CN111812600B - An adaptive terrain-related SRTM-DEM correction method - Google Patents
An adaptive terrain-related SRTM-DEM correction method Download PDFInfo
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Abstract
An adaptive terrain-dependent SRTM-DEM correction method, comprising the steps of: 1) Modeling global trend errors by constructing linear models related to geographic locations, i.e., f trend (E,N)＝a 0 +a 1 sinE+a 2 cos (90 ° -N) (1); 2) Construction of a BIC-based local terrain error correction model will be a terrain dependent error f terrain Is constructed as f terrain (S,A,Z)＝a 3 H+f TF (S, a) (2); 3) Construction of an adaptive terrain-dependent SRTMDEM correction model Δh=f trend (E,N)+f terrain (S, a, H) +Δh+δ (4); 4) Robust estimation using model parameters . Compared with the traditional SHM and MLE correction methods, the correction method has higher accuracy.
Description
Technical Field
The invention relates to a correction method of a space plane radar terrain task (SRTM) Digital Elevation Model (DEM), in particular to a self-adaptive terrain-related SRTM-DEM correction method.
Background
Digital Elevation Model (DEM) products play an important role in research and practical applications in the fields of geophysics, geology, hydrology, geodetic, urban engineering, etc. Traditional DEM products are produced by adopting point-based geodetic measures (such as GPS and precise leveling) with small working surface, high spatial resolution and high time consumption. In recent decades, the development of remote sensing optical photogrammetry technology has greatly driven the development of airborne light detection and ranging (LiDAR), satellite-borne optical photogrammetry and airborne/satellite-borne interferometric synthetic aperture radar (InSAR) DEM generation technologies. In these methods, inSAR may generate DEMs with advantages of all-day, all-weather, high spatial resolution, etc. The space plane radar topography mission (SRTM) generated a near global DEM (80% of the earth land area, between 56 ° S and 60 ° N) with a spatial resolution of about 30 meters using onboard C-and X-band SAR sensors from 11 to 22 of 2 months 2000. SRTM DEM is the first DEM product with near global homogeneity and high spatial resolution, and has been widely used in various fields such as geology, topography, water resource and hydrology, glacier, natural disaster evaluation, vegetation investigation and research since being released in 2003.
To guide this type of application, the accuracy of the SRTM-DEM is assessed using GPS receivers, corner reflector arrays, marine data and other DEM products, such as optical DEM and airborne DEM (E.Rodriguez, C.S.Morris, and J.E. Belz, "A global assessment of the SRTM performance," Photogrammetric Engineering)&Remote Sensing, vol.72, no.3, pp.249-260,2006), (S.Mukherjee, P.K.Joshi, S.Mukherjee, A.Ghosh, R.Garg, and A.Mukhopadhyy, "Evaluation of vertical accuracy of open source Digital Elevation Model (DEM)," International Journal of Applied Earth Observation and Geoinformation, vol.21, pp.205-217,2013), (Y.Gorokhovich and A.Voustianiouk, "Accuracy assessment of the processed SRTM-based elevation data by CGIAR using field data from USA and Thailand and its relation to the terrain characteristics," Remote Sensing of Environment, vol.104, no.4, pp.409-415,2006), (M.Mukul, V.Srivastava, and M.Mukul, "Accuracy analysis of the 2014-2015Global Shuttle Radar Topography Mission (SRTM) 1arc-sec C-Band height model using International Global Navigation Satellite System Service (IGS) Network," Journal of Earth System Science, vol.125, no.5, pp.909-917,2016. The results show that the absolute vertical error of the SRTM-DEM is generally less than 16 meters, and the absolute error of the circular positioning is less than 20 meters. However, it is notable that such accuracy is often manifested in plain and low vegetation areas. For mountainous or dense vegetation areas, SRTM DEM has significantly reduced accuracy (e.g., tens or hundreds of meters in elevation) (E.Berthier, Y.Arnaud, C.Vincent, and F. Remy, "Biases of SRTM in high-mountain areas: implications for the monitoring of)glacier volume changes,"Geophysical Research Letters,vol.33,no.8,2006.)，(D.Weydahl,J.Sagstuen,Dick,and H."SRTM DEM accuracy assessment over vegetated areas in Norway," International Journal of Remote Sensing, vol.28, no.16, pp.3513-3527,2007.). Previous studies have shown that errors in SRTM DEM consist mainly of three parts, (1) vegetation bias due to weak penetration of X or C band microwave sensors in forest areas (y.su and q. Guo, "A practical method for SRTM DEM correction over vegetated mountain areas," ISPRS journal of photogrammetry and remote sensing, vol.87, pp.216-228,2014.), (2) global (or long wavelength) error trend [16 ]](3) elevation, grade and slope related errors (E.Rodriguez, C.S.Morris, and J.E. Belz, "A global assessment of the SRTM performance," Photogrammetric Engineering)&Remote Sensing,vol.72,no.3,pp.249-260,2006.)，(Y.Gorokhovich and A.Voustianiouk,"Accuracy assessment ofthe processed SRTM-based elevation data by CGIAR using field data from USA and Thailand and its relation to the terrain characteristics,"Remote Sensing of Environment,vol.104,no.4,pp.409-415,2006.)，(A."Combination of SRTM3 and repeat ASTER data for deriving alpine glacier flow velocities in the Bhutan Himalaya," Remote Sensing of Environment, vol.94, no.4, pp.463-474,2005). Two common mathematical models for SRTM-DEM correction are used, namely a harmonic model for correcting global error trend, an improvement is based on a continuously defined spherical harmonic function, the whole spherical surface is modeled, and then the GNSS/ICESAT high-precision measurement data is used as input to carry out least square adjustment, and the correlation coefficient of the spherical harmonic is estimated (A.Wendleder, A.Felbier, B.Wessel, M.Huber, and A. Roth, "A method to estimate long-wave heightt errors of SRTM C-band DEM, "IEEE Geoscience and Remote Sensing Letters, vol.13, no.5, pp.696-700,2016.). Another is a multiple linear regression model that relates local terrain-related errors to terrain factors (e.g., altitude, grade, and aspect), assuming systematic deviations in the region or local SRTM, using known GPS elevation differences from the corresponding elevation of SRTM, regression methods were used to determine the deviations of the entire region (S.El. Sed. And A.H. Ali, "Improving the Accuracy of the SRTM Global DEM Using GPS data fusion and regression Model," International Journal of Engineering Research, vol.5, no.3, pp.190-196,2016.), (H.T.Elshambiky, "Using direct transformation approach as an alternative technique to fuse global digital elevation models with GPS/levelling measurements in Egypt," Journal of Applied Geodesy, vol.13, no.3, pp.159-177,2019.), (A.Zhogolev and I.Savin, "The influence correction of boreal forest vegetation on SRTM data," Geocarto International, vol.33, no.6, pp.573-586,2018.). However, both modes have some drawbacks. For example, the spherical harmonic model cannot take into account local terrain-related errors, and therefore it is typically used for relatively flat areas. The multiple linear regression model considers local terrain-related errors, but does not consider global error trends, reducing the accuracy of the corrected SRTM DEM, particularly in mountainous areas where the SRTM DEM has nonlinear terrain-related errors. To our knowledge, there is currently a lack of models that consider both global trends and local terrain dependent SRTM DEM linear/nonlinear errors.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a self-adaptive terrain-related SRTM-DEM correction method. The method may adaptively model linear/nonlinear terrain-dependent errors of the SRTM-DEM in mountainous areas based on Bayesian Information Criterion (BIC). The MLR model is thus taken as a special case of the proposed model. In addition, the proposed method solves model parameters (i.e., M-estimates) using robust estimates instead of the common least squares method used in the SHM and MLR methods to improve estimation robustness.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: an adaptive terrain-dependent SRTM-DEM correction method, comprising the steps of: 1) Modeling global trend errors by constructing linear models related to geographic locations, i.e
f trend (E,N)＝a 0 +a 1 sinE+a 2 cos(90°-N) (1)
Wherein a is 0 ,a 1 ,a 2 Is a model parameter;
2) Construction of BIC-based local terrain error correction model
Errors f to be related to the terrain terrain Is constructed as
f terrain (S,A,Z)＝a 3 H+f TF (S,A) (2)
Wherein a is 3 Is the error coefficient of the SRTM DEM and the high correlation, f TF (S, A) represents an error relating to the gradient and the direction of the gradient;
and f is true TF The order of (S, a) is determined using an adaptive strategy;
selecting the model that reaches the lowest Bayesian information criterion value, i.e. the lowest BIC value, as the best model describing the gradient and gradient-related error in the SRTM DEM;
BIC＝ln(n)k-2L (3)
where n represents the observation sample size, k is the number of independent parameters, and L is the log-likelihood of the model;
3) Construction of adaptive terrain-dependent SRTMDEM correction model
I.e. the difference deltah between the SRTM DEM elevation and the measured elevation,
ΔH＝f trend (E,N)+f terrain (S,A,H)+Δh+δ (4)
wherein E, N, H, S and A are longitude, latitude, elevation, gradient and slope directions of the SRTM DEM corresponding to all actual measurement points; Δh represents the corresponding vegetation bias, which is set to 0; delta is the residual error term. We take as an example a polynomial involving a second order slope and a fourth order slope. The complete terrain-related model constructed by this method can be expressed as
To simplify the following statement, we rewrite the matrix form as equation (6):
ΔH＝B·X (6)
where X represents model parameters and B represents model factor vectors.
4) Robust estimation of terrain-related model parameters
The robust estimation method is able to retrieve a stable solution by adaptively assigning weights to observations. Therefore, we choose a widely used robust estimation method M-estimation to solve the model parameters of the constructed model. Model parameter vectorCan be obtained by iteratively weighting equation (6) (7):
up toLess than a specified threshold (e.g., 10 -4 ). Let n be the measured elevation value, then the weight matrix at the kth iteration +.>The method comprises the following steps:
wherein the method comprises the steps ofRepresenting P k Is the ith main diagonal entry,>is the residual of the ith observation equation +.>And standard deviation delta in the kth iteration k B and c are constants (typically designated 1.5 and 2.5).
Equation (8) shows that there is a coarse difference for one (whenWhen) the M-estimate may be assigned a zero weight to eliminate its contribution to the model parameter estimate, avoiding the effect of coarse differences on the model parameter estimate. In addition, the M-estimation can adaptively assign the weight to other observed values without prior weight information, thereby improving the accuracy of model parameter estimation. This is not reached by least squares estimation. The independent variables (e.g., B) in equation (6) have different units, for example, longitude and latitude are in degrees and height is in meters. Therefore, these arguments must be normalized before model estimation.
Where B' is the normalized value of the variable B.
5) Robust estimation using model parametersThe +.about.of SRTM DEM can be implemented as follows>Pixel level correction:
wherein H is 1 Is the elevation vector of any pixel of the SRTM DEM, B 1 Is SRTM DEMAny matrix of pixel coefficients, including a matrix of coefficients for new arguments (e.g., longitude, latitude, elevation, slope, and slope).
Compared with the prior art, the invention has the advantages that: compared with the traditional SHM and MLE correction methods, the correction method has higher accuracy.
Drawings
FIG. 1 is a schematic elevation view of the SRTM DEM in an experimental area selected from the Hunan Zhang House.
FIG. 2 is a slope chart of experimental regions selected in the Hunan Zhang House of Hunan province.
FIG. 3 is a slope chart of experimental regions selected in the Hunan Zhang House.
Fig. 4 is a plot of slope error for an SRTM DEM corresponding to 1001 measured GPS points.
Fig. 5 is a slope error plot for an SRTM DEM corresponding to 1001 measured GPS points.
Fig. 6 is a graph of an algorithm corrected SRTM DEM of the present embodiment.
Fig. 7 is a residual plot of corrected SRTM DEM versus original SRTM DEM.
Detailed Description
The present invention will be described more fully hereinafter with reference to the preferred embodiments for the purpose of facilitating understanding of the present invention, but the scope of protection of the present invention is not limited to the specific embodiments described below.
It will be understood that when an element is referred to as being "fixed, affixed, connected, or in communication with" another element, it can be directly fixed, affixed, connected, or in communication with the other element or intervening elements may be present.
Unless defined otherwise, all technical and scientific terms used hereinafter have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the scope of the present invention.
An adaptive terrain-dependent SRTM-DEM correction method, comprising the steps of: 1) Modeling global trend errors by constructing a linear model related to geographic location (A.Wendleder, A.Felbier, B.Wessel, M.Huber, and A. Roth, "A method to estimate long-wave height errors of SRTM C-band DEM," IEEE Geoscience and Remote Sensing Letters, vol.13, no.5, pp.696-700,2016), i.e.)
f trend (E,N)＝a 0 +a 1 sinE+a 2 cos(90°-N) (1)
Wherein a is 0 ,a 1 ,a 2 Is a model parameter; according to Wendleder's study, global trend error is linearly related to the geographical longitude and latitude of the SRTM DEM.
2) Construction of BIC-based local terrain error correction model
Errors f to be related to the terrain terrain Is constructed as
f terrain (S,A,Z)＝a 3 H+f TF (S,A) (2)
Wherein a is 3 Is the error coefficient of the SRTM DEM and the high correlation, f TF (S, A) represents an error relating to the gradient and the direction of the gradient;
and f is true TF The order of (S, a) is determined using an adaptive strategy.
In the MLR method, f TF The (S, a) correction function is a linear model with respect to grade and direction. However, the linear (first order) model is not suitable for mountainous areas, whereas the higher order (nonlinear) model can only describe the terrain-dependent errors of the mountain SRTM DEM. To overcome this disadvantage, an adaptive strategy was proposed in this study to determine f TF (S, A) order. More specifically, we first generate a finite set of polynomials of varying order (typically one to five) for grade and slope direction. The Bayesian Information Criterion (BIC) solves this problem by introducing a penalty term as the number of parameters in the model.
Selecting the model that reaches the lowest Bayesian information criterion value, i.e. the lowest BIC value, as the best model describing the gradient and gradient-related error in the SRTM DEM;
BIC＝ln(n)k-2L (3)
where n represents the observation sample size, k is the number of independent parameters, and L is the log-likelihood of the model.
3) Construction of adaptive terrain-dependent SRTMDEM correction model
I.e. the difference deltah between the SRTM DEM elevation and the measured elevation,
ΔH＝f trend (E,N)+f terrain (S,A,H)+Δh+δ (4)
wherein E, N, H, S and A are longitude, latitude, elevation, gradient and slope directions of the SRTM DEM corresponding to all actual measurement points; Δh represents the corresponding vegetation bias, which is set to 0; delta is the residual error term.
In the present invention, the correction of vegetation bias for SRTM-DEM typically requires a large amount of highly accurate "bare" ground measurement data, but is often not satisfactory in most cases. Therefore, in this study we neglect the error component of the vegetation bias, correcting only the other two errors.
Due to the use of BIC, the proposed method can build an adaptive model for SRTM DEM error correction. We take as an example a polynomial involving a second order slope and a fourth order slope. The complete terrain-related model constructed by this method can be expressed as
To simplify the following statement, we rewrite the matrix form as an equation:
ΔH＝B·X (6)
where X represents model parameters and B represents model factor vectors.
It should be noted that the vegetation bias in the SRTM-DEM depends on terrain-related errors. Thus, equation (6) may correct for mixed errors in the SRTM DEM that are related to vegetation and ground terrain, rather than terrain-related errors alone, particularly in mountainous areas covered by vegetation.
In the present invention, a widely used robust estimation method M-estimation (f.r. hampel, "The influence curve and its role in robust estimation," Journal of the AmericanStatisticalAssociation, vol.69, no.346, pp.383-393,1974.), (p.j.huber, "Robust estimation of a location parameter," The Annals of Mathematical Statistics, vol.35, no.1, pp.73-101,1964.) was selected to solve model parameters of the constructed adaptive terrain-dependent SRTMDEM correction model;
model parameter vectorCan be obtained by iteratively weighting equation (6) (7):
up toLess than a specified threshold (e.g., 10 -4 )。
Setting the measured height value of the actual height as n, and then weighting matrix in the kth iterationThe method comprises the following steps:
wherein the method comprises the steps ofRepresenting P k Is the ith main diagonal entry,>is the residual of the ith observation equation +.>And standard deviation delta in the kth iteration k B and c are constants (typically designated 1.5 and 2.5).
Equation (8) shows that there is a coarse difference for one (whenWhen) the M-estimate may be assigned a zero weight to eliminate its contribution to the model parameter estimate, avoiding the effect of coarse differences on the model parameter estimate. In addition, the M-estimation can adaptively assign the weight to other observed values without prior weight information, thereby improving the accuracy of model parameter estimation. This is not reached by least squares estimation. The independent variables (e.g., B) in equation (6) have different units, for example, longitude and latitude are in degrees and height is in meters. Therefore, these arguments must be normalized before model estimation.
Where B' is the normalized value of the variable B.
4) Robust estimation using model parametersThe +.about.of SRTM DEM can be implemented as follows>Pixel level correction:
wherein H is 1 Is the elevation vector of any pixel of the SRTM DEM, B 1 Is any matrix of pixel coefficients for the SRTM DEM, including a matrix of coefficients for new independent variables (e.g., longitude, latitude, elevation, slope, and slope).
Overview of SHM model
According to the study of (A.Wendleder, A.Felbier, B.Wessel, M.Huber, and A.Roth, "A method to estimate long-wave height errors of SRTM C-band DEM," IEEE Geoscience and Remote Sensing Letters, vol.13, no.5, pp.696-700,2016), global trend error is linearly related to the geographic longitude and latitude of the SRTM DEM; thus, a Spherical Harmonic Model (SHM) is chosen to model trend errors, i.e
Wherein A is nm And B nm Is a dimensionless weighting coefficient; r is R nm And S is nm Is a surface spherical harmonic; m and n are the level and order of the SHM.
Overview of MLR model
MLR method corrects SRTM DEM local topography dependent errors by constructing multiple linear regression analysis
ΔH＝a 0 +a 1 S+a 2 A+a 3 H (12)
Where ΔH is the difference between the observed area SRTM DEM elevation and the measured elevation measured by leveling, GPS or ICEsat; s, A and H are the slope, slope direction and SRTM DEM elevation of the corresponding measuring points; p= [ a ] 0 ,a 1 ,L,a 3 ] T Model parameters representing the MLR model. The unknown amount P is then calculated by a method using least squares. And finally, correcting the SRTM DEM according to pixels by adopting a formula (12). Global trend errors and higher order terrain-related errors are not considered in the MLR model. Thus, the accuracy of the corrected SRTM DEM will be degraded, especially in mountainous areas where terrain-related non-linear errors exist.
It is noted that equation (12) is a special case of equation (6) in which the remaining parameters are all zero except for a0 and a 3-a 5.
Example 1
In this example, the country of Hunan province of China was selected as the study area. FIGS. 1-3 show the SRTM-DEM on a selected Region (ROI). Triangles and asterisks in fig. 1 represent experimental and verification data of the measured GPS, respectively. The North region of the ROI is relatively flat, has an elevation of about 118 to 630m, and has a slope of about 0 to 13. The south is formed as a mountain area with an elevation ranging from about 130 to 1452m and a slope ranging from 0 ° to 72 °. The various types of ground terrain in the ROI are suitable for evaluating the overall performance of the proposed method. In addition, 1051 measured elevation data were collected using a continuously running reference station or other GPS measurement means from the Hunan province (see asterisks and triangles). Model parameters may be estimated using these measured elevation data and may be used to evaluate the accuracy of the corrected SRTM-DEM.
The GPS elevation data is the world geodetic level (i.e., ellipsoidal height) of the world geodetic system 84 (WGS 84), while the SRTM-DEM elevation is the earth level (i.e., positive height) of the Earth's gravity model 96 (EGM 96). Therefore, all GPS elevation data needs to be unified for inter-data elevation reference before correcting SRTM-DEM by converting in the following way
H EGM96 ＝H WGS84 -N (13)
Wherein H is WGS84 High earth, H, corresponding to WGS-84 EGM96 Corresponding to the positive elevation of EGM96, N ground level differences.
SRTM-DEM error correction experimental result of the inventive patent algorithm
Fig. 4 and 5 show the Gao Chengwu difference of the SRTM-DEM at 1051 GPS observation points with respect to slope and direction of slope, as shown, there is no significant linear relationship between the error of the SRTM-DEM and the slope and direction, especially the latter. The results indicate that the SRTM-DEM error exhibits a non-linear relationship with respect to grade and direction. The results show that polynomials with first order height, second order slope and fourth order slope direction are optimized models as compared to other polynomials. Experiments were performed using 1001GPS real points, and 50 real points (whose geographic positions are indicated by asterisks in fig. 1) with almost uniform gradients and gradients were selected for accuracy verification. The algorithm of the invention is adopted to carry out SRTM DEM correction pixel by pixel. The experimental results are shown in FIG. 3.
Fig. 6 shows the corrected SRTM DEM, and fig. 7 shows the difference between the original (see fig. 1) and corrected SRTM DEM in the ROI. Triangles in fig. 7 are experimental points and asterisks are verification points. The results show that the maximum difference is about-50 m. To quantitatively evaluate the accuracy of the SRTM DEM error correction, we compared the corrected SRTM DEM elevation with the elevation of the selected 50 actual points, indicating good agreement between the two, a Root Mean Square Error (RMSE) of 8.1m (as shown in table 1), which indicates an improvement in accuracy of about 20% over the root mean square error (i.e., 10.1 m) of the uncorrected SRTM DEM. The result shows that the method can effectively improve the elevation precision of the SRTM DEM.
Fig. 3, (a) the algorithm of the invention corrects the SRTM DEM, (b) corrects the residual map of the SRTM DEM with the original SRTM DEM (triangles are experimental points and asterisks are verification points).
Compared with SHM and MLE algorithms
In this section, we compare the proposed method with two common methods (the SHM and MLE methods). The same 1001GPS real site was used to correct the SRTM DEM using the SHM and MLE models. Table 1 lists RMSE values for the SHM and MLE corrected SRTM DEM. For comparison purposes, the RMSE of the methods herein is added to the table. As shown in Table 1, the SHM and MLE methods also improved the accuracy of the SRTM DEM by about 2% and 4% respectively. However, the root mean square error of the SHM correction and the MLE correction were 9.9m and 9.7m higher than the RMSE (8.1 m) of the method correction herein, respectively. In other words, the accuracy of the methods presented in this study was improved by about 18.2% and 16.5%, respectively, relative to the SHM and MLE methods.
For further analysis, we calculated the Root Mean Square Error (RMSE) of the corrected SRTM DEM using these three methods at slope intervals of 0 ° to 10 °,10 ° to 20 °, and >20 °, with the results also listed in table 1. The accuracy of the SRTM DEM corrected using the SHM, MLE and methods herein is close (i.e., 7.2, 7.1 and 7.1m, respectively) for a slope range of 0 ° to 10 °. For a slope range of 10 ° to 20 °, the RMSE of the SRTM DEM corrected by the SHM and MLR is 8.2 and 7.5m, whereas the RMSE of the SRTM DEM corrected by the method presented herein is 6.5m, with an improvement in accuracy of 20.7% and 13.3%, respectively. The MLR method is consistent with the RMSE value in the interval of 0 ° to 10 °, whereas the RMSE of the SHM method is increased by about 1m, because the SHM method does not consider the terrain-related error. When the slope of the SRTM DEM is greater than 20 °, the RMSE of the SHM and MLE corrected SRTM DEM increases rapidly to 18.6 and 18.3m, respectively, while the RMSE of the proposed method increases slowly to 13.2m, with an increase in accuracy of about 29% and 7.8% relative to the SHM and MRE methods, respectively. The results indicate that the proposed method has better accuracy performance in SRTM DEM correction in mountainous areas, especially with gradients greater than 20 °.
Table SRTM DEM accuracy comparison results corrected using SHM, MLE and algorithm of the invention
Claims (2)
1. An adaptive terrain-related SRTM-DEM correction method, characterized by: the method comprises the following steps: 1) Modeling global trend errors by constructing linear models related to geographic locations, i.e
f trend (E,N)＝a 0 +a 1 sinE+a 2 cos(90°-N) (1)
Wherein a is 0 ,a 1 ,a 2 Is a model parameter;
2) Construction of BIC-based local terrain error correction model
Errors f to be related to the terrain terrain Is constructed as
f terrain (S,A,Z)＝a 3 H+f TF (S,A) (2)
Wherein a is 3 Is the error coefficient of the SRTM DEM and the high correlation, f TF (S, A) represents an error relating to the gradient and the direction of the gradient; and f is true TF The order of (S, a) is determined using an adaptive strategy;
selecting the model that reaches the lowest Bayesian information criterion value, i.e. the lowest BIC value, as the best model describing the gradient and gradient-related error in the SRTM DEM;
BIC＝ln(n)k-2L (3)
where n represents the observation sample size, k is the number of independent parameters, and L is the log-likelihood of the model;
3) Construction of adaptive terrain-dependent SRTMDEM correction model
I.e. the difference deltah between the SRTMDEM elevation and the measured elevation,
ΔH＝f trend (E,N)+f terrain (S,A,H)+Δh+δ (4)
wherein E, N, H, S and A are longitude, latitude, elevation, gradient and slope directions of the SRTM DEM corresponding to all actual measurement points; Δh represents the corresponding vegetation bias, which is set to 0; delta is the residual error term; can also be used
ΔH＝B·X (5)
Representation, wherein X represents model parameters and B represents model factor vectors;
4) Robust estimation using model parametersThe +.about.of SRTM DEM can be implemented as follows>Pixel level correction:
wherein H is 1 Is the elevation vector of any pixel of the SRTM DEM, B 1 Is any pixel coefficient matrix of the SRTMDEM, and comprises a coefficient matrix of a new independent variable; new arguments include longitude, latitude, elevation, slope, and slope.
2. The adaptive terrain-related SRTM-DEM correction method according to claim 1, wherein: selecting a widely used robust estimation method M-estimation to solve model parameters of the constructed adaptive terrain-related SRTMDEM correction model;
model parameter vectorCan be obtained by iteratively weighting equation (5) (6):
up toLess than a specified threshold.
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