**1. Introduction**

With the rapid development of space technologies, more and more Low Earth Orbit Satellites (LEOs) have been successfully used in scientific missions [1–7]. Especially, in order to obtain more detailed information about the marine environment and mapping and carry out research about the change in current global mean sea level, tens of ocean altimetry

**Citation:** Peng, H.; Zhou, C.; Zhong, S.; Peng, B.; Zhou, X.; Yan, H.; Zhang, J.; Han, J.; Guo, F.; Chen, R. Analysis of Precise Orbit Determination for the HY2D Satellite Using Onboard GPS/BDS Observations. *Remote Sens.* **2022**, *14*, 1390. https://doi.org/ 10.3390/rs14061390

Academic Editor: Xiaogong Hu

Received: 15 February 2022 Accepted: 10 March 2022 Published: 13 March 2022

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satellites have been launched. For example, there have been successful launches of Seasat, GeoSat, Topex/Poseidon, HY2A/B/C, Jason1, Jason2 and Jason3 altimetry satellites [1,8], which provide a large amount of effective and high-precision data for assessing the change in current global mean sea level. As shown by the successful use of Global Positioning System (GPS) in the precise orbit determination (POD) for Topex/Poseidon satellite [8], the spaceborne GPS technique makes it possible to obtain centimeter-level orbit products and, thus, has been widely used for LEOs [9–15]. Gao et al. [10] adopted DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) data of HY2A to analyze POD results, and showed that the radial orbit difference with the CNES (Centre National d'Etudes Spatiales) orbits is about 1.1 cm. Guo et al. [11] conducted POD of HY2A based on GPS and DORIS data, and achieved radial accuracy better than 1.0 cm. Wang et al. [16] adopted three months of GPS observations of HY2C, and achieved the radial accuracy of about 1.2 cm.

China has developed and operated the BeiDou Navigation Satellite System (BDS) independently [17]. Nowadays, there are a total of 34 BDS satellites in orbit, including 15 BDS-2 satellites (six geostationary Earth orbit (GEO) satellites, six inclined geosynchronous orbit (IGSO) satellites, and 3 medium-Earth orbit (MEO) satellites) and 19 BDS-3 satellites (two IGSO satellites and 17 MEO satellites). There are more and more LEO satellites carrying BDS receivers, and numerous studies have been carried out on the POD based on spaceborne BDS data in recent years. In 2013, the FengYun-3C (FY-3C) satellite was launched successfully, which was equipped with BDS-2 and GPS receivers simultaneously. The spaceborne BDS and GPS data of FY-3C satellite provided a great opportunity to analyze the POD performance of LEOs with BDS. Li et al. [18] conducted POD of FY-3C based on BDS-only and BDS/GPS combined; the analysis showed that the BDS-only orbits can reach a three-dimensional (3D) root mean square (RMS) of 8 cm based on the orbit overlap comparison, while the 3D RMS value of combined POD is 3.9 cm. Xiong et al. [19] achieved real-time POD with a precision of 1.24 m for the FY-3C satellite using BDS and GPS pseudo-range observations. Zhao et al. [20] used the derived POD orbits of FY-3C and regional station observations to enhance the BDS orbits and improved the accuracy from 354.3 to 63.1 cm for GEO, 22.70 to 20.0 cm for IGSO, and 20.9 to 16.7 cm for MEO. Based on the FY-3C spaceborne BDS and GPS data from 2013 to 2017, Li et al. [21] found that the combined POD (without GEO) can achieve slightly better precision than the GPS results, which indicates that when high-quality BDS orbit and clock products are used, the combined solution can improve the accuracy of POD for LEOs in comparison with the GPSonly solution. Based on the spaceborne BDS data of FY-3C, Zhang et al. [22] found that the precision of LEO orbit determination and reliability of the solution are improved through the calibration of daily orbit biases in GEO. The measurements of Tianping-1B, launched in 2018, were also collected by Zhao et al. from GPS/BDS-3. Their results indicated that the orbit consistency of the combined BDS-3/GPS solutions was below 3.5 cm [23].

In 2021, China successfully launched a new altimetry, satellite-HaiYang-2D (HY2D), which is a marine operational satellite that can provide precise ocean dynamic environmental information for the warning and forecasting of marine disaster, continuously measuring the sea surface height and sea surface wind and conducting marine scientific research. In order to guarantee the reliability of satellite orbits for radar altimetry mission, HY2D is equipped with a GPS and BDS receiver and carries a laser retro-reflector array for satellite laser ranging (SLR). Therefore, this paper adopts spaceborne GPS and BDS data to conduct research about the POD of HY2D, mainly including the model strategies used in POD processing, Global Navigation Satellite System (GNSS)-derived orbit analysis, and the validation of SLR residuals for HY2D. The relevant research results can lay an important foundation for the development of subsequent altimetry satellites, and that in turn can lay an important foundation for the development of a spaceborne BDS receiver.

This paper is structured as follows. Section 2 introduces materials and mainly consists of general information about the HY2D satellite and data collection. Section 3 mainly presents the POD method and strategies. All results and discussion obtained based on the above methods and strategies are given in Section 4. Finally, conclusions are given in Section 5.

### **2. Materials**

#### *2.1. HY2D Spacecraft*

On 19 May 2021, the HY2D satellite was launched at the Jiuquan satellite launch center successfully. The HY2D satellite adopts a non-sun-synchronous orbit with the inclination of 66◦, and the orbit altitude of about 960 km. The primary sensors comprise radar altimeter, microwave scatterometer, calibration radiometer, data collection system and ship automatic identification system [24].

Figure 1 shows the HY2D spacecraft and its payloads. It should be pointed out that the GNSS antennas consists of GPS and BDS antennas but cannot receive GPS/BDS signals simultaneously. Thus, the GPS and BDS receivers would switch to each other as needed. The X, Y and Z are the three axes of the satellite flight reference frame (SFF) in the figure, and the +X and +Z axes point toward the direction of flight and nadir, respectively. The +Y axis completes the right-hand orthogonal reference. When the satellite is at zero attitude, the SFF coincides with the satellite body reference frame (SBF), while the SFF is different from the SBF in a non-zero attitude. Table 1 lists the coordinates of the GPS and BDS antenna phase center, laser retro-array (LRA) spherical center, and center of mass in the SBF. With the help of these coordinates, we can perform phase center correction of receivers for HY2D in POD processing.

**Figure 1.** HY2D satellite and its payloads.


**Table 1.** Coordinates of the center of mass, GPS and BDS antenna phase centers and LRA spherical center in the SBF.

When the satellite is flying, surface forces acting on HY2D are mainly from atmospheric drag, earth radiation pressure and solar radiation pressure [10]. In order to model the forces precisely, having a well knowledge of the characteristics for the HY2D satellite surfaces and radiators is very necessary. Table 2 gives the parameters information of spacecraft surfaces and radiators, including the optical characteristics and projected areas. With help of the information, the solar radiation pressure of HY2D can be described with the Box-Wing model.

**Table 2.** Projected areas and optical characteristics of HY2D.


Table 2 shows that the +X and +Z axes point to the directions of flight and nadir, respectively, and -Y axis points to the direction of Sun. As the HY2D satellite belongs to a non-sun-synchronous orbit satellite, the solar arrays are always directed to the sun. Moreover, the HY2D satellite is in a non-zero attitude during the flight, and the SBF has to rotate according to the attitude following the order of yaw-roll-pitch to obtain the SFF. So, it is essential to adopt satellite attitude data to calculate the solar radiation pressure and phase center offset accurately.

Table 3 shows a part of attitude data of HY2D satellite, which is provided by National Satellite Ocean Application Service (NSOAS) at present. As can be shown from Table 3, the attitude data consist of date, time, roll angle, pitch angle, and yaw angle. In addition, the change in yaw angle works well with the increase in time, so, this study needs to use the attitude data of HY2D to correct the phase center offset and solar radiation pressure.


**Table 3.** The attitude data of HY2D satellite provided by NSOAS.

#### *2.2. Data Collection*

For evaluating the POD performances of HY2D, we selected spaceborne BDS data from July 6 to July 19, and GPS data from July 20 to August 10 to conduct experiments. Here, Figures 2 and 3 present the number of BDS and GPS satellites observed on a day, respectively.

**Figure 2.** Number of BDS satellites observed on 10 July 2021.

**Figure 3.** Number of GPS satellites observed on 21 July 2021.

As can be shown from Figure 2, most of the epochs have at least four BDS satellites available, and there are an average of five satellites. However, the smallest is 2, and the biggest is 9. As can be seen from Figure 3, compared to BDS, the usability of satellites for GPS is much better, and most epochs have more than five GPS satellites, and the maximum is up to 10 GPS satellites. This is mainly attributed to the GPS constellation consisting of 32 MEO satellites, more than the current BDS constellation, and the fact that most BDS, GEO and IGSO satellites are located within the Asia-pacific region.

#### **3. POD Method and Strategies**

This Section mainly describes the observation and dynamic model used in the POD processing of HY2D. Meanwhile, we also present the detailed dynamic and observation model in the POD for HY2D.

### *3.1. Observation Model*

The GNSS antenna of HY2D satellite only tracks the GPS or BDS signal separately at present, so we selected ionosphere-free combined observation from GPS or BDS to calculate precise orbits. Equation (1) gives ionosphere-free combined observation of GPS and BDS.

$$\begin{cases} P\_B = \rho\_B - c \cdot \delta t\_B^s + c \cdot \delta t\_B^t + \varepsilon\_{BP} \\\ L\_B = \rho\_B - c \cdot \delta t\_B^s + c \cdot \delta t\_B^t + N\_B \cdot \lambda\_B + \varepsilon\_{BL} \\\ P\_G = \rho\_G - c \cdot \delta t\_G^s + c \cdot \delta t\_G^t + \varepsilon\_{GP} \\\ L\_G = \rho\_G - c \cdot \delta t\_G^s + c \cdot \delta t\_G^t + N\_G \cdot \lambda\_G + \varepsilon\_{GL} \end{cases} \tag{1}$$

where *PB* and *PG* are the code observations of BDS and GPS, respectively, while *LB* and *LG* are the carrier phase observations of BDS and GPS, respectively; *ρ<sup>B</sup>* and *ρ<sup>G</sup>* are geometrical distance from BDS and GPS signal to receiver, respectively, *δt s <sup>B</sup>* and *δt s <sup>G</sup>* stand for satellite clock errors for BDS and GPS, *δt t <sup>B</sup>* and *δt t <sup>G</sup>* are clock errors for BDS and GPS receivers, *NB* and *NG* refer to combined ambiguity parameters of BDS and GPS observations separately, *λ<sup>B</sup>* and *λ<sup>G</sup>* refer to combined wave length of BDS and GPS observations separately, *εBP*, *εBL*, *εGP* and *εGL* stand for different type observation noise.

#### *3.2. Dynamic Model*

The equation of motion of a single LEO satellite in the inertial frame can be expressed as follows [25]: ..

$$\stackrel{\rightharpoonup}{r} = -\frac{GM}{\left|\stackrel{\rightharpoonup}{r}\right|^3}\stackrel{\rightharpoonup}{r} + a\_r + a\_{rtn} \tag{2}$$

..

where, *GM* stands for geocentric gravitational constant, - *r* and - *r* are the position and acceleration of the satellite in the inertial coordinate system, respectively; *ar* refers to main perturbation acceleration excluded Earth center gravity, that includes the Sun and Moon perturbation, atmosphere drag, solar radiation pressure, Earth radiation pressure, solid Earth tide, ocean tide and so on. *artn* refers to the periodic radial, tangential, and normal (RTN) perturbation, which can make up for these unmodeled perturbation acceleration errors [26–28]. In this study, the tangential and normal perturbation parameters are estimated for the POD processing.

In order not to affect the calculation efficiency and accuracy of orbit determination, the process of choosing the dynamic and observation model is important. For this purpose, the used dynamic model and measurement model are designed in the POD processing for the HY2D satellite refers to the above descriptions. Furthermore, this study also shows the used model information of the SLR validation for the calculated HY2D orbit. The details are given in Table 4. We adopted the 24 h arc solution based on the dynamical method orbit determination, the atmospheric drag coefficient, the solar radiation pressure coefficient, and RTN perturbation parameters are estimated per 6 h, 24 h, and 24 h, respectively. Moreover, the receiver clock parameter for HY2D is estimated with the gaussian white noise model, and the float solutions of ambiguities are also estimated.


**Table 4.** Dynamical and observation model employed in the POD for HY2D.

