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Satellite orientation modelling with quaternions and its impact on BDS-3 PPP-AR
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Ambiguity Resolution in Precise Point Positioning (PPP-AR) is important to achieving high-precision positioning in wide areas. The International GNSS (Global Navigation Satellite System) Service (IGS) and some other academic organizations have begun to provide phase bias products to enable PPP-AR, such as the integer-clock like products by Centre National d’Etudes Spatials (CNES), Wuhan University (WUM) and the Center for Orbit Determination in Europe (CODE), as well as the Uncalibrated Phase Delay (UPD) products by School of Geodesy and Geomatics (SGG). To evaluate these disparate products, we carry out Global Positioning System (GPS)/Galileo Navigation Satellite System (Galileo) and BeiDou Navigation Satellite System (BDS-only) PPP-AR using 30 days of data in 2019. In general, over 70% and 80% of GPS and Galileo ambiguity residuals after wide-lane phase bias corrections fall in ± 0.1 cycles, in contrast to less than 50% for BeiDou Navigation Satellite (Regional) System (BDS-2); moreover, around 90% of GPS/Galileo narrow-lane ambiguity residuals are within ± 0.1 cycles, while the percentage drops to about 55% in the case of BDS products. GPS/Galileo daily PPP-AR can usually achieve a positioning precision of 2, 2 and 6 mm for the east, north and up components, respectively, for all phase bias products except those based on German Research Centre for Geosciences (GBM) rapid satellite orbits and clocks. Due to the insufficient number of BDS satellites during 2019, the BDS phase bias products perform worse than the GPS/Galileo products in terms of ambiguity fixing rates and daily positioning precisions. BDS-2 daily positions can only reach a precision of about 10 mm in the horizontal and 20 mm in the vertical components, which can be slightly improved after PPP-AR. However, for the year of 2020, BDS-2/BDS-3 (BDS-3 Navigation Satellite System) PPP-AR achieves about 50% better precisions for all three coordinate components.
This paper proposes a new positioning accuracy reliability analysis method based on the differential kinematics and saddlepoint approximation to evaluate the influence of kinematic parameter uncertainties on the robotic motion. Firstly, considering the reliability analysis instability caused by complex nonlinear limit state function, the reliability model of positioning accuracy is established based on the differential kinematics and error propagation. Subsequently, the parameters of the position error distribution are deduced analytically to combine with the eigen-decomposition to complete the modeling of the cumulant generating function, thereby the kinematic reliability is yielded according to the saddlepoint approximation method. Finally, the comparative analysis of a six degrees of freedom serial industrial robot is conducted and the results of which demonstrate that the proposed method provides a better performance than the existing methods in terms of accuracy and efficiency for kinematic reliability analysis.
Energetic particles and electromagnetic radiation (EM) from solar events and galactic cosmic rays can bombard and interact with satellites' exposed surfaces, and sometimes possess enough energy to penetrate their surface. Among other known effects, the scenario can cause accelerated orbit decay due to atmospheric drag, sporadic and unexplainable errors in functions of sensitive parts, degradation of critical properties of structural materials, jeopardy of flight worthiness, transient and terminal health hazard to both onboard passengers and astronauts, and sometimes a catastrophic failure that can abruptly end satellite mission. The understanding of the dynamics of the space radiation environment and associated effects is critically important for satellites design and operation in ionospheric plasma environment, in which satellites are designed to function. In this chapter we review some satellite anomalies associated with the space radiation environment and conclude with mitigation effort that can reduce such impact.
The PRIDE Lab at GNSS Research Center of Wuhan University has developed an open-source software for GPS precise point positioning ambiguity resolution (PPP-AR) (i.e., PRIDE PPP-AR). Released under the terms of the GNU General Public License version 3 (GPLv3, http://www.gnu.org/licenses/gpl.html), PRIDE PPP-AR supports relevant research, application and development with GPS post-processing PPP-AR. PRIDE PPP-AR is mainly composed of two modules, undifferenced GPS processing and single-station ambiguity resolution. Undifferenced GPS processing provides float solutions with wide-lane and narrow-lane ambiguity estimates. Later, single-station ambiguity resolution makes use of the phase clock/bias products, which are released also by the PRIDE Lab at ftp://pridelab.whu.edu.cn/pub/whu/phasebias/, to recover the integer nature of single-station ambiguities and then carry out integer ambiguity resolution. PRIDE PPP-AR is based on a least-squares estimator to produce daily, sub-daily or kinematic solutions for various geophysical applications. To facilitate the usage of this software, a few user-friendly shell scripts for batch processing have also been provided along with PRIDE PPP-AR. In this article, we use 1 month of GPS data (days 001–031 in 2018) to demonstrate the performance of PRIDE PPP-AR software. The PRIDE Lab is committed to consistently improve the software package and keep users updated through our website.
The yaw mode history of BDS-2 IGSO/MEOs since 2016 is inferred from reverse kinematic precise point positioning. Experimental results show that C06 (IGSO-1) and C14 (MEO-6) satellites have abandoned the orbit-normal (ON) attitude mode in favor of continuous yaw-steering (CYS) mode since March and September 2017, respectively. BDS C13 (IGSO-6), launched in March 2016, and C16 (IGSO-7) always adopt the CYS mode during eclipse seasons. The majority of BDS-2 IGSO/MEOs still experience attitude switches between nominal and ON mode. Most of the attitude switches from nominal to ON mode take place when the sun elevation angle above the orbital plane (β angle) decreases below 4° \((\left| \beta \right| < 4^\circ )\). A few switches also occur for \(\left| \beta \right|\) slightly above 4°. However, most of the attitude switches from ON to nominal mode are undertaken when \(\left| \beta \right|\) increases to above 4°, but a few switches with \(\left| \beta \right|\) just below 4° happen. The exact switch condition between the two attitude modes is presented in this study. For BDS-2 IGSO/MEOs using the CYS mode, the yaw-attitude model previously established by the Wuhan University (indicated by WHU model) can basically reproduce their yaw maneuvers. However, reverse midnight-turn maneuvers occasionally occur for C13 and C14 for β angles falling into the range \((0^\circ ,0.14^\circ )\). This discrepancy in the form of a reversal in the yaw direction during the noon-turn maneuvers is first observed for C13 and C14 when the β angle is in the range of \(( - \,0.14^\circ ,0^\circ )\). The mismodeling of the satellites attitudes during reverse yaw maneuvers significantly degrades the performance of BDS precise orbit determination (POD). The phase observation residuals extracted from BDS POD reach 40 cm, which thereby leads to the misidentification of a substantial number of observations around orbital midnight and noon points as outliers when the WHU model is applied in our experiments. The WHU model is modified to reproduce the reverse yaw maneuvers of satellites in the post-processing BDS POD. The derived phase residuals decrease to normal levels, and the clock solutions become smoother relative to solutions employing the WHU model.
Five new-generation BeiDou-3 experimental satellites, called BeiDou-3e, have been launched into inclined geosynchronous orbit (IGSO) and medium orbit (MEO) since March 2015. In addition to newly designed signals and intersatellite links, different satellite buses, updated rubidium atomic frequency standards (RAFSs), and new passive hydrogen masers (PHMs) have been used. Using 15 stations, mainly in the Asia–Pacific region, we determined orbits and clock for both the BeiDou-3e and the regional BeiDou-2 satellites using the Extend CODE (Center for Orbit Determination in Europe) Orbit Model (ECOM). The orbit consistency, indicated by 3D orbit boundary discontinuity, is 50–70 and 40–60 cm for BeiDou-3e IGSO and MEO satellites, respectively, and better than 15 cm in radial component. Satellite laser ranging (SLR) validation gives about 17 and 10 cm for BeiDou-3e IGSO and MEO satellites. The BeiDou-3e satellites orbits show slightly better performance than the BeiDou-2 satellites as indicated by SLR. However, errors depending on the sun elongation angle were identified in SLR residuals for the BeiDou-3e IGSO C32 satellite, while such errors did not exist for BeiDou-2 IGSO/MEO and BeiDou-3e MEO satellites. No orbit accuracy degeneration for BeiDou-3e IGSO and MEO satellites was observed when the elevation angle (β angle) of the sun above the orbital plane was between − 4° and + 4°. In that case, the BeiDou-2 IGSO and MEO satellites are in orbit normal (ON) mode. An analysis of the yaw attitude identified that BeiDou-3e satellites did not use the ON mode, but experienced midnight- and noon-point maneuvers when the β angle is approximately between − 3° and + 3°. Compared with BeiDou-2 satellites, the onboard clocks of the BeiDou-3e IGSO satellites showed dramatic improved performance. The stability of BeiDou-3e IGSO satellites can be compared to the latest type of RAFSs employed onboard the GPS IIF satellites as well as the PHMs used onboard the Galileo satellites.
It is well known that the attitude of GNSS satellites during eclipse seasons suffers from inexact or deficient modeling. The consequences of these errors are limited but there is some impact on the measurement residuals and this partly affects the orbit quality of eclipsing satellites. In addition, it is important to have consistent models between the different Analysis Centers (ACs) in order to construct reliable combined solutions, specifically for the clocks. The IGS ACs have generally adopted specific and as realistic as possible attitude modeling to lower the effects of these errors (e.g., Kouba’s attitude laws, Dilssner’s estimated yaw rate from measurements,…). Still, we observe today noticeable differences in the clock estimates provided by the ACs during eclipses. The situation is complicated by the combination with new constellations (MGEX) and the increasing number of different attitude laws for all these GNSS. At the IGS Multi-GNSS Working Group Splinter Meeting of the EGU this year, it was decided to propose a format to exchange the attitude quaternions used to build the other delivered products (orbits/clocks). This work presents the proposed exchange format as well as a comparison of attitude laws used by different ACs. This format allows disseminating, together with the classical orbit and clock products, the attitude used to generate the products instead of leaving this assumption to users for PPP and other applications. Importantly, this format would allow comparison and future improvement of GNSS attitude modeling for all ACs and IGS users.
This article discusses the attitude modes employed by present Global (and Regional) Navigation Satellite Systems (GNSSs) and the models used to describe them along with definitions of the constellation-specific spacecraft body frames. A uniform convention for the labeling of the principal spacecraft axes is proposed by the International GNSS Service (IGS), which results in a common formulation of the nominal attitude of all GNSS satellites in yaw-steering mode irrespective of their specific orbit and constellation. The conventions defined within this document provide the basis for the specification of antenna phase center offsets and variations in a multi-GNSS version of the IGS absolute phase center model in the ANTEX (antenna exchange) format. To facilitate the joint analysis of GNSS observations and satellite laser ranging measurements, laser retroreflector array coordinates consistent with the IGS-specific spacecraft frame conventions are provided in addition to representative antenna offset values for all GNSS constellations.
Precise knowledge and consistent modeling of the yaw-attitude of GNSS satellites are essential for high-precision data processing and applications. As the exact attitude control mechanism for the satellites of the BeiDou Satellite Navigation System (BDS) is not yet released, the reverse kinematic precise point positioning (PPP) method was applied in our study. However, we confirm that the recent precise orbit determination (POD) processing for GPS satellites could not provide suitable products for estimating BDS attitude using the reverse PPP because of the special attitude control switching between the nominal and the orbit-normal mode. In our study, we propose a modified processing schema for studying the attitude behavior of the BDS satellites. In this approach, the observations of the satellites during and after attitude switch are excluded in the POD processing, so that the estimates, which are needed in the reverse PPP, are not contaminated by the inaccurate initial attitude mode. The modified process is validated by experimental data sets and the attitude yaw-angles of the BDS IGSO and MEO satellites are estimated with an accuracy of better than 9∘. Furthermore, the results confirm that the switch is executed when the Sun elevation is about 4∘ and the actual orientation is very close to its target one. Based on the estimated yaw-angles, a preliminary attitude switch model was established and reintroduced into the POD, yielding to a substantial improvement in the orbit overlap RMS.
This chapter provides an introduction to the Galileo program and architecture. It starts by presenting the program context, rationale and history, including the early definition phases and test beds and the GIOVE experimental satellites. It then presents an overview of the Galileo services. Later, an architectural overview is provided, including the Galileo segments: the Space Segment, the Ground Mission Segment, and the Ground Control Segment. The chapter also provides a description of Galileo’s contribution to the Search And Rescue services through COSPAS/SARSAT, and finalizes with an overview of the user segment and highlighting interoperability and compatibility issues with other GNSS.
Results of the estimation of azimuth-dependent phase center variations (PCVs) of GPS satellite antennas using global GPS data
are presented. Significant variations of up to ±3–4mm that are demonstrated show excellent repeatability over eight years.
The application of the azimuthal PCVs besides the nadir-dependent ones will lead to a further reduction in systematic antenna
effects. In addition, the paper focuses on the benefit of a possible transition from relative to absolute PCVs. Apart from
systematic changes in the global station coordinates, one can expect the GPS results to be less dependent on the elevation
cut-off angle. This, together with the significant reduction of tropospheric zenith delay biases between GPS and VLBI, stands
for an important step toward more consistency between different space geodetic techniques.
In Global Positioning System (GPS) data analyses, large networks are usually divided into sub-networks to solve the conflict between increasing amounts of data and limited computer resources, although an integrated analysis would provide better results. This conflict becomes even more critical with the increasing number of stations, and low-Earth-orbiting satellites and the Galileo system coming into operation. The major reason is that a huge number of ambiguity parameters are kept in the normal equation for sequential integer ambiguity fixing. In this paper, the problem is solved by a special procedure of parameter elimination for both real-valued and ambiguity-fixed solutions, based on an adapted ambiguity-fixing approach where the covariance-matrix of ambiguity parameters is not required anymore. It is demonstrated that, with the new strategy, the required memory can be reduced to one-tenth and the computation time to at least one-third compared to the existing methods, and huge GPS networks with several hundred stations can be processed efficiently on a personal computer.
Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle biases (FCBs) have been separated from the integer ambiguities in a network solution. One method to achieve these products is to estimate the FCBs by averaging the fractional parts of the float ambiguity estimates, and the other is to estimate the integer-recovery clocks by fixing the undifferenced ambiguities to integers in advance. In this paper, we theoretically prove the equivalence of the ambiguity-fixed position estimates derived from these two methods by assuming that the FCBs are hardware-dependent and only they are assimilated into the clocks and ambiguities. To verify this equivalence, we implement both methods in the Position and Navigation Data Analyst software to process 1 year of GPS data from a global network of about 350 stations. The mean biases between all daily position estimates derived from these two methods are only 0.2, 0.1 and 0.0 mm, whereas the standard deviations of all position differences are only 1.3, 0.8 and 2.0 mm for the East, North and Up components, respectively. Moreover, the differences of the position repeatabilities are below 0.2 mm on average for all three components. The RMS of the position estimates minus those from the International GNSS Service weekly solutions for the former method differs by below 0.1 mm on average for each component from that for the latter method. Therefore, considering the recognized millimeter-level precision of current GPS-derived daily positions, these statistics empirically demonstrate the theoretical equivalence of the ambiguity-fixed position estimates derived from these two methods. In practice, we note that the former method is compatible with current official clock-generation methods, whereas the latter method is not, but can potentially lead to slightly better positioning quality.
Networks of dozens to hundreds of permanently operating precision Global Positioning System (GPS) receivers are emerging at spatial scales that range from 10(exp 0) to 10(exp 3) km. To keep the computational burden associated with the analysis of such data economically feasible, one approach is to first determine precise GPS satellite positions and clock corrections from a globally distributed network of GPS receivers. Their, data from the local network are analyzed by estimating receiver- specific parameters with receiver-specific data satellite parameters are held fixed at their values determined in the global solution. This "precise point positioning" allows analysis of data from hundreds to thousands of sites every (lay with 40-Mflop computers, with results comparable in quality to the simultaneous analysis of all data. The reference frames for the global and network solutions can be free of distortion imposed by erroneous fiducial constraints on any sites.
A review of advanced fault detection and diagnosis (FDD) techniques in attitude control systems (ACSs) of spacecraft is presented. In the first part of the paper, several types of ACS failure scenarios with their practical solutions are presented. Next, the existing approaches to FDD are considered and classified based on different criteria, including applications and design techniques. The literature of this part showed that to enhance ACS operational safety, predictability of failure of an ACS and/or of its components as well as reducing the possibility of failure occurrence is imperative. In addition, fast FDD of various kinds of failures is necessary to guarantee the required reliability of an ACS. The second part of this study highlights challenges involved with different FDD approaches, emphasizing their practical applicability. Current research gaps in FDD techniques such as insensitive residual signal, process monitoring methods, accurate plant model design, easy-to-use software development, FDD tuning process, dealing with noisy sensor measurements, time taken for fault management, the sensitivity of FDD system to faults, and FDD robustness are further elaborated on. Subsequently, the state-of-the-art FDD and its future needs are reflected on. The results of this study could direct spacecraft manufacturers and ACS providers to focus on future needs and improve ground testing for enhanced operational reliability and redundancy.
Broadcasting the multi-frequency signals is one of the outstanding advantages of BDS-3 (BeiDou Navigation Satellite System). In addition to the legacy signals B1I and B3I, we are interested in the performance of two new signals B1C and B2a. For the purpose of improving the orbit accuracy of BDS-3 backbone MEOs (Medium Earth Orbits), this study focuses on Precise Orbit Determination (POD) using B1C/B2a dual-frequency measurements. First, the performance of POD will be benefit from an increasing observation quantity and qualities. Observations from the public MGEX (Multi-GNSS Experiment) network are statistically collected, and the number of stations able to track B1C and B2a signals is analyzed. In recent years, the sustainable growth number of stations is up to more than one hundred, which brings the new chance to improve the POD accuracy based on B1C/B2a linear combination. Then, the multipath and post-fit residuals of observations are compared between B1C/B2a and B1I/B3I to investigate the observation qualities. Second, as a key strategy, the ambiguities are successfully fixed during POD processing of BDS-3 MEOs. The ambiguity fixing percentage is as high as 93.1% on average using B1C/B2a combination. Compared with float solutions, the improvements of ambiguity fixed orbits reach 36.2%, 19.9% and 36.6% on the radial, along-track and cross-track components, respectively. For the fixed solutions of B1I/B3I and B1C/B2a, it is noticed that the orbits achieve further benefits from B1C/B2a combination for 8.4%, 6.9% and 8.0% on the radial, along-track and cross-track components, respectively. Finally, the performance of B1C/B2a combination POD is validated by orbital overlapping, the orbit signal-in-space range error (SISRE) analysis, independent technology Satellite Laser Ranging (SLR) and Precise Point Positioning (PPP), respectively. SLR residuals show the radial orbital accuracy has an improvement of 8.0% for C20, C21, C29 and C30 on average when employing B1C/B2a measurements. Compared with B1I/B3I, both static and kinematic PPP based on B1C/B2a orbits indicate the improvement on the vertical component. And a faster and more stable convergence performance is also observed using B1C/B2a combination.
With the completion of the BeiDou Global Navigation Satellite System (BDS-3), more available frequencies have brought opportunities for precise point positioning ambiguity resolution (PPP-AR). This research theoretically deduced the multi-frequency PPP-AR model and the rule of observable-specific signal bias (OSBs) transformation. Then 34 International GNSS Service stations were selected to investigate the multi-frequency BDS-3 and multi-GNSS PPP-AR. The results suggested that the OSBs products provided by Centre National D'Etudes Spatiales (CNES) have absorbed the impact of inter-frequency clock bias and could be directly added to the original observations to restore the integer characteristics of the multi-frequency ambiguity. Meanwhile, the antenna phase center correction should keep consistent when using the CNES OSBs to restore the Melbourne-Wübbena ambiguity. The BDS-3 quad-frequency ambiguity-fixed convergence time was 39.0 and 25.1 min for kinematic and static PPP, which was shortened by nearly 15.0 and 3.4 min than the dual-frequency ambiguity-fixed solution. The quad-system multi-frequency PPP-AR showed the optimal state, which was 0.66, 0.76 and 2.66 cm for kinematic mode while 0.31, 0.31 and 1.02 cm for static mode in east, north, and up directions, respectively.
An intra-system bias (ISB) is a necessary parameter in the BeiDou Navigation Satellite System (BDS)-2 and BDS-3 integrated precise point positioning (PPP); however, its influence in BDS-2/BDS-3 combined processing remains unclear. This paper investigates the ISB effects on the combined PPP using different precise orbit and clock products. Considering an increasing number of BDS products, a comprehensive evaluation of the products is undertaken before validating with PPP tests. Results indicate that BDS-2 Wuhan University (WUM) orbital differences outweigh Centre National d’Etudes Spatiales (CNT), Shanghai Observatory (SHA), and Information and Analysis Center (IAC) orbits. Moreover, BDS-3 constellation registers better clock performance than BDS-2 using any MGEX product. Furthermore, introducing the ISB into the combined processing of BDS-2 and BDS-3 improves both the positioning performance and convergence time for all products. The best improvement in positioning performance is achieved when Deutsches GeoForschungsZentrum (GBM) product is employed. Finally, it is found that considering the ISB in the PPP model affects the code more than the phase observations.
An effective sensor network with an appropriate sensor configuration is the first step of model updating to obtain the actual structural response. However, sensor placements based on inherent structural characteristics (such as mode shapes) alone or their optimizations only with deterministic data are unlikely to provide very good results. Therefore, using a non-probabilistic theory to characterize the uncertainty in the uncertainty propagation process for model updating, this study proposes a time-dependent, reliability-based method for the optimal load-dependent sensor placement considering multi-source uncertainties. Due to the limitations of the uncertain parameters obtained using probabilistic or statistical methods, the uncertainties tackled in this study that includes those from structural properties and measurement processes are regarded as interval variables. Using the first-passage theory in the overall time history, different crossing situations of the reduced time history responses (that is, the modal coordinates) with respect to the full ones are constructed. The difference between the modal coordinates of the reduced and the full models is defined as the objective of the optimization, which indicates the matching level. Based on the time-dependent reliability-based index and the errors of deterministic modal coordinates between the reduced and full models, the multi-objective optimization is solved using NSGA-II. A detailed flowchart of the proposed method is given, and its effectiveness is verified by two simulated engineering examples for model updating.
The orientation of GNSS satellites in space is a key quantity in GNSS data processing. It is required to correctly apply several force models and observation corrections. Incorrect or insufficient modeling of satellite attitude can lead to inconsistencies both among providers of GNSS products and between providers and users, which negatively affects the quality of combined products and positioning solutions. Exchanging satellite attitude information in the form of quaternions helps to eliminate or reduce those inconsistencies. This study presents the first systematic exchange of attitude data in a common format (called ORBEX) within the International GNSS Service (IGS). A comparison of attitude auxiliary data from seven IGS analysis centers over a one-year period shows significant differences for GPS and GLONASS satellites, but not for Galileo. These differences are mostly confined to eclipse periods but can reach up to 180°. Considering the attitude differences between analysis center solutions in an experimental clock combination significantly improved the consistency of analysis center solutions during eclipse periods. A kinematic PPP analysis covering ten globally distributed stations over one week resulted in an almost unanimous improvement when using the provided satellite attitude instead of a nominal model, with an average RMS reduction of 50% in the east and up components. The results presented in this study show that satellite attitude is important GNSS auxiliary data and making it available benefits both providers and users.
The greatest concentration of spacecraft and space debris resides in an orbital band between 100 and 2000 km altitude, classified as low‐Earth orbit (LEO). Of these space objects, those below about 1000 km all experience an appreciable drag force due to the presence of Earth's atmosphere. It has been a common approach to use LEO spacecraft orbital behavior to extract upper atmosphere properties and then reapply this atmosphere description to predict future spacecraft behavior using orbit propagators. This approach leads to mutual coupling between spacecraft response and atmosphere change that results in convoluted uncertainties. To unravel such interdependencies, a physical description of the LEO space environment and how it changes due to external influences is required independently of the physical description for atmosphere‐spacecraft interactions. The main challenge lies in attributing how much of the orbital perturbation is the result of changes in the upper atmosphere versus changes in a satellite's ballistic coefficient. Today, greater fidelity in space environment specification is required for LEO spacecraft operations, collision avoidance procedures, and space environment forecasting. This chapter highlights the remaining issues by segmenting the LEO drag environment into a lower and upper register, and describing separately the LEO environment and gas‐surface interaction in each register. In addition, advances in solar and geomagnetic drivers for improved density specification are described.
The inter-receiver pseudorange biases exist between receivers equipping with different front-end designs and correlator types. It is distinguishable from differential code biases and would affect Global Navigation Satellite System (GNSS) estimations if it is not taken into account in data processing. In this contribution, the effects of inter-receiver pseudorange biases on the regional BeiDou navigation satellite system (BDS-2) satellite precise orbit determination (POD) will be investigated. For validation purposes, 35 globally distributed Multi-GNSS Experiment ground stations for which the receivers are from three manufacturers were used to determine the precise orbits of BDS-2 satellites from day of year 154 to 163, 2017. The accuracy of orbit overlap and satellite laser ranging (SLR) residual validation comparisons show that by implementing inter-receiver pseudorange bias corrections, the POD accuracies of the BDS-2 satellites can be effectively improved. The root mean square errors of 24-h precise orbit determination overlap corresponding to the radial cross-track, and along-track components are improved by 1.4%, 2.7%, and 12.7%, respectively, after correcting the inter-receiver pseudorange biases. The standard deviations of the SLR residuals of satellite C01, C13, and C11 are reduced from 30.7, 7.1, and 3.5 cm to 30.2, 6.8, and 2.9 cm, respectively. The results also showed that inter-receiver pseudorange biases will cause an along-track bias in Geostationary Earth Orbit (GEO) satellite orbit determination. The performances of GEO POD in along-track component can be improved by considering the inter-receiver pseudorange biases.
Techniques enabling precise point positioning with ambiguity resolution (PPP-AR) were developed over a decade ago. Several analysis centers of the International GNSS Service (IGS) have implemented such strategies into their software packages and are generating (experimental) PPP-AR products including satellite clock and bias corrections. While the IGS combines individual orbit and clock products as standard to provide a more reliable solution, interoperability of these new PPP-AR products must be confirmed before they can be combined. As a first step, all products are transformed into a common observable-specific representation of biases. It is then confirmed that consistency is only ensured by considering both clock and bias products simultaneously. As a consequence, the satellite clock combination process currently used by the IGS must be revisited to consider not only clocks but also biases. A combination of PPP-AR products from six analysis centers over a one-week period is successfully achieved, showing that alignment of phase clocks can be achieved with millimeter precision thanks to the integer properties of the clocks. In the positioning domain, PPP-AR solutions for all products show improved longitude estimates of daily static positions by nearly 60% over float solutions. The combined products generally provide equivalent or better results than individual analysis center contributions, for both static and kinematic solutions.
A consistent analysis of signal-in-space ranging errors (SISREs) is presented for all current satellite navigation systems, considering both global average values and worst-user-location statistics. The analysis is based on 1 year of broadcast ephemeris messages of the Global Positioning System (GPS), GLONASS, Galileo, BeiDou and QZSS collected with a near-global receiver network. Position and clock values derived from the navigation data are compared against precise orbit and clock products provided by the International GNSS Service and its multi-GNSS experiment. Satellite laser ranging measurements are used for a complementary and independent assessment of the orbit-only SISRE contribution. The need for proper consideration of antenna offsets is highlighted and block-/constellation-specific radial antenna offset values for the center-of-mass correction of broadcast orbits are derived. Likewise, the need for application of differential code biases in the comparison of broadcast and precise clock products is emphasized. For GPS, the analysis of the legacy navigation message is complemented by a discussion of the CNAV message performance based on the first CNAV test campaign in June 2013. Global average SISRE values for the individual constellations amount to 0.7 ± 0.02 m (GPS), 1.5 ± 0.1 m (BeiDou), 1.6 ± 0.3 m (Galileo), 1.9 ± 0.1 m (GLONASS), and 0.6 ± 0.2 m (QZSS) over a 12-month period in 2013/2014.
The observed carrier phase in the Global Positioning System depends on the orientation of the antennas of the transmitter and the receiver as well as the direction of the line of sight. Two equivalent analytic formulas are derived for the correction based on the property of circularly polarized wave. The magnitude of the correction is evaluated with a simulation. Result from a GPS experiment is shown for the effect of the phase correction. A general formula useful for qualitative evaluation of the differenced measurements is given in terms of the solid angles subtended at the center of the earth by the receivers and transmitters involved.
An efficient algorithm is developed for multisession adjustment of GPS data with simultaneous orbit determination and ambiguity resolution. Application of the algorithm to the analysis of data from a five-year campaign in progress in southern and central California to monitor tectonic motions using observations by GPS satellites, demonstrates improvements in estimates of station position and satellite orbits when the phase ambiguities are resolved. Most of the phase ambiguities in the GPS network were resolved, particularly for all the baselines of geophysical interest in California.
The BeiDou attitude model for continuous yawing MEO and IGSO spacecraft
- F Dilssner
- G Laufer
- T Springer
- E Schonemann
- W Enderle
- R G Suya
- Y.-T Chen
- C F Kwong
- P Zhang
ORBEX: The Orbit Exchange Format
- S Loyer
- O Montenbruck
- S Hilla
A Guide to Using International GNSS Service (IGS) Products, Geodetic Survey Division-Natural Resources Canada
- J Kouba
Contributions to the theory of atmospheric refraction
- Saastamoinen
Global mapping function (GMF): A new empirical mapping function based on numerical weather model data
- Bohm