In-orbit Validation Research Articles

Design and Validation of a U-Net-Based Algorithm for Star Sensor Image Segmentation

The present work focuses on the investigation of an artificial intelligence (AI) algorithm for brightest objects segmentation in night sky images’ field of view (FOV). This task is mandatory for many applications that want to focus on the brightest objects in an optical sensor image with a particular shape: point-like or streak. The algorithm is developed as a dedicated application for star sensors both for attitude determination (AD) and onboard space surveillance and tracking (SST) tasks. Indeed, in the former, the brightest objects of most concern are stars, while in the latter they are resident space objects (RSOs). Focusing attention on these shapes, an AI-based segmentation approach can be investigated. This will be carried out by designing, developing and testing a convolutional neural network (CNN)-based algorithm. In particular, a U-Net will be used to tackle this problem. A dataset for the design process of the algorithm, network training and tests is created using both real and simulated images. In the end, comparison with traditional segmentation algorithms will be performed, and results will be presented and discussed together with the proposal of an electro-optical payload for a small satellite for an in-orbit validation (IOV) mission.

Drag-free control design and in-orbit validation of TianQin-1 satellite

Drag-free control (DFC) is one of the key technologies for space-borne gravitational wave detectors. For the TianQin (TQ) project, non-gravitational disturbances on the spacecraft must be suppressed by DFC. TianQin-1 (TQ-1) is the first satellite for technology verification, whose main goal is to verify the disturbances reduction technologies. In this paper, the DFC requirement and preliminary analysis for the TQ project are introduced, and then the design and the experimental validation with the TQ-1 satellite is presented. In-orbit results show a successful validation of DFC and the residual acceleration of TQ-1 satellite has been suppressed to at 10 mHz versus thruster noise.

High-precision physics-based radiation force models for the Galileo spacecraft

We present two new high-precision physics-based radiation force models for the In-Orbit Validation (IOV) and Full Operational Capability (FOC) spacecraft (s/c) of the Galileo Global Navigation Satellite System (GNSS). In both cases, the s/c bus surfaces are covered in material types, i.e., Laser Retro-reflector Array (LRA), Optical Surface Reflector (OSR) and Single-Layer Insulation (SLI) coverings, that were either not encountered or not specifically dealt with in earlier work. To address this, a number of modelling enhancements were proposed and tested, including: a specific model to account for the direct and reflected solar radiation force for LRA surfaces; a design update of the bus model computation process to allow for more than one insulation material; a specific thermal force model for OSR surfaces; a thermal force model for the Navigation Antenna (NAVANT) surface that includes a temperature model derived from on-orbit temperature measurements; and force models to account for thermal emissions from radiator panels on the +X and ±Y surfaces for both IOV and FOC, and on the -Z surface for FOC only. In the UCL2+ model each of these effects are accounted for. The theoretical impact of each modelling concept introduced is assessed, individually, by considering the magnitude of its effect in acceleration-space. The impact on orbit accuracy is confirmed through a rigorous set of Precise Orbit Determination (POD) validation tests, in which observations from all active Galileo s/c over two full years, 2017 and 2018, including during eclipsing periods, are included in the analysis. The UCL2+ approach results in day boundary discontinuities of 22 mm, 17 mm and 27 mm in the radial, across-track and along-track components, respectively. Analysis of the one-way Satellite Laser Ranging (SLR) residuals suggests that radial accuracy at better than 1 cm (3.7 mm mean residuals) and precision at better than 2 cm (17 mm root mean square (rms) error) is achievable with the UCL2+ model.

GNSS Receiver-Related Pseudorange Biases: Characteristics and Effects on Wide-Lane Ambiguity Resolution

Satellite chip shape distortions lead to signal tracking errors in pseudorange measurements, which are related to the receiver manufacturers, called receiver-related pseudorange biases. Such biases will lead to adverse effects for differential code bias (DCB) and satellite clock estimation, single point positioning (SPP) and precise point positioning (PPP) applications with pseudoranges. In order to assess the characteristics of receiver-related pseudorange biases for global positioning system (GPS), Galileo navigation satellite system (Galileo) and BeiDou navigation satellite system (BDS), seven short baselines from the Multi-GNSS experiment (MGEX) network are tested. The results demonstrate that there are significant inconsistences of pseudorange biases according to satellites, frequencies, receiver and antenna types. For the baselines using the same receivers of TRIMBLE, pseudorange biases are within ±0.2 ns with the same antennas, while they increase to ±0.6 ns with the different antennas. As for baselines with mixed receiver types, pseudorange biases can reach up to 2.5 ns. Among GPS/Galileo/BDS, Galileo shows the smallest pseudorange biases, and the obvious inconsistences of pseudorange biases are observed between BDS-2 and BDS-3, and Galileo in-orbit validation (IOV) satellites and full operational configuration (FOC) satellites. In order to validate receiver-related pseudorange biases, we carry out relative positioning experiments using short baselines. The results show that the RMS values of position errors are reduced 12.6% and 11.4% in horizontal and vertical components with biases correction. The impacts of receiver-related pseudorange biases on wide-lane (WL) ambiguity are also discussed. The results indicate that the percentage of the fractional parts within ±0.1 cycles have an obvious increase with the pseudorange biases correction, and RMS values of the fractional parts are reduced 28.9% and 67.6% for GPS and BDS, respectively.

Toward the 1-cm Galileo orbits: challenges in modeling of perturbing forces

Precise orbit determination demands knowledge of perturbing forces acting on the satellites of the Global Navigation Satellite Systems (GNSS). The metadata published by the European GNSS Agency for the Galileo satellites allow for the composition of the analytical box-wing model dedicated for coping with the direct solar radiation pressure (SRP), albedo, and infrared radiation (IR). Based on the box-wing model, we evaluated both the magnitude and the characteristic periods of accelerations caused by all the aforementioned forces. We assess which perturbations can be absorbed by the extended Empirical CODE Orbit Model (ECOM2) and what are the consequences of neglecting higher-order ECOM2 coefficients. In order to evaluate the impact of SRP, albedo, IR, and the navigation antenna thrust, we perform a series of precise Galileo orbit determination strategies for Galileo In-Orbit-Validation (IOV), Full Operational Capability (FOC), and two FOC satellites launched into eccentric orbits. The proposed box-wing model is capable of absorbing approximately 97% of the SRP in the Sun-satellite direction, whereas the rest can be mitigated by an additionally estimated small set of empirical parameters. The purely physical box-wing model does not fully handle satellite misorientation and re-radiation effects, such as Y-bias, solar panel rotation lag, that is the misalignment causing a constant acceleration perpendicular to the solar panel axis and the direction to the Sun. However, the box-wing model is especially crucial in terms of the absorption of the higher-order terms of SRP and stabilizes the orbit solutions during the eclipsing periods. Based on the SLR residual analysis, we found a systematic effect at the level up to 50 mm resulting from the omission of the high-order empirical orbit coefficients. We also found that the impact of the albedo, IR, and transmitter antenna thrust on the Galileo orbits reach the level of 5, 14, and 20 mm, respectively. Eventually, we obtain the overall accuracy of the Galileo-FOC orbits at the level of 22.5 mm, even for the eclipsing period for the solution which considers the box-wing model with the estimation of the constant empirical accelerations.

Low Earth Orbiter (LEO) Navigation Augmentation: Opportunities and Challenges

As China’s Beidou satellite navigation system (Beidou system) achieves a primary global coverage, the low earth orbiter navigation augmentation (LEO-NA) technique becomes a hot research topic, since it can easily cooperate with the Beidou system to improve the precision for global autonomous navigation and to extend the application market of the global navigation satellite systems (GNSS). This paper analyzed the demand for and status of the LEO-NA technique, and focused on the in-orbit validation of key techniques for the “Luojia-1A” satellite. It also studied the challenges faced by the LEO-NA system, including interoperability of signal frequencies after navigation augmentation, integrated design of the communication and navigation signals, control and management of the LEO constellations, acquisition and tracking of the high-dynamic augmented signals, and integration with existing GNSS systems. Considering the pressing demand for the LEO-NA techniques, the following suggestions are proposed, including enhancing the top-level design of the LEO-NA system while focusing on the synergy of the LEO-NA and Beidou systems; promoting the integration of the communications, navigation, and remote sensing functions, and building the space-based real-time service system in a stepwise and stratified manner; and planning and constructing the satellite project and the ground infrastructure in an integrated manner.

Assessing the contribution of Galileo to GPS+GLONASS PPP: Towards full operational capability

By the end of 2018, the Galileo constellation consisted of four in-orbit validation (IOV) satellites and 22 full operational capability (FOC) satellites. Except for GPS and GLONASS, the FOC of Galileo has not been reached. In 2018, four Galileo FOC satellites were launched. With these launches, most of the Galileo FOC has been reached. In this paper, the latest contribution of the Galileo constellation to GPS+GLONASS combined Multi-GNSS precise point positioning (PPP) solutions is analyzed in terms of static/kinematic accuracy and convergence time. Three different elevation cut-off angles (5°,-15°,-30°) are chosen to simulate the ideal and restricted satellite visibilities. A two-month period and a one-week period in 2019 are chosen for conducting static and kinematic PPP, respectively, using the data of 20 Multi-GNSS Experiment (MGEX) stations. Non-overlapping sessions of 24, 12, 6, 3, 1, and 0.5 h within two months are processed for static PPP to analyze the effect of the Galileo contribution to static PPP for each observation length and cut-off angle. GipsyX scientific software developed by NASA’s Jet Propulsion Laboratory (JPL) is used for PPP processes. The statistical results show that the contribution of Galileo generally becomes higher as the observing sessions become shorter, but no significant correlation between the contribution of Galileo and observing session is found for each station. The largest horizontal and vertical accuracy improvements of Galileo are observed as 8 mm/11 mm (47%/61%) and 23 mm/30 mm (20%/48%) for static and kinematic PPP, respectively. The accuracy degradation is observed more in the vertical component for some stations when adding Galileo to GPS+GLONASS combined static and kinematic PPP. The Galileo contributions to minimum, maximum, and mean convergence times are also computed for both static and kinematic PPP. The largest improvement show that mean horizontal and vertical convergence times are shortened by 24 min/24 min (52%/45%) and 61 min/23 min (89%/62%) for static and kinematic PPP, respectively. The results also show that outliers can be reduced significantly for most of the stations by adding Galileo to the GPS+GLONASS combined PPP for short observation sessions.

Quality assessment of GPS, Galileo and BeiDou-2/3 satellite broadcast group delays

The quality of broadcast group delays (BGDs) transmitted in the navigation messages of the Global Positioning System (GPS), BeiDou-2/3 and Galileo is assessed by comparison with multi-GNSS differential code bias (DCB) products generated at the Chinese Academy of Sciences (CAS). An automatic DCB (AutoDCB) realignment procedure is presented to handle discontinuities within individual BGD/DCB series. The analysis is performed over a four-year period starting from January 2014. For GPS, the consistency between broadcast timing group delays (TGDs) and CAS MGEX DCBs is 0.25 ns, and the corresponding values are 0.05, 0.3 and 0.45 ns for L1C/A, L2C and L5Q inter-signal corrections (ISCs), respectively. The best agreement between GPS L2C ISCs and CAS MGEX C1W-C2L DCBs is emphasized. The inconsistency between broadcast and post-processed C2I-C6I DCBs (=TGD1) is found to decrease from 1.5 to 0.45 ns across the entire BeiDou-2 constellation since late July 2017, indicating a significant quality improvement of BeiDou-2 transmitted TGD1 parameters. A systematic offset of around 4.0 ns is found between TGD1 reference datums of BeiDou-3 and BeiDou-2 constellations, which needs to be removed in the combined BeiDou-2/3 B1I single-frequency or B1I+B3I dual-frequency standard positioning applications. Aside from the increasingly improved repeatability of broadcast E1-E5a/5b delays, an overall agreement at the level of 0.1–0.4 ns is achieved between Galileo transmitted value and DCB metadata from European GNSS Agency (GSA) for the in-orbit validation (IOV) satellites. In the comparison of Galileo BGDs and CAS MGEX DCBs, the consistency is at the level of 0.4 and 0.3 ns for IOV and full operation capability (FOC) satellites, respectively. The requirement of the routine assessment of broadcast group delays is also emphasized, in particular for newly launched satellites of new constellations.

Analysis of Galileo/BDS/GPS signals and RTK performance

New satellites and signals become available with the modernization of GNSS, especially for Galileo and BDS. The current Galileo constellation comprises 4 IOV (in-orbit validation) and 14 FOC (full operational capability) satellites which transmit signals on five frequencies. In addition to BDS-II regional navigation system, five BDS-III experimental (BDS-IIIs) and eight BDS-III satellites have been launched. It is worthwhile to evaluate the performance of these new satellites and signals. First, these signals are assessed in regard to carrier-to-noise density ratio (C/N0), code multipath (MP) combination, and triple-frequency carrier phase ionospheric-free and geometry-free (DIF) combination. The C/N0 of Galileo IOV satellites is several dB-HZ lower than that of the FOC satellites, while that of the IOV satellite E19 is always the lowest, regardless of receiver type. As for BDS, the C/N0 of the BDS-IIIs are higher than that of BDS-II but lower than that of BDS-III. The difference of C/N0 among GPS satellites is not obvious. Among all the signals, the performance of E5 is the best which may be related to its advanced modulation scheme, while the L2 is the worst. The code multipath on E5 is independent of the satellite elevation due to its good MP suppression performance, which may be related to its wide signal bandwidth. The RMSs of MP for Galileo signals are even smaller than that of GPS. Being free of the systematic code errors of BDS-II, the RMS of BDS-IIIs MP errors is comparable with that of GPS and Galileo. In addition, the multipath errors show an obvious periodic behavior, which differs with the types of satellites. Similarly, the DIF combinations also possess elevation-dependent and periodic characteristics. Note that the inter-frequency bias variations present in BDS-II and GPS IIF satellites are absent for Galileo satellites. The accuracy of Galileo SPP is comparable to that of GPS, but better than that of BDS. Although there are no significant differences for the RTK results of the three systems, the double-differenced carrier phase and code residuals of E5 is the smallest among all the signals.

Galileo and QZSS precise orbit and clock determination using new satellite metadata

During 2016–2018, satellite metadata/information including antenna parameters, attitude laws and physical characteristics such as mass, dimensions and optical properties were released for Galileo and QZSS (except for the QZS-1 optical coefficients). These metadata are critical for improving the accuracy of precise orbit and clock determination. In this contribution, we evaluate the benefits of these new metadata to orbit and clock in three aspects: the phase center offsets and variations (PCO and PCV), the yaw-attitude model and solar radiation pressure (SRP) model. The updating of Galileo PCO and PCV corrections, from the values estimated by Deutsches Zentrum fur Luft- und Raumfahrt and Deutsches GeoForschungsZentrum to the chamber calibrations disclosed by new metadata, has only a slight influence on Galileo orbits, with overlap differences within only 1 mm. By modeling the yaw attitude of Galileo satellites and QZS-2 spacecraft (SVN J002) according to new published attitude laws, the residuals of ionosphere-free carrier-phase combinations can be obviously decreased in yaw maneuver seasons. With the new attitude models, the 3D overlap RMS in eclipse seasons can be decreased from 12.3 cm, 14.7 cm, 16.8 cm and 34.7 cm to 11.7 cm, 13.4 cm, 15.8 cm and 32.9 cm for Galileo In-Orbit Validation (IOV), Full Operational Capability (FOC), FOC in elliptical orbits (FOCe) and QZS-2 satellites, respectively. By applying the a priori box-wing SRP model with new satellite dimensions and optical coefficients, the 3D overlap RMS are 5.3 cm, 6.2 cm, 5.3 cm and 16.6 cm for Galileo IOV, FOCe, FOC and QZS-2 satellites, with improvements of 11.0%, 14.7%, 14.0% and 13.8% when compared with the updated Extended CODE Orbit Model (ECOM2). The satellite laser ranging (SLR) validation reveals that the a priori box-wing model has smaller mean biases of − 0.4 cm, − 0.4 cm and 0.6 cm for Galileo FOCe, FOC and QZS-2 satellites, while a slightly larger mean bias of − 1.0 cm is observed for Galileo IOV satellites. Moreover, the SLR residual dependencies of Galileo IOV and FOC satellites on the elongation angle almost vanish when the a priori box-wing SRP model is applied. As for satellite clocks, a visible bump appears in the Modified Allan deviation at integration time of 20,000 s for Galileo Passive Hydrogen Maser with ECOM2, while it almost vanishes when the a priori box-wing SRP model and new metadata are applied. The standard deviations of clock overlap can also be significantly reduced by using new metadata.

Estimating and assessing Galileo satellite fractional cycle bias for PPP ambiguity resolution

Due to the rapid deployment of the Galileo constellation, Galileo is now able to contribute to GNSS precise point positioning (PPP) ambiguity resolution (AR) with 17 operational satellites as of December 2017. We estimate the satellite fractional cycle bias (FCB) based on globally distributed MGEX stations and assess the Galileo FCB quality by a comparison with that of GPS and BDS. Results of 60 days indicate that the quality of Galileo wide-lane (WL) FCB is better than GPS and BDS in terms of data usage rate, residual distribution, as well as standard deviation of daily estimates. The RMS of Galileo WL FCB residuals is 0.071 cycles, while that of GPS and BDS are 0.089 and 0.117 cycles, respectively. The standard deviation of Galileo daily WL FCB is 0.010 cycles, while that of GPS and BDS is 0.018 and 0.043 cycles. We attribute the better quality of Galileo WL FCB to its signal modulation, AltBOC, which significantly compresses the multipath effect for pseudorange measurement. Within the Galileo constellation, the performance of In-Orbit Validation (IOV) satellites WL FCB is worse than that of Full Operational Capability (FOC) satellites as a result of a reduction in the power of the transmitted signal. The performance of the two highly eccentric satellites is comparable to other FOC satellites. The overall quality of Galileo narrow-lane (NL) FCB is slightly worse than that of GPS but better than that of BDS. The RMS of Galileo NL FCB residuals is 0.062 cycles, while that for GPS and BDS is 0.050 and 0.086 cycles respectively. In addition, the NL FCB quality of FOC, IOV (except E19), as well as the two eccentric satellites, shows no significant difference in terms of data usage rates and residuals. Galileo PPP AR solutions are conducted at 20 MGEX stations with 3-h sessions for 10 days. The positional biases of AR solutions are 0.7, 0.6, and 2.1 cm for east, north and up components respectively, while those for float solutions are 2.1, 1.1, and 2.7 cm, corresponding to the improvements of 67, 45, and 22%, respectively. These results demonstrate that, currently, Galileo FCB can be estimated with accuracy comparable with GPS and BDS, and the Galileo observations can bring an obvious benefit to ambiguity-fixed PPP.

In-orbit performance assessment of BeiDou intersatellite link ranging

The introduction of an intersatellite link, also called a crosslink, is considered a promising technique for improving the reliability and integrity of a global navigation satellite system. As one of the most rapidly developing satellite navigation systems, the BeiDou system launched from March 2015 to February 2016 an in-orbit validation constellation that includes two inclined geosynchronous orbit satellites and three medium earth orbit satellites equipped with an intersatellite link in the Ka band. We modeled the intersatellite measurements of BeiDou and evaluated the ranging performance of the intersatellite link based on the analysis of in-orbit measurement data. We used both residual analysis and external data comparison to assess the data. The results show that the ranging precision of the BeiDou intersatellite link is within 10 cm and is determined mainly by the thermal noise of the receiver. Moreover, the drift rate of the group delay of the transceiver channel is within 1 cm per day.

Assessing the latest performance of Galileo-only PPP and the contribution of Galileo to Multi-GNSS PPP

By the end of 2016, the Galileo constellation had 4 in-orbit validation (IOV) satellites and 14 full operational capability (FOC) satellites, 17 of which were able to transmit signal in November 2017. Galileo has already had early operational capability (EOC). To assess the latest performance of the Galileo-only precise point positioning (PPP) and the contribution of Galileo to the Multi-GNSS PPP solutions, observations collected at 16 Multi-GNSS Experiment (MGEX) stations over ten days are used to realize the various PPP cases. The statistical results show that the three-dimensional positioning accuracy of Galileo static and kinematic PPP can reach centimeter level and decimeter level after convergence, respectively. The contribution of Galileo can improve the positioning accuracy by 29.49%, 29.96% and 23.70% for GPS kinematic PPP and 11.03%, 10.59% and 11.07% for GPS/GLONASS kinematic PPP solutions in the north, east and up components, respectively. The average convergence time can be reduced by 45.48% for GPS-only kinematic PPP and by 11.04% for GPS/GLONASS solutions by adding Galileo observations. Moreover, adding Galileo observations shortens the average convergence time by 30.45% and 7.8% for GPS-only and GPS/GLONASS static PPP solutions, respectively. Although the convergent positioning results of GPS and GPS/GLONASS static PPP solutions after the addition of Galileo measurements do not demonstrate as significant improvement as those of the kinematic PPP solutions, the positioning accuracy of the GPS/Galileo static PPP solutions compared to the GPS-only static PPP still demonstrates an improvement of approximately 25% on the east component. Furthermore, the GPS/Galileo internal system time bias (ISB) and observation residual are analyzed. The results show that the noise level of the GPS L1/L2 signals and the negative impact of multipath errors on the GPS pseudo-range observations for the L1/L2 signals are greater than those of Galileo E1/E5a signals, resulting in the residuals of GPS ionosphere-free code observations larger than those of Galileo code observations. However, the phase observation residuals of GPS and Galileo are of the same magnitude. Additionally, the one-day GPS/Galileo ISB is quite stable. Its stability described by standard deviation is approximately 0.34 ns.

Elevation-dependent pseudorange variation characteristics analysis for the new-generation BeiDou satellite navigation system

To validate the new system design and the new technology of the third-generation BDS (BeiDou-3), five non-GEO experimental satellites were launched during 2015 and 2016. In addition to the B1I and B3I signals that have been emitted by BeiDou-2, three newly designed civil signals (B1C, B2a, and B2b) were first transmitted by these satellites and are planned to be partly applied to the official BeiDou-3 satellites. In this study, the signature of elevation-dependent systematic biases in code measurements, which are commonly observed from BeiDou-2 satellites, was investigated for the three new civil signals based on observations collected using different types of receivers at different locations. Our results show that the RMS of multipath combination residuals of the new civil signal B1C was statistically larger than those of B2a and B2b signals. This indicates that B1C tends to be more seriously affected by multipath effects than B2a and B2b. Furthermore, the station elevation-dependent and satellite nadir- and azimuth-dependent multipath signatures were analyzed in detail. The results show that elevation-dependent variations in code measurements of B1I and B3I signals still exist for BeiDou-2 satellites, including the latest IGSO-6 (C13) launched in 2016. Based on different receivers which are equipped with all-in-view antennas, these types of code biases seem to be absent in the legacy B1C, B2a, and B2b frequency bands for BeiDou-3 in-orbit validation satellites. However, benefited from multipath-free conditions, results from a 40-m dish antenna reveal that the satellite-induced code pseudorange variations still exist in the bands of B1C, B2a, and B2b of BeiDou-3 in-orbit validation satellites, although their variation ranges are only at a level of approximately 0.1 m.

Fast solar radiation pressure modelling with ray tracing and multiple reflections

Physics based SRP (Solar Radiation Pressure) models using ray tracing methods are powerful tools when modelling the forces on complex real world space vehicles. Currently high resolution (1 mm) ray tracing with secondary intersections is done on high performance computers at UCL (University College London). This study introduces the BVH (Bounding Volume Hierarchy) into the ray tracing approach for physics based SRP modelling and makes it possible to run high resolution analysis on personal computers. The ray tracer is both general and efficient enough to cope with the complex shape of satellites and multiple reflections (three or more, with no upper limit). In this study, the traditional ray tracing technique is introduced in the first place and then the BVH is integrated into the ray tracing. Four aspects of the ray tracer were tested for investigating the performance including runtime, accuracy, the effects of multiple reflections and the effects of pixel array resolution.Test results in runtime on GPS IIR and Galileo IOV (In Orbit Validation) satellites show that the BVH can make the force model computation 30–50 times faster. The ray tracer has an absolute accuracy of several nanonewtons by comparing the test results for spheres and planes with the analytical computations. The multiple reflection effects are investigated both in the intersection number and acceleration on GPS IIR, Galileo IOV and Sentinel-1 spacecraft. Considering the number of intersections, the 3rd reflection can capture 99.12%,99.14%, and 91.34% of the total reflections for GPS IIR, Galileo IOV satellite bus and the Sentinel-1 spacecraft respectively. In terms of the multiple reflection effects on the acceleration, the secondary reflection effect for Galileo IOV satellite and Sentinel-1 can reach 0.2 nm/s2 and 0.4 nm/s2 respectively. The error percentage in the accelerations magnitude results show that the 3rd reflection should be considered in order to make it less than 0.035%. The pixel array resolution tests show that the dimensions of the components have to be considered when choosing the spacing of the pixel in order not to miss some components of the satellite in ray tracing. This paper presents the first systematic and quantitative study of the secondary and higher order intersection effects. It shows conclusively the effect is non-negligible for certain classes of misson.

Estimation and analysis of multi-GNSS differential code biases using a hardware signal simulator

In ionospheric modeling, the differential code biases (DCBs) are a non-negligible error source, which are routinely estimated by the different analysis centers of the International GNSS Service (IGS) as a by-product of their global ionospheric analysis. These are, however, estimated only for the IGS station receivers and for all the satellites of the different GNSS constellations. A technique is proposed for estimating the receiver and satellites DCBs in a global or regional network by first estimating the DCB of one receiver set as reference. This receiver DCB is then used as a ‘known’ parameter to constrain the global ionospheric solution, where the receiver and satellite DCBs are estimated for the entire network. This is in contrast to the constraint used by the IGS, which assumes that the involved satellites DCBs have a zero mean. The ‘known’ receiver DCB is obtained by simulating signals that are free of the ionospheric, tropospheric and other group delays using a hardware signal simulator. When applying the proposed technique for Global Positioning System legacy signals, mean offsets in the order of 3 ns for satellites and receivers were found to exist between the estimated DCBs and the IGS published DCBs. It was shown that these estimated DCBs are fairly stable in time, especially for the legacy signals. When the proposed technique is applied for the DCBs estimation using the newer Galileo signals, an agreement at the level of 1–2 ns was found between the estimated DCBs and the manufacturer’s measured DCBs, as published by the European Space Agency, for the three still operational Galileo in-orbit validation satellites.

Investigation on Reference Frames and Time Systems in Multi-GNSS

Receivers able to track satellites belonging to different GNSSs (Global Navigation Satellite Systems) are available on the market. To compute coordinates and velocities it is necessary to identify all the elements that contribute to interoperability of the different GNSSs. For example the timescales kept by different GNSSs have to be aligned. Receiver-specific biases, or firmware-dependent biases, need to be calibrated. The reference frame used in the representation of the orbits must be unique. In this paper we address the interoperability issues from the standpoint of a Single Point Positioning (SPP) user, i.e., using pseudoranges and broadcast ephemeris. The biases between GNSSs timescales and receiver-dependent biases are analyzed for a set of 31 MGEX (Multi-GNSS Experiment) stations over a time span of more than three years. Time series of biases between timescales of GPS (Global Positioning System), GLONASS (Global Navigation Satellite System), Galileo, BeiDou, QZSS (Quasi-Zenith Satellite System), SBAS (Satellite Based Augmentation System) and NAVIC (Navigation with Indian Constellation) are investigated, in addition to the identification of events like discontinuity of receiver-dependent biases due to firmware updating. The GPS broadcast reference frame is shown to be aligned to the one (IGS14) realized by the precise ephemeris of CODE (Center for Orbit Determination in Europe) to within 0.1 m and 2 milliarcsec, with values dependent on whether IIR-A, IIR-B/M or IIF satellite blocks are considered. Larger offsets are observed for GLONASS, up to 1 m for GLONASS K satellites. For Galileo the alignment of the broadcast orbit to IGS14/CODE is again at the 0.1 m and several milliarcsec level, with the FOC (Full Operational Capability) satellites slightly better than IOV (In Orbit Validation). For BeiDou an alignment of the broadcast frame to IGS14/CODE comparable to GLONASS is observed, regardless of whether IGSO (Inclined Geosynchronous Orbit) or MEO (Medium Earth Orbit) satellites are considered. For all satellites, position differences according to the broadcast ephemeris relative to IGS14/CODE orbits are projected to the radial, along-track and crosstrack triad, with the largest periodic differences affecting mostly the along track component. Sudden discontinuities at the level of up to 1 m and 2–3 ns are observed for the along-track component and the satellite clock, respectively. The time scales of GLONASS, Galileo, QZSS, SBAS and NAVIC are very closely aligned to GPS, with constant offsets depending on receiver type. The offset of the BeiDou time scale to GPS has an oscillatory pattern with peak-to-peak values up to 100 ns. To characterize receiver-dependent biases the average of six Septentrio receivers is taken as reference, and relative offsets of the other receiver types are investigated. These receiver-dependent biases may depend on the individual station, or for the same station on the update of the firmware. A detailed calibration history is presented for each multiGNSS station studied.

Analysis of Galileo IOV + FOC signals and E5 RTK performance

The current Galileo constellation in April 2017 comprises both in-orbit validation and full operational capability satellites transmitting signals on five frequencies, i.e., E1, E5a, E5b, E5, and E6. We analyze the power, multipath and noise of these signals using the data collected by four short baselines of various lengths and receiver/antenna types in Perth, Australia, as well as the Netherlands. In our analysis, the Galileo signals, except E5, show different relative noise and multipath performance for different receiver/antenna types. The E5 signal, with a weak dependency on the type of receiver/antenna, shows a significantly lower level of multipath and noise with respect to the other signals. Estimations of the E5 code standard deviation based on the data of each of the mentioned baselines gives a value of about 6 cm, which is further reduced to about 1 cm once the data are corrected for multipath. Due to the superior stochastic properties of E5 signal compared to the other Galileo signals, we further analyze the short-baseline real-time kinematic performance of the Galileo standalone E5 observations. Our findings confirm that the Galileo E5 data, if corrected for the multipath effect, can make (almost) instantaneous ambiguity resolution feasible already based on the current constellation.

Validation of Galileo orbits using SLR with a focus on satellites launched into incorrect orbital planes

The space segment of the European Global Navigation Satellite System (GNSS) Galileo consists of In-Orbit Validation (IOV) and Full Operational Capability (FOC) spacecraft. The first pair of FOC satellites was launched into an incorrect, highly eccentric orbital plane with a lower than nominal inclination angle. All Galileo satellites are equipped with satellite laser ranging (SLR) retroreflectors which allow, for example, for the assessment of the orbit quality or for the SLR–GNSS co-location in space. The number of SLR observations to Galileo satellites has been continuously increasing thanks to a series of intensive campaigns devoted to SLR tracking of GNSS satellites initiated by the International Laser Ranging Service. This paper assesses systematic effects and quality of Galileo orbits using SLR data with a main focus on Galileo satellites launched into incorrect orbits. We compare the SLR observations with respect to microwave-based Galileo orbits generated by the Center for Orbit Determination in Europe (CODE) in the framework of the International GNSS Service Multi-GNSS Experiment for the period 2014.0–2016.5. We analyze the SLR signature effect, which is characterized by the dependency of SLR residuals with respect to various incidence angles of laser beams for stations equipped with single-photon and multi-photon detectors. Surprisingly, the CODE orbit quality of satellites in the incorrect orbital planes is not worse than that of nominal FOC and IOV orbits. The RMS of SLR residuals is even lower by 5.0 and 1.5 mm for satellites in the incorrect orbital planes than for FOC and IOV satellites, respectively. The mean SLR offsets equal -44.9, -35.0, and -22.4 mm for IOV, FOC, and satellites in the incorrect orbital plane. Finally, we found that the empirical orbit models, which were originally designed for precise orbit determination of GNSS satellites in circular orbits, provide fully appropriate results also for highly eccentric orbits with variable linear and angular velocities.

Galileo status: orbits, clocks, and positioning

The European Global Navigation Satellite System Galileo is close to declaration of initial services. The current constellation comprises a total of 12 active satellites, four of them belonging to the first generation of In-Orbit Validation satellites, while the other eight are Full Operational Capability (FOC) satellites. Although the first pair of FOC satellites suffered from a launch anomaly resulting in an elliptical orbit, these satellites can be used for scientific applications without relevant limitations. The quality of broadcast orbits and clocks has significantly improved since the beginning of routine transmissions and has reached a signal-in-space range error of 30 cm. Precise orbit products generated by the scientific community achieve an accuracy of about 5 cm if appropriate models for the solar radiation pressure are applied. The latter is also important for an assessment of the clock stability as orbit errors are mapped to the apparent clock. Dual-frequency single point positioning with broadcast orbits and clocks of nine Galileo satellites that have so far been declared healthy already enables an accuracy at a few meters. Galileo-only precise point positioning approaches a precision of 2 cm in static mode using daily solutions.