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For real-time (RT) precise point positioning (PPP), the state space representation (SSR) information is often delayed due to possible communication delays and specific broadcast intervals. In this case, the positioning results will diverge and re-converge due to the increase of SSR products extrapolation errors. In addition, RT orbit and clock offset accuracy, as well as their extrapolation errors, will vary in different systems and satellites. We propose a PPP with ambiguity resolution (PPP-AR) method that combines a time-differenced carrier phase (TDCP) model, in which the characteristics of the orbit and clock are considered. Under normal communication, the PPP-AR solution is obtained by fixing satellites with small SSR product errors. When the communication is abnormal, the TDCP model is utilized to extrapolate user coordinates by considering different extrapolation error characteristics of satellites. The experimental results show that GPS and Galileo SSR products have better accuracy than BDS, with signal-in-space user ranger errors (SISREs) of 2.7, 2.2, and 8.6 cm, respectively. Optimizing the PPP stochastic model based on SISREs can effectively reduce the convergence time. Under 5 min SSR delay, SISREs caused by clock and orbit extrapolation for GPS/Galileo/BDS are 3.5, 1.4, and 2.6 cm, respectively. After optimizing the TDCP stochastic model based on extrapolation errors, the horizontal and vertical positioning accuracies can be maintained at 0.7 cm and 5.0 cm. For multi-GNSS, the combination of the TDCP and PPP-AR can overcome the influence of short delay. After optimizing the stochastic model, the GPS/Galileo/BDS positioning accuracy can be maintained at about 2.4 cm under 3 min delay, showing an accuracy improvement rate of 59.3% compared with the traditional method using only PPP. Additionally, the rapid PPP convergence results can be obtained by inheriting previous filter state information when the communication recovers normally. [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]

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]

• Provide a simplified joint orbit determination (JOD) method that employs kinematic approach to determine the LEO satellites orbit. • The comparative analysis between proposed method and traditional method is analyzed based on the real data from LEO onboard GNSS receiver. • Simplified JOD method demonstrates a significant decrease in computation time and is nearly unaffected by orbital maneuvers of LEO satellites. • The proposed method is prospective to be an efficient JOD mode for future LEO navigation enhancement system. Joint orbit determination (JOD) of Global Navigation Satellite Systems (GNSS) satellites and low Earth orbit (LEO) satellites has been substantiated as an efficacious approach to compensate for the ground station geometry. In the traditional JOD, the precise orbit determination (POD) of LEO satellite is mainly processed by the reduced-dynamic approach, however, this approach involves complex calculations and the credibility of the determined positions diminishes when LEO satellites undergo orbital maneuvers. Therefore, a simplified JOD method is designed that employs kinematic approach to determine the LEO satellites orbit. To verify the effectiveness of the proposed method, the orbit of GPS satellites and LEO satellites are jointly estimated utilizing the regional and global networks. 8 LEO satellites, including GRACE-C/D, SWARM-A/B/C, SENTINEL-3A/B, and JASON-3, are chosen for JOD. The comparative analysis between the proposed method and traditional method are achieved in terms of GPS orbit accuracy, LEO orbit accuracy, computation time and the JOD performance during LEO maneuvers. Under regional station scenario, the GPS orbit accuracy determined using the proposed method and the traditional method is 3.64 cm and 2.52 cm, respectively. In the case of global station scenario, the accuracies are 1.71 cm and 1.64 cm. Additionally, the traditional method yields superior enhancement and higher accuracy of the LEO orbits. However, it exhibits a noticeable increase in computation time compared to the proposed method and the performance of JOD declines significantly when LEO satellites undergo orbital maneuvers. Alternatively, although the accuracy of the LEO orbits using the proposed method is comparatively lower, it offers a substantial reduction in the overall network computation time compared to traditional method. Moreover, the proposed method based on LEO kinematic precise orbit determination (KPOD) is nearly unaffected by orbital maneuvers of LEO satellites, presenting unique advantages in practical data processing. [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]

The service areas of the BeiDou Navigation Satellite System (BDS) are China, the Asia–Pacific, and the world via three stages of development. The BDS constellation is designed to maintain a geostationary Earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO). These orbital maneuvers yield certain difficulties for data processing, especially for the BeiDou satellites, such as a decrease in the real-time service performance, which causes a missing precise orbit product from the maneuvered satellites. The frequencies of the orbital maneuvers for the GEO and IGSO satellites are higher than those for the MEO satellites. The maneuvering time and strategy cannot be obtained by common users due to secrecy, which can yield a decline in the service performance of the BDS. Thus, in this study, we analyzed the variation in the orbital semimajor axis for the satellites. The long-term variation in the orbital semimajor axis changes linearly. The short-term variation in the orbital semimajor axis also has periodicity, which can be described by the sum of sine functions. According to the long-term variation in the orbital semimajor axis for the satellites, we propose a detection method for in-plane orbital maneuvering of the GEO, IGSO, and MEO satellites. We then propose a detection method for out-of-plane maneuvering of the GEO satellites. BDS and Global Positioning System (GPS) data from the broadcast ephemeris were analyzed to verify the proposed methods. The experimental results from 2013 to 2019 show that the frequency of orbital maneuvering is approximately once a month for the GEO satellites, once every six months for the IGSO satellites, and once every 1.4 years for the MEO satellites. [ABSTRACT FROM AUTHOR]

Abstract The on-orbit characteristics and service performance of Galileo navigation system (Galileo) has been drawn attentions since Galileo is the only one global navigation system which is normally equipped with large-scale, high precision and performance hydrogen atomic clocks. Based on a period of 1000 days' Galileo satellite clock offset products, this article analyzed the performance changes of Galileo satellite clocks when the working clock is switched to the backup clock. The onboard clock phases, frequencies, frequency drifts, the polynomial fitting residuals and the stabilities have been obtained. Results show that the frequency drifts of Galileo satellite clocks can reach up to a magnitude of 10−19 and the fitting precisions are superior to 0.3 ns, while the stabilities in the time length of ten thousand seconds can achieve 10−14. These mainly can be due to the onboard high performance and precision hydrogen atomic clocks. [ABSTRACT FROM AUTHOR]

The determination of slant total electron content (STEC) between satellites and receivers is the first step for establishing an ionospheric model. However, the leveling errors, caused by the smoothed ambiguity solutions in the carrier-to-code leveling (CCL) method, degrade the performance of ionosphere modeling and differential code bias (DCB) estimation. To reduce the leveling errors, an uncombined and undifferenced precise point positioning (PPP) method with ambiguity resolution (AR) was used to directly extract the STEC. Firstly, the ionospheric observables were estimated with CCL, PPP float-ambiguity solutions, and PPP fixed-ambiguity solutions, respectively, to analyze the short-term temporal variation of receiver DCB in zero or short baselines. Then, the global ionospheric map (GIM) was modeled using three types of ionospheric observables based on the single-layer model (SLM) assumption. Compared with the CCL method, the slight variations of receiver DCBs can be obviously distinguished using high precise ionospheric observables, with a 58.4% and 71.2% improvement of the standard deviation (STD) for PPP float-ambiguity and fixed-ambiguity solutions, respectively. For ionosphere modeling, the 24.7% and 27.9% improvements for posteriori residuals were achieved for PPP float-ambiguity and fixed-ambiguity solutions, compared to the CCL method. The corresponding improvement for residuals of the vertical total electron contents (VTECs) compared with the Center for Orbit Determination in Europe (CODE) final GIM products in global accuracy was 9.2% and 13.7% for PPP float-ambiguity and fixed-ambiguity solutions, respectively. The results show that the PPP fixed-ambiguity solution is the best one for the GIM product modeling and satellite DCBs estimation. [ABSTRACT FROM AUTHOR]

Satellite antenna phase center offsets (PCOs) and phase variations (PVs) for BeiDou-3 satellites are estimated based on the tracking data of the Multi-GNSS Experiment (MGEX) and the international GNSS Monitoring and Assessment System (iGMAS) network. However, when estimating the (PCOs) of BeiDou-3 medium Earth orbit (MEO) satellites by pure Extending the CODE Orbit Model (ECOM1), the x-offset estimations of the PCOs have a systematic variation of about 0.4 m with the elevation of the Sun above the orbital plane (β-angle). Thus, a priori box-wing solar radiation pressure (SRP) model of BeiDou-3 MEO was assisted with ECOM1. Then, the satellite type-specific PCOs and common PVs were obtained. The estimations of PCOs and PVs were compared with the MGEX PCOs from the precise orbit and clock offset. When the MGEX PCOs were used, the root mean square (RMS) of 24 h overlap was 6.76, 4.36, 1.46 cm, in along-track, cross-track, and radial directions, respectively; the RMS and standard deviations (STD) of the 24 h clock offset overlap were 0.28 and 0.15 ns; the fitting RMS of the 72 h clock offset of the quadratic polynomial was 0.243 ns. After comparing this with the estimated PCOs and PVs, the RMS of the 24 h orbit overlap was decreased by 6.5 mm (10.54%), 1.8 mm (4.4%), and 1.1 mm (8.03%) in the along-track, cross-track, and radial directions, respectively; the RMS and STD of the 24 h clock offset overlap were decreased by 0.024 ns (8.6%) and 0.020 ns (13.1%), respectively; the fitting RMS of the 72 h clock offset of the quadratic polynomial was reduced by about 0.016 ns (6.5%). [ABSTRACT FROM AUTHOR]

In the Global Navigation Satellite System (GNSS) community, the Quasi-Zenith Satellite System (QZSS) is an augmentation system for users in the Asia-Pacific region. However, the characteristics and performance of four QZSS satellite clocks in a long-term scale are unknown at present. However, it is crucial to the positioning, navigation and timing (PNT) services of users, especially in Asia-Pacific region. In this study, the characteristics and performance variation of four QZSS satellite clocks, which including the phase, frequency, frequency drift, fitting residuals, frequency accuracy, periodic terms, frequency stability and short-term clock prediction, are revealed in detail for the first time based on the precise satellite clock offset products of nearly 1000 days. The important contributions are as follows: (1) It is detected that the times of phase and frequency jump are 2.25 and 1.5 for every QZSS satellite clock in one year. The magnitude of the frequency drift is about 10−18. The periodic oscillation of frequency drift of J01 and J02 satellite clocks is found. The clock offset model precision of QZSS is 0.33 ns. (2) The two main periods of QZSS satellite clock are 24 and 12 hours, which is the influence of the satellite orbit; (3) The frequency stability of 100, 1000 and 10,000 s are 1.98 × 10−13, 6.59 × 10−14 and 5.39 × 10−14 for QZSS satellite clock, respectively. The visible "bump" is found at about 400 s for J02 and J03 satellite clocks. The short-term clock prediction accuracy of is 0.12 ns. This study provides a reference for the state monitoring and performance variation of the QZSS satellite clock. [ABSTRACT FROM AUTHOR]

In order to provide better service for the Asia-Pacific region, the BeiDou navigation satellite system (BDS) is designed as a constellation containing medium earth orbit (MEO), geostationary earth orbit (GEO), and inclined geosynchronous orbit (IGSO). However, the multi-orbit configuration brings great challenges for orbit determination. When orbit maneuvering, the orbital elements of the maneuvered satellites from broadcast ephemeris are unusable for several hours, which makes it difficult to estimate the initial orbit in the process of precise orbit determination. In addition, the maneuvered force information is unknown, which brings systematic orbit integral errors. In order to avoid these errors, observation data are removed from the iterative adjustment. For the above reasons, the precise orbit products of maneuvered satellites are missing from IGS (international GNSS (Global Navigation Satellite System) service) and iGMAS (international GNSS monitoring and assessment system). This study proposes a method to determine the precise orbits of maneuvered satellites for BeiDou GEO and IGSO. The initial orbits of maneuvered satellites could be backward forecasted according to the precise orbit products. The systematic errors caused by unmodeled maneuvered force are absorbed by estimated pseudo-stochastic pulses. The proposed method for determining the precise orbits of maneuvered satellites is validated by analyzing data of stations from the Multi-GNSS Experiment (MGEX). The results show that the precise orbits of maneuvered satellites can be estimated correctly when orbit maneuvering, which could supplement the precise products from the analysis centers of IGS and iGMAS. It can significantly improve the integrality and continuity of the precise products and subsequently provide better precise products for users. [ABSTRACT FROM AUTHOR]

Due to the cuboid satellite body of BeiDou-3 satellites, the accuracy of their orbit showed a trend of systematic variation with the sun-satellite-earth angle (ε) using the Extend CODE Orbit Model (ECOM1). Therefore, an a priori cuboid box-wing model (named the cuboid model) is necessary to compensate ECOM1. Considering that the body-dimensions and optical properties of the BeiDou-3 satellites used to construct the box-wing model have not yet been fully released, the adjustable box-wing model (ABW) was used for precise orbit determination (POD). The a priori cuboid box-wing model was directly estimated by the precision radiation accelerations, obtained from ABW POD. When using ECOM1 model, for 14 < β < 40°, a linear systematic variation of D0 related to the elevation of the sun above the orbital plane (β-angle) with a slope of 0.048 nm/s2/°, was found for C30. After adding the cuboid model to assist ECOM1 (named Cuboid + ECOM1), the slope was reduced to 0.005 nm/s2/°, and for C20 satellite, the standard deviation (STD) of D0 was improved, from 1.28 to 0.85 nm/s2 (34%). For satellite laser ranging (SLR) validation, when using the ECOM1 model, the systematic variation with the ε angle was about 14 cm for C20 and C30. After using the Cuboid + ECOM1 model, the variation was significantly reduced to about 5 cm. For C20 and C21, compared with the ECOM1 model, the root mean square (RMS) of the ECOM2 and Cuboid + ECOM1 model was improved by about 0.54 (10.3%) and 0.43 cm (8.7%). For C29 and C30, the RMS of ECOM2 and Cuboid + ECOM1 model was improved for about 0.7 (10.9%) and 1.6 cm (25.6%). Finally, the RMS of the SLR residuals of 4.37 to 4.88 cm was achieved for BeiDou-3 POD. [ABSTRACT FROM AUTHOR]

Because there are different types of BeiDou constellations with participating geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites, the maneuvering frequency of BeiDou satellites is higher than that of other navigation systems. The satellite orbital maneuvers lead to orbital parameter failure for several hours from broadcast ephemeris. Due to the missing initial orbit, the maneuvering thrust, and the period of orbital maneuvering, the orbit products of maneuvering satellites cannot be provided by the International Global Navigation Satellite System (GNSS) Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS). In addition, the period of unhealthy status and the orbital parameters of maneuvering satellites in broadcast ephemeris are unreliable, making the detection of orbital maneuver periods more difficult. Here, we develop a method to detect orbital maneuver periods involving two key steps. The first step is orbit prediction of maneuvering satellites based on precise orbit products. The second step is time period detection of orbit maneuvering. The start time detection factor is calculated by backward prediction orbit and pseudo-range observations, and the end time detection factor is calculated by forward prediction orbit and pseudo-range observations. Data of stations from the Multi-GNSS Experiment (MGEX) and iGMAS were analyzed. The results show that the period of orbit maneuvering could be detected accurately for BeiDou GEO and IGSO satellites. In addition, the orbital maneuver period of other GNSS medium Earth orbit (MEO) satellites could also be determined by this method. The results of period detection for orbit maneuvering provide important reference information for precision orbit and clock offset determination during satellite maneuvers. [ABSTRACT FROM AUTHOR]

The racking station distribution structure plays an important role in GNSS satellite orbit determination. Due to the current satellite distribution of the BeiDou satellite navigation system (BDS), the problem how to construct a reasonable distribution of tracking stations to obtain BDS satellite orbits with high precision has become a highly imperative issue. Based on the theory of dynamic orbit determination, two different station distributions were analyzed to study their impact on BDS precise and real-time orbit determination. Subsequently, the impact of Satellite Position Dilution of Precision (SPDOP) values on orbit determination was analyzed. Finally, an improved scheme for the tracking station distribution was designed based on the original scheme. The numerical results show that the SPDOP value can be used to evaluate the contribution of the tracking stations distribution on the BDS IGSO and MEO satellites orbit determination. In addition, the tracking stations which focus on the Asia-Pacific region play a key role in current BDS orbit determination. [ABSTRACT FROM AUTHOR]