Antenna Phase Center Offsets Research Articles

PCO and hardware delay calibration for LEO satellite antenna downlinking navigation signals

Augmentation of the Global Navigation Satellite System by low earth orbit (LEO) satellites is a promising approach benefiting from the advantages of LEO satellites. This, however, requires errors and biases in the satellite downlink navigation signals to be calibrated, modeled, or eliminated. This contribution introduces an approach for in-orbit calibration of the phase center offsets (PCOs) and code hardware delays of the LEO downlink navigation signal transmitter/antenna. Using the satellite geometries of Sentinel-3B and Sentinel-6A as examples, the study analyzed the formal precision and bias influences for potential downlink antenna PCOs and hardware delays of LEO satellites under different ground network distributions, and processing periods. It was found that increasing the number of tracking stations and processing periods can improve the formal precision of PCOs and hardware delay. Less than 3.5 mm and 3 cm, respectively, can be achieved with 10 stations and 6 processing days. The bias projections of the real-time LEO satellite orbital and clock errors can reach below 3 mm in such a case. For near-polar LEO satellites, stations in polar areas are essential for strengthening the observation model.

Intercomparison of multi-GNSS signals characteristics acquired by a low-cost receiver connected to various low-cost antennas

With the increasing number of low-cost GNSS antennas available on the market, there is a lack of comprehensive analysis and intercomparison of their performance. Moreover, multi-GNSS observation noises are not well recognized for low-cost receivers. This study characterizes the quality of GNSS signals acquired by low-cost GNSS receivers equipped with eight types of antennas in terms of signal acquisition, multipath error and receiver noise. The differences between various types of low-cost antennas are non-negligible, with helical antennas underperforming in every respect. Compared with a geodetic-grade station, GPS and Galileo signals acquired by low-cost receivers are typically weaker by 3–9 dB-Hz. While the L1, E1 and E5b signals are well-tracked, only 72% and 86% of L2 signals are acquired for GPS and GLONASS, respectively. The signal noise for pseudoranges varies from 0.12 m for Galileo E5b to over 0.30 m for GLONASS L1 and L2, whereas for carrier-phase observations it oscillates around 1 mm for both GPS and Galileo frequencies, but exceeds 3 mm for both GLONASS frequencies. Antenna phase center offsets (PCOs) vary significantly between frequencies and constellations, and do not agree between two antennas of the same type by up to 25 mm in the vertical component. After a field calibration a of low-cost antenna and consistent application of PCOs, the horizontal and vertical accuracy is improved to a few millimeter and a few centimeter level for the multi-GNSS processing with double-differenced and undifferenced approach, respectively. Last but not least, we demonstrate that PPP-AR is possible also with low-cost GNSS receivers and antennas, and improves the precision and convergence time. The results prove that selection of low-cost antenna for a low-cost GNSS receiver is of great importance in precise positioning applications.

Precise orbit determination of Haiyang-2D using onboard BDS-3 B1C/B2a observations with ambiguity resolution

The Haiyang-2D altimetry mission of China is one of the first Low Earth Orbit (LEO) satellites that can receive new B1C/B2a signals from the BeiDou-3 Navigation Satellite System (BDS-3) for Precise Orbit Determination (POD). In this work, the achievable accuracy of the single-receiver ambiguity resolution for onboard LEO satellites is studied based on the real measurements of new BDS-3 frequencies. Under normal conditions, six BDS-3 satellites on average are visible. However, the multipath of the B1C/B2a code observations presents some patchy patterns that cause near-field variations with an amplitude of approximately 40 cm and deteriorate the ambiguity-fixed rate. By modeling those errors, for the B2a code, a remarkable reduction of 53% in the Root Mean Square (RMS) is achieved at high elevations, along with an increase of 8% in the ambiguity-fixed rates. Additionally, an analysis of the onboard antenna's phase center offsets reveals that when compared to the solutions with float ambiguities, the estimated values in the antenna’s Z direction in the solutions with fixed ambiguities are notably smaller. The independent validation of the resulting POD using satellite laser ranging at 16 selected high-performance stations shows that the residuals are reduced by a minimum of 15.4% for ambiguity-fixed solutions with an RMS consistency of approximately 2.2 cm. Furthermore, when compared to the DORIS-derived orbits, a 4.3 cm 3D RMS consistency is achieved for the BDS-3-derived orbits, and the along-track bias is reduced from 2.9 to 0.4 cm using ambiguity fixing.

Estimation of antenna phase center offsets for BDS-3 satellites with the metadata and receiver antenna calibrations

Estimation of antenna phase center offsets for BDS-3 satellites with the metadata and receiver antenna calibrations

Consistency of Galileo satellite antenna phase center offsets

Information about satellite antenna phase center offsets (PCOs) is indispensable for high-precision applications of global navigation satellite systems. Pre-flight manufacturer calibrations of the PCOs are available for all individual Galileo satellites and each frequency. So far, geodetic usage of Galileo is focused on the ionosphere-free linear combination of the E1 and E5a signals. In view of the growing number of E5b- and E6-capable receivers and upcoming multi-frequency applications, the consistency of the PCO values for different frequencies becomes a topic of increasing importance. Galileo satellite antenna PCOs have been estimated from the ionosphere-free linear combinations of E1/E5a, E1/E5b, and E1/E6. The mean horizontal PCOs of the different frequencies agree on the few millimeter level. The X-PCOs show a bias of about 1 cm compared to the manufacturer calibrations, whereas the Y-PCOs are free of such a bias. The Z-PCOs have a systematic offset of -11 to {-15} cm w.r.t. the manufacturer calibrations due to scale inconsistencies of the current version of the International Terrestrial Reference Frame (ITRF2020) and the manufacturer calibrations. The maximum Z-PCO difference between the various linear combinations amounts to 4 cm and provides a measure of the presently achieved consistency of ground and space antenna calibrations across different frequencies. This inconsistency would translate into height differences of about 1.6 mm and associated scale differences of the terrestrial reference frame of 0.25 ppb, when adjusting station coordinates with manufacturer calibrated Galileo PCOs for different frequency pairs.

On the relation of GNSS phase center offsets and the terrestrial reference frame scale: a semi-analytical analysis

Phase center offsets (PCOs) of global navigation satellites systems (GNSS) transmit antennas along the boresight axis introduce line-of-sight-dependent range changes in the modeling of GNSS observations that are strongly correlated with the estimated station heights. As a consequence, changes in the adopted PCOs impact the scale of GNSS-based realizations of the terrestrial reference frame (TRF). Vice versa, changes in the adopted TRF scale require corrections to the GNSS transmit antenna PCOs for consistent observation modeling. Early studies have determined an approximate value of alpha =-0.050 for the ratio of station height changes and satellite PCO changes in GPS orbit determination and phase center adjustment. However, this is mainly an empirical value and limited information is available on the actual PCO-scale relation and how it is influenced by other factors. In view of the recurring need to adjust the IGS antenna models to new ITRF scales, a semi-analytical model is developed to determine values of alpha for the four current GNSSs from first principles without a need for actual network data processing. Given the close coupling of satellite boresight angle and station zenith angle, satellite PCO changes are essentially compensated by a combination of station height, zenith troposphere delay, and receiver clock offset. As such, the value of alpha depends not only on the orbital altitude of the considered GNSS but also on the elevation-dependent distribution of GNSS observations and their weighting, as well as the elevation mask angle and the tropospheric mapping function. Based on the model, representative values of alpha _text {GPS}=-0.051, alpha _text {GLO}=-0.055, alpha _text {GAL}=-0.041, and alpha _text {BDS-3}=-0.046 are derived for GPS, GLONASS, Galileo, and BeiDou-3 at a 10^circ elevation cutoff angle. These values may vary by varDelta alpha approx 0.003 depending on the specific model assumptions and data processing parameters in a precise orbit determination or precise point positioning. Likewise changes of about pm 0.003 can be observed when varying the cutoff angle between 5^circ and 15^circ .

Estimation of GPS transmitter antenna phase center offsets by integrating space-based GPS observations

The deviations of the microwave signal transmitting point of Global Navigation Satellite Systems (GNSS) satellites with respect to the corresponding center-of-mass were and still are significant bias sources for GNSS-based terrestrial reference frames (TRF). Satellite phase center offsets (PCOs) and variations (PVs) are usually derived from GNSS observations from the tracking network of the International GNSS Service (IGS). Because of the strong correlation between the scale of the TRF and the satellite PCOs in the z-direction (z-PCOs), a no-net-scale (NNT) condition relative to, for instance, the International Terrestrial Reference Frame (ITRF) is commonly applied. One approach for estimating transmitter phase centers without constraining the scale is to consider space-based GNSS observations. Within this study, we estimate the satellite PCOs of the Global Positioning System (GPS) based on zero-difference ionosphere-free observations from six low Earth orbiters (LEOs) and ground networks with different numbers of stations. The six LEOs are different in their orbits, GPS receiver equipment, and tracking characteristics. We jointly estimate orbits, station coordinates, and GPS satellite PCOs in an integrated processing. The horizontal offsets are shown to significantly benefit from the LEOs onboard observations by reducing the correlation between these offsets and the GPS satellite orbit and attitude. Without applying a no-net-scale condition to the ground network, the GPS z-PCOs are estimated. By adding six LEOs, the correlation coefficients between the GPS z-PCOs and the scale is reduced significantly (about from 0.85 to 0.3), consequently, the precision of estimation is improved. When including the six LEOs, the GPS z-PCOs estimated without applying NNS are very stable. The estimated GPS z-PCOs have a −231 mm difference in average to the values in igs14_2134.atx and the corresponding scale to IGS14 reference frame is +1.89 part per billion. The estimated GPS z-PCOs agree with previous studies based on Swarm satellites and Galileo. The improvement due to different numbers of LEOs and the impact of LEO z-PCO errors on the estimation are discussed.

Antenna Phase Center Offset and Attitude Control during Eclipse for GPS Block III Satellites

Antenna Phase Center Offset and Attitude Control during Eclipse for GPS Block III Satellites

In-flight performance analysis and antenna phase center calibration of MEMS GPS receiver on-board TianQin-1 in the nadir-pointing and Sun-pointing modes

The TianQin-1 satellite, which was launched on 20 December 2019 into a Sun-synchronous orbit with an altitude of 628 km, is the first technology demonstration satellite for the TianQin project. A micro-electro-mechanical system (MEMS) global positioning system (GPS) receiver is installed on the satellite for precise orbit determination (POD). In addition to the conventional nadir-pointing mode, a specific Sun-pointing mode was used by the satellite owing to the limitation of system resources. The in-flight performance of the MEMS GPS receiver was assessed. The average numbers of available satellites for dual-frequency navigation in the nadir-pointing and Sun-pointing modes are 7 and 5, respectively. The qualities of the P2 code and carrier phase observations are basically equal for both modes. The average root mean square of the multipath errors for C1 observations in the Sun-pointing mode is 0.29 m, slightly larger than that in the nadir-pointing mode. In the Sun-pointing mode, the body of the TianQin-1 satellite rotates around the Sun-pointing axis, which may provide favourable geometric conditions for the estimation of the antenna phase center offset (PCO) corrections in the X, Y, and Z directions. Its feasibility is demonstrated using the simulated data. The GPS measurements of TianQin-1 are then used to estimate the PCO corrections in all three directions while in the Sun-pointing mode and in the Z direction while in the nadir-pointing mode. Satellite laser ranging validation shows that the orbit accuracy of TianQin-1 is approximately 5.90 cm in the nadir-pointing mode. In the Sun-pointing mode, the three-dimensional position difference of 5-h overlap decreased from 8.87 cm to 8.73 cm when the antenna PCO corrections were used in the POD.

Estimation of GPS satellite antenna phase center offsets of the third frequency using raw observation model

Satellite antenna phase center offsets (PCOs) is an important error source in global navigation satellite system (GNSS). With GNSS observations in a global network, the PCOs estimation strategy generally uses a dual-frequency (DF) ionospheric-free (IF) combination as the observation model. This model cannot derive the PCO values at each frequency, which results in the PCOs of the third frequency being unavailable for GPS satellites in the igs14.atx product. In this contribution, the PCOs estimation method of the third frequency based on uncombined (UC) precise orbit determination (POD) model is developed. The PCOs of the first- and second frequencies are fixed to the known values while PCOs of the third frequency are regarded as estimated parameters. This method is tested on the PCO estimation of GPS L5 frequency by using 110 ground stations throughout the entire year of 2018. The averaged standard deviations of L5 PCOs over one year are derived, with x-, y-, and z-offsets being 0.2, 0.2, and 1.6 cm, respectively. The corresponding difference values of the derived weighing averaged PCOs compared to the values of the igs14.atx product are 0.2, 0.1, and 9.9 cm. The POD experiment is processed to validate the derived PCOs of L5 over a period of 50 days. Results show that the accuracy of orbits, clocks and station positions is slightly improved after using estimated PCOs.

Reference system origin and scale realization within the future GNSS constellation \u201cKepler\u201d

Currently, Global Navigation Satellite Systems (GNSS) do not contribute to the realization of origin and scale of combined global terrestrial reference frame (TRF) solutions due to present system design limitations. The future Galileo-like medium Earth orbit (MEO) constellation, called “Kepler”, proposed by the German Aerospace Center DLR, is characterized by a low Earth orbit (LEO) segment and the innovative key features of optical inter-satellite links (ISL) delivering highly precise range measurements and of optical frequency references enabling a perfect time synchronization within the complete constellation. In this study, the potential improvements of the Kepler constellation on the TRF origin and scale are assessed by simulations. The fully developed Kepler system allows significant improvements of the geocenter estimates (realized TRF origin in long-term). In particular, we find improvements by factors of 43 for the Z and of 8 for the X and Y component w. r. t. a contemporary MEO-only constellation. Furthermore, the Kepler constellation increases the reliability due to a complete de-correlation of the geocenter coordinates and the orbit parameters related to the solar radiation pressure modeling (SRP). However, biases in SRP modeling cause biased geocenter estimates and the ISL of Kepler can only partly compensate this effect. The realized scale enabling all Kepler features improves by 34% w. r. t. MEO-only. The dependency of the estimated satellite antenna phase center offsets (PCOs) upon the underlying TRF impedes a scale realization by GNSS. In order to realize the network scale with 1 mm accuracy, the PCOs have to be known within 2 cm for the MEO and 4 mm for the LEO satellites. Independently, the scale can be realized by estimating the MEO PCOs and by simultaneously fixing the LEO PCOs. This requires very accurate LEO PCOs; the simulations suggest them to be smaller than 1 mm in order to keep scale changes below 1 mm.

Two methods to determine scale-independent GPS PCOs and GNSS-based terrestrial scale: comparison and cross-check

The GPS satellite transmitter antenna phase center offsets (PCOs) can be estimated in a global adjustment by constraining the ground station coordinates to the current International Terrestrial Reference Frame (ITRF). Therefore, the derived PCO values rest on the terrestrial scale parameter of the frame. Consequently, the PCO values transfer this scale to any subsequent GNSS solution. A method to derive scale-independent PCOs without introducing the terrestrial scale of the frame is the prerequisite to derive an independent GNSS scale factor that can contribute to the datum definition of the next ITRF realization. By fixing the Galileo satellite transmitter antenna PCOs to the ground calibrated values from the released metadata, the GPS satellite PCOs in the z-direction (z-PCO) and a GNSS-based terrestrial scale parameter can be determined in GPS + Galileo processing. An alternative method is based on the gravitational constraint on low earth orbiters (LEOs) in the integrated processing of GPS and LEOs. We determine the GPS z-PCO and the GNSS-based scale using both methods by including the current constellation of Galileo and the three LEOs of the Swarm mission. For the first time, direct comparison and cross-check of the two methods are performed. They provide mean GPS z-PCO corrections of - 186 pm 25 mm and - 221 pm 37 mm with respect to the IGS values and + 1.55 pm 0.22 ppb (parts per billion) and + 1.72 pm 0.31 in the terrestrial scale with respect to the IGS14 reference frame. The results of both methods agree with each other with only small differences. Due to the larger number of Galileo observations, the Galileo-PCO-fixed method leads to more precise and stable results. In the joint processing of GPS + Galileo + Swarm in which both methods are applied, the constraint on Galileo dominates the results. We discuss and analyze how fixing either the Galileo transmitter antenna z-PCO or the Swarm receiver antenna z-PCO in the combined GPS + Galileo + Swarm processing propagates to the respective freely estimated z-PCO of Swarm and Galileo.

GNSS scale determination using calibrated receiver and Galileo satellite antenna patterns

The reference frame of a global terrestrial network is defined by the origin, the orientation and the scale. The origin of the ITRF2014 is defined by the ILRS long-term solution, the orientation by no-net rotation conditions w.r.t. the previous reference frame (ITRF2008), and the scale by the mean values from global VLBI and SLR solution series (Altamimi et al. in J Geophys Res Solid Earth 121:6109–6131, 2016). With the release of the Galileo satellite antenna phase center offsets (PCO) w.r.t. the satellites center of mass (GSA in Galileo IOV and FOC satellite metadata, 2019) and the availability of new ground antenna calibrations for GNSS receivers, based on anechoic chamber measurements or on robot calibrations, GNSS global network solutions qualify to contribute to the scale determination of terrestrial networks, as well. Our analysis is based on global multi-GNSS solutions of the years 2017 and 2018 and may be seen as “proof of concept” for the contribution of GNSS data to the scale determination of the terrestrial reference frame. In a first step, the currently used Galileo PCO estimations (Steigenberger et al. in J Geod 90:773–785, 2016) are compared to the released PCO values, which show discrepancies on the decimeter-level. Eventually, the published Galileo PCOs are used in an experimental solution as known values. GNSS-specific PCOs are estimated, as well, for GPS and GLONASS, together with the “standard” parameters set up in global GNSS solutions. From the estimated network coordinates, a time series of daily scale parameters of the terrestrial network is extracted, which shows an offset of the order of 1 ppb (parts per billion, corresponding to a height difference of 6.4 mm on the Earth’s surface) w.r.t. to the ITRF2014 network and an annual variation with an amplitude of about 0.3 ppb.

GPS III Vespucci: Results of half a year in orbit

The spacecraft nicknamed Vespucci is the first GPS III satellite launched in December 2018. Numerous receivers of the global International GNSS Service network tracked the signals of this new generation of GPS spacecraft from January to July 2019. This data set serves as the basis for analysis of broadcast ephemeris performance and clock stability, as well as solar radiation pressure and satellite antenna phase center models. Different empirical orbit models are tested, and box-wing models are developed based on approximate dimensions, mass, and assumed optical properties. The box-wing models show in general a better performance than the empirical models. Compared to Block IIF satellites, the stability of the GPS III rubidium clock is higher for integration times up to 10 s. At longer integration times, the stability of both clocks is similar but the GPS III clock does not suffer from frequency-specific line bias variations that affect the apparent IIF clock. Estimated antenna phase center offsets agree on the centimeter level with the calibrations published by the manufacturer. Measurements with a 30-m high-gain antenna revealed that the satellite did not stop signal transmission in July 2019 but switched to non-standard codes and codes beyond the tracking capabilities of commercial GNSS receivers. Prior to this hibernation mode, a 70 days test without broadcast ephemeris update was conducted during which the user range error increased to roughly 1 km.

Improved Antenna Phase Center Offsets for BDS-2 IGSO/MEO Satellites Based on MGEX Long-Term Observations

For the purpose of further improving the solution accuracies of the orbital and geodetic parameters for BDS (BeiDou Navigation Satellite System) precise applications, this paper focuses on the enhancements of antenna phase center offsets (PCOs) for BDS-2 IGSOs (Inclined Geosynchronous Satellite Orbits) and MEOs (Medium Earth Orbits) through processing observations from a global tracking network. The daily estimated horizontal and vertical PCO time series of nearly three years from DOY (Day of Year) 001 in 2018 to DOY 180 in 2020 are obtained using the PANDA (Position And Navigation Data Analysis) software. The long-term PCO time series have seasonal variations and systematic effects along with the elevation angle of the Sun with respect to the orbital plane. Then, type-specific x-offsets and y-offsets of IGSOs and MEOs are comprehensively available considering the good consistency for the same satellite type. And a set of satellite-specific vertical offsets are recommended to BDS-2 IGSOs and MEOs since the low coherence of these satellites with the same type. Validation experiments are carried out for comparison between the original MGEX (Multi-GNSS Experiment) PCOs and the newly improved values (iMGEX PCOs for short), including the Precise Orbit Determination (POD) and Precise Point Positioning (PPP). Based on the orbital overlap analysis, the qualities of BDS-2 orbits show great enhancements in the along-track, cross-track and radial components, when the iMGEX PCOs are employed. Results of the independent assessment using SLR (Satellite Laser Ranging) also indicate the improvements on the radial component for C08, C10 and C11 satellites, and most of the orbit RMSs (Root Mean Squares) of iMGEX results decreased by 40.5% on average compared with the MGEX values. Additionally, the experimental station coordinates by static PPP achieve improvements at the rate of 27.1%, 32.6% and 28.4% in the east, north, and up component, respectively, in which more than a half stations realize sub-centimeter positioning accuracy in the north component using the iMGEX PCOs.

Estimation of the Antenna Phase Center Correction Model for the BeiDou-3 MEO Satellites

Satellite antenna phase center offsets (PCOs) and phase variations (PVs) for BeiDou-3 satellites are estimated based on the tracking data of the Multi-GNSS Experiment (MGEX) and the international GNSS Monitoring and Assessment System (iGMAS) network. However, when estimating the (PCOs) of BeiDou-3 medium Earth orbit (MEO) satellites by pure Extending the CODE Orbit Model (ECOM1), the x-offset estimations of the PCOs have a systematic variation of about 0.4 m with the elevation of the Sun above the orbital plane (β-angle). Thus, a priori box-wing solar radiation pressure (SRP) model of BeiDou-3 MEO was assisted with ECOM1. Then, the satellite type-specific PCOs and common PVs were obtained. The estimations of PCOs and PVs were compared with the MGEX PCOs from the precise orbit and clock offset. When the MGEX PCOs were used, the root mean square (RMS) of 24 h overlap was 6.76, 4.36, 1.46 cm, in along-track, cross-track, and radial directions, respectively; the RMS and standard deviations (STD) of the 24 h clock offset overlap were 0.28 and 0.15 ns; the fitting RMS of the 72 h clock offset of the quadratic polynomial was 0.243 ns. After comparing this with the estimated PCOs and PVs, the RMS of the 24 h orbit overlap was decreased by 6.5 mm (10.54%), 1.8 mm (4.4%), and 1.1 mm (8.03%) in the along-track, cross-track, and radial directions, respectively; the RMS and STD of the 24 h clock offset overlap were decreased by 0.024 ns (8.6%) and 0.020 ns (13.1%), respectively; the fitting RMS of the 72 h clock offset of the quadratic polynomial was reduced by about 0.016 ns (6.5%).

The Impact of Eclipsing GNSS Satellites on the Precise Point Positioning

When satellites enter into the noon maneuver or the shadow crossing regimes, the actual attitudes will depart from their nominal values. If improper attitude models are used, the induced-errors due to the wind-up effect and satellite antenna PCO (Phase Center Offset) will deteriorate the positioning accuracy. Because different generations of satellites adopt different attitude control models, the influences on the positioning performances deserve further study. Consequently, the impact of three eclipsing strategies on the single-system and multi-GNSS (Global Navigation Satellite System) Precise Point Positioning (PPP) are analyzed. According to the results of the eclipsing monitor, 65 globally distributed MGEX (Multi-GNSS EXperiment) stations for 31-day period in July 2017 are selected to perform G/R/E/C/GR/GREC PPP in both static and kinematic modes. The results show that the influences of non-nominal attitudes are related to the magnitude of the PCO values, maximum yaw angle differences, the duration of maneuver, the value of the sun angle and the satellite geometric strength. For single-system, using modeled attitudes rather than the nominal ones will greatly improve the positioning accuracy of GLONASS-only and BDS-only PPP while slightly contributions to the GPS-only and GALILEO-only PPP. Deleting the eclipsing satellites may sometimes induce a longer convergence time and a worse solution due to the poor satellite geometry, especially for GLONASS kinematic PPP when stations are located in the low latitude and BDS kinematic PPP. When multi-GNSS data are available, especially four navigation systems, the accuracy improvements of using the modeled attitudes or deleting eclipsing satellites are non-significant.

Spaceborne GPS receiver antenna phase center offset and variation estimation for the Shiyan 3 satellite

In determining the orbits of low Earth orbit (LEO) satellites using spaceborne GPS, the errors caused by receiver antenna phase center offset (PCO) and phase center variations (PCVs) are gradually becoming a major limiting factor for continued improvements to accuracy. Shiyan 3, a small satellite mission for space technology experimentation and climate exploration, was developed by China and launched on November 5, 2008. The dual-frequency GPS receiver payload delivers 1Hz data and provides the basis for precise orbit determination within the range of a few centimeters. The antenna PCO and PCV error characteristics and the principles influencing orbit determination are analyzed. The feasibility of PCO and PCV estimation and compensation in different directions is demonstrated through simulation and in-flight tests. The values of receiver antenna PCO and PCVs for Gravity Recovery and Climate Experiment (GRACE) and Shiyan 3 satellites are estimated from one month of data. A large and stable antenna PCO error, reaching up to 10.34cm in the z-direction, is found with the Shiyan 3 satellite. The PCVs on the Shiyan 3 satellite are estimated and reach up to 3.0cm, which is slightly larger than that of GRACE satellites. Orbit validation clearly improved with independent k-band ranging (KBR) and satellite laser ranging (SLR) measurements. For GRACE satellites, the average root mean square (RMS) of KBR residuals improved from 1.01cm to 0.88cm. For the Shiyan 3 satellite, the average RMS of SLR residuals improved from 4.95cm to 4.06cm.

Relative positioning calibration method of phase center offsets of GPS signal antennas

Phase center offset (PCO) of GPS antenna has a considerable influence on the precision and accuracy of the resulting coordinates. As joint observation mode of various GPS receivers and antennas becomes increasingly universal, efficient determination of PCO values of multi-type dual-frequency GPS receiver antennas at the same time needs to be addressed urgently. According to the property of antenna PCO, a relative positioning calibration method, which is based on GPS relative positioning survey theory, is proposed. This method only needs two steps, each being a simultaneous observation of one consecutive sidereal day for the reference antenna and the calibrated antenna. Experimental results for several widely used GPS antennas show that this method greatly improves the calibration efficiency and can estimate horizontal PCOs for both frequencies. The proposed method can be fully applied to synchronously assess PCOs of multi-type dual-frequency GPS antennas in high precision position.

Estimation of satellite antenna phase center offsets for Galileo

Satellite antenna phase center offsets for the Galileo In-Orbit Validation (IOV) and Full Operational Capability (FOC) satellites are estimated by two different analysis centers based on tracking data of a global GNSS network. The mean x- and y-offsets could be determined with a precision of a few centimeters. However, daily estimates of the x-offsets of the IOV satellites show pronounced systematic effects with a peak-to-peak amplitude of up to 70 cm that depend on the orbit model and the elevation of the Sun above the orbital plane. For the IOV y-offsets, no dependence on the orbit model exists but the scatter strongly depends on the elevation of the Sun above the orbital plane. In general, these systematic effects are significantly smaller for the FOC satellites. The z-offsets of the two analysis centers agree within the 10–15 cm level, and the time series do not show systematic effects. The application of an averaged Galileo satellite antenna model obtained from the two solutions results in a reduction of orbit day boundary discontinuities by up to one third—even if an independent software package is used.