS data more accurately, with the GNSS-R Doppler phase influence removed, which proves the proposed method can improve target recognition and detection resolution performance. [ABSTRACT FROM AUTHOR]

The anomalous propagation conditions, particularly the tropospheric ducts, severely impact the regular operation and performance evaluation of radio devices in the atmospheric boundary layer. Therefore, it is necessary to provide the regional distribution of tropospheric ducts for utilizing or avoiding these abnormal propagation phenomena. As significant uncooperative signal sources, the global navigation satellite systems (GNSS) have been widely applied in the remote sensing of the ocean and atmosphere due to the greater convenience and lower cost. With the completed deployment of the BeiDou Navigation Satellite System (BDS) in 2020, an additional source can be chosen in the relevant studies. Taking the BDS as an example, since the scattered signals from the ocean surface at low satellite elevation angles can be effectively trapped by tropospheric ducts, we propose a method to invert for the regional distribution of tropospheric ducts using the received power of ocean-scattered signals in this paper. Firstly, the propagation model was built to calculate the received power, and a suite of simulations was made in various atmospheric environments. The results suggested that the received power is more sensitive to the surface duct without a base layer. Then, we made a preliminary estimation of the tropospheric ducts on the ocean nearby Qingdao utilizing the Weather Research and Forecasting (WRF) model as well as the echo data measured by a Doppler weather radar. Before the inversion, the actual satellite azimuth and elevation angles should be obtained to evaluate the bistatic scattering coefficients and the received powers of the selected satellite signals. Finally, we presented an inversion example using the proposed method. In absence of the actual measurements, the received powers pre-estimated at different SNRs served as the inputs of the inversion process and the estimated duct parameters were used to verify the validity of the proposed inversion method. For both the received power and modified refractivity profile, the fitness between the values pre-estimated using the estimated duct parameters and calculated by the inverted duct parameters gets better as the elevation angle decreases and the SNR increases. The variation of the fitness between the estimated and inverted values is slightly different for each duct parameter. Moreover, the calculation of inversion errors further explained the above behaviors, including the mean absolute error (MAE) and the root mean square error (RMSE). Despite some certain errors, the inversion results maintain the overall tendencies and most characteristics of the estimated values, thus proving the validity of the inversion method. [ABSTRACT FROM AUTHOR]

The orbit maneuver detection is crucial in Global Navigation Satellite System (GNSS) precise orbit determination, which is necessary for adjusting data processing strategies. The frequency of orbit maneuvers for the BeiDou Navigation System is significantly higher than that of other navigation systems, especially for geosynchronous orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. We propose a novel real-time and postprocessing method for detecting orbit maneuvers for BeiDou satellites based on the orbit differences between the epoch-updated orbit estimated using square root information (SRIF) and the predicted orbit according to the precise orbit estimated during non-maneuver period, as well as the orbital state difference during maneuver and non-maneuver periods. This method has significant advantages over using observation residuals and it is not affected by observation outliers, thus improving the accuracy and timeliness of orbit maneuver detection. We demonstrated that 32 orbit maneuver events of BeiDou satellites were successfully detected in 2022, of which 1 was for medium Earth orbit (MEO), 7 were for IGSO with an average detected maneuvering time of 7–8 min, and 24 were for GEO satellites with an average detected time of 4–5 min. Moreover, our method can be easily integrated into current real-time filter-based precise orbit determination (POD) processing without any extra task line, which simplifies the overall data processing. The data used in this method can be accessed easily, including GNSS observation data, broadcast ephemeris, and other open-source information files. [ABSTRACT FROM AUTHOR]

Multi Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) has become the mainstream of PPP technology. Due to the differences in the coordinates and time references of each GNSS, multi-GNSS PPP must include additional Inter-System Bias (ISB) parameters to ensure compatibility between different GNSSs. Therefore, research on the characteristics of ISB is also essential. To analyze the short- and long-term time characteristics of multi-GNSS ISBs, as well as their relationship with receiver type and receiver antenna type, the Undifferenced and Uncombined (UDUC) PPP model of Global Positioning System (GPS), BeiDou navigation satellite system (BDS), and Galileo satellite navigation system (Galileo) was rigorously derived, and the physical of ISBs was elaborated in depth. ISB parameters were estimated and analyzed using 31 days of data from the 31 Multi-GNSS Experimental stations (MGEX). The results indicate that: (1) the ISB value is dependent on the station receiver type, receiver antenna type, analysis center product utilized, and GNSS system. (2) The short-term time characteristics of ISB-COM, ISB-WUM, and ISB-GBM are similar for the same station but not for the long term. In addition, ISBs are more stable in the short term. (3) There is little correlation between the ISB time characteristics, the receiver type, and the receiver antenna type, and the day-boundary discontinuity(DBD) on the ISB can be ignored for the concussive days' process. [ABSTRACT FROM AUTHOR]

The BeiDou Global Satellite Navigation System (BDS-3) broadcast newly developed B1C and B2a signals. To provide a better service for global users, the vertical phase center offset (PCO) and phase center variation (PCV) are estimated for the B1C/B2a ionospheric-free linear combination of the BDS-3 inclined geostationary orbit (IGSO) and medium earth orbit (MEO) satellites in this study. And considering the traditional PCC estimation method needs two Precise orbit determination (POD) processing, based on the correlation between PCO z-offset and PCV, the theoretical analysis and experimental comparison have been made to discuss whether the POD procedure for the PCO estimation can be omitted. The estimated z-offset time series revealed the inadequacy of the solar radiation pressure (SRP) model for the IGSO satellites and the MEO satellites with Pseudo Random Noise code (PRN) C45 and C46. The PCVraws estimated by the traditional method and the PCO estimation omitted method have the same characteristic. The final PCO z-offsets and PCVs calculated by the two schemes agreed very well with differences can be harmlessly ignored, which confirmed that the PCO estimation can be safely omitted to save computation time. The PCC model proposed in this study has been compared with the Test and Assessment Research Center of China Satellite Navigation Office (TARC/CSNO) released model, the qualities of the orbits and BDS-only precise point positioning (PPP) solutions of the new model both show improvements, except for the IGSO orbits. The analysis of the IGSO orbits further verifies the SRP model is not suitable for the IGSO satellites. [ABSTRACT FROM AUTHOR]

With the full operation of the global BeiDou navigation satellite system (BDS-3), positioning performance can be further enhanced by BDS-3 combined with the regional BeiDou navigation satellite system (BDS-2). However, due to satellite signals being out of lock and the limited visibility of satellites, the traditional multi-frequency BDS-2/3 precise point positioning (PPP) model is unable to maintain great positioning performance under urban environmental conditions. In this study, a mixed multi-frequency undifferenced and uncombined (UDUC) BDS-2/3 PPP model is presented to improve the positioning performance under urban environmental conditions by making full use of B1I, B1C, B2I, B2a, and B3I signals from all visible BDS satellites. In this model, BDS satellites with single-, dual-, triple- and quad-frequency observations all can participate in PPP. The static and kinematic experiments were carried out using the mixed multi-frequency UDUC BDS-2/3 PPP model to fully assess the positioning performance under urban environmental conditions with comparisons to the multi-frequency model. The static experiments indicated that the mixed multi-frequency UDUC BDS-2/3 PPP could continuously achieve decimeter-level positioning accuracy at a cut-off elevation angle of 40°, but part of the BDS-3 PPP would lose resolution due to limited visible satellites. Furthermore, the initial kinematic vehicle experiment showed that mixed multi-frequency UDUC BDS-2/3 PPP had better satellite geometry and more observation redundancy than the traditional multi-frequency model. Compared with the traditional multi-frequency BDS-2/3 model, the positioning accuracy of the mixed multi-frequency model was improved by 51.6, 35.5, and 39.1%, respectively, in east, north, and up directions. The convergence time was shortened by 40%. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System interferometric reflectometry (GNSS-IR), a new and inexpensive technique, has become available to the broader scientific community for detecting surface environmental information, such as soil moisture, snow depth and vegetation growth. However, there have been limited experiments focusing on the potential of crop height retrieval, especially the performance evaluation of BeiDou Navigation Satellite System (BDS) with other GNSS. Accuracy and reliability are challenging to achieve with traditional methods utilizing a single GNSS, and few measured verification data. In this study, an improved method that includes segmentation processing and multi-GNSS fusion is proposed based on GPS/GLONASS/Galileo/BDS multi-frequency data. Furthermore, experiments were carried out on a farmland in Fengqiu County, Henan Province, China. The results show that the height retrievals from four GNSS were in good agreement with the in situ observations during the whole growth cycle of the wheat after overwintering. Meanwhile, the retrievals based on the proposed method exhibited greater correspondence than the single frequency results, the correlation coefficient was increased and the root-mean-square error (RMSE) was reduced, respectively. Therefore, this study illustrates the feasibility of the proposed method to precisely estimate wheat height and its potential for use in the early warning of wheat lodging based on GNSS-IR. [ABSTRACT FROM AUTHOR]

With the completion of the BeiDou Global Navigation Satellite System (BDS-3), the multi-system precise point positioning ambiguity resolution (PPP-AR) has been realized. The satellite phase fractional cycle bias (FCB) is a key to the PPP-AR. Compared to the combined ionosphere-free (IF) model, the undifferenced and uncombined (UDUC) model retains all the information from the observations and can be easily extended to arbitrary frequencies. However, the FCB is difficult to apply directly to the UDUC model. An observable-specific signal bias (OSB) can interact directly with the original observations, providing complete flexibility for PPP-AR for multi-frequency multi-GNSS. In this study, the OSB product generation for the GPS (G), Galileo (E), and BDS-3 (C) systems is performed using 117 globally distributed multi-GNSS experiment (MGEX) stations, and their performances are evaluated. Then, the PPP-AR comparison and analysis of the two positioning models of the UDUC and IF are conducted. The results show that the stability of OSB products of the three systems is better than 0.05 ns. For the precise point positioning (PPP) ambiguity fixed solution, with comparable positioning accuracy and convergence time to the products of both the Wuhan University (WUM) and the Centre National d'Etudes Spatials (CNES) institutions, an average fixed-ambiguity rate is over 90%. Compared to the PPP float solution, the PPP-AR has the most significant improvement in positioning accuracy in the E-direction. The average improvements in the positioning accuracy under the IF and UDUC models in the static and kinematic modes are higher than 45% and 40%, respectively. The convergence times of the IF and UDUC models are improved on average by 48% and 60% in the static mode and by 40% and 55% in the kinematic mode, respectively. Among the IF and UDUC positioning models, the former has slightly better positioning accuracy and convergence time than the latter for the PPP float solution. However, both models have comparable positioning accuracy and convergence time after the PPP-AR. The GCE multi-system combination is superior to other system combinations. The average convergence time for the static PPP fixed solution is 8.5 min, and the average convergence time for the kinematic PPP fixed solution is 16.4 min. [ABSTRACT FROM AUTHOR]

The BeiDou Navigation Satellite System (BDS) is fully operational and provides positioning, navigation, and timing services to users worldwide. To comprehensively evaluate the BeiDou-3 Navigation Satellite System (BDS-3) global real-time kinematic (RTK) positioning performance, five sets of IGS/MEGX stations with different baseline lengths are selected in this research, and the visibility of current BDS-3, BDS-2+BDS-3, and Global Positioning System (GPS) system satellites are analyzed. The single frequency, dual-frequency, and triple-frequency positioning accuracy as well as ambiguity fixing rate under short baseline and long baseline are also analyzed. The experimental results show that the positioning accuracies of B1C, BII, L1, and B3I single-frequency bands were about the same, while for band B2a it was lower. For the short baseline dual-frequency RTK positioning mode, the accuracy of BDS-3 (B1C/B2a), BDS-3 (B1I/B3I), triple-frequency BDS-3 (B1C/B2a/B3I), and GPS (L1L2) is comparable and slightly better than that of BDS-3 (B1I/B3I). With the increase in baseline length, the advantages of dual-frequency BDS-3 (B1C/B2a) and triple frequency BDS (B1C/B2a/B3I) are more obvious, with triple-frequency BDS-3 (B1C/B2a/B3I) having the best positioning accuracy. In terms of ambiguity fixing performance, dual-frequency BDS-2+BDS-3 (B1I/B3I) and dual-frequency GPS (L1L2) have the highest ambiguity fixing rate. The ambiguity fixing rate of dual-frequency BDS-3 (B1C/B2a) and triple-frequency BDS-3 (B1C/B2a/B3I) can be higher than 90% within 100 km. In the case of positioning using only the BDS-3 system, the triple-frequency BDS-3 (B1C/B2a/B3I) is superior to both the dual-frequency BDS-3 (B1I/B3I) and dual-frequency BDS-3 (B1C/B2a) in terms of both positioning accuracy and ambiguity fixing rate. The BDS-2+BDS-3 (B1I/B3I) dual-frequency RTK, which has reached a level comparable to GPS, can provide global users with real-time centimeter-level differential positioning services. [ABSTRACT FROM AUTHOR]

Integrity is one of the key indicators used to characterize the performance of the global navigation satellite systems (GNSSs) and is closely related to user safety. In order to realize real-time global integrity monitoring, the BeiDou Global Navigation Satellite System (BDS-3) has realized the "satellite autonomous integrity monitoring" (SAIM) function in its satellites for the first time. BDS-3 SAIM has the monitoring functions of signal power, pseudo-range, satellite clock frequency and phase, but not the monitoring function of broadcast ephemeris. In this study, the long-term stability and distribution characteristics of BDS-3 SAIM monitoring data were analyzed by using the actual telemetry data for the first time. The results show that the SAIM monitoring data have good long-term stability and basically follow a normal distribution, which meets the design expectations. Meanwhile, in view of the fact that BDS-3 SAIM does not have the ability to independently monitor broadcast ephemerides, which may lead to the over-tolerance of BDS-3 to the probability risk of risks of integrity in the active space environment, a SAIM enhancement design for ephemeris monitoring is proposed, which integrates three relatively independent methods, with the ephemeris extrapolated from the previous cycle, and the ephemeris generated by autonomous orbit determination, inter-satellite link distance measurement data as reference data, respectively. The three methods are analyzed and verified. The results show that each of the three methods has advantages and disadvantages in terms of monitoring accuracy and resource dependence. The integration of the three methods can combine their complementary advantages and can also provide valuable as an important reference for engineering applications. [ABSTRACT FROM AUTHOR]

The autonomous orbit determination of the navigation constellation uses only bidirectional ranging data of the inter-satellite link for data processing. The lack of space-time benchmark information related to the Earth inevitably causes overall rotational uncertainty in the constellation, leading to a decrease in orbit accuracy and affecting user positioning accuracy. This study (1) introduces a method for rotation correction in distributed autonomous orbit determination based on inter-satellite bidirectional ranging; (2) conducts constellation autonomous orbit determination and time synchronization processing experiments based on inter-satellite ranging data for the 24 medium Earth orbit (MEO) satellites in the Beidou-3 global satellite navigation system (BDS-3); and (3) makes comparative analyses on the accuracy of autonomous orbit determination based on three rotation correction cases, including a no-rotation-correction case, independent satellite constraints case, and global satellite constraints case. The experimental results are described as follows. For the no-rotation-correction case, the prediction error of the orbital inclination angle (iot, i) for the entire constellation on the 30th day was 2.11 × 10−7/rad, the prediction error of the right ascension of the ascending point (Omega,   Ω ) was 2.25 × 10−7/rad, and the average root mean square (RMS) of the user range error (URE) for the entire constellation orbit was 1.41 m. In the autonomous orbit determination experiment with independent constraints on satellites, the prediction error of i for the entire constellation on the 30th day was 5.43 × 10−7/rad, the prediction error of Ω was 2.03 × 10−7/rad, and the average RMS of the orbital URE for the entire constellation was 1.09 m. In the autonomous orbit determination experiment with global satellite constraints, the prediction error of i for the entire constellation on the 30th day was 5.31 × 10−7/rad, the prediction error of Ω was 1.95 × 10−7/rad, and the RMS of the orbital URE for the entire constellation was 0.94 m. According to the analysis of the above experimental results, compared with the autonomous orbit determination under the no-rotation-correction case, the adoption of an algorithm for independent satellite constraints to correct the overall constellation rotation weakens the constellation rotation influence; however, it may destroy the overall constellation configuration, which affects the stability of autonomous orbit determination. Finally, the algorithm based on global satellite constraints both impairs the influence of constellation rotation and maintains the overall constellation configuration. [ABSTRACT FROM AUTHOR]

Ionospheric total electron content (TEC) is important data for ionospheric morphology, and also an important parameter for ionospheric correction in Global Navigation Satellite System (GNSS) precise positioning, navigation, and radio science. In this study, we present a data assimilation model for regional ionosphere based on a local ensemble Kalman filter (LEnKF) with the International Reference Ionosphere 2016 (IRI-2016) model as the background, to assimilate ionospheric TEC observations from GNSS. To demonstrate the results, the TEC estimates from the Crustal Movement Observation Network of China (CMONOC), which is about 260 stations in China, are applied as observation. The assessments are performed against the TEC estimates from BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) and against the final products from the Center for Orbit Determination in Europe (CODE). The assimilation results are in good agreement with BDS GEO TEC and the CODE TEC on a quiet or disturbed day. The correlation coefficient after assimilation is increased by about 17% compared with that before assimilation, and the RMSE after assimilation is decreased by about 42% compared with that before assimilation. Furthermore, the assimilated method is also evaluated in the single-frequency precise point positioning (PPP). The experimental results indicate that the PPP/Assimilated method can improve the GNSS positioning accuracy more effectively in comparison to the PPP/CODE. These results reveal that the LEnKF method can be considered as a useful tool for ionospheric assimilation. [ABSTRACT FROM AUTHOR]

The BeiDou global navigation satellite system (BDS-3) has been officially providing a real-time precise point positioning (PPP) augmentation service, known as the PPP-B2b service, since 2020. Decimeter-level positioning accuracy is expected to be achieved based on the PPP-B2b service. It shows great potential for global navigation satellite system (GNSS) real-time applications, including, for example, vehicle positioning on land. However, the application of the PPP-B2b service is still full of challenges in the urban environment because of GNSS signal blockage. The inertial navigation system (INS) is a popular technology which can provide continuous positions under GNSS challenging scenarios. In this study, we constructed a BDS-3 PPP-B2b/INS loosely coupled integration system for vehicle positioning and evaluated its performance through two automotive experiments. In the first experiment, four periods of 30 s GNSS outages were simulated to evaluate the performance of PPP-B2b/INS loosely coupled integration during GNSS outages. During the simulated GNSS outages, PPP-B2b positioning did not work. Nevertheless, PPP-B2b/INS loosely coupled integration provided continues solution through INS mechanization. The averaged positioning errors at the last epoch of outages were 300.6/498.0/41.0 cm for PPP-B2b/MEMS-IMU and 18.6/21.8/6.1 cm for PPP-B2b/Tactical-IMU loosely coupled integration, in the east, north and up directions, respectively. In the second experiment, we drove the land vehicle in a complex urban environment for 15 min. During this period, two GNSS signal interruptions occurred due to the occlusion of bridges, lasting 15 s and 5 s, respectively. The results show that the improvement of positioning accuracy in the east, north, and up components were 64.1%, 77.8%, and 73.8% respectively for PPP-B2b/MEMS-IMU loosely coupled integration, and 63.9%, 79.5%, and 74.4% respectively for PPP-B2b/Tactical-IMU loosely coupled integration, as compared to the positioning accuracy of PPP-B2b only. [ABSTRACT FROM AUTHOR]

References 1 Wang M., Shan T., Zhang W., Huan H. Analysis of BDS/GPS Signals' Characteristics and Navigation Accuracy for a Geostationary Satellite. The proposed algorithm mainly focuses on the absorption of orbit and clock offset errors in the line of sight (LOS) and is applied to the GPS/BDS measurements obtained from the FngYun-3C satellite. Ref. [[4]] presented an ISCB estimation algorithm and analyzed the clustering code bias characteristics of BDS-2 and BDS-3. BDS satellites can be categorized into three stages: demonstration systems (BDS-1), regional systems (BDS-2), and global systems (BDS-3). [Extracted from the article]