Real-time Precise Orbit Research Articles

LEO real-time ambiguity-fixed precise orbit determination with onboard GPS/Galileo observations

LEO real-time ambiguity-fixed precise orbit determination with onboard GPS/Galileo observations

GREAT: A scientific software platform for satellite geodesy and multi-source fusion navigation

The software platform named GNSS + REsearch, Application and Teaching (GREAT) has been designed and developed by Wuhan University for satellite geodesy and multi-source fusion navigation. GREAT is a comprehensive software platform based on C++ language, with modular structure, cross-platform capabilities and efficient performance. The software mainly focuses on space geodetic data processing, precise positioning and orbit determination, and multi-source fusion navigation. With the integration of multiple space geodetic techniques at observation level, GREAT can achieve the determination of global geodetic parameters. Meanwhile, GREAT can also achieve real-time precise orbit and clock determination by processing GNSS data from globally distributed stations, and the accuracies are about 3–6 cm for orbit and 0.1–0.4 ns for clock. Based on high-precision orbit and clock products, centimeter-level onboard positioning accuracies can be achieved with PPP-RTK in open-sky scenarios. Furthermore, centimeter-level multi-source fusion navigation can be achieved in urban scenarios though the integrated system of PPP-RTK/MEMS/VIS/LiDAR. Additionally, efficiency optimization algorithms such as parallel computing are applied to enable the software to handle the data-intensive and calculation-intensive situations.

A new quality monitoring method for real-time precise orbit and clock products

A new quality monitoring method for real-time precise orbit and clock products

Real-Time Precise Orbit Determination of Low Earth Orbit Satellites Based on GPS and BDS-3 PPP B2b Service

This study investigates and verifies the feasibility of the precise point positioning (PPP)-B2b enhanced real-time (RT) precise orbit determination (POD) of low Earth orbit (LEO) satellites. The principles and characteristics of matching various PPP-B2b corrections are introduced and analyzed. The performance and accuracy of broadcast ephemeris and PPP-B2b signals are compared and evaluated by referring to the precise ephemeris. The root mean square (RMS) errors in the Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS)-3 broadcast ephemeris orbits in the along direction are larger than those in the other two (radial and cross) directions, and correspondingly, the along component PPP-B2b corrections are greatest. The continuity and smoothness of the GPS and BDS-3 broadcast ephemeris orbits and clock offsets are improved with the PPP-B2b corrections. The availability of PPP-B2b corrections is comprehensively analyzed for the TJU-01 satellite. Several comparative schemes are adopted for the RT POD of the TJU-01 satellite using the broadcast ephemeris and PPP-B2b corrections. The RT POD performance is improved considerably with the broadcast ephemeris corrected by the PPP-B2b signals. The RMS of the RT orbital errors in the radial, along, and cross directions is 0.10, 0.13, and 0.09 m, respectively, using BDS-3 and GPS PPP-B2b corrections, with reference to the solutions calculated with the precise ephemeris. The accuracy is improved by 5.1%, 43.9%, and 28.7% in the three directions, respectively, relative to that achieved with the broadcast ephemeris. It is concluded that a greater proportion of received PPP-B2b satellite signals corresponds to a greater improvement in the accuracy of the RT POD of the LEO satellite.

Impacts of satellite clock errors on GPS/BDS/Galileo real-time PPP time transfer

By utilizing the real-time precise orbit and clock products provided by International GNSS Service (IGS), it is feasible to calculate real-time PPP (RTPPP) time and frequency transfer. The quality of these real-time precise products has a significant effect on the performance of clock comparisons and time transfer. This paper focuses on real-time clock comparisons with IGS real-time multi-GNSS precise products, which tries to explore the potential of GNSS RTPPP time transfer in time and frequency community. By using real-time precise satellite orbit and clock products from two IGS analysis centers, i.e. CNES and WHU, the clock comparisons and time transfer performance of four time links are comprehensively investigated. It is shown that the statistical uncertainty of real-time clock comparison based on multi-GNSS is within 0.15 ns, and GPS RTPPP provides time transfer results with better performance than BDS-3 and Galileo. In addition, the deviations occur in remote time links results of BDS-3 and Galileo-only between using CNES and WHU, the maximum difference can reach up to 1.10 ns. It is shown that real-time BDS-3 and Galileo satellite products of CNES and WHU are inconsistent, and will affect the time transfer performance. The paper also investigates the receiver clock offset solutions determined by using different available satellites. The results show that there are significant satellite-related biases between different satellites, especially for BDS-3 and Galileo. Thus, the reference time scales determined by using different satellites are inconsistent, and further, the time transfer for long baseline time links will be affected as there are few common view satellites for remote stations.

A Novel Method for Improving LEO Kinematic Real-Time Precise Orbit Determination With Neural Networks

A Novel Method for Improving LEO Kinematic Real-Time Precise Orbit Determination With Neural Networks

Characterizing the fault performance of real-time precise satellite orbit and clock correction products

The a priori fault probability of the real-time precise satellite orbit and clock correction products is the critical parameter for integrity monitoring of precise point positioning (PPP). The traditional fault probability evaluation methods use the worst-case instantaneous user ranging error (IURE) as the conservative test statistic. However, the systematic biases of IURE contained in the worst-case IURE barely affect the PPP accuracy, which will undermine the statistical distribution of test statistic and reduce the sensitivity of fault detection. The fault probability will be estimated over-conservatively for the traditional methods. By clarifying the sources of the systematic biases, a new test statistic is constructed by deliberately removing the systematic biases of IURE originated from satellite orbit and clock errors. One-year Global Positioning System correction products evaluation results have demonstrated that the constructed test statistic follows the Gaussian distribution with the decreased uncertainty and the improved fault detection sensitivity. The real-world data experiments have shown that the a priori probabilities of the satellite fault and the constellation fault are at the order of 10−4 and 10−5 levels, respectively.

BDS/GPS/Galileo Precise Point Positioning Performance Analysis of Android Smartphones Based on Real-Time Stream Data

Smartphones with the Android operating system can acquire Global Navigation Satellite System (GNSS) raw pseudorange and carrier phase observations, which can provide a new way for the general public to obtain precise position information. However, only postprocessing precise orbit and clock offset products in some older smart devices are applied in current studies. The performances of precise point positioning (PPP) with the smartphone using real-time products and newly smartphones are still unrevealed, which is more valuable for real-time applications. This study investigates the observation data quality and multi-GNSS real-time PPP performance using recent smartphones. Firstly, the observed carrier-to-noise density ratio (C/N0), number of satellites and position dilution of precision (PDOP) of GNSS observations are evaluated. The results demonstrate that the C/N0 received by Huawei Mate40 is better than that of the Huawei P40 for GPS, BDS, QZSS and Galileo systems, while the GLONASS is poorer, and the PDOP of the Huawei P40 is slightly better than that of Mate40. Additionally, a comprehensive analysis of real-time precise orbit and clock offset products performance is conducted. The experiment result expresses that the orbit and clock offset performance of GPS and Galileo is better than that of BDS-3 and GLONASS, and BDS-2 is the worst. Finally, single- and dual-frequency multi-GNSS combined PPP experiments using observations received from smartphones and real-time products are conducted; the results indicate that the real-time static PPP using a smartphone can achieve decimeter-level positioning accuracy, and kinematic PPP can achieve meter-level positioning accuracy after convergence.

An improved approach for rapid filter convergence of GNSS satellite real-time orbit determination

Introduction: The real-time precise satellite orbit of Global Navigation Satellite System (GNSS) usually takes a long time to converge to a stable state using the filter method. The ultra-rapid orbit products are helpful to improve convergence speed by introducing them as external constraints. Reasonably determination of stochastic model of the constraint equation from the ultra-rapid products is the key for a better performance of convergence whereas it has not been well solved.Methods: We propose to establish the stochastic model of the orbit constraint equation by analyzing the differences between the predicted part of the ultra-rapid orbit and the filter orbit after convergence. To improve the orbit accuracy during the convergence, the constant stochastic model of the constraint equation is first determined for each system by averaging the root mean square (RMS) time-series of the differences between predicted orbit from the ultra-rapid products and the SRIF orbit after convergence in different time ranges. Besides, a time-dependent stochastic model of the constraint equation is then determined by analyzing the variation of the RMS time-series. To validate the proposed method, a month of multi-constellation data collected from 80 globally distributed stations is processed using the Square Root Information Filter (SRIF) algorithm.Results: Orbit results without introducing external orbit constraints show that the convergence time in the radial direction is 13.75, 15.25 and 17.75 h for GPS, Galileo and BDS-3 satellite, respectively. For the scheme of constant stochastic model using the average RMS over 6 h, results show that there is no significant convergence phenomenon for each system in all directions. The one-dimensional (1D) RMS during the constraint period is improved by 86.5%, 84.8%, 96.8% for GPS, Galileo and BDS-3 satellites when compared to the results without introducing external orbit constraints. As for the scheme of time-dependent stochastic model, results show that the quadratic function is suitable for modeling the RMS time-series for each system, and the accuracy of results during the constraint period has a further improvement of 1.3%, 3.7% in 1D direction for GPS, BDS-3 satellites when compared to the constant stochastic model using the average RMS over 6 h. In addition, the orbit accuracy with external orbit constraint is slightly better than those without external orbit constraint after the constraint period.Discussion: The above results show that when introducing the ultra-rapid product as the external constraint, there is basically no convergence phenomenon for GNSS satellite, while the orbit accuracy for time-dependent stochastic model has further improvement than constant stochastic model. These results indicate that the proposed method can significantly improve the convergence performance without damaging the orbit accuracy after convergence, and time-dependent stochastic model is better than constant stochastic model.

BDS Orbit Maneuver Detection Based on Epoch-Updated Orbits Estimated by SRIF

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.

Analysis of BDS-3 Real-Time Satellite Clock Offset Estimated in Global and Asia-Pacific and the Corresponding PPP Performances

The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.

Evaluation of BDS-3 B1C/B2b Single/Dual-Frequency PPP Using PPP-B2b and RTS SSR Products in Both Static and Dynamic Applications

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.

In-Flight Performance Assessment of the Single-Frequency GPS/BDS Receiver for Yaogan-30 Series Satellites Real-Time Navigation

Within the Yaogan-30 series satellites, the low-cost single-frequency Global Positioning System/BeiDou Navigation Satellite System (GPS/BDS) receiver was employed for onboard real-time navigation. This article presents the in-flight performance of the single-frequency GPS/BDS receiver, including the tracking of GPS/BDS satellites, the noise of measurements, and the orbit accuracy of onboard real-time navigation results. First, in terms of satellites tracking, no BDS-2 satellites are tracked in 30–40% of all the time, four to seven BDS-2 satellites can be observed for less than 15% of the time, and only one to three BDS-2 satellites are available for the rest time, whereas 7–12 GPS satellites are tracked for the vast majority of the time. Obviously, the GPS observations play a more important role than BDS-2 data in real-time navigation and precise orbit determination (POD). Although the receivers only provide the single-frequency C/A-code pseudorange measurements without carrier-phases output, the accuracies of postprocessed POD could arrive at the level of 10–25 cm in terms of 3-D position. Hence, the post precise orbits are used as the reference for the assessment of real-time navigation accuracy. The assessment results demonstrate that the onboard real-time navigation accuracies of 2.0–3.5 m for 3-D position and 10.0–13.0 mm/s for 3-D velocity are achievable. At the same time, the statistics on the C/A-code pseudorange residuals after POD processing reflects that the noises of measurements from GPS and BDS-2 satellites are at the same level of 0.5–1.6 m. It should be noted that there is a notable velocity deviation of up to about 7.6 mm/s. Nevertheless, even with this obvious systematic error, the current velocity accuracy could still meet the real-time requirements of the small Yaogan-30 series satellites. In addition, some offline simulative solutions with tuned strategy settings are tested to validate the potential real-time navigation accuracy improvement. The simulation experiment tests results illustrate that a higher real-time orbit accuracy of roughly 1.0 m for 3-D position and 1.0 mm/s for 3-D velocity could be obtainable, if an optimized power spectral density of estimated empirical accelerations and a slightly higher order and degree of gravity model (50×50) are adopted. All the above analyses show that the single-frequency pseudorange Global Navigation Satellite System receiver is a high cost-effective sensor and has a wide horizon of application in the aerospace market.

Real-time precise orbit and clock estimation of multi-GNSS satellites with undifferenced ambiguity resolution

Real-time precise orbit and clock estimation of multi-GNSS satellites with undifferenced ambiguity resolution

Real-Time Multi-GNSS Precise Orbit Determination Based on the Hourly Updated Ultra-Rapid Orbit Prediction Method

Offering real-time precise point positioning (PPP) services for global and large areas based on global navigation satellite systems (GNSS) has drawn more and more attention from institutions and companies. A precise and reliable satellite orbit is a core premise for multi-GNSS real-time services, especially for the GPS and GLONASS, which are undergoing modernization, whereas the Galileo, BDS and QZSS have just fulfilled the construction stage. In this contribution, a real-time precise orbit determination (POD) strategy for the five operational constellations based on the hourly updated ultrarapid orbit prediction method is presented. After combination of 72 h arc through three adjacent 24 h arc normal equations, the predicted orbits are finally generated (hourly updated). The POD results indicate that the mean one-dimensional (1-D) root mean square (RMS) values compared with the Deutsches GeoForschungsZentrum (GFZ) final multi-GNSS orbits are approximately 3.7 cm, 10.2 cm, 5.8 cm, 5.7 cm, 4.1 cm and 25.1 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The mean 1-D RMS values of the hourly updated ultrarapid orbit boundary overlapping comparison are approximately 1.6 cm, 6.9 cm, 3.2 cm, 2.7 cm, 1.8 cm and 22.2 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The satellite laser ranging (SLR) validation illuminates that the mean RMS values are approximately 4.53 cm and 4.73 cm for the four MEOs of BDS-3 and four BDS-2 satellites, respectively.

Assessment of Real-Time GPS/BDS-2/BDS-3 Single-Frequency PPP and INS Tight Integration Using Different RTS Products

Due to the virtues of low-cost and high positioning accuracy, Single-Frequency Precise Point Positioning (SF-PPP) is becoming a prospective technique. However, SF-PPP is not as widely used as dual-frequency and triple-frequency PPP at present, owing to the effect of ionospheric delay residuals after model rectification. In recent years, with the evolution of multi-constellation Global Navigation Satellite Systems (multi-GNSS, i.e., GPS, BDS-2, and BDS-3), it has become possible to obtain credible and continuous positioning results using SF-PPP. However, such performance would be significantly degraded in challenging environments (i.e., boulevards, tunnels, and tall buildings). Under these circumstances, GNSS signals are obstructed, and it is difficult to provide sufficient observations for SF-PPP. Therefore, the Inertial Navigation System (INS) is employed to promote the positioning performance of SF-PPP. The PPP/INS integration is regarded as one of the most efficient approaches in GNSS-denied environments. To satisfy the request of supplying real-time positioning information, the Real-Time Services (RTS) of the International GNSS Service (IGS) provide real-time precise orbit and clock products for globally distributed users through the internet. In this paper, a real-time GPS/BDS-2/BDS-3 SF-PPP and INS tight integration model is proposed, and it is assessed using the data gathered by vehicle and real-time products afforded by CAS (Chinese Academy of Sciences), GFZ (Deutsche GeoForschungsZentrum), and WHU (Wuhan University). The outcomes illustrate the following: (1) GPS + BDS SF-PPP/INS can provide more accurate and continuous positioning solutions compared with those of GPS + BDS SF-PPP, with improvements of 52.8%, 31.1%, and 42.8% in the north, east, and vertical components, respectively. (2) In general, the orbit and clock products’ accuracies in terms of GPS afforded by the three analysis centers are consistent with each other. For BDS, the orbit product from WHU is more accurate compared to those of CAS and GFZ. However, the accuracy of the clock product afforded by WHU is lower compared with those provided by the other two centers, especially for BDS-2 satellites. (3) The positioning accuracy in terms of Root Mean Square (RMS) values based on GFZ products are much higher than the results based on CAS and WHU products in the three directions.

Adaptive Kalman Filter for Real-Time Precise Orbit Determination of Low Earth Orbit Satellites Based on Pseudorange and Epoch-Differenced Carrier-Phase Measurements

Real-time precise orbit determination (POD) of low earth orbiters (LEOs) is crucial for orbit maintenance as well as autonomous operation for space missions. The Global Positioning System (GPS) has become the dominant technique for real-time precise orbit determination (POD) of LEOs. However, the observation conditions of near-earth space are more critical than those on the ground. Real-time POD accuracy can be seriously affected when the observation environment suffers from strong space events, i.e., a heavy solar storm. In this study, we proposed a reliable adaptive Kalman filter based on pseudorange and epoch-differenced carrier-phase measurements. This approach uses the epoch-differenced carrier phase to eliminate the ambiguities and thus reduces the significant number of unknown parameters. Real calculations demonstrate that four to five observed GPS satellites is sufficient to solve reliable position parameters. Furthermore, with accurate pseudorange and epoch-differenced carrier-phase-based reference orbits, orbital dynamic disturbance can be detected precisely and reliably with an adaptive Kalman filter. Analyses of Swarm-A POD show that sub-meter level real-time orbit solutions can be obtained when the observation conditions are good. For poor observation conditions such as the GRACE-A satellite on 8 September 2017, when fewer than five GPS satellites were observed for 14% of the observation time, 1–2 m orbital accuracy can still be achieved with the proposed approach.

GNSS real-time precise point positioning with BDS-3 global short message communication devices

Global short-message communication (GSMC) service is a new function of BeiDou-3 global navigation satellite system (BDS-3). Broadcasting precise orbit and clock corrections via GSMC provides an opportunity for real-time precise point positioning (PPP), especially in the areas where internet-based communication is not available, such as deserts and oceans. This research achieves a real-time multi-GNSS PPP based on the precise orbit and clock corrections broadcast via BDS-3 GSMC. To reduce the data size, the precise corrections of only visible GNSS satellites are broadcast, and three messages are used to broadcast the corrections of GPS, Galileo and BDS satellites. The encoding strategy of corrections is designed and a procedure for real-time PPP with BDS-3 GSMC is described. To evaluate the positioning performance of the proposed real-time PPP scheme, the simulated kinematic real-time PPP experiments with BDS-3 GSMC corrections and Centre National d’Etudes Spatiales (CNES) real-time precise orbit and clock products are carried out by using observations of 7 days from 12 globally distributed IGS stations. The positioning accuracy in E, N and U components reach up to 3.3, 3.8 and 5.9 cm with GSMC corrections, which is comparable to that with CNES real-time products. Furthermore, a vehicle real-time PPP experiment is conducted using the devices with the function of BDS-3 GSMC and the positioning accuracy reach up to 4.1, 2.2 and 7.1 cm in E, N and U components after convergence.

ANALYSIS OF THE GRAVITY MODELS IMPACT ON LEO SATELLITE ORBIT PREDICTION

Abstract. Non-spherical gravity plays a crucial role in the LEO satellite orbit determination and prediction. In recent years, several new gravity models have been proposed with more comprehensive ground and space-borne data. The impact of the gravity models has been extensively studied while its impact on the orbit prediction has not attracted enough attention. With the risen of the mega LEO constellation, new applications such as the LEO navigation requires real-time precise orbit, which increases the importance of the precise orbit prediction. In this study, we selected six popular gravity models, namely JGM3, EGM2008, EGM96, EIGEN2, GL04C, and GGM03S, and compared their performance in different LEO orbit predictions. The comparison results indicate that there is no single optimal gravity model for all LEO orbit prediction scenarios. For short-term prediction, JGM3, EGM2008, GL04C models perform better while in long-term prediction JGM3, EGM96, EIGEN2 have more potential. The results also reveal that the optimal model changed with time. In addition, the impact of the gravity order on the orbit prediction is investigated, the results indicate that for satellites with lower orbital heights, the gravitational field order required to achieve a certain truncation error is higher than for satellites with higher orbital heights. The authors also explore the effect of gravitational field-associated permanent tides on orbital prediction. In one day, for satellites with an orbital altitude of about 970km, the effect of permanent tides on 3D RMS is 6.92m; for satellites around 710km, the effect of permanent tides on 3D RMS is 4.20m; for satellites around 970km, the effect of permanent tides on 3D RMS is 2.07m.

Real-Time Precise Orbit Determination for LEO between Kinematic and Reduced-Dynamic with Ambiguity Resolution

The real-time integer-ambiguity resolution of the carrier-phase observation is one of the most effective approaches to enhance the accuracy of real-time precise point positioning (PPP), kinematic precise orbit determination (KPOD), and reduced-dynamic precise orbit determination (RPOD) for low earth orbit (LEO) satellites. In this study, the integer phase clock (IPC) and wide-lane satellite bias (WSB) products from CNES (Centre National d’Etudes Spatiales) are used to fix ambiguity in real time. Meanwhile, the three models of real-time PPP, KPOD, and RPOD are applied to validate the contribution of ambiguity resolution. Experimental results show that (1) the average positioning accuracy of IGS stations for ambiguity-fixed solutions is improved from about 7.14 to 5.91 cm, with an improvement of around 17% compared to the real-time float PPP solutions, with enhancement in the east-west direction particularly significant, with an improvement of about 29%; (2) the average accuracy of the estimated LEO orbit with ambiguity-fixed solutions in the real-time KPOD and RPOD mode is improved by about 16% and 10%, respectively, with respect to the corresponding mode with the ambiguity-float solutions; (3) the performance of real-time LEO RPOD is better than that of the corresponding KPOD, regardless of fixed- or float-ambiguity solutions. Moreover, the average ambiguity-fixed ratio can reach more than 90% in real-time PPP, KPOD, and RPOD.