Phase Center Offsets Research Articles

Absolute antenna group delay variations: estimation, single station repeatability and their influence on coordinate and float ambiguity estimation in baseline positioning

Phase center offsets and variations (PCV) are common corrections applied to global navigation satellite system (GNSS) phase observations in the context of precise point positioning. Similar to PCV are group delay variations (GDV), which affect code observations. In this paper, absolute GDVs, which are independent of a reference antenna, are estimated as antenna- and frequency-specific for the frequencies 1575.42 MHz and 1176.45 MHz, where separation of receiving and transmitting antenna GDV is possible with non-rotating antennas. Nineteen receiving and transmitting antennas of GPS, Galileo, BeiDou, and QZSS satellites, using observations from static reference stations, are considered. The single station repeatability of the receiver antenna GDV i.e., the estimation of the GDV using only one station, is evaluated for all antenna-frequency combinations. The repeatability ranges from 1.1 to 7.6 cm at a zenith angle of 80°, showing significant differences between antennas and frequencies. The estimated GDV corrections are applied to multi-GNSS baseline positioning using a total of 116 baselines. Receiver antenna GDV corrections exhibit a significant non-zero mean effect on the code-based vertical coordinate estimate. Float ambiguities are estimated using observation periods of up to 20 min. The 0.95-quantile effect of the GDV corrections on narrow lane ambiguity estimates is 2.02 cycles at the first epoch and 0.54 cycles after 5 min using 30 s observation sampling. The effect on wide lane ambiguities is constant over the 20-min period considered, with the 0.95-quantile being around 0.1 cycles for the GNSS considered.

GNSS satellite yaw attitude laws and impact on satellite clock, phase OSB and PPP-AR

Satellite yaw attitudes have significant impact on Global Navigation Satellite System (GNSS) data processing in two ways: the satellite horizontal phase center offset (PCO) corrections and phase wind-up corrections. When the Sun elevation angle is small, GNSS satellites are unable to maintain the nominal attitude and take place the yaw maneuvers. Generally, different types of satellites adopt different yaw attitudes during the yaw maneuver periods. In this research, the yaw attitude laws of different types of GPS, Galileo and BDS-3 satellites are comprehensively investigated, and the impact of yaw attitudes on satellite clock, phase observable-specific signal bias (OSB) and precise point positioning with ambiguity resolution (PPP-AR) are deeply evaluated. The main results show that for GPS Block IIF satellites, the maximum differences between the nominal yaw angles and the modeled yaw angles can reach to 360°. With the nominal attitude, the estimated phase OSB changes approximately 1 cycle and a 10 cm bias is observed in the U component positioning solutions of kinematic PPP-AR. After applying the modeled attitude, these obvious errors disappear. In addition, for BDS-3 SECM satellites, the mismodeling of the nominal attitude and CSNO modeled attitude results in 4-6 cm jumps in the detrended satellite clock residuals, and a 40 cm bias is observed in the U component positioning solutions of BDS-3 kinematic PPP-AR. After applying the modified CSNO modeled attitude to BDS-3 SECM satellites, the stability of satellite clocks and the positioning accuracy of PPP-AR are significantly improved.

Analysis of Comparability of PCV in Surveying-Grade GNSS Antenna – Topcon HIPER-VR Case Study

ABSTRACT It is well known that the phase center of a Global Navigation Satellite System (GNSS) antenna is not a stable point. For any given GNSS antenna, the phase center will change with the direction of the incoming signal from a satellite, as well as the frequency. Ignoring these phase center variations (PCVs) in GNSS data processing can lead to notable errors, especially in vertical position component determination. To avoid the problem, antenna PCV together with the phase center offset (PCO) information are recommended to be used in GNSS observation processing. We currently distinguish between individual and type-mean phase center correction (PCC) models. These models describe the variations in the phase center of the antenna as a function of the elevation angle and azimuth. In general, the primary difference between individual and type-mean models lies in their specificity. Individual models are highly precise but are valid only for a particular antenna model, while the type-mean models are more general and can be applied to a broad range of antennas of the same type, but may suffer from a lower level of precision. This paper aims to analyze the comparability of PCV in surveying-grade GNSS antennas. For the analyses, we propose to use an originally designed bench with precisely defined relative positions of the seven antenna mounting points. Preliminary studies have been performed using GPS observations on L1 and L2 frequencies recorded by seven Topcon HIPER-VR antennas. The results proved that the comparability of PCV for this antenna is high. The position error did not exceed 3 mm. It could be assumed that the type-mean PCC model could describe PCV all antennas of this type with good accuracy.

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.

Manufacturer calibrations of GPS transmit antenna phase patterns: a critical review

Over the past decade, the Global Positioning System has released pre-flight calibrations for the transmit antennas of the Block IIR/IIR-M, Block IIF, and GPS III satellites that make up the current GPS constellation. Frequency-specific phase variations (PHVs) provided as part of these data sets are of key interest for an accurate and consistent modeling of GNSS carrier phase observations in precise point positioning applications as well as orbit and clock offset determination of the GPS satellites themselves. For proper utilization of the manufacturer calibrations, complementary information on the phase center offset (PCO) from the spacecraft center-of-mass is required. We describe necessary processing steps for converting the raw phase calibrations of Lockheed Martin and Boeing into a representation compatible with antenna models of the International GNSS Service (IGS), and provide a detailed discussion of inherent assumptions for combining PHVs and PCOs from different sources. Comparison with estimated antenna data from globally distributed monitoring stations shows good consistency of PHVs and suggests the use of manufacturer-calibrated, azimuth-dependent patterns in future releases of the IGS antenna model. In terms of PCOs, the new Block IIF calibrations exhibit a systematic bias of about 12 cm from PCOs estimates based on the IGS20 reference frame. This value closely matches the bias observed for manufacturer calibrations of GPS III and Galileo satellites, and suggests a careful review of the contribution that GNSS can make to the scale definition of the International Terrestrial Reference Frame (ITRF).

Validation of GPS III transmit antenna calibrations

Accurate information about the satellite transmit antennas is essential for high-precision GNSS applications. Such metadata of the GPS III satellites were publicly made available by the manufacturer Lockheed Martin. They comprise phase center offsets (PCOs), phase patterns, and directivity patterns. These calibrations are validated with ground-based measurements of a global GPS tracking network and observations of a high-gain antenna. Phase center offsets and patterns are estimated from dual-frequency observations of a ground tracking network. The ionosphere-free L1/L2 z-PCOs show a 10 cm offset w.r.t. the manufacturer calibrations due to already known inconsistencies with the ITRF2020 scale fixed in the estimation. The standard deviation of the differences between estimated and calibrated z-PCOs is 2.7 cm. The estimated phase patterns have a 0.7 mm RMS consistency with the manufacturer calibrations after minimizing the raw patterns for nadir angles between 0° and 14°. The directivity patterns are validated with the effective isotropic radiated power (EIRP) measured with a 30 m high-gain antenna. The measured EIRP for the L1 and L2 band is affected by M-code transmission from a distinct antenna. When modeling the additional contribution of this antenna, the nadir-angle variation of the EIRP matches the calibrated directivity patterns with a precision of 0.1 dBW. Representative transmit power values of the main navigation antenna amount to 125 W, 30 W, and 85 W in the L1, L2, and L5 bands, while the L1 and L2 M-code signals are transmitted with about 30 W and 25 W, respectively.

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.

Estimating inter-satellite link Ka-band antenna phase center offsets to improve BDS-3 satellite orbit determination

Satellite antenna phase center offset (PCO) correction is essential not noly for L-band ground-tracking GNSS high-precision data processing, but also for Ka-band inter-satellite link (ISL) observations. The Ka-band ISL and L-band satellite-ground observations of 90 days from 25 November 2020 to 23 February 2021 are used for the Ka-band PCO estimation and precise orbit determination (POD) validation for BDS-3 satellites. The results show that the standard deviations of the estimated Ka-band PCOs for 29 BDS-3 satellites are 1.73, 2.63 and 3.58 cm in the X, Y and Z components, respectively. The accuracy of the Ka-band PCO estimates for medium Earth orbit satellites (MEO) is better than those of inclined geosynchronous orbit (IGSO) and geostationary Earth orbit (GEO) satellites due to a better observation geometry. The POD validation results indicate that using the estimated Ka-band PCOs can improve the ISL-based orbit determination performance. Using Ka-band ISL and L-band satellite-ground observations with 40 global stations for combined POD, the orbit overlap comparison shows that the average three-dimensional (3D) root mean square (RMS) error for 29 BDS-3 satellites is decreased from 12.6 to 6.6 cm with a reduction of 47.6%, and satellite laser ranging (SLR) validation for 4 BDS-3 satellites shows an accuracy improvement from 6 to 5 cm in RMS. When using ISL and only 7 regional ground stations are used, the average 3D RMS of orbit overlap errors is decreased from 15.9 to 10.9 cm with a reduction of 31.6%, and the RMS of SLR residuals for 4 BDS-3 satellites is decreased from 6.7 to 5.6 cm. For ISL-only POD, the average 3D RMS of orbit overlap errors is decreased from 18.0 to 12.4 cm with a reduction of 31.1%, and the RMS of SLR residuals for 4 BDS-3 satellites is decreased from 7.1 to 6.9 cm.

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.

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

Impact of ambiguity resolution on phase center offsets and hardware delay estimation for BDS-3 inter-satellite links

The Chinese BeiDou navigation satellite system (BDS) has already completed its three phases and developed into a global navigation satellite system for open positioning, navigation, and timing services. The BDS-3 satellites feature the inter-satellite link (ISL). The ISL observation-related error model and ambiguity resolution for L-band observation are the crucial factors in precise data processing. In this study, we present for the first time the impact of ambiguity resolution on phase center offsets (PCOs) and hardware delay estimation of BDS-3 inter-satellite links. Two weeks’ L-band observations from 99 globally distributed ground stations and Ka-band ISL observations are collected for experimental validation and analysis. First, network solutions with and without ISL observations are conducted to investigate the role of ISL observation in ambiguity resolution. Afterward, ISL observation-related errors, mainly PCOs and hardware delays, are estimated by processing L-band with ISL observations with and without ambiguity resolution to analyze the impact of ambiguity resolution on these two factors. Finally, orbit accuracy in the network solution is assessed to further validate the effectiveness of the estimated PCOs and hardware delays in our experiment. The result indicates that introducing the ISL can slightly improve the fixing rate compared to only L-band observations from 83.7% to 84.3%. Furthermore, ambiguity resolution has a positive influence on the stability of estimated PCOs and hardware delays in turn, although the root mean square (RMS) values basically remain unchanged. The standard deviation (STD) of the x-offset is reduced from 0.021 m to 0.012 m, a significant improvement of about 43%, and 0.022 m–0.016 m, with an improvement of about 27%, for the y-offset. There is a slight improvement of about 8% for z-offset. Similarly, around 10% improvement in the STD for hardware delays can be achieved while the RMS values almost stay the same except for C40. Orbit determination from network solutions shows high accuracy compared to the public products for the satellite with good geometry configuration, which further validates our estimates for ISL PCOs and hardware delays.

Performance of Galileo satellite products determined from multi-frequency measurements

Each Galileo satellite provides coherent navigation signals in four distinct frequency bands. International GNSS Service (IGS) analysis centers (ACs) typically determine Galileo satellite products based on the E1/E5a dual-frequency measurements due to the software limitation and the limited tracking capability of other signals in the early time. The goal of this contribution is to evaluate the quality of Galileo satellite products determined by using different dual-frequency (E1/E5a, E1/E5b, E1/E5, E1/E6) and multi-frequency (E1/E5a/E5b/E5/E6) measurements based on different sizes of ground networks. The performance of signal noise, the consistency of frequency-specific satellite phase center offsets and the stability of satellite phase biases are assessed in advance to confirm preconditions for multi-frequency processing. Orbit results from different dual-frequency measurements show that orbit precision determined from E1/E6 is clearly worse (about 35%) than that from other dual-frequency solutions. In view of a similar E1, E5a, E5b and E6 measurement quality, the degraded E1/E6 orbit performance is mainly attributed to the unfavorable noise amplification in the respective ionosphere-free linear combination. The advantage of using multi-frequency measurements over dual-frequency for precise orbit determination is clearly visible when using small networks. For instance, the ambiguity fixing rate is 80% for the multi-frequency solution while it is less than 40% for the dual-frequency solution if 150 s data sampling is employed in a 15-station network. Higher fixing rates result in better (more than 30%) satellite orbits and more robust satellite clock and phase bias products. In general, satellite phase bias products determined from a 20-station (or more) network are precise enough to conduct precise point positioning with ambiguity resolution (PPP-AR) applications. Multi-frequency kinematic PPP-AR solutions always show 5–10% precision improvement compared to those computed from dual-frequency observations.

Yaw attitudes for BDS-3 IGSO and MEO satellites: estimation, validation and modeling with intersatellite link observations

Previously disclosed satellite metadata, as well as previous estimations using the reverse kinematic precise point positioning approach with L-band data, have already demonstrated the use of a continuous yaw-steering model by the BDS-3 Medium Earth Orbit (MEO) satellites manufactured by the China Academy of Space Technology (CAST) in deep eclipse periods instead of the orbit-normal mode. However, the yaw model has not been validated for MEO satellites manufactured by the Shanghai Engineering Center of Microsatellites (SECM), as the horizontal phase center offsets are close to zero. Moreover, the attitude model has also not been confirmed for BDS-3 Inclined Geostationary Orbit (IGSO) satellites. In this study, the intersatellite link (ISL) data are used to estimate the yaw angles of BDS-3 IGSO and MEO satellites with an accuracy of approximately 3.0° to investigate their yaw behaviors, particularly in deep eclipse periods. The estimates confirm that the IGSO and MEO satellites from CAST show the same yaw behaviors, while the SECM MEO satellites do not fully comply with the attitude law published by the China Satellite Navigation Office (CSNO). The attitude transition deviates from that predicted by the CSNO yaw law and occurs when the elevation angle of the Sun above the orbital plane (beta -angle) crosses 0° and the absolute value of the yaw angle is no more than 5°. The transition is completed within three to five minutes at a rate of approximately 0.055°/s. A model is proposed to predict these behaviors, and the ISL residuals return to normal levels and become more stable adjacent to midnight and noon points when the yaw models are used.

Estimation of Vertical Phase Center Offset and Phase Center Variations for BDS-3 B1CB2a Signals

The BeiDou Global Satellite Navigation System (BDS-3) broadcast newly developed B1C and B2a signals. To provide a better service for global users, the vertical phase center offset (PCO) and phase center variation (PCV) are estimated for the B1C/B2a ionospheric-free linear combination of the BDS-3 inclined geostationary orbit (IGSO) and medium earth orbit (MEO) satellites in this study. And considering the traditional PCC estimation method needs two Precise orbit determination (POD) processing, based on the correlation between PCO z-offset and PCV, the theoretical analysis and experimental comparison have been made to discuss whether the POD procedure for the PCO estimation can be omitted. The estimated z-offset time series revealed the inadequacy of the solar radiation pressure (SRP) model for the IGSO satellites and the MEO satellites with Pseudo Random Noise code (PRN) C45 and C46. The PCVraws estimated by the traditional method and the PCO estimation omitted method have the same characteristic. The final PCO z-offsets and PCVs calculated by the two schemes agreed very well with differences can be harmlessly ignored, which confirmed that the PCO estimation can be safely omitted to save computation time. The PCC model proposed in this study has been compared with the Test and Assessment Research Center of China Satellite Navigation Office (TARC/CSNO) released model, the qualities of the orbits and BDS-only precise point positioning (PPP) solutions of the new model both show improvements, except for the IGSO orbits. The analysis of the IGSO orbits further verifies the SRP model is not suitable for the IGSO satellites.

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 .

Phase Center Offset Calibration and Multipoint Time Latency Determination for UWB Location

The ultrawideband (UWB) system generates the precise Time of Arrival (TOA) to realize precise indoor positioning for various Internet of Things (IoT) applications. However, less attention has been paid to mitigating systematic errors in the UWB positioning algorithm, which could be a significant factor that reduces the positioning accuracy. The systematic errors are introduced mainly from two aspects. First, the offsets between the antenna reference point (ARP) and the real incidence point are not carefully eliminated from the ranging observations. Second, the between-antenna time latencies used for cable-linked synchronization usually contain systematic errors at the calibration point. In this article, we present two techniques, including the antenna phase center offset (PCO) calibration and the multipoint time latency determination (MTLD), to reduce the impact of systematic errors on the UWB positioning accuracy. The experiments are carried out in an indoor parking lot. The results show that the established PCO calibration model can correct the PCO errors by 70%. The accuracy of time latency determination is improved by 10% with MTLD and further by 44% with both MTLD and PCO calibration. The static and kinematic positioning tests indicate that the horizontal accuracy is improved from 31 to 10 cm and 20 to 10 cm, respectively.

Precise orbit determination and precision comparison for FY3C and FY3D with receiver antenna GPS and BDS PCV using spaceborne BDS and GPS observation data

The FY3C and FY3D satellites were equipped with global navigation satellite occultation detector (GNOS) receivers that received both GPS and BDS-2 signals. For further improving precise orbit determination (POD) precisions, we estimated receiver GPS and BDS signal phase center variations (PCV) models with 2° and 5° resolutions and set the different weights for GPS and BDS-2 observations in the combined POD. The BDS-based POD precision using BDS-2 satellite antenna phase center offset (PCO) values from the China Satellite Navigation Office (CSNO) are not as accurate as those obtained from the International GNSS Service (IGS) Multi-GNSS experiments project (MGEX). The estimated receiver GPS and BDS PCV models with 2° and 5° resolutions were estimated from the GPS phase residuals of GPS-based POD and BDS phase residuals of combined POD, respectively. In most cases, the POD precisions using the estimated PCVs with 2° resolution are superior to those with 5° resolution. The precisions of the BDS-based POD and combined POD were both improved by introducing the receiver BDS PCV models. The weighting for GPS and BDS-2 observations can further improve the precision of the combined POD. The tested results of selected weights are better than those with equal weight in the combined POD. The experiment results show that orbital precisions of FY3C are worse than those of FY3D.

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.

Effect of PCV and attitude on the precise orbit determination of Jason-3 satellite

Abstract Satellite attitude modes and antenna phase center variations have a great influence on the Precise Orbit Determination (POD) of Low Earth Orbit satellites (LEOs). Inaccurate information about spacecraft attitude, phase center offsets and variations in the POD leads to orbital error. The Jason-3 satellite experienced complex attitude modes which are fixed, sinusoidal, ramp-up/down and yaw-flip. Therefore, it is necessary to properly construct the attitude model in the process of POD especially when there is no external attitude data. For the antenna phase center correction, the PCO which is the deviation between Antenna Reference Point (ARP) and Mean Antenna Phase Center (MAPC) usually can be calibrated on the ground accurately, but the PCV which is the deviation between Instantaneous Antenna Phase Center (IAPC) and Mean Antenna Phase Center (MAPC) will change greatly with the change of space environment. Residual approach can be used to estimate the receiver PCV map. In this paper, we collected the on-board GPS data of Jason-3 satellite from January 2019 and analyzed the impacts of PCV and spacecraft attitude on the orbit accuracy by performing the reduced-dynamic POD. Compared with the reference orbit released by the Centre National d’Études Spatiales (CNES), using the PCV map can reduce the Root Mean Square (RMS) of orbit differences in the Radial (R), Along-track (T), Cross-track (N) and 3D direction about 0.3, 1.0, 0.9, and 1.4 mm. Based on the estimated PCV map, the orbit accuracy in R, T, N and 3D direction is 1.24, 2.81, 1.17, and 3.29 cm respectively by using the measured attitude data. When using the attitude model, the orbit accuracy in R, T, N and 3D directions is 1.60, 3.54, 1.33, and 4.13 cm, respectively. The results showed that the combination of measured attitude data and modeled PCV map can obtain the better orbit solution. It is essential to build a corresponding model in high-precision orbit determination, when there is no attitude data and PCV map.