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The pointing bias of the laser altimeter would change because of the launch vibration, variations in the space environment or other factors, which is one of the most important factors affecting the geometric accuracy of a laser altimeter. To calibrate pointing bias and improve the measuring accuracy of spaceborne laser altimeter, this paper propose...
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... laser altimeter used on the ZY3-02 satellite is showed as Fig. 1. The large (lower) lens is the receiving telescope, and the small (upper) lens is the transmitting telescope. This laser altimeter is used to conduct the terrain measurement ...
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... 3: With the plane coordinates (B, L) of the laser spot P, the elevation value H of the laser spot was interpolated by the reference digital terrain data. As shown in Fig. 10, the point to be interpolated is P, and its plane coordinates are (B, ...
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... Elevation Accuracy Comparison Before and After Calibration: In order to validate the calibration accuracy, ZY3-02 laser altimeter data, 382th, 944th, and 1385th, are compared with AW3D30 before calibration, as shown in Fig. 14. The difference between ZY3-02 laser data and AW3D30 is large, and it is a systematic ...
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... elevation comparisons between the ZY3-02 laser data and AW3D30 after calibration are shown in Fig. 15. It is obviously the calibration result based on the proposed method which can improve the measurement accuracy of ZY3-02 laser altimeter. We compare the elevation error between before calibration and after calibration, and show the result as Figs. 16 and ...
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... elevation comparisons between the ZY3-02 laser data and AW3D30 after calibration are shown in Fig. 15. It is obviously the calibration result based on the proposed method which can improve the measurement accuracy of ZY3-02 laser altimeter. We compare the elevation error between before calibration and after calibration, and show the result as Figs. 16 and ...
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Citations
... Hence, only the elevation calculated with the correct pointing angle is comparable to the actual terrain data. By following this principle, a terrain-matching-based method has been proposed in some studies for on-orbit geometric calibration of satellite laser altimeters (Filin 2001, Li, Tang et al. 2017, Tang, Xie et al. 2019. In this method, the measured terrain is matched with known terrain data to correct any discrepancies in the readings by the altimeter. ...
Spaceborne laser altimetry represents a novel active remote sensing technology applicable to earth observation, which together with imaging spectroscopy and synthetic aperture radar as a core technology for data acquisition in the earth observation systems. However, the accuracy of horizontal positioning for laser footprints from spaceborne laser altimeters declines due to various factors such as the changes in the orbital environment and the deterioration of performance. Moreover, the limited frequency of in-orbit calibration of the spaceborne laser altimeters and the non-disclosure of calibration parameters mean that users are heavily reliant on positioning accuracy of the altimetry data provided. To address this issue, a new algorithm is proposed in this study for enhancing the accuracy of horizontal positioning for laser footprints in the absence of satellite altimeter pointing and ranging parameters. In this algorithm, high-resolution DSM is taken as the reference terrain data to take advantage of the higher precision in elevation over horizontal positioning of the laser footprints. By adjusting the horizontal position of the laser footprint within a small area, the algorithm achieves the optimal alignment of laser elevation data with the reference terrain. Then, the resulting shift in the horizontal position of the laser footprints is referenced to correct their horizontal positioning during that period. Based on the high-accuracy DSM data collected from the Xinjiang autonomous region in China and the data collected by the GF-7 satellite, simulation experiments are performed in this study to analyze and validate the proposed algorithm. According to the experimental results, the horizontal accuracy of the laser footprints improves significantly from 12.56 m to 3.11 m after optimization by the proposed method. With the elimination of 9.45 m horizontal error, accuracy is improved by 75.23%. This method is demonstrated as effective in further optimizing the horizontal position of laser altimetry data products in the absence of altimeter parameters and original data, which promotes the application of spaceborne laser data.
... Liu et al. utilized a waveformmatching approach to calibrate laser altimeters by aligning the emitted laser waveform with the waveform reflected from the actual terrain [16,17]. Tang and associates introduced a laser altimetry satellite pointing calibration method reliant on terrain matching that does not require ground-based instruments and leverages digital surface model (DSM) data for calibrating the laser altimeter's pointing [18]. Xie and team improved the efficiency of this method by implementing a pyramid optimization strategy [19]. ...
Satellite laser altimetry technology, a novel space remote sensing technique, actively acquires high-precision elevation information about the Earth’s surface. However, the accuracy of laser altimetry can be compromised by alterations in the satellite-ground environment, thermal dynamics, and cosmic radiation. These factors may induce subtle variations in the installation and internal structure of the spaceborne laser altimeter on the satellite platform, diminishing measurement precision. In-orbit calibration is thus essential to enhancing the precision of laser altimetry. Through collaborative calculations between satellite and ground stations, we can derive correction parameters for laser pointing and ranging, substantially improving the accuracy of satellite laser altimetry. This paper introduces a sophisticated calibration method for laser altimeter pointing and ranging that utilizes dense control points. The approach interpolates discrete ground control point data into continuous simulated terrain using empirical Bayesian kriging, subsequently categorizing the data for either pointing or ranging calibration according to their respective functions. Following this, a series of calibration experiments are conducted, prioritizing “pointing” followed by “ranging” and continuing until the variation in the ranging calibration results falls below a predefined threshold. We employed experimental data from ground control points (GCPs) in Xinjiang and Inner Mongolia, China, to calibrate the GaoFen-7 (GF-7) satellite Beam 2 laser altimeter as per the outlined method. The calibration outcomes were then benchmarked against those gleaned from infrared laser detector calibration, revealing disparities of 1.12 s in the pointing angle and 2 cm in the ranging correction value. Post validation with ground control points, the measurement accuracy was refined to 0.15 m. The experiments confirm that the proposed calibration method offers accuracy comparable to that of infrared laser detector calibration and can facilitate the updating of 1:10,000 topographic maps utilizing stereo optical imagery. Furthermore, this method is more cost-effective and demands fewer personnel for ground control point collection, enhancing resource efficiency compared to traditional infrared laser detector calibration. The proposed approach surpasses terrain-matching limitations when calibrating laser ranging parameters and presents a viable solution for achieving frequent and high-precision in-orbit calibration of laser altimetry satellites.
... As depicted in Tables 1 and 2, artificial ground marker calibration method comprise the Laser Ground Detector (LGD) method (Magruder et al. 2001;Tang et al. 2021), airborne infrared camera imaging calibration method (Magruder et al. 2010), Corner Cube Retroreflector (CCR) calibration method (Magruder et al. 2007). The natural surface calibration method includes satellite attitude maneuver calibration method (Luthcke et al. 2005;Luthcke et al. 2002;Luthcke et al. 2000;Rowlands et al. 1999), slope terrain calibration method , as well as terrain matching calibration method (Tang et al. 2019). The advantages and disadvantages of various calibration methods are described in detail in Tables 1 and 2. Terrain matching calibration method is one of the effective means to achieve highfrequency on-orbit geometry calibration of satellite lasers. ...
The satellite laser geometry calibration method based on terrain matching (terrain matching calibration) has been extensively employed in satellite laser geometry calibration for its simplicity and lack of need for ground probes. In this study, the key factors for the accuracy of the above-mentioned calibration method, i.e. namely the terrain slope and the number of laser points, are examined with the GaoFen-7 (GF-7) satellite as an example. Terrain is classified into six levels in according with the slope classification standards, i.e. Flat (<2°), Micro-slope (2°–5°), Gentle-slope (5°–15°), Moderate-slope (15°–25°), Slope (25°–35°) and Steep-slope (35°–55°). Moreover, a different number of laser points are randomly selected from each the respective terrain slope for calibration. The accuracy of calibration is verified using the true laser pointing obtained based on the ground detector calibration method. As indicated by the experimental results, the terrain matching calibration achieves the optimal experimental conditions when there are over 50 laser points with a terrain slope greater than 15°, or there exist over 20 laser points with a terrain slope greater than 25°. In both cases, the laser pointing accuracy after calibration can exceed 3 arc seconds. This study can provide technical guidance for high-precision terrain matching calibration.
... Magruder et al. successfully tagged ATLAS return photon clouds using corner-cube retroreflectors (CCRs) and verified a mean ICESat-2 geolocation measurement accuracy of 3.5 m ± 2.1 m (Magruder et al. 2021). Tang et al. (2019a) proposed a satellite laser pointing calibration method based on terrain matching. By traversing the laser pointing angles, the laser pointing angle with the smallest elevation residual between the laser and digital surface mode (DSM) was determined as the optimal pointing angle. ...
... By traversing the laser pointing angles, the laser pointing angle with the smallest elevation residual between the laser and digital surface mode (DSM) was determined as the optimal pointing angle. Building on the research of Tang et al (2019a)., Liu et al. completed the calibration of GF-7 satellite lasers using a field-free calibration method based on the separation between satellite laser pointing and ranging (CMSPR) (Liu et al. 2022). This method compensates for the problem where a terrain matching method cannot be used to calibrate the ranging error, but there is still an error of 2 arcsec in the laser pointing following calibration. ...
After being launched into orbit, the geometric calibration of a satellite laser altimeter will reduce errors in laser pointing and ranging caused by satellite vibrations during launch, environmental changes, and thermal effects during long-term operation, which guarantees the accuracy of measurement data. In this study, a satellite laser geometric calibration method combining infrared detectors and corner-cube retroreflectors (CCRs) is proposed. First, a CCR-based laser ranging error calibration method was established, and then a laser pointing error calibration model was derived based on a single infrared detector array. Taking GaoFen-7 (GF-7) satellite laser beam 2 as the experimental object, laser geometric calibration was realized using an infrared detector and CCR-measured data. Then, the accuracy of the proposed method was compared with that of other calibration methods, the CMLID and the CMSPR. The results show that the accuracy of the proposed calibration method is equivalent to that of the CMLID and higher than that of the CMSPR. Among them, the accuracy of the laser pointing after calibration using the proposed method is better than 0.8 arcsec, and the elevation accuracy of the laser on flat, sloping, and mountainous terrains is better than 0.11 m, 0.30 m, and 1.80 m, respectively.
... Secondly, the proposed accuracy verification meth-64 ods regard the laser track as a whole without considering the individual differences of 65 photons. 66 At present, the verification methods for the horizontal accuracy of satellite-based li-67 dar include GPS/GNSS differential technology [9], analysis method based on echo wave-68 form [10,11], and matching with the high-accuracy digital elevation model (DEM)\digital 69 surface model (DSM) [12,13]. By comparing the GNSS and ATL03 photon-based heights, 70 Brunt et al. [14] proved that the current accuracy of ATL03 is better than 5 cm, and the 71 surface measurement accuracy is better than 13 cm. ...
... Therefore, it is feasi-78 ble to use high-accuracy DSM to check the accuracy of the ICESat-2 data. Tang et al. [13] 79 proposed a terrain-matching method based on a hierarchical pyramid searching for satel-80 lite-based laser altimeters. Using Tang's method, the best matching position can be quickly 81 determined. ...
... 306 To further evaluate the effectiveness of our method, we use two alternative methods 307 in the same study site to make a comparative study. Tang's method utilizes the pyramid 308 iteration method [13]. It determines the window and step sizes according to the terrain 309 characteristics to determine the minimum elevation difference of DSM and improve the 310 geolocation accuracy. ...
The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2), launched in September 2018, has been widely used in forestry and surveying. A high-accuracy digital elevation model (DEM)/digital surface model (DSM) for terrain matching can effectively evaluate the ICESat-2 design requirements and provide essential data support for further study. The conventional terrain-matching methods regard the laser ground track as a whole, ignoring the individual differences caused by the interaction of photons during flight. Therefore, a novel terrain-matching method using a two-dimensional affine transformation model was proposed to describe the deformation of laser tracks. The least-square optimizes the model parameters with the high-accuracy terrain data to obtain the best matching result. The results in McMurdo Dry Valley (MDV), Antarctica, and Zhengzhou (ZZ), China, demonstrate that the proposed method can verify geolocation accuracy and indicate that the average horizontal accuracy of ICESat-2 V5 data is about 3.86 m in MDV and 4.67 m in ZZ. It shows that ICESat-2 has good positioning accuracy, even in mountainous areas with complex terrain. Additionally, the random forest (RF) model was calculated to analyze the influence of four factors on geographic location accuracy. The slope and signal-to-noise ratio (SNR) are considered the crucial factors affecting the accuracy of ICESat-2 data.
... Therefore, due to the limitations of the plane accuracy verification in the experiment, verification of relative plane accuracy was conducted for the calibration results only. However, the plane accuracy and elevation accuracy of GF-7 satellite laser are closely correlated [34,35]. In other words, the elevation accuracy can also reflect the plane accuracy. ...
On-orbit geometric calibration of satellite-borne laser based on infrared detectors is the key tool to ensure the elevation measurement accuracy, and the accuracy of on-orbit geometric calibration is directly determined by laser spots captured by detectors. Mathematical methods, such as gray-scale barycenter, are widely applied for centroid extraction of spots captured by infrared detectors and completely depend on the energy values at points measured by detectors, which have low precision and are greatly affected by the consistency of the detectors and other factors at present. Based on the above question, considering the consistency between the real laser footprint shape and spot captured by detectors, a centroid extraction method of laser spots captured by infrared detectors combining laser footprint images and detector observation data is proposed for making up this defect to some extent. First, the self-adaptive “two-step method” is used to denoise footprint images hierarchically to obtain the real shape of footprints for constraining the spots captured by detectors, and then the centroids of spots are extracted by using the energy-weighted barycenter method based on regional blocks. In the experiment, Gaofen-7 (GF-7) satellite is taken as the research object, and the proposed method, as well as the other six methods, are used for the centroid extraction of laser spots captured by detectors, the calculation of calibration parameters based on the single-beam and dual-beam laser calibration models, the positioning of laser footprints, and cross verification. According to the results, the plane accuracy of centroid extraction using the proposed method is as follows: 0.34 grids for Beam 1 and 0.33 grids for Beam 2. In addition, on flat terrain, the elevation accuracy of Beam 1 and Beam 2 in 2021 is 5.2 cm and 5.0 cm, respectively, 0.6 cm and 4.2 cm higher than those in the most accurate one among other methods; the elevation accuracy in 2020 is 23.3 cm and 7.1 cm, respectively, 7.7 cm and 2.7 cm higher than those in the most accurate one among other methods. On slopes and gentle slopes, the method proposed is also superior to other methods. Since the change of pointing angle caused by satellite jitter, atmosphere, etc., between different years, the accuracy drops when laser footprints of 2020 are located using the parameters of 2021. In summary, under different terrains and years, the results fully demonstrate the effectiveness and accuracy of the proposed method, which has more significant advantages than other traditional methods.
... The simulation waveform matching calibration method [12] has some uncertainties with high requirements for the local terrain type, and the reliability is low. The traditional terrain matching calibration method [13] cannot calibrate laser range errors, and the calibration accuracy is low. Additionally, there is an iterative pointing angle calibration method based on small-range terrain matching [14]. ...
... and the surface elevation was the same within approximately 100 m of this feature. The satellite laser pointing accuracy is normally approximately 30 m [13] after the first terrain matching calibration. Within this error range, the actual elevation of the ground for the selected laser footprints would not change, and the selected ranging calibration area was reasonable. ...
... The detailed implementation process of the algorithm is shown in Figure 7. When the range of the pointing grid is large or the grid spacing is small, the experimental processing speed is slow, and the reference [13] can be used to improve the pointing calibration processing speed by using a pyramid method. ...
Satellite laser altimeters have been widely used in the surveying, mapping, forestry, and polar regions and by other industries due to their excellent elevation measurement accuracy. Satellite laser on-orbit geometry calibration is a necessary means to ensure elevation accuracy. This study proposes an iterative geometry calibration method for satellite laser altimeter pointing and ranging separation that does not require the use of field detectors. The DSM data were first used to complete the laser pointing calibration, and then the laser footprint elevation was measured accurately to complete the laser ranging calibration. The iterative calibration experiment was repeated until the convergence condition (i.e., the laser point difference was less than 1× 10-5 degrees and the laser ranging difference was less than 0.01 m) was met, with the calibrated laser pointing angle and ranging separation used as the input parameters. In this work, the GaoFen-7 (GF-7) satellite laser was used as the test object and the actual laser pointing and ranging values derived from ground detector calibrations. The results verified that the pointing accuracy of the GF-7 beam 1 was 2 arcsec and that the ranging accuracy was 2 cm after applying the calibration method presented in this paper. The pointing accuracy of the GF-7 beam 2 was 2.2 arcsec, and the ranging accuracy was approximately 1 cm. This analysis demonstrated that the GF-7 laser mission exceeded its pointing angle requirement of 3 arcsec after laser pointing and ranging separation iterative calibrations were applied. Finally, ground control points were used to verify the calibrated elevation accuracy of the GF-7 satellite laser, and its accuracy on flat terrain was 0.18 m. In summary, it was proven that the satellite laser geometry calibration method proposed in the article is effective.
... Yi et al. [20] proposed a spaceborne laser altimeter pointing on-orbit calibration method based on the analysis of natural surface ranging residuals, which avoids satellite attitude maneuvering but requires the digital elevation map of the calibration field as reference data. Tang et al. [21] proposed a method for spaceborne laser altimeter calibrating by using published digital terrain data as reference data to match with stripes of a point cloud obtained by the geolocation model of the laser altimeter. After calibration, the elevation error is less than 3 m, and the efficiency of the method is 10 times higher than the previous algorithm. ...
For a multi-mode Earth observation satellite carrying a line array camera and a multi-beam line array LiDAR, the relative installation attitude of the two sensors is of great significance. In this paper, we propose an on-orbit calibration method for the relative installation attitude of the camera and the LiDAR with no need for the calibration field and additional satellite attitude maneuvers. Firstly, the on-orbit joint calibration model of the relative installation attitude of the two sensors is established. However, there may exist a multi-solution problem in the solving of the above model constrained by non-ground control points. Thus, an alternate iterative method by solving the pseudo-absolute attitude matrix of each sensor in turn is proposed. The numerical validation and simulation experiments results show that the relative positioning error of the line array camera and the LiDAR in the horizontal direction of the ground can be limited to 0.8 m after correction by the method in this paper.
... In addition to the above methods of scan maneuvers and directly obtaining the actual footprint locations, other kinds of calibration/ validation methods based on the known topographic information were investigated Filin, 2003;Filin, 2006;Shuman et al., 2006;Siegfried et al., 2011;Yi et al., 2016;Zhang et al., 2018;Brunt et al., 2019;Nan et al., 2019;Neuenschwander and Magruder, 2019;Tang et al., 2019;Malambo and Popescu, 2021;Liu et al., 2021). Generally, these methods benefiting from the known topographic information can be divided into: (1) Sigefried et al. and Burnt et al. validated the elevation accuracy of ICESat and ICESat-2 by using highresolution ground-based GPS measurements (Siegfried et al., 2011;Brunt et al., 2019). ...
... (3) The terrain matching methods were investigated, which estimate the systematic bias or evaluate the geolocation accuracy by matching the known ground truth profiles with the observed profiles from laser altimeters (an observed profile was constructed by successive laser footprints on the ground) (Filin, 2003(Filin, , 2006Yi et al., 2016;Nan et al., 2019;Neuenschwander and Magruder, 2019;Tang et al., 2019;Malambo and Popescu, 2021;Liu et al., 2021). Specifically, Filin derived the basic principle of terrain matching method for the calibration of spaceborne laser altimeters (Filin, 2003(Filin, , 2006. ...
... Yi et al. analyzed the conditions of satisfaction for the used topography when conducting terrain matching methods (Yi et al., 2016). Tang et al. made a coarse calibration for laser altimeter data using the terrain matching method and pyramid-search strategy, where the Advanced Land Observation Satellite (ALOS) Word 3D 30 m (AW3D30) digital surface model (DSM) was used as the known topographic information (Tang et al., 2019). Nan et al. proposed a terrain matching method for the on-orbit calibration of photon-counting laser altimeters with high-resolution Digital Elevation Model (DEM) (Nan et al., 2019). ...
Precisely estimating on-orbit laser ranging and pointing systematic bias plays a significant role in obtaining high accuracy data product for spaceborne laser altimeters. Current terrain matching methods were mainly used to estimate the systematic bias for analog (or full waveform) laser altimeters or to evaluate the geolocation accuracy for both analog and photon-counting laser altimeters. The new generation photon-counting laser altimeter provides unprecedented high-density laser points on the ground and can obtain the along-track surface profiles even when observing terrains with complex topography. In this study, we propose a terrain matching algorithm to iteratively estimate the laser pointing and laser ranging systematic biases for spaceborne photon-counting laser altimeters. With the help of the ground truth topography, the systematic biases are obtained by matching the observed ranging profiles from a spaceborne photon-counting laser altimeter with the expected ranging profiles calculated from a reasonable model. Meanwhile, the theoretical model of the estimation precision is derived and denoted as confidence intervals. The data products and system parameters of the only current spaceborne photon-counting laser altimeter, i.e. Ice, Cloud, and Land Elevation Satellite-2 Advanced Topographic Laser Altimeter System (ICESat-2 ATLAS), are used to test the performance of the proposed method in Lianyungang City, China with local ground truth Digital Elevation Model (DEM). This method is proved that it can be further used to validate the geolocation accuracy, and the results show that the mean horizontal accuracy of ICESat-2 is approximately 1.7 m in the study site. It indicates that ICESat-2 has very good geolocation accuracy, even though the study site is a mountainous region with complex topography. In addition, the ranging model difference between analog and photon-counting laser altimeters is derived and quantitatively analyzed in this study. The proposed method can be not only used in the validation of geolocation accuracy but also as a potential calibration method for spaceborne photon-counting laser altimeters.
... 等激光测高数据与遥感影像结合实现对火星、月球表面的形貌测绘，以解决火星、月球表面 缺少控制数据的问题 [7][8][9][10] 。随后，结合 ICESat 卫星获取的激光测高数据，开展了针对地球的 联合区域网平差技术研究，显著提高了我国资源三号 [11][12][13] 、天绘一号 [ [20][21][22] ...
Block adjustment technology can improve image positioning accuracy, but the lack of ground control points limits the block adjustment technology. Considering that satellite-based LiDAR can provide global ground control points, using satellite laser altimeter data to improve positioning accuracy of optical stereo images is a feasible idea. The research on satellite laser altimetry in China is not sufficient compared with USA, which needs more attention. The DEM area element trajectory matching is performed on satellite-based LiDAR photon data to establish the correspondence between the trajectory of laser altimetry points and the DSM generated by remote sensing stereo images. Then, selected ground photons and high-resolution optical remote sensing images are jointed with block adjustment, and based on the iterative solution method considering coordinate error of laser altimetry points, stereo positioning accuracy promotion of satellite remote sensing can be realized. Satellite-based LiDAR data ATL03, GF-7 and TH-3 satellite remote sensing images were used to verify the performance of the method. The experimental results showed that the proposed method can effectively improve stereo positioning accuracy of satellite remote sensing images without ground control points, and the root mean square error of the elevation accuracy can reach 1.258 m.
