TanDEM-X DEM Error Correction Method Based on Least Squares Configuration

Abstract

A TanDEM-XDEM error correction method based on least square configuration, comprising the following steps: 1) TanDEM-XDEM data is generated from TanDEM-X / TerraSAR-X data, and ICESat-2 data is acquired; 2) the error of any point of DEM is divided into systematic error and random error, and an error correction model based on least square configuration is established; L=BX+GY+Delta;(1) 3) the error estimation value obtained in step 2) is subtracted from the original TanDEM-XDEM, and the corrected DEM can be obtained. The method can correct the systematic error and random error of TanDEM-XDEM simultaneously. The results show that the average error absolute value of TanDEM-XDEM in the region is reduced from 2.019 m to 0.058 m after correction by the method, and the root mean square error is reduced from 6.141 m to 3.851 m, and the accuracy is improved by 37.3%.

Description

Technical Field

[0001] This invention relates to a method for processing DEM data, and more particularly to a TanDEM-XDEM error correction method based on least squares configuration. Background Technology

[0002] Digital Elevation Models (DEMs) are crucial foundational data for various geoscientific analyses and are widely used in fields such as hydrology, geology, meteorology, and military. In recent years, with the continuous development of aerospace technologies such as InSAR and LiDAR, the ability to acquire large-scale global DEM data has been increasingly enhanced. Consequently, more and more global digital terrain models with different scales, resolutions, and accuracies have been publicly released, such as ASTER GDEM, ALOS AW3D30 DEM, SRTM DEM, and TanDEM-X DEM. These publicly available DEMs provide important topographic reference information for geoscientific research and have been widely applied. However, the accuracy of the generated DEM data is inevitably affected by differences in observation techniques (such as optical, radar, and photogrammetry), topography, and land cover types during the observation and generation processes. For example, the ASTER GDEM and ALOS AW3D30 DEM generated based on optical image stereo pairing technology have disadvantages such as difficulty in penetrating clouds and fog due to their short wavelengths, and susceptibility to noise and outliers. Meanwhile, the SRTM DEM and TanDEM-X DEM generated based on synthetic aperture radar interferometry (InSAR) technology are more susceptible to the influence of large terrain tilt angles because their observation mode is side-view imaging, and are prone to forming data holes in steep areas with large slopes.

[0003] In October 2018, the German Aerospace Center (DLR) publicly released the global TanDEM-X DEM dataset (90m resolution). This dataset was acquired using InSAR (Infrared SAR) technology and meets the HRTE-3 (High Resolution Terrain Elevation, Level-3) standard set by the National Geospatial-Intelligence Agency (NGA), exhibiting high elevation accuracy. Currently, the TanDEM-X DEM dataset has been applied in various geoscientific studies, such as glacier change analysis, mining area surveys, and reservoir storage estimation. However, it is currently only publicly available at a resolution of 90m, with an error range of 8–16 meters, and in mountainous areas, the error can even reach nearly 100 meters. Therefore, this directly impacts the application potential and scope of the TanDEM-X DEM data.

[0004] To fully explore the application value of publicly released TanDEM-XDEM and broaden its application in various fields, many scholars have conducted research on improving the accuracy of TanDEM-XDEM. Currently, the research mainly focuses on two aspects. The first is to fuse multi-source DEMs, combining the advantages of DEMs from different observation methods to generate a more accurate, complete, and reliable dataset than a single DEM. For example, Yue Guodong et al. proposed a rising-falling ... For example, Kim et al. explored a scheme to improve the TanDEM-XDEM (12-meter resolution) of German Aerospace Corporation using artificial neural networks (ANNs). This method uses the backpropagation algorithm to train the network and minimizes the error between the target layer and the output layer by utilizing the mean square error of the cost function (Kim DE, Liu J, Liong SY, et al. Satellite DEM Improvement Using Multispectral Imagery and an Artificial Neural Network[J]. Water, 2021, 13(11): 1551.). However, although the theories and algorithms in these two aspects can eliminate the influence of spatially large-scale trending systematic errors, they do not consider the improvement of random errors in DEM by high-precision point data, and cannot fully utilize the role of high-precision point data in improving the accuracy of TanDEM-XDEM. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a TanDEM-XDEM error correction method based on least squares configuration to improve the accuracy of TanDEM-XDEM.

[0006] To solve the above-mentioned technical problems, the technical solution proposed by this invention is as follows: a TanDEM-XDEM error correction method based on least squares configuration, comprising the following steps: 1) generating TanDEM-XDEM data from TanDEM-X / TerraSAR-X data and obtaining ICESat-2 data; TanDEM-X DEM data represented by raster data, where the value of each raster can be regarded as the observation value of a point data, and a DEM data can be represented by the set of all raster point data observation values ​​on the DEM surface;

[0007] DEM data is divided into overlapping points and non-overlapping points. The raster points that overlap with ICESat-2 data can be called overlapping points, and the raster points that do not overlap with any ICESat-2 data can be called non-overlapping points.

[0008] 2) The error at any point in the DEM is divided into systematic error and random error, and a TanDEM-XDEM error correction model based on least squares configuration is established;

[0009] The least-squares configuration TanDEM-XDEM error correction model is expressed as follows:

[0010] L=BX+GY+Δ (1)

[0011] Where L represents the observed value obtained by observing the error at any point of the DEM, that is, the error value at that point;

[0012] B represents the coefficient matrix, which is an m-row, m-column identity matrix where m is the number of coincidence points; X represents the random error component of the model, which can be represented as [X'X″]. T , where X' represents the random error at the coincident point and X″ represents the random error at the non-coincident point;

[0013] GY represents the systematic error part of the model, where G is the coefficient matrix of the systematic error model and Y is the parameter matrix of the systematic error model;

[0014] Δ represents observation noise;

[0015] 3) Subtract the error estimate L obtained in step 2) from the original TanDEM-XDEM to obtain the corrected DEM.

[0016] In this invention, the random component of the TanDEM-XDEM grid point error can be expressed as:

[0017] L X' =X'+Δ (2)

[0018] L X″ =X″+Δ (3)

[0019] Together with equation (1), we establish the adjustment model of least squares collocation theory, namely:

[0020]

[0021] Where the coefficient matrix B is an m-row, m-column identity matrix, and m is the number of overlapping points; D' represents the random error component of overlapping grid points, and D″ represents the random error component of non-overlapping grid points; the systematic error component of TanDEM-X DEM is determined by a polynomial relating to grid position, elevation, and slope, i.e.:

[0022]

[0023] Y=[a0 a1 a2 a3 a4 a5 a6 a7 a8] T (6)

[0024] x, y, h, and s represent the coordinates of the coincident points on the x and y axes, as well as their elevation and slope.

[0025] Combining equation (4), we can obtain the error equation for the least-squares-configured TanDEM-X DEM error correction model:

[0026]

[0027] Considering that noise Δ and D', D″ are usually independent of each other, i.e., D ΔX' =0,D ΔX″ =0,D ΔX' This refers to the variance of noise and random errors at coincidence points, D. ΔX″ This refers to the variance of noise and random errors at non-coincident points; according to the principle of indirect adjustment, the solution of the unknown parameters in formula (7) can be calculated by the following formula:

[0028]

[0029] In the formula, D X' D Δ Let D represent the variances of X' and Δ, respectively. X'X″ This represents the covariance between coincident and non-coincident points.

[0030] After simplifying equation (8), we can obtain the fitting and estimation formulas for the systematic error and random error components in TanDEM-X DEM:

[0031]

[0032] in, To estimate the fitting values ​​of the unknown parameters of the systematic error model. and These are the fitted estimates of random errors at coincident and non-coincident points, respectively; D X'X' Let D be the autocovariance matrix of the coincident points. X″X' Let be the cross-covariance matrix between coincident and non-coincident points.

[0033] Compared with existing technologies, the advantages of this invention are as follows: the TanDEM-XDEM error correction (LSC-TXC) method based on least squares configuration can simultaneously correct both systematic and random errors of TanDEM-X DEM. Using southwestern Europe as the experimental region, experimental results show that the average absolute value of the TanDEM-X DEM error corrected by the method in this region decreased from 2.019m to 0.058m; the root mean square error decreased from 6.141m to 3.851m, improving the accuracy by 37.3%. Attached Figure Description

[0034] Figure 1 This is a map showing the location of the study area in Example 1.

[0035] Figure 2 This is a satellite impact map of the study area.

[0036] Figure 3 The TanDEM-X DEM image shows the study area.

[0037] Figure 4 This is a topographic slope map of the study area.

[0038] Figure 5 This is a flowchart of the error correction method in Example 1.

[0039] Figure 6 shows the original TanDEM-X DEM image.

[0040] Figure 7 shows the TanDEM-XDEM image after correction using the error correction method of Example 1.

[0041] Figure 8 shows the difference between the corrected TanDEM-X DEM and the original TanDEM-X DEM.

[0042] Figure 9 The error histograms of TanDEM-X DEM before and after correction relative to ICESat-2 data are shown. Detailed Implementation

[0043] To facilitate understanding of the present invention, the present invention will be described more fully and in detail below with reference to preferred embodiments, but the scope of protection of the present invention is not limited to the following specific embodiments.

[0044] It should be noted that when a component is described as being "fixed to, attached to, connected to or connected to" another component, it can be directly fixed to, attached to, connected to or connected to the other component, or it can be indirectly fixed to, attached to, connected to or connected to the other component through other intermediate connectors.

[0045] Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by those skilled in the art. The technical terms used herein are for the purpose of describing particular embodiments only and are not intended to limit the scope of the invention.

[0046] Example 1

[0047] The study area for Embodiment 1 of this invention is located in southwestern Europe, between 41°28′ and 42°58′ north latitude and 1°59′ and 3°46′ west longitude, covering an area of ​​approximately 26,244 square kilometers. The location of the study area is as follows: Figure 1 As shown in the rectangular area. Figure 2 It can be seen that the land cover types in this area are diverse. From Figure 3 The TanDEM-X DEM data reveals diverse topographic features and a wide elevation range, dominated by hills and mountains. The southern part of the area is higher in elevation, while the northern part is lower and flatter. Furthermore, the distribution of slope gradients within the study area is highly varied, exhibiting significant slope variability. It includes mostly flat areas as well as numerous steep regions, such as... Figure 4 The topographic slope of the study area is shown.

[0048] TanDEM-X / TerraSAR-X data

[0049] TerraSAR-X and TanDEM-X are German radar satellites from DLR (German Aerospace Center). The first of the two satellites, TerraSAR-X (TSX), has been successfully operating in space since 2007, followed by the almost identical TanDEM-X (TDX) in 2010; both satellites are still operational. This paper uses SAR data acquired by the TDX / TSX interferometric pair in bistatic mode. In this mode, one satellite transmits a signal, which is then received simultaneously by two satellites. The corresponding terrain information is obtained by analyzing the phase difference between the received echo signals. Furthermore, due to the unique imaging geometry of TDX / TSX in bistatic mode, and the close proximity (<400m) between the two satellites in this dual-satellite system, the time interval between the two SAR images acquired by the TDX and TSX satellites is extremely small, i.e., the time baseline is almost zero. Therefore, TDX / TSX interferometry is less affected by factors such as weather changes and time decorrelation, resulting in a more accurate TanDEM-X DEM and thus obtaining more precise information.

[0050] This paper selects 20 pairs of TDX / TSX imagery within the experimental area as experimental data. These imagery pairs are the data acquired during the ascent of orbit in 2019, and the coverage area of ​​each pair of TDX / TSX imagery is approximately 58km*61km.

[0051] ICESat-2 altimeter data

[0052] On September 15, 2018, the ICESat-2 (Ice, Cloud and Elevation Satellite-2) satellite was successfully launched from California. This satellite is NASA's next-generation spaceborne lidar satellite, launched after the failure of the ICESat-1 satellite. ICESat-2 altimetry data is primarily used to measure changes in the height of global ice sheets, clouds, and land, with a resolution of approximately 17 meters, a significant improvement over previous lidar data (such as ICESat-1). ICESat-2 data also features global coverage, which is of great significance for studying global surface height changes. ICESat-2 altimetry data can be applied to research in glaciers, ice sheets, oceans, and land, including sea-level change, ice sheet melting, surface deformation, and changes in surface water storage. Furthermore, ICESat-2 data can be fused with other remote sensing data (such as DEM data) to improve its accuracy and application value.

[0053] NASA's ICESat-2 data products describe the heights of sea ice, land ice, forest vegetation, water levels, urban areas, and more, with data observations spanning from the end of 2018 to the present. In this paper, we used the ATLAS / ICESat-2 L3ALand and Vegetation Height, Version 5 (ATL08) dataset, which contains the line-of-sight heights of the ground and canopy surfaces above the WGS84 ellipsoid (ITRF2014 reference frame).

[0054] TanDEM-X DEM Error Correction Model Based on Least Squares Configuration

[0055] Least Squares Configuration (LSC) originally referred to a mathematical method for combining various data to study the Earth's shape and gravitational field. In the study of Earth's shape and gravity, the general form of the configuration is that its functional model includes both a random component and a non-random component (also called the tendency parameter). This situation, involving both determining the signal and the tendency parameter, often arises in other measurement adjustment problems. Adjusting these problems using the generalized least squares adjustment principle is called least squares configuration, or simply the configuration method. Furthermore, in Earth's shape, gravitational field, and other adjustment problems, it is often necessary to determine the optimal estimates of the estimated signal and the tendency parameter. Since the tendency parameter is often the coefficient of a fitted function, the configuration method is also called a fitted estimation.

[0056] In previous studies using least squares collocation to estimate non-stationary spatial random fields in gravity research, quadratic surfaces or Gaussian functions were often chosen as the tendency component in the function model. However, when applying least squares collocation theory to improve the accuracy of DEMs, these fitted surfaces fail to fully reflect the actual surface changes, leading to biases in the empirical covariance function estimation and potentially incorrect estimation results. Experimental analysis shows that the systematic error of TanDEM-XDEM exhibits a positive linear correlation with elevation and a quadratic function relationship with terrain slope. Based on this correlation, a TanDEM-XDEM systematic error model is established and used as the tendency component to more comprehensively reflect the actual surface changes. Then, the error at any point in the DEM is divided into systematic and random errors. The established TanDEM-XDEM error correction model (LSC-TXC error correction model) based on least squares collocation can be expressed as:

[0057] L=BX+GY+Δ (1)

[0058] Where L represents the observed value obtained by observing the error at any point in the DEM, i.e., the error value at that point.

[0059] B represents the coefficient matrix, which in most cases can be the identity matrix. X represents the random error component of the model, which can be represented as [X'X″]. T , where X' represents the random error at the coincident point, and X″ represents the random error at the non-coincident point. GY represents the systematic error part of the model, where G is the coefficient matrix of the systematic error model, Y is the parameter matrix of the systematic error model; Δ is the observation noise.

[0060] LSC-TXC error correction model solution

[0061] First, for TanDEM-X DEM data represented by raster data, the value of each raster can be considered as an observation of a point data point. A DEM data point can be represented by the set of all raster point data observations on the DEM surface. Therefore, DEM data can be divided into overlapping points and non-overlapping points. The raster points that overlap with ICESat-2 data can be called overlapping points, and the raster points that do not overlap with any ICESat-2 data points can be called non-overlapping points. Therefore, according to stochastic process theory, the stochastic component of the TanDEM-X DEM raster point error can be expressed as:

[0062] L X' =X'+Δ (2)

[0063] L X″ =X″+Δ (3)

[0064] Together with equation (1), we establish the adjustment model of least squares collocation theory, namely:

[0065]

[0066] Where the coefficient matrix B is an m-row, m-column identity matrix, and m is the number of overlapping points; X' represents the random error component of overlapping grid points, and X″ represents the random error component of non-overlapping grid points; the systematic error component of TanDEM-X DEM is determined by a polynomial relating to grid position, elevation, and slope, i.e.:

[0067]

[0068] Y=[a0 a1 a2 a3 a4 a5 a6 a7 a8] T (6)

[0069] x, y, h, and s represent the coordinates of the coincident points on the x and y axes, as well as their elevation and slope.

[0070] Combining equation (4), we can obtain the error equation of the LSC-TXC algorithm:

[0071] Where X' represents the random error component of the overlapping grid points, and X″ represents the random error component of the non-overlapping grid points; the corresponding error equation for this model can be obtained:

[0072]

[0073] Considering that noise Δ and X', X″ are usually independent of each other, i.e., D ΔX' =0,D ΔX″ =0,D ΔX' This refers to the variance of noise and random errors at coincidence points, D. ΔX″ This refers to the variance of noise and random errors at non-coincident points; according to the principle of indirect adjustment, the solution of the unknown parameters in formula (7) can be calculated by the following formula:

[0074]

[0075] In the formula, D X' D Δ Let D represent the variances of X' and Δ, respectively. X'X″ This represents the covariance between coincident and non-coincident points.

[0076] After simplifying equation (8), we can obtain the fitting and estimation formulas for the systematic error and random error components in TanDEM-X DEM:

[0077]

[0078] in, To estimate the fitting values ​​of the unknown parameters of the systematic error model. and These are the fitted estimates of random errors at coincident and non-coincident points, respectively; D X'X' Let D be the autocovariance matrix of the coincident points. X″X' Let be the cross-covariance matrix between coincident and non-coincident points.

[0079] To obtain the fitted estimates of the systematic and random error components of the TanDEM-X DEM, it is necessary to first obtain the unknown part D in equation (9) above. X'X' and D X″X'This can be calculated by fitting the covariance function. Since the fitting accuracy of the covariance function directly affects the estimation accuracy of the least squares collocation theory, only by ensuring that the estimated field is a stationary random field and eliminating the trend can the covariance function correctly reflect the actual situation of the estimated field. Therefore, in order to ensure the stationarity of the data and eliminate the trend of the data, the error value of the systematic error at the coincidence point is obtained by subtracting the value of the systematic error trend surface from the difference of the coincidence point, that is, the initial value of the random error (signal) at the coincidence point. Then, the spatial correlation structure between the signals is calculated according to the spatial distribution of the signals at the coincidence point. The prior covariance between the signals can be calculated according to Equation (10):

[0080]

[0081] Where C r It is the prior covariance between coincident points i and j whose distance is less than or equal to the interval distance r, N r P is the total number of paired coincident points that are separated by a distance r. i P j It is the product of the signals at the coincidence points i and j.

[0082] This allows us to derive the distance and prior covariance between each pair of coincident points. Then, least-squares curve fitting is used to estimate the optimal curve function to describe the relationship between the distance between each pair of coincident points and their prior covariance. The function for these fitted curves can be a Gaussian function model, a Cauchy function model, an exponential function model, or a Markov function model, etc. Subsequently, based on the obtained optimal fitted curve or covariance function, the variance-covariance matrix (VCM) between the two signals at the coincident and non-coincident points can be generated. The VCM can be expressed as follows:

[0083]

[0084] Among them, D X'X' Let D be the autocovariance matrix of the coincident points. X″X' Let D be the cross-covariance matrix between coincident and non-coincident points. X″X″ It is the autocovariance matrix between non-coincident points.

[0085] Finally, the autocovariance matrix D of the coincident points in the VCM is calculated. X'X' The cross-covariance matrix D between coincident and non-coincident points X″X' Substituting into equation (9), the fitted estimation values ​​of the parameter matrix of the TanDEM-X DEM systematic error model can be obtained respectively. and the fitting estimate of random error and By substituting the obtained fitted estimation value back into equation (1), the error value of all grid points in the entire TanDEM-XDEM can be obtained. Then, by subtracting the obtained error value from the original TanDEM-X DEM, the corrected DEM can be obtained. The specific process of the LSC-based TanDEM-X DEM error correction method (LSC-TXC algorithm) in this paper is as follows: Figure 5 As shown. Analysis of TanDEM-X DEM correction results.

[0086] This paper selects ICESat-2 data (23,250 points) observed in the study area in 2021 as experimental data. Then, 12,036 ICESat-2 data points in the study area in 2022 were randomly selected as validation data to evaluate the accuracy changes of TanDEM-X DEM before and after correction. The main evaluation indicators are mean error (ME) and root mean square error (RMSE).

[0087] ME and RMSE are respectively represented as:

[0088]

[0089]

[0090] Where n is the number of verification data points, x is the elevation value of the verification data, and y is the elevation value of the DEM. The unit of elevation data is meters.

[0091] Figure 6 shows the original TanDEM-X DEM of the study area, Figure 7 shows the TanDEM-X DEM of the study area after correction using the LSC-TXC model, and Figure 8 shows the elevation difference between the original and corrected TanDEM-X DEM. The results show that the differences are mostly concentrated between -20m and 30m, but the grid point with the largest difference reaches -257.255m, and dozens of grid points have differences greater than 100m. Analysis revealed that the original TanDEM-X DEM contained a small number of data holes in these areas with excessively large differences. After correction using the proposed LSC-TXC model, these data holes were filled based on the spatial correlation between errors, resulting in excessively large abnormal differences.

[0092] An error histogram can be obtained by calculating the difference in elevation between the corresponding points in the ICESat-2 validation data and the TanDEM-X DEM before and after correction. Figure 9As shown. Before correction, the TanDEM-X DEM exhibited a certain degree of negative bias, with an average error ME of -2.019 m, indicating that the average elevation of the TanDEM-X DEM was higher than that of the ICESat-2 point. This result is expected to be due to the observation center of the TDX radar satellite being located between the canopy of vegetation and the bare ground. The root mean square error (RMSE) before correction was 6.141 m, similar to some other regions; for example, Gdulová K et al. showed an RMSE of 11.99 m for the TanDEM-X DEM in some mountainous parts of Europe (Gdulová K, J, V. Accuracy assessment of the global TanDEM-X digital elevation model in a mountain environment[J]. Remote Sensing of Environment, 2020, 241: 111724.), Yu Jianing et al. found that the RMSE value of TanDEM-X DEM in China was 7.87m (Yu Jianing, Liu Kai, Zhang Bingyue, Huang Ying, Fan Chenyu, Song Chunqiao, Tang Guoan. Evaluation of elevation accuracy of TanDEM-X 90m DEM in China and its applicability analysis[J]. Journal of Geoinformation Science, 2021, 23(04): 646-657.).

[0093] After correction, the vertical error of the TanDEM-X DEM exhibits a symmetrical distribution near zero. Compared to before correction, the vertical error of the TanDEM-X DEM is closer to zero, with an average error ME value of 0.058m. Figure 9 As can be seen, the number of points with large error values ​​was significantly reduced after correction compared to before correction. Simultaneously, the root mean square error (RMSE) of TanDEM-X DEM relative to the validation data ICESat-2 also decreased to 3.851m after correction. Specifically, after correction using the TanDEM-X DEM error correction (LSC-TXC) algorithm based on least squares collocation theory, the RMSE of TanDEM-X DEM decreased by 37.3%, indicating that the proposed model significantly improved the quality of TanDEM-X DEM.

[0094] Model performance comparison analysis

[0095] Table 1 shows the accuracy improvement effect of the TanDEM-X DEM Error Correction (LSC-TXC) algorithm based on least squares configuration compared with the performance of several other DEM accuracy improvement algorithms.

[0096] Table 1. Correction results of TanDEM-X DEM under different algorithms

[0097]

[0098] It can be observed that, after using the TanDEM-X DEM error correction algorithm (LSC-TXC) based on least squares collocation theory, random forest (RF) (Chen C, Yang S, Li Y. Accuracy assessment and correction of SRTMDEM using ICESat / GLAS data under data coregistration[J]. Remote sensing, 2020, 12(20):3435.), height difference fitting neural network (HDFNN) (Shen Huanfeng, Liu Lu, Yue Linwei, Li Xinghua, Zhang Liangpei. High-quality seamless DEM generationblending SRTM-1, ASTER GDEM v2 and ICESat / GLAS observations[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2018, 47(06):854-863.), and backpropagation neural network (BPNN) (Yue L, Shen H, Zhang L, et al. High-quality seamless DEM generationblending SRTM-1, ASTER GDEM v2 and ICESat / GLAS observations[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2020, 12(20):3435.), the results are significantly improved. (Sensing, 2017, 123:20-34.) The average error (ME) and root mean square error (RMSE) of the improved DEMs from these four algorithm models are all lower than those of the original TanDEM-X DEM (ME = -2.019m, RMSE = 6.141m), meaning that all four models have improved the accuracy of the original TanDEM-X DEM in this experimental area to varying degrees. However, in terms of ME, the ME value of Random Forest (RF) (-0.033m) is better than the ME value of the LSC-TXC model in this paper (0.058m).

[0099] In terms of RMSE, the LSC-TXC algorithm in this paper significantly improves the accuracy of DEM compared to the other three algorithms. Specifically, the accuracy of LSC-TXC is 6.5%, 7.6%, and 18.1% higher than that of Random Forest (RF), High Difference Fitting Neural Network (HDFNN), and Backpropagation Neural Network (BPNN), respectively. Among these three algorithms, Random Forest (RF) performs best, mainly because RF regression uses a bootstrap aggregation scheme, collecting some data from all samples to train the model and using other data to validate the model. This strategy avoids the overfitting problem, which often confuses linear regression methods with classical machine learning methods (Zhao W, Wu H, Yin G, et al. Normalization of the temporal effect on the MODIS land surface temperature product using random forest regression[J]. ISPRS Journal of Photogrammetry and Remote Sensing,2019,152:109-118.). However, since RF includes four stages, each of which is time-consuming, the computational cost of this model is very high.

[0100] This invention proposes a least-squares configuration-based TanDEM-X DEM error correction (LSC-TXC) algorithm, which can simultaneously correct both systematic and random errors in TanDEM-X DEM. Using southwestern Europe as the experimental region, experimental results show that the average absolute error of TanDEM-X DEM corrected by the proposed method in this region decreased from 2.019m to 0.058m; the root mean square error decreased from 6.141m to 3.851m, improving accuracy by 37.3%. Furthermore, the correction results were compared with three commonly used methods (random forest, elevation difference fitting neural network, and BPNN), revealing that the accuracy of TanDEM-X DEM corrected using the proposed method improved by 6.5%, 7.6%, and 18.1%, respectively.

Claims

1. A TanDEM-X DEM error correction method based on least squares configuration, characterized by; Includes the following steps: 1) Generate TanDEM-X DEM data from TanDEM-X / TerraSAR-X data and acquire ICESat-2 data; represent TanDEM-X DEM data using raster data, where the value of each raster is regarded as the observation value of a point data, and a DEM data is represented by the set of all raster point data observation values ​​on the DEM surface; The DEM data is divided into overlapping points and non-overlapping points. The raster points that overlap with ICESat-2 data are called overlapping points, and the raster points that do not overlap with any ICESat-2 data are called non-overlapping points. 2) The error at any point in the DEM is divided into systematic error and random error, and a TanDEM-X DEM error correction model based on least squares configuration is established; The least-squares configuration TanDEM-X DEM error correction model is expressed as follows: ； wherein, represents the observed value obtained by observing the error of any point of the DEM, i.e. the error value of the point; B represents the coefficient matrix, which is an m-row, m-column identity matrix where m is the number of overlapping points. The random error component of the model is represented as... ,in This represents the random error at the point of overlap. This represents the random error at non-coincident points; Represents the systematic error component of the model, where It is the coefficient matrix of the system error model. It is the parameter matrix of the system error model; To observe noise; 3) Subtract the error estimate obtained in step 2) from the original TanDEM-X DEM. Then the corrected DEM can be obtained; The random component of the TanDEM-X DEM grid point error is represented as follows: ； Together with equation (1), we establish the adjustment model of least squares collocation theory, i.e.; ； The systematic error component of the TanDEM-X DEM is determined by a polynomial relating grid location, elevation, and slope, i.e.: ； （6）； , , , The coordinates of the horizontal and vertical axes, elevation, and slope of the point of coincidence are represented. Combining equation (4), we can obtain the error equation of the least squares-configured TanDEM-X DEM error correction model: ； Considering noise and , They are independent of each other, that is =0, =0, This refers to the variance of noise and random errors at coincidence points. This refers to the variance of noise and random errors at non-coincident points; according to the principle of indirect adjustment, the solution of the unknown parameters in formula (7) can be calculated by the following formula: ； In the formula, , They represent and The variance; After simplifying equation (8), we can obtain the fitting and estimation formulas for the systematic error and random error components in TanDEM-X DEM: ； in, To estimate the fitting values ​​of the unknown parameters of the systematic error model. and These are the fitted estimates of random errors at coincident and non-coincident points, respectively. The autocovariance matrix of the coincident points. Let be the cross-covariance matrix between coincident and non-coincident points.

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