The satellite gravimetry technology effectively recovers the global Earth’s gravity field.Since 2000s,HL-SST satellite CHAMP,LL-SST satellite GRACE,Gravity Gradient Measurement(GGM)satellite GOCE have been launched s...The satellite gravimetry technology effectively recovers the global Earth’s gravity field.Since 2000s,HL-SST satellite CHAMP,LL-SST satellite GRACE,Gravity Gradient Measurement(GGM)satellite GOCE have been launched successfully,producing some Earth’s gravity models solely from satellites data.However,the space and time resolution of the Earth’s gravity fields do not adequately satisfy scientific objectives.The main reason is that the gravimetry satellites are not enough and observation data insufficient.The paper outlines the current and future status of Chinese gravity satellite missions.The Chinese gravimetry satellite system,named Chinese Gravimetry augment and Mass change exploring mission(ChiGaM),successfully launched in Dec.2021 after four years of production and over a year of calibration and valiation.The accelerometer,K-band ranging system and the three stellar sensors,among others,were precisely calibrated and trimmed.The satellite mass center was determined and coordinated with the proof center of accelerometer with an accuracy 100μm.The inter-satellite ranging system and BDS/GPS receiver operate together seamlessly.The range and range rate noise is less than 3μm/Hz^(1/2) and 1μm/s/Hz^(1/2),respectively,in band of 0.025~0.1 Hz.The electrostatic suspension accelerometer is working well.Its high-sensitive axis noise level is 3×10^(-10) m/s^(2)/Hz^(1/2)near the frequency 0.1 Hz,and 1×10^(-9) m/s^(2)/Hz^(1/2) for the less-sensitive axis.Meanwhile the BDS/GPS receiver is used to achieve data for precise orbit determination,yielding an orbit result with accuracy better than 2 cm.When compared with KBR observations,the RMS of the bias is less than 1 mm.Besides above mission,next gravimetric satellite is being developed now.TQ-2 mission is designed as a totally experimental satellite for gravitational wave detection at low Earth orbit,which can detect the Earth’s gravity field simultaneously.The Bender-type mission is considered the most promising configuration for TQ-2 and consists of two polar satellites and two inclined satellites.Due to the extra observations at the east-west direction derived from the inclined satellite pair,significant improvements has been made in detecting temporal signals with higher accuracy and spatial-temporal resolution.To achieve the scientific goal,the ACC MBW can shift from 0.001~0.1 Hz to 0.004~0.1 Hz for ACC,and the LRI MBW can shift from 0.01~1 Hz to 0.1~1 Hz.For future research,a gravimetric potential survey using cold-atomic-clock based on the general relativity theory,cold atom gradiometer should be pursued.Gravimetric technologies should be mined and researched,and the gravimetry satellite constellation should be developed,so as to improve the time resolution and space resolution for meeting the requirements of geophysics,geodesy,earthquake,water resources environment,oceanography,etc.展开更多
After implementing CGCS2000,establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in m...After implementing CGCS2000,establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in mapping applications.Consequently,a grid model for high-accuracy coordinate transformation of CGCS2000 is proposed.Specifically,we firstly analyze a minimum curvature equation of coordinate transformation,which possesses the characteristics of both the global and local smoothness,achieving better consistency with the consecutive smoothness for the coordinate transformation of map’s linear feature.Then an iterative calculation method of grid nodes and an approach for establishing regional grid models based on collocation by two-step minimization are proposed.Meanwhile,a data structure of grid model is constructed.Finally we give the optimized grid interval and transformation accuracy in China corresponding to the proposed grid model.Using 48 433 points of 2000 National Geodetic Control Network of China,we take the proposed model into practice by constructing grid models for coordinate transformation from BJS54 and XAS80 to CGCS2000,and the external positional accuracies for both models are 0.26 m and 0.03 m respectively.展开更多
Editor-in-Chief Jianya GONG,Wuhan University,China Associate Editors-in-Chief Yuanxi YANG,Xi'an Research Institute of Surveying and Mapping,China Jiancheng LI,Wuhan University,China Zhilin II,The Hong Kong Polytec...Editor-in-Chief Jianya GONG,Wuhan University,China Associate Editors-in-Chief Yuanxi YANG,Xi'an Research Institute of Surveying and Mapping,China Jiancheng LI,Wuhan University,China Zhilin II,The Hong Kong Polytechnic University,HongKong China Wenzhong SHI,The Hong Kong Polytechnic Unitersity,.HongKong China.展开更多
In this study,we provide a summary of research advances in the field of maritime target detection using DP(dualpolarimetric)SAR(Synthetic Aperture Radar)imagery,accomplished during the European and China collaboration...In this study,we provide a summary of research advances in the field of maritime target detection using DP(dualpolarimetric)SAR(Synthetic Aperture Radar)imagery,accomplished during the European and China collaboration in the framework of the Dragon-4 program ID 32235.The main innovative contribution is twofold:(1)We addressed ship detection proposing an improved GP-PNF(Geometrical Perturbation-Polarimetric Notch Filter),termed as IGP-PNF,that is characterized by a new feature vector that includes three new scattering features;(2)We addressed oil platform detection by contrasting singlepolarization SAR methods with polarimetric ones in order to quantify the extra-benefit carried on polarimetric information.The proposed theoretical framework is tested against actual multi-polarization SAR data.In particular,ship detection methods are verified against a Sentinel-1 SAR scene where a large number of ships is present;while,oil platform detection is discussed using Terra SAR-X SAR data.Experimental analysis shows that:(1)The IGP-PNF method performs best in terms of clutter-to-target ratio;(2)Coherent polarimetric information significantly outperforms single-polarization SAR measurements in highlighting targets in challenging cases.展开更多
Compared with the pair-wise registration of point clouds,multi-view point cloud registration is much less studied.In this dissertation,a disordered multi-view point cloud registration method based on the soft trimmed ...Compared with the pair-wise registration of point clouds,multi-view point cloud registration is much less studied.In this dissertation,a disordered multi-view point cloud registration method based on the soft trimmed deep network is proposed.In this method,firstly,the expression ability of feature extraction module is improved and the registration accuracy is increased by enhancing feature extraction network with the point pair feature.Secondly,neighborhood and angle similarities are used to measure the consistency of candidate points to surrounding neighborhoods.By combining distance consistency and high dimensional feature consistency,our network introduces the confidence estimation module of registration,so the point cloud trimmed problem can be converted to candidate for the degree of confidence estimation problem,achieving the pair-wise registration of partially overlapping point clouds.Thirdly,the results from pair-wise registration are fed into the model fusion to achieve the rough registration of multi-view point clouds.Finally,the hierarchical clustering is used to iteratively optimize the clustering center model by gradually increasing the number of clustering categories and performing clustering and registration alternately.This method achieves rough point cloud registration quickly in the early stage,improves the accuracy of multi-view point cloud registration in the later stage,and makes full use of global information to achieve robust and accurate multi-view registration without initial value.展开更多
According to the characteristics of the road features,an Encoder-Decoder deep semantic segmentation network is designed for the road extraction of remote sensing images.Firstly,as the features of the road target are r...According to the characteristics of the road features,an Encoder-Decoder deep semantic segmentation network is designed for the road extraction of remote sensing images.Firstly,as the features of the road target are rich in local details and simple in semantic features,an Encoder-Decoder network with shallow layers and high resolution is designed to improve the ability to represent detail information.Secondly,as the road area is a small proportion in remote sensing images,the cross-entropy loss function is improved,which solves the imbalance between positive and negative samples in the training process.Experiments on large road extraction datasets show that the proposed method gets the recall rate 83.9%,precision 82.5%and F1-score 82.9%,which can extract the road targets in remote sensing images completely and accurately.The Encoder-Decoder network designed in this paper performs well in the road extraction task and needs less artificial participation,so it has a good application prospect.展开更多
The exploration of building detection plays an important role in urban planning,smart city and military.Aiming at the problem of high overlapping ratio of detection frames for dense building detection in high resoluti...The exploration of building detection plays an important role in urban planning,smart city and military.Aiming at the problem of high overlapping ratio of detection frames for dense building detection in high resolution remote sensing images,we present an effective YOLOv3 framework,corner regression-based YOLOv3(Correg-YOLOv3),to localize dense building accurately.This improved YOLOv3 algorithm establishes a vertex regression mechanism and an additional loss item about building vertex offsets relative to the center point of bounding box.By extending output dimensions,the trained model is able to output the rectangular bounding boxes and the building vertices meanwhile.Finally,we evaluate the performance of the Correg-YOLOv3 on our self-produced data set and provide a comparative analysis qualitatively and quantitatively.The experimental results achieve high performance in precision(96.45%),recall rate(95.75%),F1 score(96.10%)and average precision(98.05%),which were 2.73%,5.4%,4.1%and 4.73%higher than that of YOLOv3.Therefore,our proposed algorithm effectively tackles the problem of dense building detection in high resolution images.展开更多
Target detection technology of synthetic aperture radar(SAR)imageis widely used in the field of military reconnaissance and surveillance.The traditional SAR image target detection methods need to be provided a lot of ...Target detection technology of synthetic aperture radar(SAR)imageis widely used in the field of military reconnaissance and surveillance.The traditional SAR image target detection methods need to be provided a lot of empirical knowledge because the characteristics of SAR images in different configurations(attitude,pitch angle,imaging parameters,etc.)will change greatly,resulting in high generalization error.Currently,deep learning method has achieved great success in the field of image processing.Research shows that deep learning can achieve a more intrinsic description of the data,while the model has a stronger ability of modeling and generalization.In order to solve the problem of insufficient data in SAR data sets,an experimental system for acquiring SAR image data in real scenes was built.Then the transfer learning method and the improved convolution neural network algorithm(PCA+Faster R-CNN)are applied to improve the target detection precision.Finally,experimental results demonstrate the significant effectiveness of the proposed method.展开更多
Reliable and prompt information on forest above-ground biomass(AGB)and tree diameter at breast height(DBH)are crucial for sustainable forest management.Remote sensing technology,especially the Light Detection and Rang...Reliable and prompt information on forest above-ground biomass(AGB)and tree diameter at breast height(DBH)are crucial for sustainable forest management.Remote sensing technology,especially the Light Detection and Ranging(LiDAR)technology,has been proven to estimate important tree variables effectively.This study proposes predicting DBH and AGB from tree height and other LiDAR data extracted metrics.In the suggested DBH prediction,we developed a nonlinear estimation equation using the total tree height.As for the AGB prediction approach,we used regression methods such as multiple linear regression(MLR),random forest(RF)and support vector machine for regression(SVR).We conducted the study for the Gudao forest area dominated by Robinia Pseudoacacia trees,located in the Yellow River Delta(YRD),China.For our developed approaches,we used Unmanned Aerial Vehicle(UAV)and Backpack LiDAR point cloud datasets obtained in June 2017,and three field data measurements gathered in June 2017 and 2019 and October 2019,all from the same study area.The results demonstrate that:①The LiDAR data individual tree segmentation(ITS)from which we extracted individual tree information like tree location and tree height,was carried out with an overall accuracy F=0.91;②We used the ITS height data from the field stand in 2019 as a fit and developed a nonlinear DBH estimation equation with Root Mean Square Error(RMSE)=3.61 cm,later validated by the 2017 dataset;③Forest AGB at stand level was estimated with the MLR,RF and also SVR regression methods,and results show that the SVR method gave higher accuracy with R2=0.82 compared to the R2=0.72 of RF and the R2=0.70 of the MLR.Calculated AGB at plot level using the 2017 LiDAR data was used to validate both models’accuracy.Combining the UAV LiDAR data and the Backpack LiDAR significantly improved the overall ITS.The UAV LiDAR ability to provide high accuracy tree height abstraction,the DBH of the regression equation and other extracted LiDAR metrics showed high accuracy in estimating the forest AGB.This study shows that being cost-free is not the only advantage of free available software.In the performance of ITS and the LiDAR,metrics extraction proved to be as good as the commercially available software.展开更多
Currently,deep convolutional neural networks have made great progress in the field of semantic segmentation.Because of the fixed convolution kernel geometry,standard convolution neural networks have been limited the a...Currently,deep convolutional neural networks have made great progress in the field of semantic segmentation.Because of the fixed convolution kernel geometry,standard convolution neural networks have been limited the ability to simulate geometric transformations.Therefore,a deformable convolution is introduced to enhance the adaptability of convolutional networks to spatial transformation.Considering that the deep convolutional neural networks cannot adequately segment the local objects at the output layer due to using the pooling layers in neural network architecture.To overcome this shortcoming,the rough prediction segmentation results of the neural network output layer will be processed by fully connected conditional random fields to improve the ability of image segmentation.The proposed method can easily be trained by end-to-end using standard backpropagation algorithms.Finally,the proposed method is tested on the ISPRS dataset.The results show that the proposed method can effectively overcome the influence of the complex structure of the segmentation object and obtain state-of-the-art accuracy on the ISPRS Vaihingen 2D semantic labeling dataset.展开更多
Shallow water multi-beam echo sounders(MBESs)are characterized by their high resolution and high density,and MBES data processing is a hotspot in modern marine surveying.The Combined Uncertainty and Bathymetry Estimat...Shallow water multi-beam echo sounders(MBESs)are characterized by their high resolution and high density,and MBES data processing is a hotspot in modern marine surveying.The Combined Uncertainty and Bathymetry Estimator(CUBE)is the mainstream MBES data processing algorithm,although little is known about its core theories and parameters.In this paper,the basic principle,mathematical model,key parameters,and main processing steps of CUBE are described systematically.A parameter group optimization method that combines CUBE with a surface filter is established.Additionally,an example is given that shows the steps for parameter group optimization,including selection of a typical area,parameter group testing,and comparative analysis,and the method is then applied to shallow water MBES data processing.The results show that the method can improve the accuracy and efficiency of automatic data processing effectively,and it is thus of engineering application value.展开更多
This paper is intended to report on the progresses made during the Dragon-4 project Three and Four-Dimensional Topographic Measurement and Validation(ID:32278),sub-project Multi-baseline SAR Processing for 3 D/4 D Rec...This paper is intended to report on the progresses made during the Dragon-4 project Three and Four-Dimensional Topographic Measurement and Validation(ID:32278),sub-project Multi-baseline SAR Processing for 3 D/4 D Reconstruction(ID:322782).The work here reported focuses on two important aspects of SAR remote sensing of tropical forests,namely the retrieval of forest biomass and the assessment of effects due to changing weather conditions.Recent studies have shown that by using SAR tomography the backscattered power at 30 m layer above the ground is linearly correlated to the forest Above Ground Biomass(AGB).However,the two parameters that determine this linear relationship might vary for different tropical forest sites.For purpose of solving this problem,we investigate the possibility of using Li DAR derived AGB to help training the two parameters.Experimental results obtained by processing data from the Tropi SAR campaign support the feasibility of the proposed concept.This analysis is complemented by an assessment of the impact of changing weather conditions on tomographic imaging,for which we simulate BIOMASS repeat pass tomography using ground-based Tropi SCAT data with a revisit time of 3 days and rainy days included.The resulting backscattered power variation at 30 m is within 1.5 d B.For this forest site,this error is translated into an AGB error of about 50~80 t/hm^(2),which is 20%or less of forest AGB.展开更多
A novel tie point matching algorithm of aerial images with the assistance of airborne LiDAR point clouds and POS data is proposed Firstly,the conjugate point searching strategy used in traditional correlation coeffici...A novel tie point matching algorithm of aerial images with the assistance of airborne LiDAR point clouds and POS data is proposed Firstly,the conjugate point searching strategy used in traditional correlation coefficient matching is improved and a fast algorithm is presented.Secondly,an automatic camera boresight misalignment calibration method based on virtual ground control points is proposed,and then the searching range of image matching is adaptively determined and applied to the image matching of the entire surveying area.Test results verified that the fast correlation coefficient matching algorithm proposed in this paper can reduce approximately 25% of the matching time without the loss of matching accuracy.The camera boresight misalignment calibration method can effectively increase the accuracy of exterior orientation elements of images calculated from POS data,and thus can significantly improve the predicted position of conjugate point for tie point matching.Our proposed image matching algorithm can achieve superior matching accuracy with multi-scale,multi-view,and cross-flight aerial images.展开更多
Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces sever...Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces several forms of topographic effects: direct effect on gravity, secondary indirect effect on gravity and indirect effects on the (quasi-) geoid, respectively. To strike a balance between computation accuracy and numerical efficiency, the global integration region of topographic effects is usually divided into near zone and far zone. We focus on the computation of near-zone topographic effects, which are functions of actual topographic masses and condensed masses. Since there have already been mature formulas for gravitational attraction and potential of actual topographic masses using rectangular prism model, we put forward surface element model for condensed masses. Afterwards, the formulas for near-zone direct and indirect effects are obtained easily by combining the rectangular prism model and surface element model. To overcome the planar approximation errors involved with the new formulas for near-zone topographic effects, the Earth’s curvature can be taken into account. It is recommended to apply the formulas based on the rectangular prism and surface element considering the Earth’s curvature to calculate near-zone topographic effects for high-accuracy demand to determine geoid and quasi-geoid.展开更多
Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduct...Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.展开更多
The Global Navigation Satellite Systems(GNSS)broadcast radio signals are continuously at two or more frequencies in the L-band,and the multipath signals from sea surface recorded by off-the-shelf geodetic receivers ha...The Global Navigation Satellite Systems(GNSS)broadcast radio signals are continuously at two or more frequencies in the L-band,and the multipath signals from sea surface recorded by off-the-shelf geodetic receivers have been demonstrated they can be used to estimate sea level,using a technology called GNSS multipath reflectometry(GNSS-MR).Before proceeding to estimate reflection parameters,the azimuth range and elevation angle range are needed to be defined,as only with suitable azimuths and elevation angles the sensing zones can be guaranteed on water.So,this study presents an angle dependence analysis method to jointly select the azimuth range and elevation angle range based on wavelet analysis which can describe the nonstationary power of different sinusoidal oscillations changed with elevation angle.The key of this method is to use one grid model to screen the spectrum power of multipath oscillation on different elevation angles and azimuths in this work.Then the elevation angles and the azimuths can be determined by searching grids with greater power.The GPS and GLONASS data of two MultiGNSS Experiment(MGEX)stations named BRST and MAYG was analyzed and used to retrieve.Firstly,the angle dependence analysis was carried out to determine the elevation range and azimuth range.Secondly,the sea levels were retrieved from individual signals.Finally,the retrievals of individual signals are combined to form a 10-min sea level retrieval series.The RMSEs of the combined retrievals are both less than 15 cm.The results show the effectiveness of the selection of angle range based on the angle dependence analysis method.展开更多
Influence of Range Gate Width on Detection Probability and Ranging Accuracy of Single Photon Laser Altimetry Satellite Guoyuan LI 1,3,Fanghong YE 1,2,Xinming TANG 1,Dongping XIE 1,Jiapeng HUANG 1,Genhua HUANG 31.Land ...Influence of Range Gate Width on Detection Probability and Ranging Accuracy of Single Photon Laser Altimetry Satellite Guoyuan LI 1,3,Fanghong YE 1,2,Xinming TANG 1,Dongping XIE 1,Jiapeng HUANG 1,Genhua HUANG 31.Land Satellite Remote Sensing Application Center,Ministry of Natural Resources,Beijing 100048,China;2.School of Resource and Environmental Sciences,Wuhan University,Wuhan 430079,China;3.Key Laboratory of Space Active Opto-electronics Technology,Chinese Academy of Sciences,Shanghai 200038,China Abstract:The influence of the single photon laser altimeter range-gate width on the detection probability and ranging accuracy is discussed and analyzed,according to the LiDAR equation,single photon detection equation and the Monte Carlo method to simulate the experiment.The simulated results show that the probability of detection is not affected by the range gate,while the probability of false alarm is relative to the gate width.When the gate width is 100 ns,the ranging accuracy can accord with the requirements of satellite laser altimeter.But when the range gate width exceeds 400 ns,ranging accuracy will decline sharply.The noise ratio will be more as long as the range gate gets larger,so the refined filtering algorithm during the data processing is important to extract the useful photons effectively.In order to ensure repeated observation of the same point for 25 times,we deduce the quantitative relation between the footprint size,footprint,and frequency repetition according to the parameters of ICESat-2.The related conclusions can provide some references for the design and the development of the domestic single photon laser altimetry satellite.展开更多
In order to meet the requirements of high-precision vehicle positioning in complex scenes,an observation noise adaptive robust GNSS/MIMU tight fusion model based on the gain matrix is proposed considering static zero ...In order to meet the requirements of high-precision vehicle positioning in complex scenes,an observation noise adaptive robust GNSS/MIMU tight fusion model based on the gain matrix is proposed considering static zero speed,non-integrity,attitude,and odometer constraint models.In this model,the robust equivalent gain matrix is constructed by the IGG-Ⅲmethod to weaken the influence of gross error,and the on-line adaptive update of observation noise matrix is carried out according to the change of actual observation environment,so as to improve the solution performance of filtering system and realize high-precision position,attitude and velocity measurement when GNSS signal is unlocked.A real test on a road over 600 km demonstrates that,in about 100 km shaded environment,the fixed rate of GNSS ambiguity resolution in the shaded road is 10%higher than that of GNSS only ambiguity resolution.For all the test,the positioning accuracy can reach the centimeter level in an open environment,better than 0.6 m in the tree shaded environment,better than 1.5 m in the three-dimensional traffic environment,and can still maintain a positioning accuracy of 0.1 m within 10 s when the satellite is unlocked in the tunnel scene.The proposal and verification of the algorithm model show that low-cost MIMU equipment can still achieve high-precision positioning when there are scene feature constraints,which can meet the problem of high-precision vehicle navigation and location in the urban complex environment.展开更多
This paper is devoted to the development and testing of the optimal procedures for retrieving biophysical crop variables by exploiting the spectral information of current multispectral optical satellite Sentinel-2 and...This paper is devoted to the development and testing of the optimal procedures for retrieving biophysical crop variables by exploiting the spectral information of current multispectral optical satellite Sentinel-2 and Venus and in view of the advent of the new Sino-EU hyperspectral satellite(e.g.,PRISMA,EnMAP,and GF-5).Two different methodologies devoted to the estimation of biophysical crop variables Leaf area index(LAI)and Leaf chlorophyll content(Cab)were evaluated:non-kernel-based and kernel-based Machine Learning Regression Algorithms(MLRA);Sentinel-2 and Venus data comparison for the analysis of the durum wheat-growing season.Results show that for Sentinel-2 data,Gaussian Process Regression(GPR)was the best performing algorithm for both LAI(R 2=0.89 and RMSE=0.59)and Cab(R 2=0.70 and RMSE=8.31).Whereas,for PRISMA simulated data the Kernel Ridge Regression(KRR)was the best performing algorithm among all the other MLRA(R 2=0.91 and RMSE=0.51)for LAI and(R 2=0.83 and RMSE=6.09)for Cab,respectively.Results of Sentinel-2 and Venus data for durum wheat-growing season were consistent with ground truth data and confirm also that SWIR bands,which are used as tie-points in the PROSAIL inversion,are extremely useful for an accurate retrieving of crop biophysical parameters.展开更多
A systematic and comprehensive comparison of the five commonly used earth radii in geodesy and cartography is carried out,and the differences between the most common points of the earth radii,their corresponding maxim...A systematic and comprehensive comparison of the five commonly used earth radii in geodesy and cartography is carried out,and the differences between the most common points of the earth radii,their corresponding maximum values,and the latitudes of equal points between them are derived with the help of computer algebraic systems.The symbolic expressions are expressed as a power series of the first eccentricity.Taking the CGCS2000 ellipsoid as an example,the differences between the commonly used earth radii are clarified to numerical values.The results show that the difference between the commonly used earth radii has a maximum at 90 degrees and a minimum at 0 degree.The difference between the average radius of curvature and the rectifying sphere radius is the biggest,and the difference between the average radius of curvature and the average sphere radius is the smallest.These results can provide a theoretical basis for corresponding research in the geosciences,space science,navigation and positioning.展开更多
基金National Key R&D Program of China(No.2021YFB3900604)。
文摘The satellite gravimetry technology effectively recovers the global Earth’s gravity field.Since 2000s,HL-SST satellite CHAMP,LL-SST satellite GRACE,Gravity Gradient Measurement(GGM)satellite GOCE have been launched successfully,producing some Earth’s gravity models solely from satellites data.However,the space and time resolution of the Earth’s gravity fields do not adequately satisfy scientific objectives.The main reason is that the gravimetry satellites are not enough and observation data insufficient.The paper outlines the current and future status of Chinese gravity satellite missions.The Chinese gravimetry satellite system,named Chinese Gravimetry augment and Mass change exploring mission(ChiGaM),successfully launched in Dec.2021 after four years of production and over a year of calibration and valiation.The accelerometer,K-band ranging system and the three stellar sensors,among others,were precisely calibrated and trimmed.The satellite mass center was determined and coordinated with the proof center of accelerometer with an accuracy 100μm.The inter-satellite ranging system and BDS/GPS receiver operate together seamlessly.The range and range rate noise is less than 3μm/Hz^(1/2) and 1μm/s/Hz^(1/2),respectively,in band of 0.025~0.1 Hz.The electrostatic suspension accelerometer is working well.Its high-sensitive axis noise level is 3×10^(-10) m/s^(2)/Hz^(1/2)near the frequency 0.1 Hz,and 1×10^(-9) m/s^(2)/Hz^(1/2) for the less-sensitive axis.Meanwhile the BDS/GPS receiver is used to achieve data for precise orbit determination,yielding an orbit result with accuracy better than 2 cm.When compared with KBR observations,the RMS of the bias is less than 1 mm.Besides above mission,next gravimetric satellite is being developed now.TQ-2 mission is designed as a totally experimental satellite for gravitational wave detection at low Earth orbit,which can detect the Earth’s gravity field simultaneously.The Bender-type mission is considered the most promising configuration for TQ-2 and consists of two polar satellites and two inclined satellites.Due to the extra observations at the east-west direction derived from the inclined satellite pair,significant improvements has been made in detecting temporal signals with higher accuracy and spatial-temporal resolution.To achieve the scientific goal,the ACC MBW can shift from 0.001~0.1 Hz to 0.004~0.1 Hz for ACC,and the LRI MBW can shift from 0.01~1 Hz to 0.1~1 Hz.For future research,a gravimetric potential survey using cold-atomic-clock based on the general relativity theory,cold atom gradiometer should be pursued.Gravimetric technologies should be mined and researched,and the gravimetry satellite constellation should be developed,so as to improve the time resolution and space resolution for meeting the requirements of geophysics,geodesy,earthquake,water resources environment,oceanography,etc.
基金The National Natural Science Foundation Program(41674019)The National Plan on Key Basic Research and Development of China(2016YFB0501701).
文摘After implementing CGCS2000,establishing grid models for high-accuracy coordinate transformation which are mainly used to transform border lines and coordinate grids of topographic maps becomes an important issue in mapping applications.Consequently,a grid model for high-accuracy coordinate transformation of CGCS2000 is proposed.Specifically,we firstly analyze a minimum curvature equation of coordinate transformation,which possesses the characteristics of both the global and local smoothness,achieving better consistency with the consecutive smoothness for the coordinate transformation of map’s linear feature.Then an iterative calculation method of grid nodes and an approach for establishing regional grid models based on collocation by two-step minimization are proposed.Meanwhile,a data structure of grid model is constructed.Finally we give the optimized grid interval and transformation accuracy in China corresponding to the proposed grid model.Using 48 433 points of 2000 National Geodetic Control Network of China,we take the proposed model into practice by constructing grid models for coordinate transformation from BJS54 and XAS80 to CGCS2000,and the external positional accuracies for both models are 0.26 m and 0.03 m respectively.
文摘Editor-in-Chief Jianya GONG,Wuhan University,China Associate Editors-in-Chief Yuanxi YANG,Xi'an Research Institute of Surveying and Mapping,China Jiancheng LI,Wuhan University,China Zhilin II,The Hong Kong Polytechnic University,HongKong China Wenzhong SHI,The Hong Kong Polytechnic Unitersity,.HongKong China.
基金supported by ESA-NRSCC Dragon-4 project ID 32235 entitled“Microwave satellite measurements for coastal area and extreme weather monitoring”。
文摘In this study,we provide a summary of research advances in the field of maritime target detection using DP(dualpolarimetric)SAR(Synthetic Aperture Radar)imagery,accomplished during the European and China collaboration in the framework of the Dragon-4 program ID 32235.The main innovative contribution is twofold:(1)We addressed ship detection proposing an improved GP-PNF(Geometrical Perturbation-Polarimetric Notch Filter),termed as IGP-PNF,that is characterized by a new feature vector that includes three new scattering features;(2)We addressed oil platform detection by contrasting singlepolarization SAR methods with polarimetric ones in order to quantify the extra-benefit carried on polarimetric information.The proposed theoretical framework is tested against actual multi-polarization SAR data.In particular,ship detection methods are verified against a Sentinel-1 SAR scene where a large number of ships is present;while,oil platform detection is discussed using Terra SAR-X SAR data.Experimental analysis shows that:(1)The IGP-PNF method performs best in terms of clutter-to-target ratio;(2)Coherent polarimetric information significantly outperforms single-polarization SAR measurements in highlighting targets in challenging cases.
文摘Compared with the pair-wise registration of point clouds,multi-view point cloud registration is much less studied.In this dissertation,a disordered multi-view point cloud registration method based on the soft trimmed deep network is proposed.In this method,firstly,the expression ability of feature extraction module is improved and the registration accuracy is increased by enhancing feature extraction network with the point pair feature.Secondly,neighborhood and angle similarities are used to measure the consistency of candidate points to surrounding neighborhoods.By combining distance consistency and high dimensional feature consistency,our network introduces the confidence estimation module of registration,so the point cloud trimmed problem can be converted to candidate for the degree of confidence estimation problem,achieving the pair-wise registration of partially overlapping point clouds.Thirdly,the results from pair-wise registration are fed into the model fusion to achieve the rough registration of multi-view point clouds.Finally,the hierarchical clustering is used to iteratively optimize the clustering center model by gradually increasing the number of clustering categories and performing clustering and registration alternately.This method achieves rough point cloud registration quickly in the early stage,improves the accuracy of multi-view point cloud registration in the later stage,and makes full use of global information to achieve robust and accurate multi-view registration without initial value.
基金National Natural Science Foundation of China(Nos.61673017,61403398)and Natural Science Foundation of Shaanxi Province(Nos.2017JM6077,2018ZDXM-GY-039)。
文摘According to the characteristics of the road features,an Encoder-Decoder deep semantic segmentation network is designed for the road extraction of remote sensing images.Firstly,as the features of the road target are rich in local details and simple in semantic features,an Encoder-Decoder network with shallow layers and high resolution is designed to improve the ability to represent detail information.Secondly,as the road area is a small proportion in remote sensing images,the cross-entropy loss function is improved,which solves the imbalance between positive and negative samples in the training process.Experiments on large road extraction datasets show that the proposed method gets the recall rate 83.9%,precision 82.5%and F1-score 82.9%,which can extract the road targets in remote sensing images completely and accurately.The Encoder-Decoder network designed in this paper performs well in the road extraction task and needs less artificial participation,so it has a good application prospect.
基金National Natural Science Foundation of China(No.41871305)National Key Research and Development Program of China(No.2017YFC0602204)+2 种基金Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(No.CUGQY1945)Open Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education and the Fundamental Research Funds for the Central Universities(No.GLAB2019ZR02)Open Fund of Laboratory of Urban Land Resources Monitoring and Simulation,Ministry of Natural Resources,China(No.KF-2020-05-068)。
文摘The exploration of building detection plays an important role in urban planning,smart city and military.Aiming at the problem of high overlapping ratio of detection frames for dense building detection in high resolution remote sensing images,we present an effective YOLOv3 framework,corner regression-based YOLOv3(Correg-YOLOv3),to localize dense building accurately.This improved YOLOv3 algorithm establishes a vertex regression mechanism and an additional loss item about building vertex offsets relative to the center point of bounding box.By extending output dimensions,the trained model is able to output the rectangular bounding boxes and the building vertices meanwhile.Finally,we evaluate the performance of the Correg-YOLOv3 on our self-produced data set and provide a comparative analysis qualitatively and quantitatively.The experimental results achieve high performance in precision(96.45%),recall rate(95.75%),F1 score(96.10%)and average precision(98.05%),which were 2.73%,5.4%,4.1%and 4.73%higher than that of YOLOv3.Therefore,our proposed algorithm effectively tackles the problem of dense building detection in high resolution images.
基金Foundation for Innovative Research Groups of the National Natural Science Foundation of China(No.61621005)。
文摘Target detection technology of synthetic aperture radar(SAR)imageis widely used in the field of military reconnaissance and surveillance.The traditional SAR image target detection methods need to be provided a lot of empirical knowledge because the characteristics of SAR images in different configurations(attitude,pitch angle,imaging parameters,etc.)will change greatly,resulting in high generalization error.Currently,deep learning method has achieved great success in the field of image processing.Research shows that deep learning can achieve a more intrinsic description of the data,while the model has a stronger ability of modeling and generalization.In order to solve the problem of insufficient data in SAR data sets,an experimental system for acquiring SAR image data in real scenes was built.Then the transfer learning method and the improved convolution neural network algorithm(PCA+Faster R-CNN)are applied to improve the target detection precision.Finally,experimental results demonstrate the significant effectiveness of the proposed method.
文摘Reliable and prompt information on forest above-ground biomass(AGB)and tree diameter at breast height(DBH)are crucial for sustainable forest management.Remote sensing technology,especially the Light Detection and Ranging(LiDAR)technology,has been proven to estimate important tree variables effectively.This study proposes predicting DBH and AGB from tree height and other LiDAR data extracted metrics.In the suggested DBH prediction,we developed a nonlinear estimation equation using the total tree height.As for the AGB prediction approach,we used regression methods such as multiple linear regression(MLR),random forest(RF)and support vector machine for regression(SVR).We conducted the study for the Gudao forest area dominated by Robinia Pseudoacacia trees,located in the Yellow River Delta(YRD),China.For our developed approaches,we used Unmanned Aerial Vehicle(UAV)and Backpack LiDAR point cloud datasets obtained in June 2017,and three field data measurements gathered in June 2017 and 2019 and October 2019,all from the same study area.The results demonstrate that:①The LiDAR data individual tree segmentation(ITS)from which we extracted individual tree information like tree location and tree height,was carried out with an overall accuracy F=0.91;②We used the ITS height data from the field stand in 2019 as a fit and developed a nonlinear DBH estimation equation with Root Mean Square Error(RMSE)=3.61 cm,later validated by the 2017 dataset;③Forest AGB at stand level was estimated with the MLR,RF and also SVR regression methods,and results show that the SVR method gave higher accuracy with R2=0.82 compared to the R2=0.72 of RF and the R2=0.70 of the MLR.Calculated AGB at plot level using the 2017 LiDAR data was used to validate both models’accuracy.Combining the UAV LiDAR data and the Backpack LiDAR significantly improved the overall ITS.The UAV LiDAR ability to provide high accuracy tree height abstraction,the DBH of the regression equation and other extracted LiDAR metrics showed high accuracy in estimating the forest AGB.This study shows that being cost-free is not the only advantage of free available software.In the performance of ITS and the LiDAR,metrics extraction proved to be as good as the commercially available software.
基金National Key Research and Development Program of China(No.2017YFC0405806)。
文摘Currently,deep convolutional neural networks have made great progress in the field of semantic segmentation.Because of the fixed convolution kernel geometry,standard convolution neural networks have been limited the ability to simulate geometric transformations.Therefore,a deformable convolution is introduced to enhance the adaptability of convolutional networks to spatial transformation.Considering that the deep convolutional neural networks cannot adequately segment the local objects at the output layer due to using the pooling layers in neural network architecture.To overcome this shortcoming,the rough prediction segmentation results of the neural network output layer will be processed by fully connected conditional random fields to improve the ability of image segmentation.The proposed method can easily be trained by end-to-end using standard backpropagation algorithms.Finally,the proposed method is tested on the ISPRS dataset.The results show that the proposed method can effectively overcome the influence of the complex structure of the segmentation object and obtain state-of-the-art accuracy on the ISPRS Vaihingen 2D semantic labeling dataset.
基金National Natural Science Foundation of China(Nos.4190606941830540)+1 种基金The Scientific Research Fund of the Second Institute of Oceanography,Ministry of Natural Resources(Nos.JG2005SZ2002)。
文摘Shallow water multi-beam echo sounders(MBESs)are characterized by their high resolution and high density,and MBES data processing is a hotspot in modern marine surveying.The Combined Uncertainty and Bathymetry Estimator(CUBE)is the mainstream MBES data processing algorithm,although little is known about its core theories and parameters.In this paper,the basic principle,mathematical model,key parameters,and main processing steps of CUBE are described systematically.A parameter group optimization method that combines CUBE with a surface filter is established.Additionally,an example is given that shows the steps for parameter group optimization,including selection of a typical area,parameter group testing,and comparative analysis,and the method is then applied to shallow water MBES data processing.The results show that the method can improve the accuracy and efficiency of automatic data processing effectively,and it is thus of engineering application value.
文摘This paper is intended to report on the progresses made during the Dragon-4 project Three and Four-Dimensional Topographic Measurement and Validation(ID:32278),sub-project Multi-baseline SAR Processing for 3 D/4 D Reconstruction(ID:322782).The work here reported focuses on two important aspects of SAR remote sensing of tropical forests,namely the retrieval of forest biomass and the assessment of effects due to changing weather conditions.Recent studies have shown that by using SAR tomography the backscattered power at 30 m layer above the ground is linearly correlated to the forest Above Ground Biomass(AGB).However,the two parameters that determine this linear relationship might vary for different tropical forest sites.For purpose of solving this problem,we investigate the possibility of using Li DAR derived AGB to help training the two parameters.Experimental results obtained by processing data from the Tropi SAR campaign support the feasibility of the proposed concept.This analysis is complemented by an assessment of the impact of changing weather conditions on tomographic imaging,for which we simulate BIOMASS repeat pass tomography using ground-based Tropi SCAT data with a revisit time of 3 days and rainy days included.The resulting backscattered power variation at 30 m is within 1.5 d B.For this forest site,this error is translated into an AGB error of about 50~80 t/hm^(2),which is 20%or less of forest AGB.
基金The National Natural Science Foundation of China under Grants(41171292,41322010)The National Basic Research Program of China(973 Program)(2012CB719904).
文摘A novel tie point matching algorithm of aerial images with the assistance of airborne LiDAR point clouds and POS data is proposed Firstly,the conjugate point searching strategy used in traditional correlation coefficient matching is improved and a fast algorithm is presented.Secondly,an automatic camera boresight misalignment calibration method based on virtual ground control points is proposed,and then the searching range of image matching is adaptively determined and applied to the image matching of the entire surveying area.Test results verified that the fast correlation coefficient matching algorithm proposed in this paper can reduce approximately 25% of the matching time without the loss of matching accuracy.The camera boresight misalignment calibration method can effectively increase the accuracy of exterior orientation elements of images calculated from POS data,and thus can significantly improve the predicted position of conjugate point for tie point matching.Our proposed image matching algorithm can achieve superior matching accuracy with multi-scale,multi-view,and cross-flight aerial images.
基金The National Natural Science Foundation of China (41674025,41674082)The Independent Research Foundation of State Key Laboratory of Geo-information Engineering (SKLGIE2018-ZZ-10).
文摘Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces several forms of topographic effects: direct effect on gravity, secondary indirect effect on gravity and indirect effects on the (quasi-) geoid, respectively. To strike a balance between computation accuracy and numerical efficiency, the global integration region of topographic effects is usually divided into near zone and far zone. We focus on the computation of near-zone topographic effects, which are functions of actual topographic masses and condensed masses. Since there have already been mature formulas for gravitational attraction and potential of actual topographic masses using rectangular prism model, we put forward surface element model for condensed masses. Afterwards, the formulas for near-zone direct and indirect effects are obtained easily by combining the rectangular prism model and surface element model. To overcome the planar approximation errors involved with the new formulas for near-zone topographic effects, the Earth’s curvature can be taken into account. It is recommended to apply the formulas based on the rectangular prism and surface element considering the Earth’s curvature to calculate near-zone topographic effects for high-accuracy demand to determine geoid and quasi-geoid.
基金National Natural Science Foundation of China(Nos.42071444,42101444)。
文摘Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.
基金National Natural Science Foundation of China(Nos.42004018,41830110)Natural Science Foundation of Jiangsu Province(No.BK20190496)Fundamental Research Funds for the Central Universities(No.B200202015)。
文摘The Global Navigation Satellite Systems(GNSS)broadcast radio signals are continuously at two or more frequencies in the L-band,and the multipath signals from sea surface recorded by off-the-shelf geodetic receivers have been demonstrated they can be used to estimate sea level,using a technology called GNSS multipath reflectometry(GNSS-MR).Before proceeding to estimate reflection parameters,the azimuth range and elevation angle range are needed to be defined,as only with suitable azimuths and elevation angles the sensing zones can be guaranteed on water.So,this study presents an angle dependence analysis method to jointly select the azimuth range and elevation angle range based on wavelet analysis which can describe the nonstationary power of different sinusoidal oscillations changed with elevation angle.The key of this method is to use one grid model to screen the spectrum power of multipath oscillation on different elevation angles and azimuths in this work.Then the elevation angles and the azimuths can be determined by searching grids with greater power.The GPS and GLONASS data of two MultiGNSS Experiment(MGEX)stations named BRST and MAYG was analyzed and used to retrieve.Firstly,the angle dependence analysis was carried out to determine the elevation range and azimuth range.Secondly,the sea levels were retrieved from individual signals.Finally,the retrievals of individual signals are combined to form a 10-min sea level retrieval series.The RMSEs of the combined retrievals are both less than 15 cm.The results show the effectiveness of the selection of angle range based on the angle dependence analysis method.
文摘Influence of Range Gate Width on Detection Probability and Ranging Accuracy of Single Photon Laser Altimetry Satellite Guoyuan LI 1,3,Fanghong YE 1,2,Xinming TANG 1,Dongping XIE 1,Jiapeng HUANG 1,Genhua HUANG 31.Land Satellite Remote Sensing Application Center,Ministry of Natural Resources,Beijing 100048,China;2.School of Resource and Environmental Sciences,Wuhan University,Wuhan 430079,China;3.Key Laboratory of Space Active Opto-electronics Technology,Chinese Academy of Sciences,Shanghai 200038,China Abstract:The influence of the single photon laser altimeter range-gate width on the detection probability and ranging accuracy is discussed and analyzed,according to the LiDAR equation,single photon detection equation and the Monte Carlo method to simulate the experiment.The simulated results show that the probability of detection is not affected by the range gate,while the probability of false alarm is relative to the gate width.When the gate width is 100 ns,the ranging accuracy can accord with the requirements of satellite laser altimeter.But when the range gate width exceeds 400 ns,ranging accuracy will decline sharply.The noise ratio will be more as long as the range gate gets larger,so the refined filtering algorithm during the data processing is important to extract the useful photons effectively.In order to ensure repeated observation of the same point for 25 times,we deduce the quantitative relation between the footprint size,footprint,and frequency repetition according to the parameters of ICESat-2.The related conclusions can provide some references for the design and the development of the domestic single photon laser altimetry satellite.
基金Youth Program of National Natural Science Foundation of China (No. 41904029)Scientific Research Project of Beijing Educational Committee (No. KM202010016009)。
文摘In order to meet the requirements of high-precision vehicle positioning in complex scenes,an observation noise adaptive robust GNSS/MIMU tight fusion model based on the gain matrix is proposed considering static zero speed,non-integrity,attitude,and odometer constraint models.In this model,the robust equivalent gain matrix is constructed by the IGG-Ⅲmethod to weaken the influence of gross error,and the on-line adaptive update of observation noise matrix is carried out according to the change of actual observation environment,so as to improve the solution performance of filtering system and realize high-precision position,attitude and velocity measurement when GNSS signal is unlocked.A real test on a road over 600 km demonstrates that,in about 100 km shaded environment,the fixed rate of GNSS ambiguity resolution in the shaded road is 10%higher than that of GNSS only ambiguity resolution.For all the test,the positioning accuracy can reach the centimeter level in an open environment,better than 0.6 m in the tree shaded environment,better than 1.5 m in the three-dimensional traffic environment,and can still maintain a positioning accuracy of 0.1 m within 10 s when the satellite is unlocked in the tunnel scene.The proposal and verification of the algorithm model show that low-cost MIMU equipment can still achieve high-precision positioning when there are scene feature constraints,which can meet the problem of high-precision vehicle navigation and location in the urban complex environment.
基金This paper was supported by European Space Agency(ESA)contract 4000121195-Ministry of Science and Technology(MOST),Dragon 4 cooperation(ID:32275).Specifically,Subproject1-Topic1“Algorithm Development Exploiting Multitemporal and Multi Sensor Satellite Data for Improving Crop Classification,Biophysical and Agronomic Variables Retrieval and Yield Prediction”and by the Italian Space Agency(ASI)project PRISCAV(PRISMA Calibration/Validation).
文摘This paper is devoted to the development and testing of the optimal procedures for retrieving biophysical crop variables by exploiting the spectral information of current multispectral optical satellite Sentinel-2 and Venus and in view of the advent of the new Sino-EU hyperspectral satellite(e.g.,PRISMA,EnMAP,and GF-5).Two different methodologies devoted to the estimation of biophysical crop variables Leaf area index(LAI)and Leaf chlorophyll content(Cab)were evaluated:non-kernel-based and kernel-based Machine Learning Regression Algorithms(MLRA);Sentinel-2 and Venus data comparison for the analysis of the durum wheat-growing season.Results show that for Sentinel-2 data,Gaussian Process Regression(GPR)was the best performing algorithm for both LAI(R 2=0.89 and RMSE=0.59)and Cab(R 2=0.70 and RMSE=8.31).Whereas,for PRISMA simulated data the Kernel Ridge Regression(KRR)was the best performing algorithm among all the other MLRA(R 2=0.91 and RMSE=0.51)for LAI and(R 2=0.83 and RMSE=6.09)for Cab,respectively.Results of Sentinel-2 and Venus data for durum wheat-growing season were consistent with ground truth data and confirm also that SWIR bands,which are used as tie-points in the PROSAIL inversion,are extremely useful for an accurate retrieving of crop biophysical parameters.
基金National Natural Science Foundation of China(Nos.41771487,41971416,41871376)Natural Science Foundation for Distinguished Young Scholars of Hubei Province of China(No.2019CFA086)。
文摘A systematic and comprehensive comparison of the five commonly used earth radii in geodesy and cartography is carried out,and the differences between the most common points of the earth radii,their corresponding maximum values,and the latitudes of equal points between them are derived with the help of computer algebraic systems.The symbolic expressions are expressed as a power series of the first eccentricity.Taking the CGCS2000 ellipsoid as an example,the differences between the commonly used earth radii are clarified to numerical values.The results show that the difference between the commonly used earth radii has a maximum at 90 degrees and a minimum at 0 degree.The difference between the average radius of curvature and the rectifying sphere radius is the biggest,and the difference between the average radius of curvature and the average sphere radius is the smallest.These results can provide a theoretical basis for corresponding research in the geosciences,space science,navigation and positioning.