**4. Results and Discussion**

For the sake of analyzing the orbit determination accuracy of the HY2D satellite, we selected spaceborne BDS data from 6 July to 19 July, and GPS data from 20 July to 10 August for determination orbit. Then, we analyzed the residual variation of the POD processing for the HY2D satellite, presented the overlap orbit precision and compared the calculated orbits with precise orbit products provided by CNES, and showed the SLR validation results.

#### *4.1. POD Residuals Analysis*

Because the change in daily residuals of POD is basically similar for the HY2D satellite, we present the residual variation of observations for two days of data calculated by the above method and model strategies. Additionally, the selected days are, respectively, July 10 and 21, 2021 for BDS and GPS. Figure 4 shows the residual variation in spaceborne BDS phase observations from HY2D satellite on 10 July 2021. As can be seen from the figure, about 96.41 percent of residual values are located within ±15.00 mm. The average value and standard deviation of residuals are 0.036 mm and 9.12 mm, respectively, which show that these residuals have no significant deviations.

**Figure 4.** Variation of residuals in the POD for HY2D using spaceborne BDS data.

Moreover, Figure 5 shows the residuals variation in spaceborne GPS phase observations from the HY2D satellite on 21 July 2021. As can be seen from the figure, about 97.21 percent of residuals values are located within ±15.00 mm, similar to BDS. After the statistical calculation of these residuals, their average value and standard deviation are 0.026 mm and 8.53 mm, respectively, and there are also no obvious systematic errors in the residuals of GPS.

**Figure 5.** Variation of residuals in the POD for HY2D using spaceborne GPS data.

#### *4.2. POD Precision Analysis for HY2D*

In this study, we also compare the calculated orbit using spaceborne BDS and GPS data with the precise Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS)-derived orbits provided by CNES. Figures 6 and 7, respectively, show the position differences in Radial (R), Tangential (T), and Normal (N) directions between the calculated orbit and the precise orbit.

**Figure 6.** The variation in errors for the HY2D satellite using spaceborne BDS data compared with CNES orbit.

**Figure 7.** The variation in errors for the HY2D satellite using spaceborne GPS data compared with CNES orbit.

As can be seen from Figures 6 and 7, the variations in the radial direction have smaller fluctuation, which are basically located within ±0.03 m. However, the fluctuation in the tangential direction is relatively bigger, and this may be related to the used models of atmospheric drag and solar pressure, which are hard to estimate exactly. It should be noted that the normal fluctuations of GPS are relatively smaller than BDS; this is related to the number of GPS satellites, which are more than the BDS satellites and the orbit precision of GEO and IGSO satellites is lower. To analyze the precision visually, Table 5 gives the accuracy statistics of the HY2D satellite using spaceborne BDS and GPS data. We can find that the mean values are close to zero, which illustrate that these error values are basically unbiased and have no obvious systematic errors. For spaceborne BDS data, the radial, tangential, normal and 3D accuracy can achieve 1.5 cm, 4.1 cm, 3.0 cm, and 5.3 cm, respectively, and the radial, tangential, normal and 3D accuracy are, respectively 1.5 cm, 3.5 cm, 2.0 cm, and 4.3 cm for spaceborne GPS data. However, because of the fewer satellites available, the consistency the BDS-derived orbits are slightly worse than the GPS-derived orbits.


**Table 5.** Accuracy statistics of POD for HY2D using spaceborne BDS and GPS data (unit: cm).

For validating the reliability of the used method and model strategies, we also utilize more spaceborne BDS and GPS data to conduct POD solutions for HY2D satellite, and the results of comparison with precise orbit provided by CNES are shown in Figures 8 and 9 in radial, tangential, normal and 3D directions.

**Figure 8.** The RMS values for HY2D satellite using spaceborne BDS data.

R T N 3DRMS

**Figure 9.** The RMS values for HY2D satellite using spaceborne GPS data.

As can be shown from Figures 8 and 9, the radial RMS values are basically 1.4~1.5 cm for BDS and GPS data, and the tangential and normal accuracies are slightly poorer compared to the radial direction. Overall, the precision based on spaceborne GPS data are slightly better than that of spaceborne BDS data, and the results are in agreement with the previous analysis, which shows that the used method and model strategies have a certain reliability. Moreover, Tables 6 and 7 show the accuracy statistics of HY2D. As can be shown from Tables 6 and 7, the average radial accuracy based on spaceborne BDS and GPS data are, respectively, 1.5 cm and 1.4 cm, the average three-dimensional accuracy are 5.3 cm and 4.3 cm, respectively. These results illustrate that the HY2D satellite, using spaceborne BDS and GPS data, can achieve the radial precision of 1.4~1.5 cm, the 3D position precision better than 5.5 cm, and the radial precision can satisfy high-precision altimetry applications.


**Table 6.** The precision statistics of HY2D satellite using spaceborne BDS data (unit: cm).

**Table 7.** The statistics of accuracy for HY2D satellite using spaceborne GPS data (unit: cm).


#### *4.3. SLR Validation for the POD of HY2D*

SLR is an independent measurement technique compared to GNSS, and thus SLR validation can validate objectively the accuracy and reliability of GNSS-derived orbits [11,38]. Here, we select the SLR normal point data from the corresponding periods of the HY2D satellite (download: ftp://edc.dgfi.tum.de/pub/slr/data/npt\_crd/, accessed on 10 February 2022). The SLR residual results cannot verify the accuracies of the components in each direction or orbital position directly, but they denote that the distance precision between the given SLR station and the validated satellite. When the higher cut-off angle is set, the SLR residuals can better reflect the radial accuracy. Because HY2D is an altimetry satellite, its radial precision is our primary concern. In this study, we set the cut-off angles as 20, and give the time series of SLR residuals in Figure 10.

**Figure 10.** The variation of SLR residuals for HY2D satellite.

As can be seen from Figure 10, most of the residual values are located within ±8.0 cm, and have no obvious abnormal value. The orbits of the first 14 days are calculated using spaceborne BDS data, and the next 22 days orbits are calculated using spaceborne GPS data. The range of SLR residuals for BDS-derived orbits is slightly bigger than that of GPS-derived orbits, which is related to that the precision based on spaceborne GPS data are slightly better than that of spaceborne BDS data. After the statistical calculation of these residuals, their average value and standard deviation are, respectively, −0.7 cm and 3.3 cm, which illustrate that these residuals have no significant deviations. The results also indicate that the orbital accuracy of HY2D satellite can satisfy the current high-precision altimetry requirements.

#### **5. Conclusions**

Based on the spaceborne BDS and GPS data of the newly launched HY2D satellite, this paper conducts research into POD using one month of data. The model strategies are developed to solve the precise orbits of the HY2D satellite, and this study selects a month of real onboard GPS and BDS data to validate the developed model strategies. The main conclusions of the study are given in the following:


As an example of the HY2D satellite, this study adopts spaceborne BDS and GPS data to conduct POD research. Eventually, the model strategies are developed to solve the precise orbit of the HY2D satellite. Meanwhile, we use the external DORIS-derived precise orbit of the HY2D satellite and SLR normal point data to validate the calculated orbit, and the results show that the HY2D satellite can achieve 1 cm radial precision.

**Author Contributions:** C.Z. provided the initial idea for this research; H.P., C.Z., S.Z. and X.Z. collected the experimental data and conducted the experiment; C.Z., H.P., S.Z., B.P., H.Y. analyzed the results of the experiment; C.Z., J.Z., J.H., F.G. and R.C. wrote the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Key Research Program of China "Collaborative Precision Positioning Project" (No. 2016YFB0501900), the National Natural Science Foundation of China (Grant No. 42174222, 41904165, 62101219, 41804019), the State Key Laboratory of Geodesy and Earth's Dynamics self-deployment project (No. S21L6101, S21L8101), the Natural Science Foundation of Hubei Province (No. 2017CFB372), the Natural Science Foundation of Jiangsu Province (No. BK20210921), the Natural Science Foundation of Fujian Province (No. 2018J01480).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors acknowledge the satellite information of HY2D provide by NSOAS. Our sincere thanks to the NSOAS for providing space-borne GPS and BDS data for HY2D; CODE for providing GPS satellite orbits, clocks and Earth rotation parameters; the CNES for providing precise orbits for HY2D; the ILRS for providing SLR data of the HY2D satellite. Meanwhile, we would like to thank the anonymous reviewers for their valuable comments.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

#### **References**

