CN111812600A - Self-adaptive terrain-dependent SRTM-DEM correction method - Google Patents

Self-adaptive terrain-dependent SRTM-DEM correction method Download PDF

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CN111812600A
CN111812600A CN202010607023.4A CN202010607023A CN111812600A CN 111812600 A CN111812600 A CN 111812600A CN 202010607023 A CN202010607023 A CN 202010607023A CN 111812600 A CN111812600 A CN 111812600A
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CN111812600B (en
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周璀
张贵
杨泽发
朱建军
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Central South University of Forestry and Technology
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    • G—PHYSICS
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
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Abstract

An adaptive terrain-dependent SRTM-DEM correction method, comprising the steps of: 1) construction of a linear model related to geographical location to model global trend errors, i.e. ftrend(E,N)＝a0+a1sinE+a2cos (90-N) (1); 2) construction of a BIC-based local terrain error correction model for terrain-dependent errors fterrainIs constructed as fterrain(S,A,Z)＝a3H+fTF(S, A) (2); 3) constructing a self-adaptive terrain-dependent SRTMDEM correction model delta H ═ ftrend(E,N)+fterrain(S, a, H) + Δ H + (4); 4) robust estimation using model parameters
Figure DDA0002561208760000012
Figure DDA0002561208760000011
. Compared with the traditional SHM and MLE correction methods, the correction method provided by the invention has higher precision.

Description

Self-adaptive terrain-dependent SRTM-DEM correction method
Technical Field
The invention relates to a method for correcting a radar terrain task (SRTM) Digital Elevation Model (DEM) of a space shuttle, in particular to a method for correcting an SRTM-DEM related to a self-adaptive terrain.
Background
Digital Elevation Model (DEM) products play an important role in research and practical application in the fields of geophysical, geological, hydrology, geodetic surveying, urban engineering and the like. The traditional DEM products are mostly produced by adopting a point-based geodetic measuring method (such as GPS and precision leveling) with small working surface, high spatial resolution and large time consumption. In recent decades, the development of remote sensing optical photogrammetry technology has greatly pushed 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 can generate DEMs with the advantages of time-of-day, weather, high spatial resolution, etc. The space shuttle radar terrain mapping mission (SRTM) generated a near global DEM (80% of the earth' S 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 months and 2 months of 2000. The SRTM DEM is the first nearly-global homogeneous DEM product with high spatial resolution, and is widely applied to many fields such as geology, landform, water resource and hydrology, glacier science, natural disaster evaluation, vegetation investigation and research and the like since the release in 2003.
To guide this type of application, the accuracy of SRTM-DEMs (e.rodriguez, c.s.morris, and j.e.belz, "a global assessment of SRTM performance," photonic engineering, "is evaluated using GPS receivers, corner reflector arrays, marine data, and other DEM products, such as optical DEMs and airborne DEMs&RemoteSensing,vol.72,no.3,pp.249-260,2006.)，(S.Mukherjee,P.K.Joshi,S.Mukherjee,A.Ghosh,R.Garg,and A.Mukhopadhyay,"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,"Accuracyassessment oftheprocessed SRTM-based elevation data by CGIAR using field data from USA andThailand and its relation to the terrain characteristics,"RemoteSensingofEnvironment,vol.104,no.4,pp.409-415,2006.)，(M.Mukul,V.Srivastava,and M.Mukul,"Accuracy analysis of the2014–2015Global ShuttleRadar Topography Mission(SRTM)1arc-sec C-Band height model using the 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 noteworthy that this accuracy is typically manifested in plain and low vegetation areas. For mountainous or vegetation-dense areas, the accuracy of SRTM DEMs drops significantly (e.g., tens or even hundreds of meters in altitude) (e.g., berthier, y.arnaud, c.vision, and f.remy, "Biases of SRTM in high-mobility areas: improvements for the monitoring of geographical of volumetric volumefhanges," geophysic research trees, vol.33, No.8,2006.), (d.weydahl, j.sagstun,
Figure BDA0002561208740000021
Dick,and H.
Figure BDA0002561208740000022
"SRTM DEM acquisition assessment over derived areas in Norway," International journal of removal sensing, vol.28, No.16, pp.3513-3527,2007.). Previous studies have shown that the errors of SRTM DEM mainly include three components, namely vegetation deviation due to weak penetration of X or C band microwave sensors in forest areas (y.su and q.guo, "a positive method for SRTM DEM correlation over collected surface areas," isps journal of photomethetryandrendremosensing vol, 87, pp.216-228,2014.), and global (or long wavelength) error tendency [16](iii) errors associated with elevation, slope and direction of slope (E.Rodriguez, C.S. Morris, and J.E.Belz, "A glass assessment Soft words SRTM Performance," Photogrammestric engineering&RemoteSensing,vol.72,no.3,pp.249-260,2006.)，(Y.Gorokhovich and A.Voustianiouk,"Accuracyassessment of the processed SRTM-based elevation data by CGIAR using fielddata from USA and Thailand and its relation to the terrain characteristics,"Remote Sensing of Environment,vol.104,no.4,pp.409-415,2006.)，(A.
Figure BDA0002561208740000023
"Combination of SRTM3 and repeat ASTER data for differentiating the apple binder flowvelocities in the Bhutan Himalaya, "remotesensingof environmental, vol.94, No.4, pp.463-474,2005.). The general mathematical models for SRTM-DEM correction are two, one is a harmonic model for correcting global error tendency, the improvement is based on continuously defined spherical harmonics, the whole spherical surface is modeled, then the GNSS/ICESAT high-precision measurement data is used as input, least square adjustment is carried out, and the correlation coefficient of the spherical harmonics is estimated (A.Wendleder, A.Felbier, B.Wessel, M.Huber, and A.Roth, "A method to estimate equation-wave errors of SRTM C-band DEM," IEEEGeosCineceand remotesensing Leters, vol.13, No.5, pp.696-700,2016.). The other is a multivariate linear regression Model that relates local terrain-related errors to surface terrain factors (such as height, slope and aspect), and uses The known difference between GPS elevation and corresponding SRTM elevation to find The deviation of The whole area by regression method (S.ElSayed and A.H.Ali., "Improving The Accuracy of The SRTM Global GPS data and regression Model," International journal of engineering research, vol.5, No.3, pp.190-196,2016., (H.T.Elshmaibaky, "Using direct transformation of The actual GPS data and conversion technology to The Global position of The geographic elevation, and" conversion of The GPS elevation, 13. J.13. conversion, J.13. Zymid and A.32. The difference between The local terrain related errors and The corresponding elevation of The SRTM, "conversion of The GPS elevation, and conversion Model, and The difference of The overall elevation of The area, volume, and The difference of The GPS elevation of The area, V.13. The GPS elevation of The area, The geographic area of The geographic area, The geographic. However, both modes have some disadvantages. For example, the spherical harmonic model cannot account for 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 trend, so that the accuracy of the SRTM DEM after correction is reduced, and particularly in a mountain area with nonlinear terrain related errors in the SRTM DEM. To our knowledge, there is currently a lack of models that consider both global trends and terrain-dependent local srtmdam linear/nonlinear errors.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art and provide a self-adaptive terrain-dependent SRTM-DEM correction method. The method can be used for adaptively modeling the linear/nonlinear terrain-related errors of the SRTM-DEM in the mountainous area based on Bayesian Information Criterion (BIC). This makes the MLR model a specific case of the proposed model. In addition, the proposed method solves for model parameters (i.e., M-estimation) using robust estimation instead of the ordinary 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) building a linear model related to geographical location to model global trend errors, i.e.
ftrend(E,N)＝a0+a1sinE+a2cos(90°-N) (1)
Wherein a is0,a1,a2Is a model parameter;
2) construction of local terrain error correction model based on BIC
Error f to be related to terrainterrainIs constructed as
fterrain(S,A,Z)＝a3H+fTF(S,A) (2)
Wherein a is3Is the SRTMDEM height-dependent error coefficient, fTF(S, a) represents an error relating to the gradient and the slope direction;
in fact fTFThe order of (S, A) is determined by adopting an adaptive strategy;
selecting a model reaching the lowest Bayesian information criterion value, namely selecting the model reaching the lowest BIC value as an optimal model for describing the error related to the gradient and the gradient in the SRTMDEM;
BIC＝ln(n)k-2L (3)
where n represents the observed 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 srtmdam elevation and the measured elevation,
ΔH＝ftrend(E,N)+fterrain(S,A,H)+Δh+ (4)
wherein E, N, H, S and A are longitude, latitude, elevation, gradient and slope of SRTMDEM corresponding to all real measuring points; Δ h represents the corresponding vegetation bias, which is set to 0; is a residual error term. We take as an example a polynomial that relates to the second order slope and the fourth order slope. The complete terrain-dependent model constructed by this method can be represented as
Figure BDA0002561208740000041
To simplify the following statement, we rewrite the matrix form to equation (6):
ΔH＝B·X (6)
where X represents the model parameters and B represents the model factor vectors.
4) Robust estimation of terrain-dependent model parameters
A robust estimation method is able to retrieve a stable solution by adaptively assigning weights to the observations. Therefore, we choose a widely used robust estimation method M-estimation [24,25]]To solve for the model parameters of the constructed model. Model parameter vector
Figure BDA00025612087400000410
The robust estimation value of (2) can be obtained by iteratively weighting equation (7) with respect to equation (6):
Figure BDA0002561208740000042
up to
Figure BDA0002561208740000043
Less than a specified threshold (e.g.,10-4). Setting the measured elevation value as n, and then in the weight matrix of the k iteration
Figure BDA0002561208740000044
There may be literature [26 ]]Obtaining:
Figure BDA0002561208740000045
wherein
Figure BDA0002561208740000046
Represents PkThe ith main diagonal entry of (a),
Figure BDA0002561208740000047
is the residual of the ith observation equation
Figure BDA0002561208740000048
And standard deviation in the kth iterationkB and c are constants (typically designated 1.5 and 2.5).
Equation (8) indicates that there is a gross error for one (when
Figure BDA0002561208740000049
Time), the estimate of M may assign a zero weight to eliminate its contribution to the estimation of the model parameters, avoiding the effect of gross error on the estimation of the model parameters. In addition, M-estimation can adaptively assign weights to other observations without prior weight information, thereby improving the accuracy of model parameter estimation. This is not achievable with least squares estimation. The argument in equation (6), such as B, has different units, e.g., longitude and latitude in degrees and altitude in meters. Therefore, these arguments must be normalized before the model estimation.
Figure BDA0002561208740000051
Where B' is the normalized value of the variable B.
5) Robust estimation using model parameters
Figure BDA0002561208740000052
SR can be realized by the following wayOf TM DEM
Figure BDA0002561208740000053
Pixel level correction:
Figure BDA0002561208740000054
wherein H1Is the elevation vector of an arbitrary pixel of SRTMDEM, B1Is an arbitrary pixel coefficient matrix for the SRTM DEM, containing a coefficient matrix of 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 provided by the invention has higher precision.
Drawings
FIG. 1 is a SRTMDEM elevation map of an experimental area selected from Zhang Jiajie, Hunan province.
FIG. 2 is a slope diagram of an experimental area selected by Zhang Jiajie in Hunan province.
FIG. 3 is a slope diagram of an experimental area selected by Zhang Jiajie in Hunan province.
FIG. 4 is a slope error diagram of SRTMDEM corresponding to 1001 measured GPS points.
FIG. 5 is a graph of slope error for SRTMDEM corresponding to 1001 measured GPS points.
FIG. 6 is the SRTMDEM graph corrected by the algorithm of this embodiment.
FIG. 7 is a graph of the residual error of the corrected SRTMDEM and the original SRTMDEM.
Detailed Description
In order to facilitate an understanding of the present invention, the present invention will be described more fully and in detail with reference to the preferred embodiments, but the scope of the present invention is not limited to the specific embodiments described below.
It should be particularly noted that when an element is referred to as being "fixed to, connected to or communicated with" another element, it can be directly fixed to, connected to or communicated with the other element or indirectly fixed to, connected to or communicated with the other element through other intermediate connecting components.
Unless otherwise defined, all terms of art 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 limit the scope of the present invention.
An adaptive terrain-dependent SRTM-DEM correction method, comprising the steps of: 1) a linear model related to geographical location is constructed to model global trend errors (A.Wendleder, A.Felbier, B.Wessel, M.Huber, and A.Roth, "A method to estimate long-wave height errors of SRTM C-band DEM," IEEEGeoscience and remove sensing errors, vol.13, No.5, pp.696-700,2016.), namely
ftrend(E,N)＝a0+a1sinE+a2cos(90°-N) (1)
Wherein a is0,a1,a2Is a model parameter; according to the Wendleder study, global trend errors are linearly related to the geographic longitude and latitude of SRTMDEM.
2) Construction of local terrain error correction model based on BIC
Error f to be related to terrainterrainIs constructed as
fterrain(S,A,Z)＝a3H+fTF(S,A) (2)
Wherein a is3Is the SRTMDEM height-dependent error coefficient, fTF(S, a) represents an error relating to the gradient and the slope direction; in fact fTFThe order of (S, A) is determined using an adaptive strategy.
In the MLR method, fTFThe (S, A) correction function is a linear model with respect to the slope and the direction of the slope. However, linear (first order) models are not applicable to mountainous areas, while high order (non-linear) models can only describe terrain-dependent errors of mountainous areas srtmdex. To overcome this drawback, an adaptive strategy was proposed in this study to determine fTFThe order of (S, A). More specifically, we first generate a finite set of polynomials of varying order (typically one to five) for the slope and dip. Bayesian Information Criterion (BIC) is introduced into model by penalty termTo solve this problem.
Selecting a model reaching the lowest Bayesian information criterion value, namely selecting the model reaching the lowest BIC value as an optimal model for describing the error related to the gradient and the gradient in the SRTMDEM;
BIC＝ln(n)k-2L (3)
where n represents the observed 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 srtmdam elevation and the measured elevation,
ΔH＝ftrend(E,N)+fterrain(S,A,H)+Δh+ (4)
wherein E, N, H, S and A are longitude, latitude, elevation, gradient and slope of SRTMDEM corresponding to all real measuring points; Δ h represents the corresponding vegetation bias, which is set to 0; is a residual error term.
In the present invention, vegetation bias correction of SRTM-DEM typically requires a large amount of high precision "bare" geodetic measurement data, but is generally not satisfactory in most cases. Therefore, in this study, we neglected the error component of the vegetation bias and corrected 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 that relates to the second order slope and the fourth order slope. The complete terrain-dependent model constructed by this method can be represented as
Figure BDA0002561208740000071
To simplify the following statement, we rewrite the matrix form to an equation:
ΔH＝B·X (6)
where X represents the model parameters and B represents the model factor vectors.
It should be noted that vegetation bias in SRTM-DEM depends on terrain-dependent errors. Thus, equation (6) may correct for blending errors in the SRTM DEM that are related to vegetation and ground terrain, rather than terrain-only errors, particularly in mountainous areas where vegetation is covered.
In The present invention, a widely used Robust estimation method M-estimation (f.r. hampel, "The Robust and its roll in Robust estimation," Journal of American statistical association, vol.69, No.346, pp.383-393,1974.) (p.j.huber, "Robust estimation of The evaluation parameter," The analog of statistical statistics, vol.35, No.1, pp.73-101,1964.) is selected to solve The model parameters of The constructed adaptive terrain-dependent srtmdme correction model;
model parameter vector
Figure BDA0002561208740000072
The robust estimation value of (2) can be obtained by iteratively weighting equation (7) with respect to equation (6):
Figure BDA0002561208740000073
up to
Figure BDA0002561208740000074
Less than a specified threshold (e.g.,10-4)。
Setting the measured elevation value as n, and then in the weight matrix of the k iteration
Figure BDA0002561208740000075
There may be literature [26 ]]Obtaining:
Figure BDA0002561208740000081
wherein
Figure BDA0002561208740000082
Represents PkThe ith main diagonal entry of (a),
Figure BDA0002561208740000083
is the residual of the ith observation equation
Figure BDA0002561208740000084
And standard deviation in the kth iterationkB and c are constants (typically designated 1.5 and 2.5).
Equation (8) indicates that there is a gross error for one (when
Figure BDA0002561208740000085
Time), the estimate of M may assign a zero weight to eliminate its contribution to the estimation of the model parameters, avoiding the effect of gross error on the estimation of the model parameters. In addition, M-estimation can adaptively assign weights to other observations without prior weight information, thereby improving the accuracy of model parameter estimation. This is not achievable with least squares estimation. The argument in equation (6), such as B, has different units, e.g., longitude and latitude in degrees and altitude in meters. Therefore, these arguments must be normalized before the model estimation.
Figure BDA0002561208740000086
Where B' is the normalized value of the variable B.
4) Robust estimation using model parameters
Figure BDA0002561208740000087
The SRTM DEM can be implemented in the following way
Figure BDA0002561208740000088
Pixel level correction:
Figure BDA0002561208740000089
wherein H1Is the elevation vector of an arbitrary pixel of SRTMDEM, B1Is an arbitrary pixel coefficient matrix of the SRTM DEM, containing new arguments (e.g. longitude, latitude, elevation, slope and declination)A matrix of coefficients.
Overview of SHM model
According to the study (A.Wendleder, A.Felbier, B.Wessel, M.Huber, and A.Roth, "A method of until estimate long-wave height errors of SRTM C-band DEM," IEEEGeosensinceand remotesensing leaves, vol.13, No.5, pp.696-700,2016.), the global trend error is linearly related to the geographical longitude and latitude of the SRTM DEM; thus, the Spherical Harmonic Model (SHM) was chosen to model the trend error, i.e.
Figure BDA00025612087400000810
Wherein A isnmAnd BnmIs a dimensionless weighting coefficient; rnmAnd SnmIs a surface spherical harmonic; m and n are the rank and order of the SHM.
Overview of MLR model
MLR method corrects SRTMDEM errors related to local terrain by constructing multiple linear regression analysis
ΔH＝a0+a1S+a2A+a3H (12)
Wherein Δ H is a difference between an elevation of the observation area SRTMDEM and an actually measured elevation measured by leveling, GPS or ICEsat; s, A and H are the gradient, the slope direction and the elevation of the SRTMDEM of the corresponding measuring point; p ═ a0,a1,…,a3]TRepresenting model parameters of the MLR model. The unknown quantity P is then calculated by using a least squares method. Finally, the SRTMDEM is corrected according to the pixel by adopting a formula (12). Global trend errors and higher order terrain-related errors are not considered in the MLR model. Therefore, the accuracy of the corrected SRTMDEM will be degraded, especially in mountainous areas where terrain-dependent non-linear errors exist.
It is noted that equation (12) is a special case of equation (6) where the remaining parameters are all zero except a0 and a 3-a 5.
Example 1
In the embodiment, Zhang Jiajie in Hunan province of China is selected as a research area. Fig. 1-3 show SRTM-DEM over a selected Region (ROI). The triangles and asterisks in fig. 1 represent experimental data and validation data, respectively, of the actual measured GPS. The terrain in the north of the ROI is relatively flat, varying from approximately 118 to 630m in elevation, and varying from 0 to 13 in slope. The southern terrain is a mountainous area with an elevation range of about 130 to 1452m and a slope of 0 to 72. Various types of ground topography in the ROI are suitable for evaluating the overall performance of the proposed method. In addition, 1051 measured elevation data (see asterisks and triangles) were collected using a continuously operating reference station or other GPS measurement means in the south of Hunan province. Using these measured elevation data, model parameters may be estimated and used to evaluate the accuracy of the corrected SRTM-DEM.
The GPS elevation data is the world geodetic system 84(WGS 84) geodetic plane (i.e., ellipsoidal height), and the SRTM-DEM elevation is the Earth's gravity model 96(EGM96) geodetic plane (i.e., positive height). Therefore, all GPS elevation data needs to be unified for inter-data elevation references before correcting SRTM-DEM, and conversion is performed in the following manner
HEGM96＝HWGS84-N (13)
Wherein HWGS84Corresponding to the ground height, H, of WGS-84EGM96Corresponding to a positive height of EGM96, N is a geodetic difference.
SRTM-DEM error correction experimental result of patent algorithm of the invention
FIGS. 4 and 5 show elevation error values for the SRTM-DEM at 1051 GPS observation points versus grade and incline, as shown, there is no significant linear relationship between the error of the SRTM-DEM and the grade and incline, particularly the latter. The results show that the SRTM-DEM error shows a nonlinear relationship with respect to the slope and the sloping direction. The results show that a polynomial with a first order height, a second order slope and a fourth order slope is an optimization model compared to other polynomials. Experiments were performed with 1001GPS real-world points, and 50 real-world points (whose geographical locations are indicated by asterisks in fig. 1) with nearly uniform slope and slope were selected for accuracy verification. The algorithm of the invention is adopted to carry out SRTM DEM correction pixel by pixel. The results of the experiment are shown in FIG. 3.
Fig. 6 shows the corrected SRTM DEM, and fig. 7 shows the difference in ROI between the original (see fig. 1) and corrected SRTM DEMs. In fig. 7, the triangles are experimental points and the asterisks are verification points. The results show a maximum difference of about-50 m. To quantitatively assess the accuracy of the SRTM DEM error correction, we compared the corrected SRTM DEM elevation to the elevations of the selected 50 actual measurement points, and the results showed good agreement between the two, with a Root Mean Square Error (RMSE) of 8.1m (as shown in Table 1), which indicates an improvement of about 20% in accuracy over the root mean square error (i.e., 10.1m) of the SRTM DEM without correction. The result shows that the method can effectively improve the elevation precision of the SRTM DEM.
FIG. 3 (a) is a graph of the residual error between the corrected SRTMDEM and the original SRTMDEM (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 commonly used methods (the SHM and MLE methods). The SRTM DEM was corrected using the SHM and MLE models using the same 1001GPS real points. Table 1 lists RMSE values for SHM and MLE corrected srtmdef. For ease of comparison, 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 srtmdef by about 2% and 4%, respectively, on average. However, the root mean square errors of the SHM and MLE correction results were 9.9m and 9.7m higher, respectively, than the RMSE (8.1m) of the correction results of the method herein. In other words, the accuracy of the method proposed in this study was improved by about 18.2% and 16.5% relative to the SHM and MLE methods, respectively.
To further analyze the results, 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 °, and the results are 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 the slope range of 0 ° to 10 °. For a range of slopes from 10 ° to 20 °, the RMSE of the SRTM DEM corrected by SHM and MLR was 8.2 and 7.5m, while the RMSE of the SRTM DEM corrected by the method proposed herein was 6.5m, with 20.7% and 13.3% improvement in accuracy, respectively. The MLR method is consistent with the RMSE values in the interval of 0 deg. to 10 deg., whereas the RMSE of the SHM method increases by about 1m because the SHM method does not take into account terrain-related errors. When the slope of the SRTM DEM is greater than 20 deg., 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 improvement of about 29% and 7.8% in accuracy over the SHM and MRE methods, respectively. The results show that the proposed method has better accuracy performance in the SRTM DEM correction in mountainous areas (especially with slopes greater than 20 °).
Table SRTM DEM precision comparison results corrected using SHM, MLE and the algorithm of the invention
Figure BDA0002561208740000111

Claims (2)

1. A self-adaptive terrain-dependent SRTM-DEM correction method is characterized by comprising the following steps: the method comprises the following steps: 1) building a linear model related to geographical location to model global trend errors, i.e.
ftrend(E,N)＝a0+a1sinE+a2cos(90°-N) (1)
Wherein a is0,a1,a2Is a model parameter;
2) construction of local terrain error correction model based on BIC
Error f to be related to terrainterrainIs constructed as
fterrain(S,A,Z)＝a3H+fTF(S,A) (2)
Wherein a is3Is the SRTMDEM height-dependent error coefficient, fTF(S, a) represents an error relating to the gradient and the slope direction; in fact fTFThe order of (S, A) is determined by adopting an adaptive strategy;
selecting a model reaching the lowest Bayesian information criterion value, namely selecting the model reaching the lowest BIC value as an optimal model for describing the error related to the gradient and the gradient in the SRTMDEM;
BIC＝ln(n)k-2L (3)
where n represents the observed 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 srtmdam elevation and the measured elevation,
ΔH＝ftrend(E,N)+fterrain(S,A,H)+Δh+ (4)
wherein E, N, H, S and A are longitude, latitude, elevation, gradient and slope of SRTMDEM corresponding to all real measuring points; Δ h represents the corresponding vegetation bias, which is set to 0; is a residual error term; it can also be represented by Δ H ═ B · X (5), where X represents the model parameters and B represents the model factor vectors;
4) robust estimation using model parameters
Figure FDA0002561208730000011
The SRTM DEM can be implemented in the following way
Figure FDA0002561208730000012
Pixel level correction:
Figure FDA0002561208730000013
wherein H1Is the elevation vector of an arbitrary pixel of SRTMDEM, B1Is an arbitrary pixel coefficient matrix of the SRTM DEM, and comprises a coefficient matrix of a new independent variable; the new arguments include longitude, latitude, elevation, grade, and slope.
2. The adaptive terrain-dependent SRTM-DEM correction method of claim 1, wherein: selecting a widely used steady estimation method M-estimation [24,25] to solve model parameters of the constructed adaptive terrain-dependent SRTMDEM correction model;
model parameter vector
Figure FDA0002561208730000014
May be estimated by iterating equation (5)The weighted equation (6) obtains:
Figure FDA0002561208730000021
up to
Figure FDA0002561208730000022
Less than a specified threshold (e.g.,10-4)。
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