Orbit Accuracy Research Articles

SLR Validation and Evaluation of BDS-3 MEO Satellite Precise Orbits

Starting from February 2023, the International Laser Ranging Service (ILRS) began releasing satellite laser ranging (SLR) data for all BeiDou global navigation satellite system (BDS-3) medium earth orbit (MEO) satellites. SLR data serve as the best external reference for validating satellite orbits, providing a basis for comprehensive evaluation of the BDS-3 satellite orbit. We utilized the SLR data from February to May 2023 to comprehensively evaluate the orbits of BDS-3 MEO satellites from different analysis centers (ACs). The results show that, whether during the eclipse season or the yaw maneuver season, the accuracy was not significantly decreased in the BDS-3 MEO orbit products released from the Center for Orbit Determination in Europe (CODE), Wuhan University (WHU), and the Deutsches GeoForschungsZentrum (GFZ) ACs, and the STD (Standard Deviation) of SLR residuals of those three ACs are all less than 5 cm. Among these, CODE had the smallest SLR residuals, with 9% and 12% improvement over WHU and GFZ, respectively. Moreover, the WHU precise orbits exhibit the smallest systematic biases, whether during non-eclipse seasons, eclipse seasons, or satellite yaw maneuver seasons. Additionally, we found some BDS-3 satellites (C32, C33, C34, C35, C45, and C46) exhibit orbit errors related to the Sun elongation angle, which indicates that continued effort for the refinement of the non-conservative force model further to improve the orbit accuracy of BDS-3 MEO satellites are in need.

A kinematic real-time PPP approach with estimating signal in space range errors

Since 2013, the International GNSS Service (IGS) real-time service (RTS) has been providing precise orbit and clock corrections for ten years, which enables real-time positioning at the decimeter level. High precision positioning relies heavily on accurate orbit and clock. However, constrained by the relatively short observation duration, the accuracy of real-time products are often worse than the final products. Previous studies indicate that compensating for errors in orbit and clock can improve positioning accuracy. Based on this theory, we proposed an improved positioning model, which incorporates the signal-in-space range error (SISRE) into the ionosphere-free combination observation equation and treats it as a parameter in the Kalman filter. Through the analysis of SISRE, we find that the time-varying characteristic of the parameter follows a random walk assumption. To find the optimal parameter settings of the SISRE parameters, a two-dimensional sensitivity analysis is employed, and a set of recommended values are provided. In the simulated kinematic positioning experiments, the proposed method achieves positioning accuracies of 17.3 cm, 19.6 cm, and 18.0 cm for GPS, BDS-3, and Galileo, respectively, representing a 10–20 % improvement over traditional methods. In real-time PPP experiment, the accuracy reaches 21.7 cm, indicating a 12.9 % improvement compared to traditional methods.

A simplified GNSS/LEO joint orbit determination method

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.

Analysis and diagnosis of abnormal SLR validation results for BeiDou-3 SECM-B MEO C225 and C226 satellite orbits

Satellite laser ranging (SLR) is the only stand-alone and external tool for verifying the accuracy of microwave-based GNSS orbits. On February 2, 2023, the International Laser Ranging Service initiated the SLR global tracking campaign for the complete BeiDou-3 medium Earth orbit (MEO) constellation. This initiative provides an opportunity to unveil the potential issue for BeiDou-3 MEO orbit modeling. An examination of the SLR validation results of precise BeiDou-3 MEO orbits across different IGS/Multi-GNSS Experiment (MGEX) analysis centres (ACs) reveals that the SLR residual standard deviation for BeiDou-3 SECM-B MEOs C225 and C226 orbits reaches 18 cm. This figure is approximately four to nine times those for other BeiDou-3 MEOs. This contradicts the fact that the orbit quality of C225 and C226 is comparable to other satellites. By analyzing the correlation between SLR residuals and de-trend clock residuals, detector-specific bias performance, and the distribution characteristics of SLR residuals relative to satellite azimuth and nadir angles, we diagnose that abnormal SLR validation results for C225 and C226 originate from a large deviation in the official horizontal offsets for the laser retroreflector arrays (LRAs) in the satellite reference frame. LRA horizontal offsets for C225 and C226 are estimated based on SLR residuals. With our adjusted LRA offset estimates, the SLR residual metrics for C225 and C226 orbits (across various IGS/MGEX ACs) are comparable to the results obtained for other BeiDou-3 MEOs. Additionally, our adjustments enable the identification of their orbit modeling errors across different IGS/MGEX ACs according to the pattern of SLR residual variation. From the study, spacecraft manufacturers should be encouraged to conduct a comprehensive review of ground calibrations for BeiDou LRA offsets. This is crucial for optimizing BeiDou orbit model and enhancing its applications in high-precision geosciences.

Improved GRACE-FO kinematic orbit determination with epoch-difference KBR during the GPS flex power period

The flex power technology in satellite navigation systems enhances anti-jamming capabilities but can impact the quality of GPS observations and the accuracy of low Earth orbit determination, such as GRACE Follow-On (GRACE-FO) mission. This study investigates the influence of GPS flex power on Hatch-Melbourne-Wübbena (HMW) linear combinations and GRACE-FO kinematic orbits from January 1 to September 30, 2020. Epoch-differenced K-Band Ranging (KBR) data is introduced in orbit determination during the flex power period to improve both absolute and inter-satellite relative accuracy. The analysis indicates that the influence of early flex power (before February 13, 2020) on HMW combinations and orbits is minimal, whereas the effect of later flex power (after February 14, 2020) is significant: (1) HMW combinations exhibit notable systematic discontinuities even with elevation angles greater than 50 degrees, causing the fixing rate of wide-lane ambiguities to drop from 96 % to 80 %. (2) Kinematic absolute orbits show significant deteriorations of approximately 9 mm and 4 mm in the three-dimensional direction for float and integer ambiguity resolution (FAR and IAR), while relative accuracy of FAR and IAR orbits decreases by 50 % and 46 %, respectively. However, using epoch-differenced KBR (DKBR) data, the accuracy of absolute orbits could be increased by up to 15 % and the accuracy of relative orbits could be improved by at least 69 %, which showcases a positive effect. Thus, this can be considered as an alternative method to improve the accuracy of GRACE-FO orbit during the flex power period.

Sentinel-6 Michael Freilich precise orbit determination using PODRIX and TriG receiver measurements

The Sentinel-6 Michael Freilich altimetry mission flies two GNSS receivers: a primary multi-GNSS (GPS plus Galileo) PODRIX receiver and a GPS-only TriG receiver. Each of these receivers is independently capable of supporting the precise orbit determination (POD) requirement for < 1.5 cm radial rms error. In this study, we characterize the performance of single-receiver solutions and evaluate the benefits of a combined TriG and PODRIX orbit solution. The availability of both sets of receiver observations revealed a 10 mm in-track difference between orbit solutions derived independently from TriG and PODRIX tracking data. Based on satellite laser ranging (SLR) residuals, this bias has been isolated to an apparent inconsistency between the estimated TriG receiver clock and observation time-tags of approximately 1.3 μs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu \\hbox {s}$$\\end{document}, which is equivalent to a common range error of roughly 400 m in the TriG observations. After applying this calibration, the TriG and PODRIX displayed similar performance in terms of orbit overlap precision. PODRIX-Galileo observations showed lower code and phase tracking residual rms values compared to the GPS observations. Overall, processing the calibrated TriG and PODRIX observations separately results in highly accurate orbit solutions with radial orbit accuracies better than 1 cm rms as indicated by one-way SLR residual rms of 7.2 mm or better for each solution. Orbit solution accuracy is slightly improved by processing both TriG and PODRIX observations together, resulting in one-way SLR residual rms of 7.0 mm.

GPS-Based Precise Orbit Determination of LEO Satellites Using Space-Based Double-Differenced Observations

One of the important GPS applications in space is precise orbit determination (POD) of Low-Earth Orbit (LEO) satellites. Thousands of LEO satellites are currently in orbit. One of the challenges is how to efficiently and precisely determine the orbits to satisfy the relative and absolute accuracy needs of missions. Currently, GPS-based POD of LEO satellites can be performed using either un-differenced (UD) or ground-based double-differenced (DD) observations. The UD POD needs both precise GPS satellite orbits and clocks; the DD POD needs not only the precise orbits, but also global ground reference receivers. Therefore, the GPS-based LEO POD is based on either global ground stations or precise GNSS clocks, which are not convenient for near real-time or real-time data processing. The GPS orbits can be precisely predicted in certain time; the clocks are not. For some formation flying satellite missions (two or more LEO satellites), the absolute orbit accuracy requirements are not as stringent as the relative requirements. The problem is how to perform LEO POD without global station data and precise GPS clocks in near real-time or real-time to achieve the mission orbit accuracy requirement. Based on this motivation, we investigated the GPS-based LEO POD using space-based DD observations without using global ground station GPS data and precise GPS clock products. For this study, we processed the real GPS observations from two LEO satellites. The absolute and relative orbit accuracy is assessed using several tests, including analysis of the orbit fits, external orbit comparisons, Satellite Laser Ranging (SLR) and K-band Ranging (KBR) residuals.

Comparing city size distributions: Gridded population versus nighttime lights

AbstractThis paper compares the size distributions of cities when they are measured using gridded population and nighttime lights (NTLs) data. To do so, we exploit recent and accurate satellite imagery to proxy urban economic activity. Similarly to related studies, our results suggest that population is more equally distributed than lights at the country level. However, and calling assumptions established for urban NTLs into question, our findings do not support a Pareto function for their distribution. We also obtain evidence of a nonlinear and heterogeneous link between population and lights for a global sample of cities. Grounded on our empirical analysis, we develop a simple theoretical framework that relates the difference between the distributions of population and light emissions to the strength of agglomeration economies.

Earth Rotation Parameters Derived from BDS-3 New Signals B1C/B2a Dual-Frequency Combination Observations

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.

Orbit determination of Earth-Moon libration point navigation constellation based on Inter-satellite links

Earth-Moon libration point navigation constellation has a merit of fully covering the cislunar space and providing navigation services with merely a small number of satellites. Furthermore, this type of constellation itself can achieve orbit determination by using only its Inter-satellite links (ISL) owing to the well-known gravitational asymmetry near the libration points. This paper adopts a representative four-satellite navigation constellation including three satellites located near the libration point L3, L4, L5, and an extra one in Distant Retrograde Orbit (DRO), and studies the orbit determination accuracy of the constellation under two conditions: establishing ISLs within itself (called Solely libration point satellites) and establishing additional ISLs with BeiDou Navigation Satellite System (BDS) (called Libration + BeiDou satellites). The simulation results indicate that, for the Solely libration point satellites scenario with the 1 m range error and solar radiation pressure (SRP) error with the level of 10% deviation between ball model and macro model, the final orbit accuracies for L3, L4, L5, and DRO satellites can respectively achieve 11.3 m, 12.7 m, 12.6 m, and 7.3 m. Reducing the link interval can significantly shorten the arc length to achieve final accuracy, whileas it has less impact on the final orbital accuracy. When the link interval is set as 240, 60, 10, and 2 min, the arc lengths at the final accuracy of better than 15 m are about 35, 29, 23, and 20 days, respectively. To balance the communication burden and the orbit determination arc length, the recommended ISL building interval is 10 min. Errors coming from range measurement model and dynamic model, in addition, are key factors in orbit determination, which can result in meters to tens of meters of orbital accuracy. For the Libration + BeiDou satellites scenario, the augmented ISLs to BDS can substantially improve constellation orbital accuracy and shorten the orbit determination arc length. When the DRO satellite attached to the Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) satellites of BDS respectively, the improved accuracy are 37.1%, 61.2%, and 42.2%, while the shortened arc length are 20.1%, 28.3%, and 28.1%, respectively. The research findings presented in this paper can serve as a reference for the construction and assessment of navigation constellations in the Earth-Moon system.

Performance comparison of orbit and clock augmentation corrections from PPP-B2b, HAS and CLAS

Precise Point Positioning (PPP) augmentation corrections can enhance the accuracy of Global Navigation Satellite System (GNSS) positioning. Three prominent PPP augmentation services: the third generation of BeiDou Navigation Satellite System (BDS-3) PPP-B2b, Europe's Galileo High Accuracy Service (HAS) and Quasi-Zenith Satellite System (QZSS) Centimeter Level Augmentation Service (CLAS), are evaluated and compared, contributing to the optimal utilization of these services. Based on a 25-day dataset in March 2023, all the three services have made significant improvements in GPS orbit accuracy compared to the broadcast ephemeris. Galileo HAS achieved the highest three-dimension (3D) orbit accuracy for both GPS and Galileo (10.5 and 10.4 cm), followed by CLAS (48.1 and 16.3 cm) and PPP-B2b (GPS: 73.0 cm, BDS-3: 44.6 cm). This distinct performance of PPP-B2b orbits is found for the first time to be related to the large constellation rotation errors, which accounts for roughly half of the orbit errors of along and cross components. Regarding clock errors, PPP-B2b and HAS enhanced GPS clock accuracy to 0.20 ns (70 %) and 0.17 ns (74 %), respectively, over the broadcast clock (0.66 ns), while CLAS shows a much smaller improvement. Moderate correlations of 0.3–0.8 between orbit and clock errors are observed for the three augmentation corrections. For signal in space ranging error (SISRE), HAS (GPS:5.5 cm, Galileo:4.9 cm) outperforms PPP-B2b (GPS:14.3 cm, BDS-3:8.9 cm) and CLAS (GPS:23.6 cm, Galileo:13.7 cm). The 2-hourly kinematic positioning results with an accuracy of better than 20 cm (95th percentile) for the horizontal and vertical component, could be achieved for both PPP-B2b and HAS within 20 min within their service area. It is not recommended rely solely on the orbit/clock/code bias of CLAS for precise positioning, as the positioning accuracy is influenced by the SISRE. PPP-RTK of CLAS achieves horizontal 10 cm (95th percentile) and rapid convergence of mostly less than a minute by incorporating phase bias and atmospheric corrections.

Update of SB9 orbits using HERMES/Mercator radial velocities

Aims. By combining astrometric orbits (delivered in large numbers by the Gaίa mission) with spectroscopic orbits for systems with two observable spectra (SB2), it is possible to derive the masses of both stellar components. However, to get masses with a good accuracy requires accurate spectroscopic orbits, which is the primary aim of the present paper. A subsidiary aim is to discover SB2 systems hiding among known SB1 systems and even though this search may often prove unsuccessful, the acquired radial velocities may still be used to improve the existing spectroscopic orbits. Methods. New radial velocities for 58 binary systems from the Ninth Catalogue of Spectroscopic Binary Orbits (SB9), obtained using the high-resolution HERMES spectrograph installed on the 1.2 m Mercator telescope, were used to possibly identify hitherto undetected SB2 systems. For SB1 systems with inaccurate orbits, we used these new radial-velocity measurements to improve the orbital accuracy. Results. This study provides 51 orbits (41 SB1 and 10 SB2) that have been improved with respect to the solution listed in the SB9 catalogue, out of the 58 SB9 orbits studied, which belong to 56 stellar systems. Among them, there are five triple and four quadruple systems. Despite the high resolution of HERMES, the only system we detected as anew SB2 system is HIP 115142 A. The B component of the visual binary HIP 92726 has now been found to be a spectroscopic system as well, which makes HIP 92726 a newly discovered quadruple system (SB 1+SB 1). Moreover, the high resolution of HERMES has enabled us to better isolate the signature of the secondary component of HIP 12390, HIP 73182, and HIP 111170. Thus, we derived more accurate masses for them. Among the 30 SB also present in Gaia Data Release 3 (DR3), with periods shorter than the Gaia DR3 time span (~1000 d), only five had been flagged as binaries by DR3. Various DR3 selection criteria are responsible for this discrepancy.

Sun-Earth system Lagrange point spacecraft orbit computation by numerical method and deep learning technique

In this article, the Lagrange points locations are computed in the Rotating Lagrangian Point (RLP) as well as in J2000 inertial reference frames. The well-known Sun-Earth system is considered for the circular restricted three-body problem (CRTBP). In the synodic frame, the Sun-Earth Lagrangian L1 point halo orbit is computed via Differential Correction and Lindstedt-Poincaré (LP) methods. The periodic halo orbits are expressed with respect to barycenter, heliocenter and geocenter, respectively. The deep learning-based model is further explored for the orbit accuracy obtained by the numerical method considering the third, fourth and fifth order LP method.

Error Analysis for Rotating-drift-scan Charge-coupled Device Observation of Near-Earth Asteroids

The apparent velocities of near-Earth asteroids (NEAs) are usually high when they pass by Earth. Observing these fast-moving objects with long exposure times would cause their images to streak and significantly decrease the precision of astronomical measurements. The rotating-drift-scan (RDS) charge-coupled device technique is a promising approach to observe fast-moving NEAs during their close approaches to Earth. By rotating the camera of a telescope, an NEA can be observed in the time delay integration mode. This allows the asteroid to be imaged as a point source, even with a long exposure time. Here, we thoroughly present the RDS follow-up observation and orbit determination of a newly discovered NEA 2023 BJ7. This technique makes an impactful contribution to improving the NEA's orbit accuracy by extending the observation arc. A detailed statistical analysis of the astrometric error was conducted, revealing that RDS observations can achieve a competitive accuracy with an rms error of 0.″24 in right ascension and 0.″32 in declination. The instability of the telescope is thought to be the main reason affecting the internal precision. Furthermore, the RDS technique excels at observing fast-moving NEAs, as well as newly discovered NEAs without accurate ephemerides. For NEAs with rates of motion exceeding 10 deg day−1, the rms of RDS observation residuals is 0.″35 in the along-track direction and 0.″23 in the cross-track. With this technique, a network of small-aperture telescopes would substantially benefit our global NEAs monitoring system to ensure Earth’s safety from any asteroid impacts.

Koopman Operator theory applied to Lambert’s problem with a spectral behavior analysis

Lambert’s problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work presents an approximate-analytical solution to Lambert’s problem using the Koopman Operator (KO). In contrast to previous methods in the literature, the KO provides the analysis of a nonlinear system by seeking a transformation that embeds the nonlinear dynamics into a global linear representation. The new methodology to solve for Lambert solutions proposed in this paper considers the position of the system’s eigenvalues on the phase plane, evaluating accurate state transition polynomial maps for a computationally efficient propagation of the dynamics. The minimum-energy and minimum-Δv solutions to Lambert’s problem are found using the KO. The spectral behavior of the solutions is studied and a deeper understanding of the dynamical system is provided. The methodology and solutions are compared in accuracy and performance with other techniques found in the literature, highlighting the benefits of the newly developed analytical approach over classical numerical methodologies.

Impacts of Hydrology and Extreme Events on Dissolved Organic Carbon Dynamics in a Heavily Urbanized Estuary and Its Major Tributaries: A View From Space

AbstractDissolved organic matter and its colored component, Colored Dissolved Organic Matter (CDOM), play a major role in global carbon budgets, and their fluxes provide an essential link between terrestrial and aquatic biogeochemical cycles. Satellite observations can uniquely capture the hydro‐biogeochemical connectivity of terrestrial and aquatic landscapes, across scales. Yet, accurate satellite retrievals of CDOM and dissolved organic carbon (DOC) dynamics remain challenging in urbanized estuaries and coasts. Here, we present an advanced unified algorithm for space‐based retrieval of coastal CDOM and DOC dynamics and its application in Long Island Sound—one of the world's most heavily urbanized estuaries that is becoming increasingly vulnerable to climate change stressors. A rich bio‐optical data set, encompassing a wide range of environmental conditions, was integrated into the algorithm training to retrieve DOC concentrations and CDOM spectral shape (i.e., spectral slope S275–295)—a proxy for DOC quality. The new algorithms were applied to full‐resolution satellite imagery from the Sentinel‐3 Ocean and Land Color Instrument (OLCI) after thoroughly evaluating the performance of six ocean color atmospheric correction approaches (ACOLITE, BAC, C2RCC, MUMM, l2gen, and Polymer). Evaluation of the algorithms yielded mean absolute percent differences of 28%, 12%, and 10% for aCDOM(300), S275–295, and DOC, respectively. Application of the algorithms to multi‐year satellite OLCI imagery captured, for the first time, the coupled impact of seasonal transitions, wind regimes, freshwater inputs, anthropogenic disturbances, and hydrological extremes (both intense precipitation and droughts) on DOC fluxes and CDOM quality at the ecosystem scale. Results have important implications for improved predictions of coastal biogeochemical fluxes in complex urban−estuary systems.

Investigating the Global Performance of the BDS-2 and BDS-3 Joint Real-Time Undifferenced and Uncombined Precise Point Positioning Using RTS Products from Different Analysis Centers

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.

SISRE of BDS-3 MEO: Evolution as well as Comparison between D1 and B-CNAV (B-CNAV1, B-CNAV2) Navigation Messages

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%.

Solar Radiation Gridded Satellite data comparison in Gran Canaria Island

During the last years solar energy has been increasing the percentage of the total energy production around the world and it is expected it persists growing notably [1]. In insular grids, such as Canary Islands, the knowledge of solar radiation behaviour is one of the most important variables in order to ensure the stability for power systems. In this paper we study the suitability of Gridded Satellite data for modelling solar radiation for both PV and CSP purposes. The analysis and comparison is performed using hourly Global and Direct Solar radiation from the satellite model CM SAF database and four ground measurement stations in Gran Canaria. This study could give us a better knowledge of solar radiation behavior in a wide spatial and temporal coverage. Moreover, an accurate satellite radiation data could improve solar radiation forecasting for power systems manage systems [2].

Validation of long arc orbit determination method based on orbital residuals analysis and determination of coordinates of Chinese SLR stations using the LAGEOS satellites

Satellite Laser Ranging (SLR) technology is one of the main technologies in the field of space geodesy, it has played an extremely important role in laser ranging data application and research. As a commonly used geodynamic satellites, the main contribution of LAGEOS and LAGEOS-2 is the solution of orbit determination and station coordinates. At present, there are 8 analysis centers of the International Laser Ranging Service (ILRS) to release the precise orbit products for the two LAGEOS satellites. However, there is currently no relevant research on the analysis of the consistency of these orbits. So, the authors would evaluate the accuracies of them, and the results show that the orbital accuracies of the two LAGEOS satellites are 3 ∼ 5 cm. SLR is regarded as one of the important input data of the International Terrestrial Reference Frame (ITRF), the analysis center of ILRS provides weekly solutions of station coordinates for ITRF. But, due to the limitation of SLR observation conditions, for example most observations of Chinese SLR stations can be made at night, and laser ranging test cannot be conducted in rainy days, the orbit solution of the seven-day arc may have the problem of less data. Therefore, this paper proposed a method for computing the station coordinates based on long arc orbit determination, and we developed the LAODGEO software (Long Arc Orbit Determination Software for Geodynamic Satellite), which is used to solve the orbits of two LAGEOS satellites and station coordinates of five SLR stations in China. The results show that the obtained orbital precision is basically superior to 3.70 cm, and the 3DRMS values between station coordinates solved by us and the coordinates published by SLRF2014 are mostly smaller than 0.013 m, which is consistent with research results domestic and overseas.