Centimeter-level precise orbit determination for the HY-2A satellite using DORIS and SLR tracking data
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- Kong, Q., Guo, J., Sun, Y. et al. Acta Geophys. (2017) 65: 1. doi:10.1007/s11600-016-0001-x
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The HY-2A satellite is the first ocean dynamic environment monitoring satellite of China. Centimeter-level radial accuracy is a fundamental requirement for its scientific research and applications. To achieve this goal, we designed the strategies of precise orbit determination (POD) in detail. To achieve the relative optimal orbit for HY-2A, we carried out POD using DORIS-only, SLR-only, and DORIS + SLR tracking data, respectively. POD tests demonstrated that the consistency level of DORIS-only and SLR-only orbits with respect to the CNES orbits were about 1.81 cm and 3.34 cm in radial direction in the dynamic sense, respectively. We designed 6 cases of different weight combinations for DORIS and SLR data, and found that the optimal relative weight group was 0.2 mm/s for DORIS and 15.0 cm for SLR, and RMS of orbit differences with respect to the CNES orbits in radial direction and three-dimensional (3D) were 1.37 cm and 5.87 cm, respectively. These tests indicated that the relative radial and 3D accuracies computed using DORIS + SLR data with the optimal relative weight set were obviously higher than those computed using DORIS-only and SLR-only data, and satisfied the requirement of designed precision. The POD for HY-2A will provide the invaluable experience for the following HY-2B, HY-2C, and HY-2D satellites.
KeywordsHY-2A satellite Precise orbit determination DORIS SLR Weight
HY-2A was launched on August 16, 2011, and as the first mission of the earth observation satellite HY-2 series (including HY-2A, HY-2B, HY-2C, and HY-2D) focuses on monitoring the marine dynamic environment with microwave sensors to detect sea surface wind field, height, and temperature. It can provide important measures to address climate change. HY-2B has just been approved and will be launched at the end of 2016 and HY-2C will be in 2019 on schedule. Therefore, the precise orbit determination (POD) for HY-2A will provide invaluable experiences for the subsequent satellites. To achieve the orbit radial accuracy up to the centimeter level, the HY-2A satellite loads a Doppler Orbit Determination and Radio positioning Integrated by Satellite (DORIS) receiver, a dual-frequency Global Positioning System (GPS) receiver, and a Satellite Laser Ranging (SLR) retro-reflector array (Zhao et al. 2013; Guo et al. 2013a; Kong et al. 2014).
DORIS is an excellent satellite tracking system supporting precise orbit determination of satellites (Tapley et al. 1994; Tavernier et al. 2006; Zelensky et al. 2010). The DORIS system is jointly developed and deployed by the Centre National d’Etudes Spatiales (CNES), Institut national de l’information géographique et forestière (IGN), and Groupe de Recherche de Géodésie Spatiale (GRGS), France. It is based on the one-way measurement of Doppler frequency shift. The selection of a one-way system (uplink) allows fully automated operation of beacons and easy communication within the whole system. The signal is transmitted by ground beacons and received by the onboard DORIS package when the satellite transits over the sky above the ground beacons (Seeber 1993). The data are processed on the ground to support the centimeter-level orbit determination for the satellite. DORIS data are also processed on board to provide real-time satellite positioning with an accuracy of some tens of centimeters. DORIS was originally designed to perform the precise orbit determination especially for TOPEX/Poseidon, and the high accuracy orbit derived from this technique played a critical role in ocean altimeter experiments (Choi 2003; Jiang et al. 2014) with an accuracy of 10 cm (Willis 1995). The TOPEX/Poseidon satellite was equipped with the first generation DORIS receiver, and achieved 13 cm radial orbit accuracy for POD (Tapley et al. 1994). With the first flight of the DGXX generation receiver on-board Jason-2, DORIS entered a new era of POD capability (Auriol and Tourain 2010; Zelensky et al. 2010). Zelensky et al. (2010) achieved an average fit value of 1.02 cm in radial direction for Jason-2 using DORIS-only data. The current DGXX generation DORIS receiver onboard HY-2A can simultaneously track 7 DORIS beacons with 2 × 7 channels (Mercier et al. 2010). This capability can increase the observation quantity, improve the coverage of observations, enhance the geometric strength, and hence improve the accuracy of orbit determination. All of these advantages will help the POD community to achieve the centimeter-level radial accuracy goal.
As a high precise tracking and positioning space geodetic technique, the SLR system is based on a two-way range principle and can provide the absolute range from tracking station to satellite. The international laser ranging service (ILRS) is responsible for the simultaneous observation and scientific product delivery of all satellites equipped with the laser retro-reflector array (LRA) (Pearlman et al. 2002; Gurtner et al. 2005). For nearly four decades, SLR has provided the primary tracking data for numerous geodetic missions such as LAGEOS, TOPEX/Poseidon, Jason, Envisat, HY-2A, and so on. On the panel of HY-2A, a dedicated LRA is equipped facing the Earth. LRA onboard HY-2A is similar to those on Envisat, ERS-2, and Jason-1/2, and plays an important role in proving a calibration tool and improving the POD solution (Luthcke et al. 2002, 2003; Urschl et al. 2005; Zhao et al. 2013; Kong et al. 2014).
If SLR data are combined with the other independent space geodetic data, the geometric structures will be strengthened, the solution will be more stable than those using the single geodetic technique, and the systematic error will be compensated to some extent. Thus, the accuracy of POD will be significantly improved (Zhang et al. 2000). Recent researches focus on using multi-geodetic techniques to estimate satellite orbit (e.g., Choi 2003; Lemoine et al. 2010; Zelensky et al. 2010; Cerri et al. 2010; Melachroinos et al. 2011; Peng et al. 2012; Thaller et al. 2013; Sheng et al. 2014; Hackel et al. 2015; Sosnica et al. 2015). Recent orbit accuracy based on DORIS + SLR data can reach about 2 cm in the radial direction thanks to the development of tracking instruments and the gradual perfection of the physics-based force models. Some of researchers have achieved 1 cm using SLR/DORIS in the radial direction (e.g., Choi 2003; Lemoine et al. 2010; Zelensky et al. 2010; Cerri et al. 2010; Couhert et al. 2015). Radial orbit accuracies for ERS-1 and ERS-2 have reached 2–3 cm (Rudenko et al. 2012). 6 cm of 3D RMS (root mean square error) was achieved for Jason-2 using DORIS + SLR data (Peng et al. 2012). Accuracy better than 2 cm in the radial direction was obtained for Jason-2 using combined GPS, SLR, and DORIS data (Sheng et al. 2014). One decimeter orbit accuracy was achieved for the first two Galileo In-Orbit Validation (IOV) satellites using combined GNSS + SLR observations (Hackel et al. 2015).
To achieve the precise orbit determination for HY-2A, a lot of work has been carried out. Zhao et al. (2013) and Wang et al. (2014) showed that the radial accuracy can be better than 3 cm using SLR-only data. Zhu et al. (2013) showed the radial accuracy of about 2 cm using DORIS-only data. Lin et al. (2014) and Guo et al. (2013b) demonstrated that the radial accuracy better than 2 cm can be achieved using GPS-only data. Jiang et al. (2014) have achieved 4.40 cm radial accuracy using combined DORIS and SLR data.
The precise orbit of HY-2A can provide a reference frame for the oceanic science research of this mission. To achieve the centimeter-level radial accuracy, independent DORIS and SLR data are selected to determine the HY-2A satellite orbit with the dynamic method. Section 2 of this paper addresses the factors related to HY-2A; Sect. 3 analyzes the performance of DORIS and SLR; Sect. 4 describes the POD strategies; Sect. 5 focuses on analyzing the RMS of orbit differences between the achieved orbits using DORIS-only, SLR-only, and DORIS + SLR data with respect to the precise CNES orbits, and compares the orbit difference RMS between DORIS-only, SLR-only, and DORIS + SLR data. Finally, the optimal relative weights for DORIS and SLR data are recommended for the optimal solution.
The HY-A satellite description
The HY-2A mission was approved jointly by the Ministry of Finance and State Administration of Science, Technology and Industry for National Defense of PRC in January, 2007. This satellite is the first ocean dynamic environment monitoring satellite sponsored by the State Oceanic Administration of China (SOA), and is the third Chinese ocean satellite after HY-1A and HY-1B. The HY-2A mission is one of the key civil space projects in the 11th Five-Year Plan of China. It runs in a near sun-synchronous orbit with a lifetime of more than 3 years. It has an orbital inclination of 99.3°, altitude of 971 km, and an equator crossing time on descending node at 6:00 a.m. In the first stage, its repeat cycle is 14 days with an intersection period of 104.46 min and it runs 13 + 11/14 revolutions every day. In the second stage, it will cover 13 + 131/168 revolutions every day with the repeat cycle of 168 days. The main remote sensor payloads on it include one radar altimeter, one microwave scatterometer, one microwave scanning radiometer, one microwave calibrating radiometer, etc.
The attitude error of a satellite can degrade the accuracy of the computed orbit to a great extent (Tseng et al. 2012) because attitude models can not exactly describe the observed attitude in real time and cannot reflect the time lag (Sheng et al. 2014). Normally, attitudes should be taken into consideration in POD strategy. Usually, adjustment of attitude angles of roll, pitch, and yaw is required to compensate the impact of attitude maneuver. For HY-2A satellite, the attitude controller is stable inertial wheels, which can make three-axis pose stability lower than 0.003 °/s, pointing precision lower than 0.1°, and measurement precision lower than 0.05° in pitch, roll, and yaw in local orbital frame (Kong et al. 2014). The satellite is three-axis stabilized, and is non-spinning relative to the satellite reference frame.
During the operational stage, the satellite mass and the mass center change during the HY-2A maneuver. The detailed information about mass and mass center is available from IDS.1
Positions of LRA optical center, DORIS and LRA phase centers in the satellite reference frame (m)
DORIS receiver phase center
LRA phase center
LRA spherical center
The optical and infrared properties of the macro-model and the plate surfaces
Normal in satellite reference frame
Doris and SLR tracking data performance
In this paper, we applied DORIS range rate data and SLR normal point data from September 8, 2012 to December 21, 2012 to compute the precise orbits of HY-2A. During these 105 days, HY-2A was tracked by 50 DORIS beacon stations and 25 SLR stations. 50 DORIS beacon stations are evenly distributed over the globe, whereas most SLR tracking sites are concentrated in Europe and North America, with a few stations in Asia and the southern hemisphere. The DORIS system has no weather restriction and beacons are designed to operate for a long time with little human intervention. Therefore, sufficient observations are available from the HY-2A satellite. However, only 3 DORIS beacon stations have tracked HY-2A on October 26, 2012. We have not computed the orbits for HY-2A on this day using DORIS-only and DORIS + SLR data.
For the low Earth orbit satellite, the SLR tracking normal point data are rare. Gaps of several hours occur very frequently because of bad weather conditions near SLR stations. During these 105 days, 25 SLR stations have tracked this mission. There are 11 days in which the number of SLR passes per day is less than 6, and we have not solved the orbits in these days for HY-2A using SLR-only data. The SLR data used in the process of POD are normal point data compressed from original tracking data for HY-2A.
HY-2A pod strategy using Doris and SLR data
POD was carried out using 10 s integrated Doppler data and the normal point data of SLR from September 8, 2012 to December 21, 2012. The accuracy of orbit determination is affected by several factors, such as tracking station distribution, quantity and quality of precise tracking data, and the accuracy of available forces and measurement models (e.g., gravity field, atmospheric drag, solar radiation pressure, phase center corrections, station coordinates, etc.) (Tapley et al. 1994). The even beacon distribution and the high precise observations of DORIS provide the possibility of POD. Considering the quantity of observation and the strength of the geometric structure of tracking stations (Švehla and Rothacher 2003; Kong et al. 2014), the dynamic method was selected for POD of HY-2A. Dynamic orbit determination is a very precise method, and the accuracy of the derived orbit for HY-2A strongly depends on the accuracy of force models. The exact modeling of ocean tides of the Earth is a difficult problem because of the complex hydrodynamic response to the tidal forces. Approximately the same as the solid Earth tides, the dynamical effect of ocean tides is most easily described as periodic variations in the normalized geopotential coefficients. Both solar radiation and Earth albedo radiation have significant influence on the low Earth orbit satellite and neither of them can be neglected (Zelensky et al. 2010). For DORIS and SLR data, the tropospheric refraction corrections were computed using the modified Hopfield model (Goad and Goodman 1974) and the Mendes-Pavlis model (Mendes et al. 2002; Mendes and Pavlis 2004), respectively. Remaining errors of the non-gravitational force models can cause secular and long-term changes in the orbital elements, which can be effectively compensated with the RTN empirical force model (Doornbos et al. 2002; Kang et al. 2006; Liu 2013; Kong et al. 2014). Cowell II numerical integration (Balmino and Barriot 1989) was used during the HY-2A satellite orbit determination, and the integration step size was 20 s in Geodyn II software. The output interval of orbit ephemeris was 60 s.
In the process of POD, all unknown parameters were estimated simultaneously, including the coordinates, velocities, atmospheric drag coefficients, solar radiation coefficients, and empirical acceleration coefficients. The RTN (R: Radial direction; T: Along-track direction; N: Cross-track direction) empirical force model was used (Colombo 1989), and coefficients of one-cycle-per-revolution empirical accelerations were estimated every day in the cross-track. Bias, cosine, and sine terms were computed in the cross-track direction. The initial state vectors were estimated per orbital arc. The MSIS86 model (Hedin 1987) was used and the coefficients Cd were estimated per 6 h. The Box-wing solar radiation pressure model was applied and the coefficients were estimated per 6 h. In the iterative computation, the least square estimation method was applied to estimate the initial parameters of position/velocity of this satellite. The computation continued until the residuals between the derived results of two adjacent iterations were less than the designed tolerance values (Tapley et al. 1994, Kong et al. 2014).
10° and 15° were the cutoff elevation angles of DORIS and SLR data, respectively. During the process of POD, UTC time was used. SLR tracking data time is UTC time, and DORIS tracking data time is TAI time. The constant offset (leap second) of 35 s was introduced when DORIS data were applied.
Adopted dynamic models and measurements in orbit determination for HY-2A
The coordinates of DORIS beacon stations and DORIS measurements
The coordinates of SLR tracking stations and SLR data
ILRS; SLR normal point data
Earth gravity model
EGM2008 (Pavlis et al. 2012), 80 × 80
JPL DE403 (Standish 1998)
Solid Earth tides
IERS2010 (Petit and Luzum 2010)
Ocean tides and ocean tides loading
FES2004 (Lyard et al. 2006)
IERS2003 (McCarthy and Petit 2033)
Solar radiation pressure
Box-Wing (Rim 1992)
Earth albedo radiation
Knocke–Ries–Tapley (Knocke et al. 1988)
MSIS86 (Hedin 1987)
Cut off angle
DORIS: 10°; SLR: 15°
Usually, for the missions equipped with a DORIS receiver, the computed orbit solutions would be compared with the CNES orbits,3 which were solved using combined DORIS, GPS, and SLR data (Peng et al. 2012; Cerri et al. 2013; Couhert et al. 2015; Gao et al. 2015) and achieved about 1.1 cm radial accuracy (Gao et al. 2015; Zhang and Vincent 2011) for HY-2A satellite. The precise CNES orbit and the one we derived may have used different models, and we can examine the validity of the models we applied by comparing our orbits with the CNES ones. The disadvantage is that we can achieve the relative accuracy and check the orbit consistency with respect to the CNES orbit.
POD using DORIS and SLR data for HY-2A
POD using DORIS-only data for HY-2A
Statistics of orbit difference RMS with respect to CNES orbits using DORIS-only data (cm)
Figure 2 and Table 4 show that the radial direction has the smallest RMS of orbit difference with respect to the CNES orbits among these three directions, and the RMS in this direction is 1.81 cm, which meets the radar altimeter requirement for science research and applications. The difference RMS value of the cross-track direction is a little bigger than that of the radial direction, and the biggest difference RMS value is that of the along-track direction, and the RMS in this direction is 6.17 cm. This experiment indicates that high density of beacon stations and highly precise HY-2A DORIS tracking data guarantee DORIS the high POD capability. The test results suggest that DORIS-only POD achieved better than 2 cm level relative accuracy in the radial direction during the observation time, and the relative accuracy is higher than the result achieved by Zhu et al. (2013) using DORIS-only data in 30 days, and is a little lower than the result achieved by Gao et al. (2015) using DORIS-only data in 93 days, and both of which were compared with the CNES obits.
POD using SLR-only data for HY-2A
Statistics of orbit difference RMS with respect to CNES orbits using SLR-only data (cm)
Figure 3 and Table 5 indicate that the RMS of differences with respect to the CNES orbits is 3.34 cm in the radial direction, and the RMS in the cross-track direction is 5.69 cm, while in the along-track direction, the RMS is 10.62 cm. From these test results, we know that the highest orbit precision is in the radial direction, mainly because the SLR data measure the absolute range between tracking station and satellite. Generally, the 3D RMS can reach 11.96 cm in position. Though the precision achieved using SLR-only data is lower than that derived from DORIS data, SLR data is of capability in calibration (Kong et al. 2014), validation, and improvement of the DORIS-based POD solutions. We have achieved similar RMS difference level to the results achieved by Zhao et al. (2013) and Wang et al. (2014) in 30-day arcs with respect to CNES in radial direction.
POD using DORIS + SLR data for HY-2A
For the POD using combined DORIS and SLR data, the weights for each kind of data play a crucial role in the accuracy of POD. Choi (2003) selected 10 cm as the fixed weight for SLR data and 2 mm/s for DORIS data during the process of POD for Jason-1and then combined with GPS data. Zelensky et al. (2010) adopted 10 cm and 3 mm/s as the weights of SLR and DORIS for Jason-1 and Jason-2 and achieved 1 cm radial accuracy. With the improvement of accuracy of SLR tracking data and DORIS receivers, Peng et al. (2012) selected 5 cm and 0.50 mm/s as weights for SLR and DORIS data to achieve POD for Jason-2 and 1.55 cm radial accuracy has been achieved. Doornbos et al. (2002) adopted 0.45 and 0.55 mm/s as the DORIS data weights and 3 cm as the SLR data weights for Jason-1 and Envisat, respectively.
A realistic way of seeking the optimal relative weights is to set the weights according to the RMS of post-fit residuals of different data types. The RMS of post-fit residuals for DORIS data is about 0.31 mm/s, and that for SLR-only data are about 3.2 cm. These data can serve as the references for the prior standard deviations for these two types of data. The sigmas should be adjusted to determine the best orbit solution, because the amount of DORIS data is large and the DORIS beacon stations are distributed evenly over the global. Conversely, the amount of SLR data is small and the tracking stations are distributed unevenly. The a priori sigma for DORIS is set around the observation level while that for SLR is set about 3–5 times larger than the post-fit residual RMS of SLR data (Choi 2003).
Statistics of the mean orbit difference RMS with respect to CNES orbits using DORIS + SLR data with different relative weights (cm)
DORIS Weight: 0.2 mm/s; SLR weight: 5.0 cm
DORIS Weight: 0.3 mm/s; SLR weight: 5.0 cm
DORIS Weight: 0.2 mm/s; SLR weight: 10.0 cm
DORIS Weight: 0.3 mm/s; SLR weight: 10.0 cm
DORIS Weight: 0.2 mm/s; SLR weight: 15.0 cm
DORIS Weight: 0.3 mm/s; SLR weight: 15.0 cm
There is a breakpoint in Fig. 4 because we did not compute the orbit on 26 October, 2012 in convenience of comparison between orbits derived using DORIS-only and DORIS + SLR data, and the statistics of the mean orbit difference RMS derived from 104 days are listed in Table 6.
From Fig. 4 we can notice that there are large residuals between 56,208 and 56,255 MJD. According to Mansoori et al. (2015) and Li et al. (2016), there are two geomagnetic storms on days 56208 and 56244. Both geomagnetic storms can produce positive significant effects on the ionospheric delay during the disturbed geomagnetic conditions. So the large residuals between days 56,208 and 56,255 have the close relation to higher ionosphere activity.
Figure 4 and Table 6 demonstrate that the RMS of orbit difference in the radial direction is the smallest among three directions. From Table 6, we can know that giving SLR the fixed weight, the values of RMS difference with respect to CNES orbits in radial direction will increase if we decrease the weight of DORIS, conversely, the RMS values will be decreased with increasing the weight of DORIS data. At the same time, we can see that the mean agreement between the computed orbits and the CNES orbits in the radial direction is about 1.5 cm with every weight setting. The smallest RMS of the computed orbit in the radial direction is 1.37 cm, and the relative weights of DORIS and SLR are 0.2 mm/s and 15.0 cm, respectively. The smallest 3D RMS is 5.87 cm and the relative weights are 0.2 mm/s and 15.0 cm for DORIS and SLR, respectively. Therefore, the optimal relative weight group is 0.2 mm/s and 15.0 cm for DORIS and SLR, respectively. We can also conclude that a large weight should be given to DORIS in the orbit determination with the dynamic strategy using SLR + DORIS data. Table 6 indicates that DORIS plays a dominant role in the precise orbit determination. The SLR + DORIS solutions rely more heavily on the DORIS data than SLR data since DORIS beacon stations have better temporal and spatial coverage than SLR tracking stations and there are more DORIS data than SLR data. We have achieved higher relative radial accuracy than those achieved using combined DORIS and SLR data in 30 days by Jiang et al. (2014) which were also compared with the CNES orbit.
Comparison between orbit difference RMS using DORIS-only, SLR-only, and DORIS + SLR data
From Tables 4, 5 and Fig. 5, we can see that in the radial direction, the RMS difference between DORIS-only and SLR-only orbits can reach 1.53 cm. The RMS differences are 4.45 and 1.65 cm in the along-track and the cross-track direction, respectively, and the 3D RMS difference is 4.27 cm. The RMS difference of the derived orbit using DORIS-only data is smaller than those from SLR-only data with respect to the CNES orbit, and the RMS in the radial direction is better than 2.0 cm for the DORIS-only orbit which can meet the needs of the altimeter payload on HY-2A. Tables 4, 6 and Fig. 5 indicate the RMS improvements of 4.4 and 18.2 mm from DORIS-only solution to DORIS + SLR solution with weights 0.2 mm/s and 15.0 cm for DORIS and SLR in the radial direction and 3D RMS. Therefore, this analysis demonstrates that SLR data can directly contribute to the overall POD accuracy, and the combined DORIS + SLR technique can produce more accurate solution than DORIS-only and SLR-only. This significant improvement of precision is owed to the high accurate observation of DORIS and SLR, which can significantly improve the data density and then significantly improve the POD capability.
HY-2A is the first ocean dynamic environment monitoring satellite of China following the Jason-1 and Jason-2 altimetry missions. A highly precise radial orbit is the fundamental requirement for accurate monitoring of sea surface topography with the altimetry satellite mission. Since GPS data are unavailable on internet, we focused on POD using DORIS and SLR tracking data and the combination of these two space geodetic techniques.
To obtain the optimal solution, we estimated orbits using DORIS-only, SLR-only, and DORIS + SLR data, respectively, and analyzed the orbit difference RMS with respect to CNES orbits. We achieved 1.81 cm radial RMS difference and 7.69 cm 3D RMS difference with the dynamic method using DORIS-only data with respect to the CNES orbit, and 3.34 cm radial RMS difference and 11.96 cm 3D RMS difference using SLR-only data with respect to the CNES orbit, respectively. There are mainly three possible reasons for the smaller RMS of orbit difference in radial direction derived from DORIS-only data than those derived from SLR-only data with respect to the CNES orbit: first, the DORIS beacon stations are distributed more evenly than those of SLR tracking stations; second, there are more measurements of DORIS than SLR; finally there are more tracking stations for DORIS than SLR.
To take advantage of the high accuracy of SLR data, we have set 6 cases of weight groups for DORIS and SLR data, and found that the optimal relative weight group was 0.2 mm/s for DORIS and 15.0 cm for SLR, and 1.37 cm of radial RMS difference and 5.87 cm of 3D RMS difference could be achieved with respect to the CNES orbit. These experiments demonstrated that the orbits determined using DORIS-only, SLR-only, and DORIS + SLR data were all stable and reliable. We also found that DORIS played a dominant role and SLR provided a strong distance constraint in POD using DORIS + SLR data. Figures 4, 5 and Table 6 also indicated that the consistency to the CNES orbit in the radial direction was better than those in the other two directions. There are three possible reasons: first, the accuracy of the force model in the radial direction is more accurate than that in the other two directions; second, the range rate of DORIS Doppler measurements varies mainly in the radial direction; and third, SLR tracks the absolute range between tracking station and satellite.
It should be recognized that SLR data also played a great role in the improvement of the orbit determination, especially for the 3D position, because they enhanced the spatial and temporal distribution of tracking data. In addition, the special attention should be given to the weight setting for different space geodetic data to achieve highly precise orbit. POD from DORIS + SLR data requires further investigation in terms of measurement bias, troposphere bias, and DORIS network time bias. The fruitful experience of POD for HY-2A will provide a reference for the following HY-2B, HY-2C, and HY-2D satellites.
We thank anonymous reviewers for their helpful comments. We express our gratitude to CNES for providing HY-2A precise orbit and CDDIS for providing DORIS and SLR data. This work was supported by the National Natural Science Foundation of China (Nos. 41374009 & 41201381), the Public Benefit Scientific Research Project of China (No. 201412001), International Science and Technology Cooperation Program of China (No. 2009DFB00130), the Shandong Natural Science Foundation of China (No. ZR2013DM009), the Basic Science and Technology Research Project of China (Grant No. 2015FY310200), and Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province (Changsha University of Science and Technology) (No. kfj150605).