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Abstract
To monitor the spectral position drift, expansion and contraction of the full width at half maximum (FWHM) of the satellite calibration spectrometer (SCS) of the HY-1C satellite during on-orbit operation, an onboard spectral calibration method based on a wavelength diffuser is proposed in this paper. This method uses the wavelength diffuser reflectance measured prelaunch as the standard spectrum, convolves it with the spectral response function of the SCS to obtain a reference spectrum, uses the measured data of the onboard SCS as the measured spectrum, and obtains the spectral drift and variation of the FWHM through spectral line matching. Generally, the spectral response function of a hyperspectral remote sensor follows a Gaussian model, and so does that of the SCS. The spectral calibration results obtained based on the onboard wavelength diffuser are validated and evaluated in comparison to calibration based on an oxygen absorption line. Preliminary results show that (1) the SCS spectral drift is negative, indicating a shift in the shortwave direction, and its absolute value is gradually decreasing with increasing on-orbit operation time; (2) the mean values of the central wavelength and FWHM errors between the two calibration methods are 0.08 nm and 0.20 nm, respectively, indicating that the spectral calibration method based on the wavelength diffuser has high accuracy and reliability; and (3) the SCS spaceborne spectral calibration error has the greatest impact on radiometric calibration in Band 18, with an uncertainty of 0.99%, while the uncertainty in the other bands is less than 0.33%, indicating that the spectral calibration uncertainty meets radiometric calibration accuracy requirements.
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1. Introduction
Hyperspectral remote sensing, which is an abbreviation for hyper-spectral-resolution remote sensing, realizes the organic integration of the two-dimensional spatial features and spectral features of ground objects in images. Because of its high spectral resolution, wide spectral coverage, and rich image information, hyperspectral remote sensing is playing an increasingly important role in the fields of environmental monitoring, resource exploration and national defense [1–5]. High-precision radiometric and spectral calibrations determine the depth and breadth of the quantitative application of hyperspectral remote sensing data. However, the spectral response characteristics of hyperspectral remote sensors that are calibrated before launch will change due to the vibrations during launch, space radiation, and changes in the working temperature during on-orbit operation. Therefore, onboard spectral calibration is needed. The purpose of spectral calibration is to determine the central wavelength and full width at half maximum (FWHM) of each band of the remote sensor, which serves as not only the premise and basis for radiometric calibration but also the necessary conditions for the remote sensor to accurately obtain the spectral information of target ground objects [6].
The shape of the spectral response function is determined by the slit width and optical system parameters. Depending on the shape of the spectral response function, different mathematical models, such as a triangle function or a Gaussian function, can be used to describe it. The spectral response function is commonly assumed to be Gaussian in shape; although this is known to not always be the best description, it can meet the spectral calibration accuracy requirements of most hyperspectral remote sensors. Therefore, a normalized Gaussian mathematical model was originally used to describe the spectral response function of the satellite calibration spectrometer (SCS) of the HY-1C satellite [7–10].
There are several main methods of onboard spectral calibration: (1) Based on the characteristic atmospheric absorption peak method, a hyperspectral sensor can be calibrated by using gas channels with characteristic absorption peaks, such as oxygen, carbon dioxide, and water vapor channels, combined with hyperspectral images. Gao used spectral matching technology, using the retrieved apparent reflectance as the measured spectrum and the atmospheric transmittance simulated based on a radiative transfer model as the reference spectrum, to realize the onboard spectral calibration of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), the Portable Hyperspectral Imager for Low-Light Spectroscopy (PHILLS), Hyperion, and other hyperspectral sensors [11]. Geffen et al. used the solar Fraunhofer lines to realize the spectral calibration of the Global Ozone Monitoring Experiment (GOME), the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY), and other hyperspectral imagers [12]. Spectral calibration based on characteristic atmospheric absorption peaks does not require additional calibration equipment or optical path design, but the spectral calibration accuracy is limited because the available absorption peaks are limited in number, have an uneven distribution, and are easily affected by altitude and atmospheric pressure. (2) Based on a characteristic absorption peak filter or monochromator method, the onboard spectral calibration of the Japanese hyperspectral sensor on the satellite known as the Advanced Land Observing Satellite-3 (ALOS-3) is realized using a quartz tungsten halogen lamp as an illumination source in combination with a National Institute of Standards and Technology (NIST) Standard Reference Material (SRM) 206 filter and Mylar film [13]. (3) The Moderate Resolution Imaging Spectroradiometer (MODIS) uses a spaceborne monochromator to realize spectral calibration [14]. With this method, the design of the optical path for onboard calibration must be modified, especially that of the moving parts, which greatly affects the complexity and reliability of the instrument. (4) Based on a rare-earth-doped wavelength diffuser, the Medium Resolution Imaging Spectrometer (MERIS) of the European Space Agency (ESA) uses the sun as the illumination source [15–16] to form a reflection spectrum with characteristic absorption peaks to realize onboard spectral calibration. Compared with other onboard spectral calibration methods, the use of a rare-earth-doped wavelength diffuser has the following advantages: (1) depending on the wavelength range and characteristics of the spectrometer channel to be calibrated, different rare earth elements and quantities can be selected to adjust the positions and quantity of the characteristic absorption peaks of the diffuser, and (2) this method is not affected by the atmosphere and can realize high-frequency and high-precision onboard spectral calibration for hyperspectral remote sensors.
As the successor to the Haiyang-1B (HY-1B) satellite, HY-1C was successfully launched from the Taiyuan Satellite Launch Center on September 7, 2018, and is mainly used for the high-precision and large-area exploration of global oceans. To overcome the disadvantages of cross-calibration between multiple sensors and ensure the onboard calibration accuracy of the other sensors on the same platform, an SCS designed by the Beijing Institute of Space Mechanics & Electricity is installed on the HY-1C satellite platform to perform standard cross-calibration of the other loads on the same platform, such as the Chinese Ocean Color and Temperature Scanner (COCTS) and the Coastal Zone Imager (CZI) [17–19]. As the radiometric calibration standard for these instruments, the SCS needs to possess high-precision spectral and radiometric calibration capabilities. To this end, the Hefei Institutes of Physical Science, Chinese Academy of Sciences (CASHIPS) designed an onboard calibration system for the SCS [20]. This paper first introduces the relevant parameters of the SCS, the onboard calibration system, and the calibration process and then introduces the principle of spectral calibration based on a wavelength diffuser. Finally, through the processing of the onboard spectral calibration data, the changes in the spectral drift and FWHM are obtained. The onboard calibration results are validated in reference to an oxygen absorption line, and the onboard spectral calibration accuracy is analyzed and evaluated.
2. Methods
2.1 Instrument design overview
The SCS has a scanning swath of approximately 12 km, a spatial resolution at nadir of 1.1 km, and a field angle within a range of ± 0.5°. A schematic diagram of the main SCS structure is shown in Fig. 1(a). Figure 1(b) shows a simplified block diagram of the design, which illustrates how the SCS observes the Earth and the solar diffuser. The SCS employs a rotating telescope assembly (RTA) and a half-angle mirror (HAM) on the optical path. The light enters the instrument through the RTA and is reflected from the rotating HAM to the fixed aft optical subsystem. There, the light is spectrally separated by a grating assembly and directed to the focal plane assembly (FPA). Through the rotation of the RTA and HAM, light reflected from different targets (i.e., the Earth and the solar diffuser) can be directed into the FPA to realize different tasks (Earth observation and onboard calibration, respectively) [21–22].
Fig. 1. Schematic of the SCS: (a) SCS mechanical module schematic; (b) simplified block diagram of the SCS.
By means of the grating assembly, the SCS obtains 101 bands of continuous spectral image information at a spectral resolution of 5 nm, covering a visible and near-infrared spectral range of approximately 400–900 nm. The spectral response function curves of Band 66–88 are shown in Fig. 2(a).
Fig. 2. (a) Spectral response function curves of B66–B88; (b) schematic diagram of the onboard calibration system.
The SCS onboard calibration system (Fig. 2(b)) consists of a calibration wheel and a solar attenuation screen for the attenuation of incident solar energy. The calibration wheel is equipped with a calibration solar diffuser (CSD) for high-frequency applications, a reference solar diffuser (RSD) for low-frequency applications, an erbium-doped wavelength diffuser (EWD) for spectral calibration, and an empty plate for dark current acquisition. Radiometric calibration, degradation monitoring, spectral calibration, and dark current acquisition are realized by rotating the CSD, RSD, EWD, and empty plate, respectively, to the front end of the SCS optical path. The radiometric calibration sequence, executed once a day, starts with dark current acquisition, with the empty plate on the calibration wheel rotated to the front of the SCS, followed by radiometric calibration with the CSD deployed, and ends with another round of dark current acquisition. For daily calibration, the exposure time of the CSD is 20 s. The CSD degradation monitoring sequence, executed every month, is realized by means of sequential observation through the CSD and RSD throughout one orbit. The spectral calibration sequence, also executed every month, is similarly realized by means of sequential observation through the CSD and EWD throughout one orbit. The spectral calibration uncertainty requirements, spectral resolution and other technical specification of the SCS are shown in Table 1.
Table 1. Technical Specification of the SCS (B18–B118)
2.2 Spectral calibration theory
The SCS has only 11 pixels per band. The onboard spectral calibration process mainly determines the central wavelength drift and FWHM. The calibration process is shown in Fig. 3. (1) First, the measured spectral reflectance is obtained by processing the calibration image data of the SCS. (2) Then, with the FWHM remaining unchanged, the standard spectrum is convolved with the SCS spectral response function for a set of different central wavelength shifts in a range of -5 nm to +5 nm in accordance with a fixed step size (such as 0.01 nm) to obtain the corresponding reference spectral reflectance. The measured spectral reflectance is then matched with the reference spectral reflectance. The number of steps corresponding to the optimal matching result is the spectral drift. (3) Finally, with the position of the central wavelength remaining unchanged, the FWHM is varied in accordance with a fixed step size (such as 0.01 nm) in a range of -2.5 nm to +2.5 nm. Similarly, by combining the SCS spectral response function and a reference spectrum with a high spectral resolution measured in the laboratory, the corresponding reference spectral reflectance under different FWHM values are obtained, and the measured spectral reflectance is matched with the reference spectral reflectance. When the matching result is optimal, the corresponding number of steps is the variation in the FWHM, and spectral calibration is complete.
For most hyperspectral remote sensors, the spectral response function can be expressed as a normalized Gaussian function [23]:
For onboard spectral calibration, the known high-resolution spectrum is used as the standard spectrum, and the reference spectrum is obtained by convolving this standard spectrum with the spectral response function. In this paper, the spectral reflectance of the wavelength diffuser measured with high precision prior to launch is taken as the standard spectrum; accordingly, the reference spectrum can be expressed as:
By processing the images measured by the SCS with the EWD and the CSD, the measured spectrum is obtained, which can be expressed as:
Since the radiometric response of the instrument postlaunch is different from the prelaunch response and the optical properties of the EWD and CSD are also different from their prelaunch properties, there will be differences in amplitude between the measured and reference spectra of the SCS, which will affect the spectrum matching accuracy. To improve the accuracy of spectral calibration, the measured spectrum needs to be processed to minimize the difference between the measured and reference spectra [24]. First, the reference spectrum is divided by the measured spectrum:
Then, polynomial fitting is performed on the result obtained from Eq. (4), as follows:
For the SCS with grating splitting, the spectral calibration formula can be expressed as a polynomial. Generally, a quadratic polynomial can meet the requirements for the spectral calibration accuracy. The initial calibration model for the instrument can be expressed as:
According to research results, the variations in the channel spectral characteristics of grating hyperspectral remote sensors are mainly characterized by drift of the central wavelength and contraction or expansion of the FWHM. The FWHM is determined by the width of the light inlet slit, the focal length of the spectrometer and other factors. Ideally, the FWHM of each band should be the same, and when spectral degradation occurs, the change in the FWHM of each band should also be the same [25]. Therefore, the calibration formula after spectral drift can be expressed as:
The Pearson correlation coefficient method is used to judge how well the results match. When the correlation coefficient between the reference and measured spectra is the highest, the matching of the results is the best. The Pearson correlation coefficient can be expressed as:
The absolute value of ${r_{{\rm{Pearson}}}}$ ranges from 0 to 1. The larger this value is, the stronger the correlation and the better the spectral line matching result.
3. Onboard calibration results
The standard spectral reflectance of the EWD was measured by a high-precision, high-spectral-resolution Fourier spectrometer prelaunch at wavelength intervals of 0.10 nm. The results are shown in Fig. 4. Obvious absorption peaks were observed near 490 nm, 523 nm, 655 nm and 805 nm.
The spectrum of the SCS was calibrated at 0.2 nm wavelength intervals with a tungsten halogen lamp as the light source combined with a monochromator. The calibration results were fitted with a quadratic polynomial. The results can be expressed as follows:
where j represents the band serial number, which ranges from 18 to 118, covering all visible to near-infrared bands.When the central wavelength and FWHM change after a period of on-orbit operation, the corresponding spectral calibration model can be expressed as:
As an example, the satellite calibration data from September 13, 2018, were processed in accordance with Eq. (3). The results are shown in Fig. 5(a). There is a large difference in reflectance amplitude between the reference curve and the measured spectrum. Accordingly, the measured spectrum is corrected in accordance with Eq. (4)–(7), as shown in Fig. 5(b). The polynomial fitting coefficients are as follows:
Fig. 5. Adjusted measured spectrum and reference spectral reflectance: (a) comparison between the reference spectrum and the original measured spectrum; (b) comparison between the reference spectrum and the adjusted measured spectrum
In this paper, a series of reference spectrum curves are obtained by setting different values, and then the correlation coefficients between the reference spectra and the measured spectrum are calculated. The results are shown in Fig. 6. In this figure, the Y-axis (Alpha) represents the drift of the measured spectrum, with a positive value (negative value) indicating that the offset direction is in the longwave (shortwave) direction; the X-axis (Beta) represents the change in the FWHM, with a positive value (negative value) representing expansion (contraction) of the FWHM, that is, a reduction (improvement) in the spectral resolution; and the Z-axis (Correlation Coefficient) representing the correlation coefficient between the measured and reference spectra.
When the spectral drift is -2.77 nm and the change in the FWHM is -0.55 nm, the correlation coefficient reaches its maximum, indicating the best matching results. Accordingly, the figure shows that in this first onboard spectral calibration postlaunch, the central wavelength of the SCS had shifted in the shortwave direction by a drift value of -2.77 nm and the FWHM had shrunk by 0.55 nm compared with that before launch. The calibration result is:
Following the above process, 10 onboard spectral calibration datasets collected from September 2018 to May 2021 were processed, and the results are shown in Fig. 7. It can be seen that (1) with an increase in the on-orbit operation time, the spectral drift of the SCS in the shortwave direction gradually decreased, that is, the spectrum tended to drift in the longwave direction, and (2) the FWHM varied randomly between 4.00 nm and 4.50 nm.
4. Validation and analysis
4.1 Validation based on an oxygen absorption peak
Combined with Earth observation remote sensing images, a remote sensor may be calibrated by using gases with characteristic absorption peaks. The main signature of the commonly used oxygen absorption channel is at 760 nm, and the water vapor absorption channel has signatures at 940 nm, 1140 nm, and 1380 nm. Of these possibilities, the oxygen absorption channel has become one of the main bases for spectral calibration in the visible and near-infrared bands because of the stable wavelength position and distinctive characteristics of its absorption peak [26–31]. Therefore, in this paper, the oxygen absorption line is selected as the reference for calibrating the SCS spectrum. By comparing the two spectral calibration results obtained based on the oxygen absorption line and the proposed method, verification of the latter is achieved. The verification process is shown in Fig. 8. (1) First, the measured reflectance at the top of the atmosphere is obtained by combining the onboard radiometric calibration coefficients and remote sensing images. (2) Then, the SCS spectral response function obtained by varying the central wavelength and FWHM with a step size of 0.01 nm is convoluted with the spectral reflectance at the top of the atmosphere obtained from a 6S simulation, and the correlation coefficient between the reference spectral reflectance and the measured equivalent reflectance is calculated. The spectral drift and FWHM values corresponding to the maximum correlation coefficient are taken as the spectral calibration results. (3) Finally, the spectral calibration results obtained based on the oxygen absorption peak and the proposed wavelength diffuser technique are compared to evaluate the spectral calibration accuracy.
The top-of-atmosphere spectral reflectance data obtained from the 6S simulation were used as the standard spectrum, combined with the Earth observation image acquired by the SCS on April 17, 2019, to verify the onboard spectral calibration results on April 26, 2019. By suitably processing the data of the SCS from Band88–Band93, the measured spectrum based on the image and the reference spectrum based on the oxygen absorption peak were obtained. The normalized results are shown in Fig. 9(a). There is a large difference between the measured spectrum and the original reference spectrum before spectral calibration, indicating that the central wavelength and FWHM have changed. The correlation coefficient between the reference and measured spectra can be obtained as shown in Fig. 9(b). When the spectral drift is -1.88 nm and the change in the FWHM is -0.92 nm, the correlation coefficient reaches the maximum, indicating the best matching results. The reference spectrum after spectral calibration and the measured spectrum are compared in Fig. 9(c). Compared with the results in Fig. 9(a), the difference between the two spectra is reduced, while the spectral position of the absorption peak remains the same, indicating that the spectral changes in the SCS can be effectively calibrated based on the oxygen absorption peak.
Fig. 9. Spectral calibration results based on the oxygen absorption peak, April 17, 2019: (a) the normalized results; (b) correlation coefficients between the reference and measured spectra; (c) results after spectral calibration.
Similarly, Earth observation images from December 25, 2018; June 7, 2019; and October 13, 2019, were processed to validate the reliability and accuracy of the EWD spectral calibration results on December 10, 2018; June 27, 2019; and October 3, 2019, respectively. The results are shown in Fig. 10. In this figure, the blue triangular dotted line represents the original reference spectrum, and the red dotted line represents the measured spectrum. There are obvious differences in the positions of the absorption peaks in the two spectra. The black rectangular dotted line represents the reference spectrum after calibration, which matches well with the absorption peak position in the measured spectrum.
Fig. 10. Comparison between the measured and reference spectra near the 760 nm oxygen absorption peak: (a) 2018/12/25; (b) 2019/6/7; (c) 2019/10/13.
The results of the two calibration methods based on the oxygen absorption peak and the EWD are summarized in Table 2, and the calculated error between the two calibration results on each date is reported. It can be seen that (1) the central wavelength of the SCS initially drifted in the shortwave direction relative to the prelaunch calibration and then tended to drift in the longwave direction with increasing on-orbit operation time; (2) compared to the prelaunch value, the FWHM of the SCS decreased after launch; and (3) the maximum and average central wavelength errors between the two calibration methods are 0.13 nm and 0.08 nm, respectively, while the maximum and average FWHM errors are 0.40 nm and 0.20 nm, respectively, which shows that the spectral calibration results based on the EWD are reliable and can meet the requirements for the spectral calibration accuracy of the SCS.
Table 2. Validation results
4.2 Uncertainty analysis of spectral calibration
When the EWD is used for spectral calibration, the error caused by the response of the calibration spectrometer is eliminated, and such provides multiple absorption peaks to help meet the calibration accuracy requirements of the spectrometer. By analyzing the principle and process of onboard calibration based on the EWD, it can be seen that the main factors affecting the calibration accuracy are as follows:
- (1) The standard spectrum of the EWD is measured by a Fourier spectrometer in the laboratory. During this test, the illumination source remains unchanged, and the reference diffuser and the wavelength diffuser are alternately measured by changing the optical path. Finally, ratio processing is carried out to obtain the reference spectral reflectance of the EWD. Subsequently, onboard spectral calibration is realized by collecting observations with the SCS using the EWD and the CSD successively in the same orbit. During this time interval, the change in the zenith angle of the sun will lead to a change in the incident energy. The amplitude difference between the measured spectrum and the reference spectrum will affect the spectral calibration accuracy. Although the amplitude difference between the measured and reference spectra at the absorption peak is reduced by ratio processing and fitting, this cannot eliminate the amplitude error caused by the given standard result.
- (2) For the spectral response function model, an ideal Gaussian function is adopted in this paper. However, due to factors such as the difference in the FWHM and the calibration accuracy in the laboratory, an ideal Gaussian response function model cannot truly reflect the spectral response of the SCS. Therefore, it is necessary to improve the Gaussian response function model in accordance with the sensor parameter characteristics to improve the spectral and radiometric calibration accuracy.
- (3) Other factors, such as the accuracy of the spectral offset determined via the correlation coefficient method, the influence of stray light on the calibration system, the instrument signal-to-noise ratio, and the laboratory measurement accuracy of the reference spectral reflectance, will also introduce uncertainty into the given calibration results.
4.3 Influence of Spectral Calibration on Radiometric Calibration Accuracy
During the onboard operation of the SCS, the CSD is used to realize radiometric calibration. The reflected radiance of the CSD can be expressed as:
Fig. 11. Results: (a) solar spectral constant; (b) relative deviations under different combinations of $\varDelta \beta$ and $\varDelta \alpha = 0$; (c) relative deviations under different combinations of $\varDelta \beta$ and $\varDelta \alpha = 0.08{\rm{nm}}$; (d) relative deviations under different combinations of $\varDelta \beta$ and $\varDelta \alpha ={-} 0.08{\rm{nm}}$.
Table 3. List of center wavelength and FWHM error combinations
The relative deviations of the equivalent solar constant under the combinations of different central wavelength errors and FWHM errors listed in Table 3 are plotted in Fig. 11(b)–(d).
- (1) As shown in Fig. 11(b), when the center wavelength error is 0 and the FWHM errors are 0.20 nm and -0.20 nm respectively, the relative deviation of Band 18 at 400 nm is approximately 0.45%, and those of the other bands are less than 0.30%.
- (2) As shown in Fig. 11(c), when the center wavelength error is 0.08 nm and the FWHM errors are 0 nm, 0.20 nm, and -0.20 nm respectively, the relative deviation of Band 18 at 400 nm is greater than 1.00%, and those of the other bands are less than 0.45%.
- (3) As shown in Fig. 11(d), when the center wavelength error is -0.08 nm and the FWHM errors are 0 nm, 0.20 nm, and -0.20 nm respectively, the relative deviation of Band 18 at 400 nm is greater than 1.00%, and those of the other bands are less than 0.45%.
The equivalent solar constant obtained near the absorption peak position is very sensitive to changes in the central wavelength position and FWHM, mainly because the equivalent solar constant is obtained via the convolution of the spectral response function and the solar spectral constant. Consequently, drift in the central wavelength and the expansion or contraction of the FWHM lead to strong changes in the equivalent solar constant at the absorption peak.
The mean relative deviations in the equivalent solar constant caused by different spectral calibration errors are shown in Fig. 12 for the different spectral bands. The relative deviation in Band 18 is the largest, with a value of 0.99%, which is mainly due to the drastic change in the solar spectral constant near a wavelength of 400 nm. The relative deviations in the other bands are less than 0.33%, indicating that except in Band 18, the uncertainty of the radiometric calibration produced by the SCS based on the spectral calibration error of the EWD is better than 0.33%, meeting the accuracy requirements for radiometric calibration.
5. Conclusion
First, this paper introduces a detailed onboard spectral calibration method and data processing flow for the SCS of the HY-1C satellite based on the EWD. This method mainly uses the high-precision spectral reflectance of the EWD measured prelaunch as a standard spectrum and obtains spectral calibration results by combining observations collected by the SCS with the EWD and CSD during on-orbit operation. Then, the oxygen absorption peak is also used as a reference for spectral calibration to verify the accuracy and reliability of the proposed spectral calibration method based on the EWD. Results obtained based on data from HY-1C show that (1) the central wavelength drift of the SCS is negative, indicating that the spectrum is shifted in the shortwave direction, and the absolute value of the spectral drift is gradually decreasing with increasing onboard operation time; (2) the mean values of the central wavelength and FWHM errors between the two calibration methods are 0.08 nm and 0.20 nm, respectively, showing that the proposed method based on the EWD exhibits high accuracy and reliability and can be used to carry out high-precision spectral calibration for the SCS during on-orbit operation; and (3) the error of the SCS onboard spectral calibration results in the largest radiometric calibration uncertainty in Band 18, where this uncertainty is 0.99%, whereas the uncertainty in the other bands is less than 0.33%. Thus, the spectral calibration error meets the requirements for high-precision radiometric calibration.
According to this analysis, the amplitude differences between the measured and reference spectra, the spectral response function model, the spectral calibration model, and the change in the FWHM are found to be the main factors affecting the accuracy of spectral calibration based on the EWD. Therefore, in future work, it will be necessary to optimize the spectral response function model and select different spectral calibration models in combination with the wavelength diffuser and the oxygen absorption line to further improve the SCS spectral calibration accuracy during onboard on-orbit operation.
Funding
the Youth Foundation of the Hefei Institute of Material Sciences, Chinese Academy of Sciences (E23Y0G46).
Acknowledgments
The authors would like to thank the Editor and anonymous reviewers for their constructive comments and suggestions on this manuscript and the National Satellite Ocean Application Service for providing data support. Finally, we thank the Beijing Institute of Space Mechanics & Electricity for providing SCS prelaunch test data.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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