Search Results (30)

A satellite laser ranging (SLR) system uses lasers to measure the range from ground stations to space objects with millimeter-level precision. Recent advances in SLR systems have increased their use in space surveillance and tracking (SST). The problem we are addressing, the precise orbit determination (POD) using one-dimensional range observations within a single arc, is challenging owing to infinite solutions because of limited observability. Therefore, general orbit determination algorithms struggle to achieve reasonable accuracy. The proposed algorithm redefines the cost value for orbit determination by leveraging residual tendencies in the POD process. The tendencies of residuals are quantified as R-squared values using Fourier series fitting to determine velocity vector information. The algorithm corrects velocity vector errors through the grid search method and least squares (LS) with a priori information. This approach corrects all six dimensions of the state vectors, comprising position and velocity vectors, utilizing only one dimension of the range observations. Simulations of three satellites using real data validate the algorithm. In all cases, the errors of the two-line element data (three-dimensional position error of 1 km and velocity error of 1 m/s, approximately) used as the initial values were reduced by tens of meters and the cm/s level, respectively. The algorithm outperformed the general POD algorithm using only the LS method, which does not effectively reduce errors. This study offers a more efficient and accurate orbit determination method, which improves the safety, cost efficiency, and effectiveness of space operations. Full article

The Haiyang-2D (HY2D) satellite is the fourth ocean dynamics environment monitoring satellite launched by China. The satellite operates on a re-entry frozen orbit, which necessitates orbital maneuvers to maintain its designated path once the satellite’s sub-satellite point deviates beyond a certain threshold. However, the execution of orbit maneuvers presents a significant challenge to the field of Precise Orbit Determination (POD). The thesis selects the on-board GPS data of HY2D satellite in December 2023 and five maneuvering days of that year. Employing a multifaceted approach that includes the assessment of observational data quality, orbit overlap, external orbit validation, and SLR (Satellite Laser Ranging) verification, the research delves into precise orbit determination during both maneuver and non-maneuver periods. The results indicate that: (1) The average number of satellites tracked by the receiver is 6.4; (2) During the non-maneuver periods, the average RMS (Root Mean Square) value of the radial difference in the 6-h overlapping arc segment is 0.66 cm, and the three-dimensional position difference is about 1.16 cm; (3) When compared with the precision science orbits (PSO) provided by CNES (Centre National d’Études Spatiales), the average values of the RMS values of the differences in the radial (R), transverse (T), and normal (N) directions during the non-maneuver and maneuver periods are respectively 1.32 cm, 2.31 cm, 1.92 cm and 3.04 cm, 8.78 cm, 2.72 cm. (4) The SLR verification of the orbit revealed a residual RMS of 2.24 cm. This suggests that by incorporating the modeling of maneuver forces during the maneuver periods, the impact of orbital maneuvers on orbit determination can be mitigated. Full article

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. Full article

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. Full article

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

As an essential infrastructure that provides positioning, navigation, and timing services, China constructed the BeiDou Navigation Satellite System (BDS). The last BDS satellite was launched in June 2020, which represents the completion of BDS. BDS’s constellation consists of Medium Earth Orbit (MEO), Inclined Geosynchronous Orbit (IGSO), and Geostationary Orbit satellites. The precise modeling of non-conservative forces for BDS satellites is a challenging task. As an independent observation, Satellite Laser Ranging (SLR) is an important validation method of GNSS orbit modeling. In this paper, we validated the precise orbit products of different Analysis Centers (ACs) by using SLR observations, focusing on the BDS orbit modeling. By comparing BDS precise orbit products generated by four ACs with respect to SLR observations for the period of February 2017 to March 2021, we proved that an obvious satellite signature effect exists in the SLR residuals of BDS observed by multi-photon stations. The result indicates that multi-photon stations have a root mean square (RMS) of SLR residuals about 5 mm lower than that of single-photon detectors. The slope of SLR residuals with regard to nadir angle of IGSO satellites for single-photon and multi-photon stations is −2.0 and −2.5 mm/deg, respectively, while the slope of MEO satellites for these stations is about −0.6 to −0.3 and −1.0 to −0.4 mm/deg, respectively. To assess the effect of non-conservative force modeling, we selected seven high-performing stations, including five single-photon and two multi-photon stations. By comparing the SLR residuals of four ACs’ orbits, we analyzed the effect of the solutions of orbit processing, especially solar radiation pressure (SRP) models. We found that some centers may have modeling defects, including BDS-3 orbits of the Deutsches GeoForschungsZentrum and BDS-2 orbits of the European Space Agency, inferred from the large RMS of SLR residuals. Modeling the SRP of BDS satellites is challenging, while an appropriate prior box-wing model can improve the accuracy of SRP modeling and provide a more stable performance. Full article

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. Full article

Haiyang-2D (HY-2D) is the fourth satellite in the marine dynamic satellite series established by China. It was successfully launched on 19 May 2021, marking the era of the 3-satellite network in the marine dynamic environment satellite series of China. The satellite’s precision orbit determination (POD) and validations are of great significance for ocean warning and marine altimetry missions. HY-2D is equipped with a laser reflector array (LRA), a satellite-borne Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) receiver, and a satellite-borne dual-frequency GPS receiver named HY2 that was independently developed in China. In this paper, the quality of GPS data collected by the HY2 is analyzed based on indicators such as the multipath effect, cycle slips, and data completeness. The results suggest that the receiver can be used in POD missions involving low-Earth-orbit (LEO) satellites. The precise orbits of HY-2D are determined by the reduced-dynamics (RD) method. Apart from POD, validation of orbit accuracy is another important task for LEO POD. Therefore, two external validation methods are proposed, including carrier differential validation using one GPS satellite and inter-satellite differential validation using two GPS satellites. These are based on space-borne carrier-phase data, and the GPS satellites used for POD validation do not participate in orbit determination. The results of SLR range validation cannot illustrate the orbit accuracy in x, y, and z directions particularly, so to make validation results more intuitive, the SLR three-dimensional (3D) validation is proposed based on SLR range validation, and the RMSs in x, y, and z directions are 2.66, 3.32, and 2.69 cm, respectively. The results of SLR 3D validation are the same as those of SLR range validation, which proves that the new external validation method provided by SLR 3D is reliable. The RMSs of carrier differential validation and inter-satellite differential validation are 0.68 and 1.06 cm, respectively. The proposed validation methods are proved to be reliable. Full article

Low Earth Orbit (LEO) satellites can be used for remote sensing and gravity field recovery, while precise orbit determination (POD) is vital for LEO satellite applications. However, there are some systematic errors when using the LEO satellite orbits released by different agencies in multi-satellite-based applications, e.g., Swarm and Gravity Recovery and Climate Experiment-Follow-On (GRACE-FO), as different GNSS precise orbit and clock products are used as well as processing strategies and software. In this paper, we performed undifferenced kinematic PODs for Swarm and GRACE-FO satellites simultaneously over a total of 14 days by using consistent International Global Navigation Satellite System (GNSS) Service (IGS) precise orbit and clock products. The processing strategy based on an undifferenced ionosphere-free combination and a least squares method was applied for Swarm and GRACE-FO satellites. Furthermore, the quality control for the kinematic orbits was adopted to mitigate abrupt position offsets. Moreover, the accuracy of the kinematic orbits solution was evaluated by carrier phase residual analysis and Satellite Laser Ranging (SLR) observations, as well as comparison with official orbits. The results show that the kinematic orbits solution is better than 4 cm, according to the SLR validation. With quality control, the accuracy of the kinematic orbit solution is improved by 2.49 % for the Swarm-C satellite and 6.98 % for the GRACE-D satellite when compared with their precise orbits. By analyzing the accuracy of the undifferenced kinematic orbit solution, the reliability of the LEO orbit determination is presented in terms of processing strategies and quality control procedures. Full article

The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou Navigation Satellite System (BDS-2), for which apparent deficiencies of non-conservative models are identified and evidenced in the Satellite Laser Ranging (SLR) residuals. The orbit errors derived from the empirical 5-parameter Extended CODE Orbit Model (ECOM) as well as a semi-analytical adjustable box-wing model show prominent dependency on the Sun elongation angle, even in the yaw-steering attitude mode. Hence, a periodic acceleration in the normal direction of the +X surface, presumably generated by the mismodeled thermal radiation pressure, is introduced. The SLR validations reveal that the Sun elongation angle-dependent systematic errors were significantly reduced, and the orbit accuracy was improved by 10–30% to approximately 4.5 cm and 3.0 cm for the BDS-2 IGSO and MEO satellites, respectively. Full article

Global navigation services from the quad-constellation of GPS, GLONASS, BDS, and Galileo are now available. The international GNSS monitoring and assessment system (iGMAS) aims to evaluate the navigation performance of the current quad systems under a unified framework. In order to assess impact of orbit and clock errors on the positioning accuracy, the user range error (URE) is always taken as a metric by comparison with the precise products. Compared with the solutions from a single analysis center, the combined solutions derived from multiple analysis centers are characterized with robustness and reliability and preferred to be used as references to assess the performance of broadcast ephemerides. In this paper, the combination method of iGMAS orbit and clock products is described, and the performance of the combined solutions is evaluated by various means. There are different internal precisions of the combined orbit and clock for different constellations, which indicates that consistent weights should be assigned for individual constellations and analysis centers included in the combination. For BDS-3, Galileo, and GLONASS combined orbits of iGMAS, the root-mean-square error (RMSE) of 5 cm is achieved by satellite laser ranging (SLR) observations. Meanwhile, the SLR residuals are characterized with a linear pattern with respect to the position of the sun, which indicates that the solar radiation pressure (SRP) model adopted in precise orbit determination needs further improvement. The consistency between combined orbit and clock of quad-constellation is validated by precise point positioning (PPP), and the accuracies of simulated kinematic tests are 1.4, 1.2, and 2.9 cm for east, north, and up components, respectively. Full article

Satellite laser ranging (SLR) observations provide an independent validation of the global navigation satellite system (GNSS) orbits derived using microwave measurements. SLR residuals have also proven to be an important indicator of orbit radial accuracy. In this study, SLR validation is conducted for the precise orbits of eight Galileo satellites covering four to eight years (the current longest span), provided by multiple analysis centers (ACs) participating in the multi-GNSS experiment (MGEX). The purpose of this long-term analysis (the longest such study to date), is to provide a comprehensive evaluation of orbit product quality, its influencing factors, and the effect of perturbation model updates on precise orbit determination (POD) processing. A conventional ECOM solar radiation pressure (SRP) model was used for POD. The results showed distinct periodic variations with angular arguments in the SRP model, implying certain defects in the ECOM system. Updated SRP descriptions, such as ECOM2 or the Box-Wing model, led to significant improvements in SLR residuals for orbital products from multiple ACs. The standard deviation of these residuals decreased from 8–10 cm, before the SRP update, to about 3 cm afterward. The systematic bias of the residuals was also reduced by 2–4 cm and the apparent variability decreased significantly. In addition, the effects of gradual SRP model updates in the POD were evident in orbit comparisons. Orbital differences between ACs in the radial direction were reduced from the initial 10 cm to better than 3 cm, which is consistent with the results of SLR residual analysis. These results suggest SLR validation to be a powerful technique for evaluating the quality of POD strategies in GNSS orbits. Furthermore, this study has demonstrated that perturbation models, such as SRP, provide a better orbit modeling for the Galileo satellites. Full article

Haiyang-2C (HY-2C) is a dynamic, marine-monitoring satellite that was launched by China and is equipped with an onboard dual-frequency GPS receiver named HY2_Receiver, which was independently developed in China. HY-2C was successfully launched on 21 September 2020. Its precise orbit is an important factor for scientific research applications, especially for marine altimetry missions. The performance of the HY2_Receiver is assessed based on indicators such as the multipath effect, ionospheric delay, cycle slip and data utilization, and assessments have suggested that the receiver can be used in precise orbit determination (POD) missions involving low-Earth-orbit (LEO) satellites. In this study, satellite-borne GPS data are used for POD with a reduced-dynamic (RD) method. Phase centre offset (PCO) and phase centre variation (PCV) models of the GPS antenna are established during POD, and their influence on the accuracy of orbit determination is analysed. After using the PCO and PCV models in POD, the root mean square (RMS) of the carrier-phase residuals is around 0.008 m and the orbit overlap validation accuracy in each direction reaches approximately 0.01 m. Compared with the precise science orbit (PSO) provided by the Centre National d’Etudes Spatiales (CNES), the RD orbit accuracy of HY-2C in the radial (R) direction reaches 0.01 m. The accuracy of satellite laser ranging (SLR) range validation is better than 0.03 m. Additionally, a new method is proposed to verify the accuracy of the RD orbit of HY-2C by using space-borne Doppler orbitography and radiopositioning integrated by satellite (DORIS) data directly. DORIS data are directly compared to the result calculated using the accurate coordinates of beacons and the RD orbit, and the results indicate that the external validation of HY-2C RD orbit has a range rate accuracy of within 0.0063 m/s. Full article

Precise knowledge of the phase center location of the global navigation satellite system (GNSS) antenna is a prerequisite for precise orbit determination (POD) of the low Earth orbit (LEO) satellite. The phase center offset (PCO) and phase center variation (PCV) values for the LEO antenna obtained from ground calibration cannot reflect the error sources encountered in the actual spacecraft environment. PCV corrections are estimated by ionosphere free (IF) carrier phase post-fit residuals of reduced dynamic orbit determination. Ambiguity resolution (AR) plays a crucial role in achieving the best orbit accuracy. The single receiver AR concept is realized using wide-lane (WL) and narrow-lane (NL) bias products. Single difference (SD) observations between satellites are applied to remove the receiver dependent phase bias. SD AR and traditional double difference (DD) AR methods are applied to fix the ambiguities. The recovered SD and DD IF ambiguities are taken as pseudo-observations to constrain the undifferenced IF ambiguity parameters in the POD process. The LEO orbits based on float ambiguity (FA), SD, AR, and DD AR are investigated. One year’s data collected by the Gravity Recovery And Climate Experiment Follow-On (GRACE-FO) mission and GPS precise products provided by the Center for Orbit Determination in Europe (CODE) were analyzed. Precise orbit generated by the Jet Propulsion Laboratory (JPL), independent satellite laser ranging (SLR), and K-band ranging (KBR) measurements were utilized to assess the orbit accuracy. More than 98% of SD WL and 95% of SD NL ambiguities are fixed, which confirms the good quality of the bias products and correctness of the SD AR method. With PCV corrections, the average phase residuals of DD and SD AR solutions are 0.13 and 0.41 mm, which indicates improved consistency between applied models and observations. Compared with JPL’s orbit, the SD AR orbits achieve the accuracy of 6.0, 6.2, and 5.1 mm in along-track, cross-track, and radial directions. The SD AR solutions show an average improvement of 18.3% related to the FA orbits while 6.3% is gained by the DD AR approach. The root mean squares (RMSs) of SLR residuals for FA, DD AR, and SD AR solutions are 11.5, 10.2, and 9.6 mm, which validate the positive effect of AR on POD. Standard deviation (STD) of KBR residuals for SD AR orbits is 1.8 mm while 0.9 mm is achieved by the DD AR method. The explanation is that the phase bias products used for SD AR are not free of errors and the errors may degrade the KBR validation. In-flight PCV calibration and ambiguity resolution improve the LEO orbit accuracy effectively. Full article

The Haiyang 2B (HY-2B) satellite requires precise orbit determination (POD) products for geodetic remote sensing techniques. An improved set of reduced-dynamic (RD) orbit solutions was generated from the onboard Global Positioning System (GPS) measurements over a 14-month period using refined strategies and processing techniques. The key POD strategies include a refined empirical acceleration model, in-flight calibration of the GPS antenna, and the resolution of single-receiver carrier-phase ambiguities. In this study, the potential periodicity of empirical acceleration in the HY-2B POD was identified by spectral analysis. In the along-track direction, a noticeable signal with four cycles per revolution (CPR) was significant. A mixed spectrum was observed for the cross-track direction. To better understand the real in-flight environment, a refined empirical acceleration model was used to cope with the time variability of empirical accelerations in HY-2B POD. Three POD strategies were used for the reprocessing for superior orbit quality. Validation using over one year of satellite laser ranging (SLR) measurements demonstrated a 5.2% improvement in the orbit solution of the refined model. Reliable correction for the GPS antenna phase center was obtained from an over-420-day dataset, and a trend in radial offset change was observed. After application of the in-flight calibration of the GPS antenna, a 26% reduction in the RMS SLR residuals was achieved for the RD orbit solution, and the carrier phase residuals were clearly reduced. The integer ambiguity resolution of HY-2B led to strong geometric constraints for the estimated parameters, and a 15% improvement in the SLR residuals could be inferred compared with the float solution. Full article