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Abstract
The two-beam GaoFen-7 (GF-7) laser altimeter is China's first formal spaceborne laser altimeter system for Earth observations. In this article, a calibration method based on simulation waveform matching is proposed to correct the laser pointing error now that the satellite is in orbit. In the method, the optimal position of the laser footprint is searched using simulated and actual waveforms. Then, the laser pointing is calibrated based on the laser footprint optimal position. In this paper, after calibration of the GF-7 laser pointing, infrared detectors are used to capture laser footprints for accuracy verification. The results show that the GF-7 laser pointing accuracy is greatly improved by the method; the laser pointing accuracy of beam 1 is approximately 5.4 arcsec, and that of beam 2 is approximately 5.7 arcsec. Subsequently, two laser footprints are selected for GF-7 laser calibration in the Helan Mountains, China, and AW3D30 digital surface model (DSM) and GPS/RTK data are used to verify the laser elevation measurement accuracy (EMA). The results show that the EMA of the GF-7 laser is significantly improved after calibration. Over flat terrain, the EMA of the GF-7 laser is improved by 10 times, from 3.74 ± 0.55 m to 0.35 ± 0.50 m, verifying the effectiveness of the proposed method.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The GaoFen-7 (GF-7) satellite, launched on November 3rd, 2019, carries China’s first laser altimeter system officially used for Earth observation [1]. Like Geoscience Laser Altimeter System (GLAS) [2–4], the GF-7 satellite laser is a linear mode, profiling lidar. However, the GF-7 satellite laser altimeter system (GFLAS) adopts two-beam simultaneous measurements; it employs four lasers (two of which are backups) and two laser footprint cameras to obtain laser footprint images [1]. A working diagram of the system is shown in Fig. 1 [5]. At present, the emission energy of beam 1 is approximately 85.7 mJ, and that of beam 2 is approximately 93.9 mJ. The wavelength, working frequency, pulse width, and divergence angle of each laser beam are 1064 nm, 3 Hz (maximum, 6 Hz), 4 ns, and 30 $\mathrm{\mu}\textrm{rad}$, respectively. Additional parameters are detailed in Table 1 [6].
Table 1. Basic design parameters of the GF-7 laser altimeter.
Table 2. The positioning accuracy based on GF-7 laser pointing
Table 3. The elevation difference mean and RMSE data in Fig. 7.
The nadir angle of each beam of the GFLAS is 0.7 degrees, and each beam has an approximately 15-m diameter footprint with an across-track sampling interval of 12.25 km to capture Earth surface elevation. The GF-7 laser-receiving telescope, with an aperture of 600 mm, collects echo signals from the Earth’s surface, which are converted into echo waveforms. Each laser beam produces a particular echo waveform. Its waveform can be used for research on surface slopes [7–9], forests [10–12], sea ice [13–15], etc. The GF-7 spaceborne laser altimeter observes approximately 8 tracks a day, and each track lasts at most 15 min.
To improve spaceborne laser positioning accuracy, field calibration tests are usually carried out after the satellite is in orbit [16–20], but the associated costs are very large, and personnel, equipment or funds are required. Considering that the GFLAS can record the echo waveform, we propose a new method for full-waveform laser on-orbit calibration based on simulation waveform matching. First, airborne lidar data are used to simulate the GFLAS echo waveform at the laser footprint initial position and to calculate the Pearson correlation coefficient (PCC) between the simulated and actual waveforms. Then, a waveform simulation test is carried out by moving the laser footprint position again and recording the PCC between all simulated waveforms and the actual waveform. The Earth surface position with the maximum PCC is regarded as the optimal position of the laser footprint. Last, the optimal position coordinate is substituted into the spaceborne laser pointing calibration model to calibrate the pointing of the GF-7 laser. In this paper, after pointing calibration, the GF-7 laser absolute elevation measurement accuracy (AEMA) on flat terrain is evaluated for the first time in this article by using Global Positioning System/ Real-Time Kinematic (GPS/RTK) data to measure the laser footprint surface elevation. Moreover, three-track laser data from the GF-7 satellite were used to verify the laser relative elevation measurement accuracy (REMA) through comparison with the ALOS World 3D-30 m (AW3D30) DSM elevation. The resulting accuracy verification results can guide other researchers in using the data.
2. Materials
2.1 Study area
In this work, the Helan Mountains in Ningxia Province, China, were selected as the calibration area. A suburb of Zhaodong city, Heilongjiang Province, was used as the verification area for the AEMA of the GF-7 laser. The 154th, 856th, and 868th laser track data of the GF-7 satellite were used as test data to verify the GF-7 laser REMA. The test data and area are shown in Fig. 2.
Fig. 2. Test data and area distribution diagram. (a) Enlarged view of the 701st laser track passing the Helan Mountains area. The laser point in the blue dotted rectangle is the calibration laser point, and the lidar range is the data range of the airborne lidar point cloud. (b) Enlarged view of the 246th laser track passing the suburb of Zhaodong city. (c) Photograph of an individual using a GPS/RTK device to measure the laser footprint surface elevation.
Fig. 3. The layout scheme and an in situ photograph of the GF-7 laser infrared detector. (a) The detector layout scheme of GF-7 beam 1 and beam 2. (b) An in situ photograph of the detector layout.
2.2 Calibration data
Two laser footprints were used in the GF-7 laser calibration; these are shown in Fig. 2(a) in the blue dotted rectangles of the 701st track on the ridge of the Helan Mountains. The change in the laser footprint with topography is sensitive to the laser echo waveform. The laser data were measured on December 19, 2019. The timecode of the GF-7 beam 1 calibration laser point is 188222006.0, and that of beam 2 is 188222003.3; the timecode is the accumulated seconds since January 1, 2014.
The airborne lidar point cloud data were used for GF-7 laser waveform simulation, and their range is shown as “Lidar range” in Fig. 2(a); the data are from OpenTopography. These data were obtained in 2014 and have a point cloud density of 7.59 pts/m2. Although the time interval between the airborne point cloud and GF-7 laser data is 5 years, the mountain surface is bare rock, and the change in the surface elevation with time during this period can be ignored.
2.3 Elevation accuracy verification data
The AW3D30 DSM, with an elevation nominal accuracy of 5 m [21], was used for GF-7 laser REMA verification before and after calibration. Then, the data from the three laser-tracks (the 154th, 856th, and 868th tracks) of the GF-7 satellite were selected, as shown in Fig. 2. The 154th lase track traverses the Inner Mongolia grassland to the south of Beijing; 449 laser points were collected by beam 1, and 453 laser points were collected by beam 2. The 856th laser track passes through the Taklimakan Desert in Xinjiang and the Tibetan Plateau from north to south, with beam 1 obtaining 367 laser points and beam 2 obtaining 341 laser points. The 868th laser track traverses the high mountain region of Shanxi, China, with beam 1 obtaining 243 laser points and beam 2 obtaining 233 laser points. In summary, 1059 and 1027 laser points were selected for beam 1 and beam 2, respectively, for verification of the REMA.
To verify the AEMA of the GF-7 laser after calibration, GPS/RTK was used to measure the surface elevation of 22 laser points (as shown in Fig. 2(b), “beam 2”) of beam 2. Figure 2(c) is an in situ photograph of GPS/RTK measurement. Figure 2(b) shows the suburbs of Zhaodong city, Heilongjiang Province, China, which has flat terrain, and the elevation measurement accuracy (EMA) of GPS/RTK in this area is better than 10 cm.
2.4 Laser pointing accuracy verification data
To directly determine the location of the laser footprint, we can use an infrared detector to capture the laser footprint; the triggered detector position is the actual position of the laser footprint. Therefore, we placed an infrared detector array on the ground of Sonid Youqi, China, on June 14, 2020, which successfully captured two footprints of the 3402nd track laser of the GF-7 satellite. The laser number of beam 1 is 203600254.0, and that of beam 2 is 203600253.3. The layout scheme of the GF-7 laser infrared detector is shown in Fig. 3.
3. Methodology
3.1 Echo simulation model of the spaceborne laser altimeter
As the working principle of a spaceborne laser altimeter, a laser transmitter emits a laser beam to a surface target, which returns to the satellite laser-receiving system and therefore passes through the atmosphere twice. Simultaneously, the echo waveform is generated in the laser-receiving system. Spaceborne laser echo simulation focuses on two parts: 1) laser emission pulse simulation and 2) laser echo signal simulation [22].
- 1. Laser emission pulse simulation
The spaceborne laser emission pulse energy satisfies one-dimensional and two-dimensional Gaussian distributions in the time and airspace domains, with the following expressions [23]:
$$E(t) = \frac{Q}{{\sqrt {2\pi } {\delta _t}}}\exp \left( { - \frac{{{t^2}}}{{2\delta_t^2}}} \right),$$where $E(t)$ is the laser emission energy; $I(x,y)$ is the laser emission energy intensity at position $(x,y)$; Q is the energy of a single pulse; ${\delta _t}$ is the laser pulse width; and l is the laser footprint diameter. - 2. Laser echo signal simulation
Theoretically, the echo waveform of the spaceborne laser is formed by the convolution of the time distribution function (Eq. (1)) of the laser emission pulse and the surface echo signal. The laser echo signal is affected by the laser transmitting range, atmospheric transmittance, surface reflectance and slope, laser system efficiency and hardware indicators. After fully considering all the above factors, we derived the calculation expression of the spaceborne laser echo signal ${V_d}$ as follows [22,24].
$${V_d} = I\frac{{TD_r^2D_{tar }^2}}{{4{R^4}{\gamma ^2}}}\frac{{G\lambda e{R_L}}}{{hc}}\cos (S + \beta )\eta _{\textrm{atm }}^2{\eta _{\textrm{tra }}}{\eta _{\textrm{sys }}}{\eta _{APD}}$$where I is the laser emission energy intensity (Eq. (2)); T is the surface spectral reflectance; ${D_r}$ is the laser-receiving aperture; ${D_{tar}}$ is the laser footprint actual diameter; $R$ is the laser transmitting range; $\gamma $ is the laser divergence angle; G is the gain factor of the avalanche photodiode (APD) detector; $\lambda $ is the laser wavelength; e is the electronic power; ${R_L}$ is the load resistance; h is the Planck constant; c is the speed of light; $S$ is the target average slope; $\beta $ is the laser nadir angle; ${\eta _{atm}}$ is the atmospheric transmittance; ${\eta _{\textrm{tra }}}$ is the system emission efficiency; ${\eta _{\textrm{sys }}}$ is the system receiving efficiency; and ${\eta _{APD}}$ is the quantum efficiency of the APD detector.The laser echo waveform is the result of the convolution of the echo signal and time distribution of the transmitted pulse, and its formula is shown below [22].
Where $W(t)$ is the laser echo waveform, $E(t)$ is Eq. (1), and ${V_d}$ is Eq. (3).
3.2 Laser footprint positioning based on simulation waveform matching
The laser pointing and its working conditions changed when the satellite was launched, and the laser pointing after the change was unknown. Therefore, we used only the laboratory measurement pointing to calculate the laser footprint position, which is not the actual surface position. However, the laser echo waveform has a unique correspondence with the terrain, so we propose a method to search the optimal laser footprint position using the simulated waveform to match the actual waveform. The basic idea is to carry out echo simulation in a square test area with the initial position of the laser footprint as the center and then use the simulated waveform match the actual waveform to find the optimal position of the laser footprint. In actual operation, we adopted the method based on pyramid layers to improve the test efficiency, and we carried out the repeated simulation waveform matching test by narrowing the test range and grid spacing. It is faster to obtain the optimal position by using a multilayered smaller test grid than by dividing a small grid in a large range. A schematic diagram of the principle is shown in Fig. 4.
Fig. 4. Schematic diagram based on pyramid waveform matching. (a) Square test area for waveform simulation. The red ellipse is the laser footprint initial position. (b) The PCC surface of the simulated and actual waveforms. (c) Simulated and actual waveforms at the maximum PCC in each layer.
The method, illustrated in Fig. 4, can be summarized into the following 5 steps:
- 1. According to laser laboratory pointing, laser ranging value, attitude, orbit data and other auxiliary data, the laser footprint initial surface position ${P_0}$ is calculated [25].
- 2. Laser echo waveform simulation: First, formula (2) is used to simulate the internal energy of the laser footprint, which is substituted into formula (3) to simulate the laser echo signal. Then, formula (4) is used to convolve the transmitted pulse simulated by formula (1) with the echo signal of formula (3), which generates a simulated waveform.
- 3. The first layer test of the pyramid: With ${P_0}$ as the center, a square test area with a side length of ${l_{side}}$ is determined as the first layer test area, and the first layer test area is divided into grids with spacing $\Delta l$. The initial value of the side length (${l_{side}}$) can be determined by the empirical value and the laser pointing error measured in the laboratory, and it can be set larger. The initial value of spacing ($\Delta l$) should not exceed 5 m. An echo waveform simulation is carried out at each grid point in the test area. Then, the actual waveform is used to match the simulated waveform at each grid point one by one. The PCC is used to quantify the similarity between the simulated and actual waveforms. The PCC formula is as follows:$$\textrm{Corr} (\Phi ,\Psi ) = \frac{{n\sum \varphi \psi - \sum \varphi \sum \psi }}{{\sqrt {n\sum {{\varphi ^2}} - {{\left( {\sum \varphi } \right)}^2}} \sqrt {n\sum {{\psi ^2}} - {{\left( {\sum \psi } \right)}^2}} }}.$$where $\Phi $ and $\Psi $ represent the actual and simulated waveform data, respectively; n is the number of samples of the waveform; and $\varphi $ and $\psi $ are the values of the actual and simulated waveforms, respectively.
To eliminate the inestimable energy loss during laser transmission, which may affect the PCC, we normalize the simulation and the actual waveform before calculating the PCC. The grid point position of the maximum PCC in the first pyramid is considered to be the optimal position of the laser point of the first layer, which is ${P_1}$.
Aligning the simulated waveform with the actual waveform is important for accurately calculating the PCC between them. In this article, the peak value alignment method is used to calculate the PCC of the two waveforms. First, we align the peak value positions of the simulated waveform and the actual waveform and fill both ends of the simulated waveform with zero values according to the actual waveform length. In so doing, we ensure that the length of the simulated waveform is consistent with the actual waveform.
- 4. The second layer test of the pyramid: A square grid test area is determined with ${P_1}$ as the center, ${l_{side}}/3$ as the side length and $\Delta l/3$ as the spacing. The second layer of the pyramid test involves repeating the first layer test to find the optimal position of the laser footprint, which is ${P_2}$.
The $N$-th layer test of the pyramid: With the laser optimal position ${P_{N - 1}}$ as the center, a square grid test area with side length ${l_{side}}/{3^{N - 1}}$ and pitch $\Delta l/{3^{N - 1}}$ is determined. The $N - th$ layer test is similar to the first layer. Since the positioning accuracy of the spaceborne laser altimeter is at the meter level, the Advanced Topographic Laser Altimeter System (ATLAS) requirement for geolocation knowledge is 6.5 m [26]. Therefore, the test termination condition is set to $\Delta l/{3^{N - 1}}$< 0.5 m. The optimal position at the $N - th$ layer is the optimal surface position of the laser footprint, which is ${P_{optimal}}$.
3.3 Calibration model of the spaceborne laser altimeter
According to the instantaneous orbit position and attitude of the satellite, the surface position of the laser footprint, and the laser pointing angle at the time the laser fire, a laser measurement geometric model is constructed between the satellite and surface [20,27,28]. Based on the laser measurement geometric model, the calibration model of spaceborne laser pointing can be derived, as shown in the following formula [20]:
4. Results and discussion
4.1 Calibration of GF-7 laser
According to the selected GF-7 laser calibration points in the Helan Mountains (as shown in Fig. 2(a)), in this paper, the pyramid used to carry out simulation waveform matching is divided into three layers. We set ${l_{side}}$ = 900 m, $\Delta l$ = 3 m in the first layer, ${l_{side}}$ = 300 m, $\Delta l$ = 1 m in the second layer, and ${l_{side}}$ = 100 m, $\Delta l$ = 0.3 m in the third layer. Then, we carry out waveform simulations on beam 1 and beam 2 according to the above parameters and search the maximum PCC between the simulated waveform and the actual waveform in each layer. Thus, the optimal surface positions of beam 1 and beam 2 are searched based on the maximum PCC. The test results at each layer are shown in Fig. 5.
Fig. 5. The test result graphs for finding the laser optimal position based on layered simulation waveform matching. From left to right in the figure are the initial position coordinates of the laser footprint; the optimal position coordinates of the first, second, and third layers; the simulated waveform and the actual waveform; and their PCC values. (a) Simulated and actual waveforms of the optimal position in each layer for laser point 188222006.0 of beam 1. (b) Simulated and actual waveforms of the optimal position in each layer for laser spot 188222003.3 of beam 2.
As shown in Fig. 5, regardless of whether the selected beam is beam 1 or beam 2, the simulation waveform at the initial laser position is obviously different from the actual waveform, and the PCC value is low. The principal reason is that the initial position of the laser footprint in the test is far from the actual position. There is a large topographic difference between the initial position of the footprint and the actual footprint, which results in a large difference between the actual waveform and the simulated waveform. The maximum PCC value is significantly higher than the PCC value at the initial position after the first layer test of the pyramid, and the simulated waveform is similar to the actual waveform. We believe that the surface position at the maximum PCC is the optimal position of the first layer of the laser footprint, which is closer to the actual position of the laser footprint. In addition, as shown in Fig. 5, the test results of the next layer are better than those of the previous layer, and the simulated waveform is more similar to the actual waveform. The simulated waveforms of the third and second layers are very similar to the actual waveform, but the third layer test results are better because the optimal position of the third layer of the laser footprint is closer to the potential actual position. The spacing of each grid point of the third layer is less than 0.5 m, and there is reason to believe that the optimal surface position of the laser footprint is the optimal position in the third pyramid layer, which is ${P_3}$.
Thus, the optimal position of the laser footprint (${P_3}$) is input into formula (6), and based on the satellite attitude and orbit data, the GF-7 beam 1 and 2 pointing biases are calibrated after eliminating the tidal and atmospheric correction. The GF-7 beam pointing bias values $(\Delta \alpha ,\Delta \beta )$ between the laboratory pointing and calibrated pointing are as follows: beam 1 laser pointing bias, (0.03°, −0.04°); beam 2 laser pointing bias, (0.109°, −0.046°).
4.2 Accuracy verification of the calibration of GF-7 laser pointing
On June 14, 2020, the two-beam laser footprints of the GF-7 satellite were successfully captured by infrared detectors. We used RTK to measure the coordinates of the triggered detector. Based on the coordinates and energy value displayed by the detector, the Gaussian surface fitting method was used to fit the GF-7 laser footprint, as shown in Fig. 6. The coordinates of the maximum energy value of the fitted footprint in Fig. 6 are considered to represent the actual center of the laser footprint.
Fig. 6. The fitting surface of the GF-7 laser footprint. (a) The laser footprint fitting surface of point 203600254.0 of beam 1. (b) The laser footprint fitting surface of point 203600253.3 of beam 2.
After obtaining the actual position of the laser footprint center, we used the pointing before and after the calibration of the GF-7 laser beams 1 and 2 to calculate the position above the two laser footprints triggered by the detectors. Then, the laser pointing accuracy after calibration was verified by comparing the distance between the footprint position before and after the calibration and its actual position. The results are shown in Table 2. DPA represents the distance between the center of the footprint calculated by the laser pointing and its actual position.
Laser point 203600254.0 in Table 2 represents beam 1 of the GF-7 laser, and laser point 203600253.3 represents beam 2 of the GF-7 laser. As indicated in Table 2, the positioning accuracy of beam 1 is 424.2 m based on the pointing before calibration, and that of beam 2 is 1018.8 m; these results mean that before calibration, the laser pointing accuracy of GF-7 beam 1 is approximately 169.7 arcsec and that of GF-7 beam 1 is approximately 407.5 arcsec. After calibration, the laser positioning accuracy of the GF-7 satellite has been significantly improved; the positioning accuracy of beam 1 is 13.6 m, and that of beam 2 is 14.3 m.
In summary, after the calibration of simulation waveform matching, the pointing accuracy of beam 1 of the GF-7 satellite laser has been improved by more than 30 times, from 169.7 arcsec to 5.4 arcsec, and that of beam 2 has been improved by more than 70 times, from 407.5 arcsec to 5.7 arcsec.
4.3 Accuracy verification of GF-7 laser elevation measurement
4.3.1 Verification of elevation accuracy based on GPS/RTK data
To accurately assess the EMA of the GF-7 laser after calibration, we commissioned the Bureau of Surveying and Mapping of Heilongjiang Province (BSMHLJ) to use the GPS/RTK technique to measure the surface elevation of the 246th laser track footprint near Zhaodong city, as shown in Fig. 2(c). Due to restrictions in the field environment, the BSMHLJ measured only the surface elevation of 22 laser footprints of GF-7 beam 2, which are labeled “Beam 2” in Fig. 2(b). Then, we calculated the elevation difference (ED) between the 22 laser points and the GPS/RTK data before and after calibration to verify the AEMA of the GF-7 laser. The results are shown in Table 4.
Table 4. GF-7 laser elevation measurement accuracy before and after calibration
According to the results in Table 4, the EMA of beam 2 of the GF-7 satellite 246th track has been significantly improved. The laser points listed in Table 4 are located over flat terrain, as shown in Fig. 2(b) and 2(c). The EMA of GF-7 beam 2 on flat terrain has increased by 10 times after calibration, from the original value of 3.74 ± 0.55 m to 0.35 ± 0.50 m. Based on the test results of a large amount of laser data, shown in Fig. 7, we know that the EMA of GF-7 beam 2 is lower than that of beam 1 before calibration, and that the laser EMAs of beams 1 and 2 are similar after calibration. Therefore, we have reason to believe that the AEMA of GF-7 laser beam 1 is similar to that of beam 2 over flat terrain. We will continue to measure the elevation of GF-7 laser beams 1 and 2 over different types of terrain using drones, GPS/RTK devices and other instruments in the future to evaluate the EMA of the GF-7 spaceborne lasers over flat, hilly, mountainous and alpine areas.
Fig. 7. Graphs of REMA of the GF-7 laser before and after calibration. (a) The 154th track elevation difference between the laser and AW3D30 DSM. (b) The 1856th track elevation difference between the laser and AW3D30 DSM. (c) The 868th track elevation difference between the laser and AW3D30 DSM. (d) The elevation difference mean value and RMSE of each track.
4.3.2 Verification of elevation accuracy based on AW3D30 DSM
For the selected 154th, 856th and 868th laser track data of the GF-7 satellite, we first calculated the surface coordinates $({{B_b},{L_b},{H_b}} )$ of all laser points of these three tracks based on the GF-7 laser laboratory pointing and obtained the AW3D30 DSM elevation (${H_{AW3D\_b}}$) of each laser point. Similarly, the coordinates $({{B_a},{L_a},{H_a}} )$ of all the test laser points were calculated again by using the calibrated GF-7 laser pointing, and the laser footprint elevation (${H_{AW3D\_a}}$) was calculated from the AW3D30 DSM. Finally, we calculated the elevation difference ($Deta\_H$) between the laser and the AW3D30 DSM elevation before and after calibration as $Deta\_{H_b} = {H_b} - {H_{AW3{D_ - }b}}$ and $Deta\_{H_a} = {H_a} - {H_{AW3{D_ - }a}}$, respectively. Comparison charts of the elevation differences of all laser points before and after calibration are shown in Fig. 7(a–c). Additionally, we calculated the mean value and root mean square error (RMSE) of the elevation difference before and after the calibration of beams 1 and 2 at each track, and the results are shown in Fig. 7(d). The data plotted in Fig. 7(d) are displayed in Table 3.
In comparison with Fig. 2, the elevation difference curve (EDC) of Fig. 7(a – c) can directly reflect terrain information. As shown in Fig. 7(a), the front and back ends of the laser EDC of track 154 are largely stable, but the middle part fluctuates greatly, especially before calibration. The reason for this fluctuation is that the laser point in the middle part is located in the mountains in northern Beijing. Therefore, the laser elevation difference is significantly larger due to the pointing error before the calibration; the EMA is significantly improved after the calibration. Figure 7(b) presents the results for the 856th laser track. The first half of the laser passes through the Taklimakan Desert in Xinjiang, and the second half passes through the mountainous Tibetan Plateau. Because the desert terrain is gentler than the mountain terrain, the laser elevation accuracy in the first half is greater than that in the second half. The laser EMA on the flat desert in Fig. 7(b) is still worse than that in Fig. 7(a). The main reason for this result is that the AW3D30 DSM was measured in 2011, whereas the GF-7 laser data were obtained in 2019; between 2011 to 2019, the desert surface elevation changed. The GF-7 868th laser track spans the high mountainous area of Shanxi Province. The EDC fluctuates greatly before calibration, as shown in Fig. 7(c), but the accuracy is significantly dimproved after calibration.
It can be seen from Fig. 7 that for either beam 1 or beam 2, the EMA of the GF-7 laser is significantly improved after calibration, especially in mountainous areas. As shown in Fig. 7(a-c), the EDC of the GF-7 laser fluctuates greatly before calibration, especially in mountainous areas. The EDC of the GF-7 laser is significantly stable after calibration and fluctuates approximately around 0. Figure 7(d) shows that the mean and RMSE of the laser elevation difference after calibration are better than those before calibration, and the EMA of GF-7 beam 2 is only half that of beam 1 before calibration. However, the EMAs of beam 1 and beam 2 can be improved to the same level after calibration. According to the RMSE results in Fig. 7(d), the EMA of the 154th track beam 1 can be increased by 3 times after calibration, and that of beam 2 can be increased by 6 times; the highest EMA is −0.03 ± 3.86 m on flat terrain. The EMA of the 856th track beam 1 can be increased by 2 times after calibration, and that of beam 2 can be increased by 4 times; the highest EMA is −0.95 ± 6.60 m on mountain terrain. Similarly, the EMA of the 856th track beam 1 is improved by 3 times, that of beam 2 is improved by 6 times, and the highest EMA is 0.58 ± 9.80 m on high mountain terrain. However, the mean values in Fig. 7(d) show that the laser elevation maximum error after calibration is still −2.17 m because the AW3D30 DSM's own error is within 5 m, so it is necessary to verify the laser AEMA. The EMA over mountains is significantly worse than that over flat terrain after calibration, which indicates that a small pointing error remains after calibration; the laser elevation measurement error is obviously magnified over mountains. In summary, the laser EMA has been significantly improved after calibration using the method proposed in this article.
4. Conclusion
In this paper, proposes a calibration method for laser pointing of the GF-7 spaceborne laser altimeter is proposed and applied to laser pointing calibration of GF-7 beams 1 and 2. After calibration, the method of capturing laser footprints by ground-based detectors is used for laser pointing accuracy verification, the AEMA of the GF-7 laser is verified by using the GPS/RTK measurements data, and the AW3D30 DSM is used to verify the REMA of the GF-7 laser. The conclusions are as follows:
- (1) After calibration, the laser pointing accuracy of the GF-7 satellite is improved by several times. The laser pointing accuracy of beam 1 is approximately 5.4 arcsec, and that of beam 2 is approximately 5.7 arcsec.
- (2) After the AEMA verification of GF-7 laser beam 2, the EMA of GF-7 beam 2 is increased by 10 times after calibration, from 3.74 ± 0.55 m to 0.35 ± 0.50 m.
- (3) The REMAs of GF-7 beams 1 and 2 are greatly improved after calibration. The EMA of GF-7 laser beam 1 is twice that of beam 2 before calibration, but after calibration, GF-7 laser beams 1 and 2 have similar EMAs.
In summary, the new method proposed in this paper can significantly improve the EMA of the spaceborne laser and can be used for monitoring spaceborne laser pointing changes. However, the method proposed in this article does not correct the laser ranging error. In the future, we will use high-precision terrain data for ranging error correction and adopt additional measurement methods to obtain the surface elevation of the GF-7 satellite lasers in typical types of terrain, to evaluate the EMA of the GF-7 lasers in flat, hilly, mountainous, and alpine areas.
Funding
Research on Satellite Observation Systems and Application Schemes for the Fine and Fast Stereo-monitoring of Land Space Project by the Innovative Youth Talents Program, MNR (12110600000018003930); Multibeam Laser Terrain Detection Radar technology and Application Project (D040105); Active and Passive Composite Mapping Technology and Application Project with Visible, Infrared and Laser Sensors (D040106); National Natural Science Foundation of China (41571440, 41771360, 41971426); Authenticity Validation Technology of Elevation Accuracy of GF-7 Laser Altimeter (42-Y20A11-9001-17/18); High-Resolution Remote Sensing, Surveying and Mapping Application Demonstration System (42-Y30B04-9001-19/21); Research and development of forest resources dynamic monitoring and forest volume estimation using LiDAR remote sensing (2020YFE0200800).
Acknowledgments
The authors thank the Bureau of Surveying and Mapping of Heilongjiang Province for assisting in measuring the GF-7 laser surface elevation in situ. We would also like to acknowledge OpenTopography (https://portal.opentopography.org/datasets.) for providing airborne lidar data and the Japan Aerospace Exploration Agency (JAXA) for providing AW3D30 DSM (https://www.eorc.jaxa.jp/ALOS/en/aw3d30/data/index.htm).
Disclosures
The authors declare no conflicts of interest.
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