Slope displacement estimation method based on ground-based interferometric radar, storage medium and equipment

Abstract

The present application relates to the technical field of slope deformation prediction, in particular to a slope displacement estimation method based on ground-based interferometric radar, a storage medium and an electronic device. The method comprises observing radar images of the slope area before and after deformation at each station; after multi-stage processing of the radar images before and after deformation, the deformation variable in the radar line-of-sight direction is obtained; then the deformation variable is decomposed into three-direction components in the geographic coordinate system, after constructing the corresponding function model and processing by the least square method, the best estimate of three-dimensional ground deformation in the geographic coordinate system is obtained; after rotation, three-direction components in the slope coordinate system are obtained, and combined with the best estimate of three-dimensional ground deformation in the geographic coordinate system, the corresponding function model is constructed; after processing by the least square method, the best estimate of three-dimensional ground deformation in the slope coordinate system is obtained, and the target function is constructed to solve the three-direction displacement of the slope. The present application can obtain three-dimensional displacement in the slope coordinate system, and meet the fine monitoring requirements of small and medium-sized slope engineering.

Description

Technical Field

[0001] This invention relates to the field of slope deformation prediction technology, specifically to a slope displacement estimation method, storage medium, and electronic device based on multi-view ground-based interferometric radar. Background Technology

[0002] Slope instability is a common geological hazard in highway construction, which can not only cause traffic disruptions but also easily trigger secondary risks such as landslides. Long-term slope stability monitoring is of great significance for ensuring traffic safety.

[0003] Interferometric Synthetic Aperture Radar (InSAR) technology offers non-contact, all-weather observation capabilities, enabling the acquisition of large-area surface deformation information within the satellite's field of view. Compared to conventional ground-based measurement methods such as Global Navigation Satellite System (GNSS), inclinometers, and displacement gauges, it boasts advantages such as low cost, large-scale coverage, and area measurement, and has gradually become one of the mainstream methods for monitoring surface deformation. However, a single satellite-borne InSAR system can only acquire one-dimensional deformation information along the radar line of sight (LOS), failing to fully characterize the three-dimensional deformation features of highway slopes. Its accuracy is limited by the spatial resolution of the satellite data, making it unsuitable for the refined monitoring needs of small to medium-sized slopes (where slope length and width are generally within tens of meters).

[0004] Unlike spaceborne InSAR technology, ground-based interferometric SAR (GB-InSAR) is a radar remote sensing method that monitors surface deformation by transmitting and receiving electromagnetic signals from a ground platform and acquiring interferometric images using an antenna along a track-based synthetic aperture. GB-InSAR offers the advantages of both high temporal frequency (time interval less than 10 minutes) and high spatial resolution (less than 1 meter), significantly suppressing temporal correlation errors. Furthermore, the fixed base of the ground-based radar further reduces spatial correlation errors caused by differences in the observation angles of the primary and secondary radar images. Therefore, under favorable observation conditions, GB-InSAR can achieve sub-millimeter-level monitoring accuracy in the line-of-sight (LOS) direction.

[0005] For highway slope deformation monitoring, ground-based interferometric radar technology allows for flexible selection of station locations and the setting of observation time intervals based on target characteristics. Its ultra-high time-frequency observation capabilities are particularly suitable for emergency real-time monitoring of slope engineering. However, limited by the geometric observation framework of a single platform and a single orbit, both a single spaceborne InSAR and a single ground-based radar can only acquire one-dimensional deformation in the LOS direction. Ground-based interferometric radar, due to its flexibility, can conduct observations from different stations and perspectives during slope monitoring. By setting the observation time-frequency and perspective, it can acquire SAR (synthetic aperture radar) images of the slope surface with the same spatiotemporal resolution. Therefore, each observation from a different perspective can be considered as SAR observation data from an independent platform. Based on deformation observations from three or more different perspectives, three-dimensional deformation can be calculated without relying on other data sources, providing a more convenient means for three-dimensional deformation monitoring of small and medium-sized slope engineering projects.

[0006] Furthermore, for slope engineering monitoring, in addition to vertical displacement, lateral horizontal displacement and aspect displacement perpendicular to the road direction are extremely important indicators. However, current 3D deformation estimation using multi-platform, multi-source data combined with spaceborne InSAR is still limited to the inversion of east-west and north-south displacements in the geographic coordinate system, which cannot meet the calculation requirements of 3D deformation for small and medium-sized slopes. If ground-based interferometric radar measurement technology is used, the lateral horizontal displacement and aspect displacement of each point in the slope coordinate system can be derived by combining the geometric movement law of slope surface coordinates and the viewing parameters of ground-based radar during on-site observation. This provides a new approach to expanding the application of InSAR technology in slope engineering.

[0007] In summary, it is necessary to develop a slope displacement estimation method, storage medium, and electronic equipment based on multi-view ground-based interferometric radar to solve the following problems existing in the technology: 1) A single spaceborne InSAR can only acquire one-dimensional deformation information in the radar LOS direction, which cannot fully characterize the three-dimensional deformation features of highway slopes; 2) The spatial resolution accuracy of spaceborne InSAR data is insufficient, which cannot meet the refined monitoring needs of small and medium-sized slope projects; 3) The three-dimensional deformation estimation of spaceborne InSAR is still limited to the inversion of east-west and north-south displacements in the geographic coordinate system, which cannot meet the calculation needs of three-dimensional deformation of small and medium-sized slopes. Summary of the Invention

[0008] The purpose of this invention is to provide a slope displacement estimation method, storage medium, and electronic device based on ground-based interferometric radar. The specific technical solution is as follows:

[0009] In a first aspect, the present invention provides a slope displacement estimation method based on ground-based interferometric radar, comprising:

[0010] Step S1: Select at least three stations around the outer perimeter of the slope area and deploy multiple artificial corner reflectors on the slope area; use a single ground-based interferometric radar to sequentially observe the radar images of the slope area before deformation and after deformation at each of the stations.

[0011] The deformation of the slope area is formed by moving at least two of the artificial corner reflectors to a preset deformation.

[0012] Step S2: Perform pixel-by-pixel complex multiplication on the radar images before and after deformation corresponding to each station to form an interferogram; extract phase information from the interferograms of each station to obtain a phase map; perform filtering and phase unwrapping on the phase maps of each station in sequence to obtain a phase image with continuous real phase; extract the unwrapped phase from the pixel positions of each artificial corner reflector in the phase image of each station, and perform transformation processing to obtain the deformation in the radar line-of-sight direction of the corresponding station.

[0013] Step S3: Decompose the deformation along the radar line of sight at each station into three components in the geographic coordinate system, and construct a three-dimensional deformation observation equation function model in the geographic coordinate system containing a coefficient matrix B; wherein, the coefficient matrix B is a coefficient matrix after singular value decomposition and regularization; then, use the least squares method to process the three-dimensional deformation observation equation function model in the geographic coordinate system to obtain the best estimate of the three-dimensional surface deformation in the geographic coordinate system.

[0014] Step S4: Rotate the three-dimensional components in the geographic coordinate system to obtain the three-dimensional components in the slope coordinate system of the slope area. Combine this with the optimal estimate of the three-dimensional surface deformation in the geographic coordinate system to obtain the three-dimensional deformation observation equation function model in the slope coordinate system containing the coefficient matrix A. The coefficient matrix A is the coefficient matrix after singular value decomposition and regularization. Subsequently, the least squares method is used to process the three-dimensional deformation observation equation function model in the slope coordinate system to obtain the optimal estimate of the three-dimensional surface deformation in the slope coordinate system. The three-dimensional displacement of the slope is obtained by constructing an objective function and solving it.

[0015] Optionally, in step S1, the baseline length between any two adjacent stations is greater than 10m, and the stations are not collinear; each station has a line of sight to the slope area.

[0016] The observation time interval between any two adjacent stations of the ground-based interferometric radar is no greater than 2 minutes.

[0017] The deformation direction of the preset deformation includes the direction along the slope, the direction perpendicular to the slope, and the horizontal direction; wherein, the horizontal direction is the direction perpendicular to the road direction.

[0018] Optionally, in step S2, the expression for the phase diagram is represented by equation (1):

[0019]

[0020] In equation (1), The original interference phase of the phase diagram is represented by arg; arg represents the complex phase function; I(x, y) represents the complex value of the interference diagram.

[0021] The phase image is represented by equation (2):

[0022]

[0023] In equation (2), Represents the interference phase after unwrapping, in radians; Unwrap represents the phase unwrapping algorithm function, used to remove 2π jumps and restore phase continuity;

[0024] The conversion process is represented by equation (3):

[0025]

[0026] In equation (3), D LOS λ0 represents the deformation along the radar line of sight at a certain station; λ0 represents the radar wavelength of the ground-based interferometric radar. This represents the unwrapped phase difference between the radar image before and after deformation at a certain station.

[0027] Optionally, in step S3, the three-dimensional deformation observation equation function model in the geographic coordinate system is represented by equation (4):

[0028]

[0029] In equation (4), These represent the deformation along the radar line-of-sight direction obtained from station 1, station 2 to station i, respectively; the value of i is greater than or equal to 3; D E D N and D U These represent the east-west, north-south, and vertical deformations in the geographic coordinate system, respectively; B represents the coefficient matrix B after the singular value decomposition and regularization processes.

[0030] The coefficient matrix B before the singular value decomposition and regularization processes is B0, which is represented by equation (5):

[0031]

[0032] In equation (5), θ 1 θ 2 ...θ i α represents the incident angle of the ground-based interferometric radar at stations 1, 2, and i, respectively; 1 α 2 ...α i These represent the azimuth angles of the ground-based interferometric radar at points 1 and 2 to 1, respectively.

[0033] From equation (4), we obtain the matrix expression (6):

[0034] D LOS =B*D ENU (6);

[0035] In equation (6), D LOS It is by The transpose of a single-column matrix formed by combination; D ENU This represents the three-dimensional surface deformation in a geographic coordinate system, which is caused by D E D N and D U The transpose of a single-column matrix formed by combination;

[0036] The least squares method is used to process equation (6) to obtain the optimal estimate of three-dimensional surface deformation in the geographic coordinate system shown in equation (7):

[0037] D ENU =[D E D N D U ]=(B T B) -1 B T D LOS (7).

[0038] Optionally, in step S4, the three-dimensional components in the geographic coordinate system are rotated using equation (8) to obtain the three-dimensional components in the slope coordinate system of the slope area:

[0039]

[0040] In equation (8), D K D T and D I These represent the slope direction displacement, perpendicular slope direction displacement, and normal displacement in the slope coordinate system, respectively; μ represents the slope of the slope region; β represents the aspect angle of the slope region.

[0041] The three-dimensional deformation observation equation function model in the slope coordinate system is represented by matrix expression (9):

[0042] D LOS=A*D KTI (9);

[0043] In equation (9), D KTI D represents K D T and D I The transpose of the single-column matrix formed by the combination; A represents the coefficient matrix A after the singular value decomposition and regularization processes;

[0044] The coefficient matrix A before the singular value decomposition and regularization processes is A0, which is represented by equation (10):

[0045]

[0046] The least squares method is used to process equation (9) to obtain the optimal estimate of the three-dimensional surface deformation in the slope coordinate system shown in equation (11):

[0047] D KTI =(A T A) -1 A T D LOS (11);

[0048] D is obtained from equation (11) K D T and D I Regularization;

[0049] Using D K and D I The horizontal displacement D is obtained by regularization from equation (12). H :

[0050] D H =D K cosμ-D I sinμ (12);

[0051] By D U D K and D H The displacements of the slope in three directions are obtained.

[0052] Optionally, in step S4, the singular value decomposition process is performed on the coefficient matrix A0 using equation (13):

[0053] A0=U∑V T (13);

[0054] In equation (13), U and V are orthogonal matrices, i.e., satisfying U T U=I and V TV = I; I represents the identity matrix; U represents the set of left singular vectors; V represents the set of right singular vectors; ∑ is a diagonal matrix whose diagonal elements are the singular values ​​of A0;

[0055] From equation (13), it can be seen that after the singular value decomposition, the pseudo-inverse matrix of the coefficient matrix A0 is V∑ as shown in equation (14). + U T ;∑ + It is a pseudo-inverse matrix of ∑;

[0056] The pseudo-inverse matrix V∑ of the coefficient matrix A0 after the singular value decomposition is... + U T Substituting into equation (9), we obtain equation (15):

[0057] D KTI =V∑ + U T D LOS (15):

[0058] The singular value decomposition and regularization methods used to obtain the coefficient matrix B are the same as those used to obtain the coefficient matrix A.

[0059] Optionally, in step S4, the method for constructing the objective function includes:

[0060] By introducing a regularization term into equation (15), we obtain the objective function shown in equation (16):

[0061] J(D KTI )=||A·D KTI -D LOS || 2 +λ·(L·D KTI ) 2 (16);

[0062] In equation (16), J(D) KTI A·D represents the total error of three-dimensional deformation in the slope coordinate system; KTI -D LOS || 2 λ·(L·D) represents the square of the difference between the inverted value and the observed value of the deformation along the radar line of sight. KTI ) 2 is the regularization term, representing the regularization constraint; λ represents the regularization weight parameter, with a value range of 0 to 0.2; L represents the regularization matrix, which is taken as the identity matrix;

[0063] In the objective function shown in equation (16), D KTITaking the partial derivative and setting it to zero, we obtain the regularized solution expression shown in equation (17):

[0064] D KTI =(A T A+λ·L T L) -1 ·A T D LOS (17);

[0065] At the preset deformation point, D calculated by equation (17) KTI Preset true values ​​of three-directional displacements in the known slope coordinate system Compare the two, and use equation (18) to calculate the error term e(λ):

[0066]

[0067] By combining equations (17) and (18), multiple different values ​​of λ are input into equation (17), and equation (18) is solved repeatedly until the error term e(λ) in equation (18) converges to the minimum, thereby determining the optimal value of λ.

[0068] Substituting the optimal value of λ into equation (17), the optimal three-dimensional surface deformation result D in the slope coordinate system is then calculated. KTI ; to make the optimal D KTI Substituting into equation (11), we obtain the optimal D. K D T and D I Regularization; to achieve optimal D K and D I Substituting the regularized solution into equation (12) yields the optimal lateral horizontal displacement D. H Finally, by D U Optimal D K and D H The displacements of the slope in three directions are obtained.

[0069] Optionally, the slope width of the slope area is 10 to 500 m, and the slope length is 10 to 500 m.

[0070] In a second aspect, the present invention provides a storage medium storing a computer program, the computer program including program instructions that, when executed by a processor, cause the processor to perform the slope displacement estimation method based on ground-based interferometric radar.

[0071] In a third aspect, the present invention provides an electronic device including a processor and a memory interconnected thereto, wherein the memory is used to store a computer program supporting the electronic device, the computer program including program instructions, and the processor is configured to invoke the program instructions to execute the slope displacement estimation method based on ground-based interferometric radar.

[0072] The application of the technical solution of the present invention has at least the following beneficial effects:

[0073] This invention provides a slope displacement estimation method based on ground-based interferometric radar. In step S1, a single ground-based interferometric radar is used to sequentially observe radar images of the slope area before and after deformation at each of the aforementioned stations. In step S2, the radar images before and after deformation at each of the aforementioned stations are processed through multiple stages to obtain the deformation in the radar line-of-sight direction at the corresponding stations. In step S3, the deformation in the radar line-of-sight direction at each of the aforementioned stations is decomposed into three-dimensional components in the geographic coordinate system. After constructing a corresponding function model and processing with the least squares method, the optimal estimate of the three-dimensional surface deformation in the geographic coordinate system is obtained. In step S4, the three-dimensional components in the geographic coordinate system are rotated to obtain the three-dimensional components in the slope coordinate system of the slope area. Combined with the optimal estimate of the three-dimensional surface deformation in the geographic coordinate system, a corresponding function model is constructed. After processing the function model with the least squares method, the optimal estimate of the three-dimensional surface deformation in the slope coordinate system is obtained. The three-dimensional displacement of the slope is obtained by solving the objective function. Therefore, the present invention, by combining steps S1 to S4, can obtain three-dimensional displacement in the slope coordinate system, meeting the calculation requirements for three-dimensional deformation of small and medium-sized slopes. This solves the problem that the three-dimensional deformation estimation using spaceborne InSAR is still limited to the inversion of east-west and north-south displacements in the geographic coordinate system, failing to meet the calculation requirements for three-dimensional deformation of small and medium-sized slopes. Furthermore, the present invention uses a single ground-based interferometric radar to acquire three-dimensional deformation information of the slope area by changing the station, thus fully characterizing the three-dimensional deformation features of highway slopes. This solves the problem that a single spaceborne InSAR can only acquire one-dimensional deformation information in the radar LOS direction, failing to fully characterize the three-dimensional deformation features of highway slopes. The spatial resolution accuracy of the ground-based interferometric radar used in this invention is approximately five times that of spaceborne InSAR, meeting the refined monitoring requirements of small and medium-sized slope projects. This solves the problem that the spatial resolution accuracy of spaceborne InSAR data is insufficient to meet the refined monitoring requirements of small and medium-sized slope projects.

[0074] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0075] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0076] Figure 1 This is a flowchart of a slope displacement estimation method based on ground-based interferometric radar in one of the embodiments;

[0077] Figure 2 This is a layout diagram of the ground-based interferometric radar and artificial corner reflectors;

[0078] Figure 3 It is a geometric relationship diagram in a geographic coordinate system;

[0079] Figure 4 This is a geometric diagram in the slope coordinate system (S in the diagram). sum "" represents the actual vector displacement in three-dimensional space;

[0080] Figure 5 This is a diagram showing the deformation of each station in Test 1 in the radar line-of-sight direction after CR3 moves to the preset deformation direction (where group 1, group 2, and group 3 represent three repeated tests in Test 1);

[0081] Figure 6 This is a diagram showing the deformation of each station in Test 1 in the radar line-of-sight direction after CR4 moves to the preset deformation (groups 1, 2, and 3 represent three repeated tests in Test 1).

[0082] Figure 7 This is a diagram showing the deformation of each station in Experiment 2 in the radar line-of-sight direction after CR3 moves to the preset deformation (groups 1, 2, and 3 represent three repeated experiments in Experiment 2).

[0083] Figure 8 This is a diagram showing the deformation of each station in Experiment 2 in the radar line-of-sight direction after CR4 moves to the preset deformation (groups 1, 2, and 3 represent three repeated experiments in Experiment 2).

[0084] Figure 9 This is a diagram showing the three-directional displacement of the slope at each station in Experiment 1 after CR3 moved to the preset deformation.

[0085] Figure 10 This is a diagram showing the three-directional displacement of the slope at each station in Experiment 1 after CR4 moved to the preset deformation.

[0086] Figure 11 This is a diagram showing the three-directional displacement of the slope at each station in Experiment 2 after CR3 moved to the preset deformation.

[0087] Figure 12This is a diagram showing the three-directional displacement of the slope at each station in Experiment 2 after CR4 moved to the preset deformation.

[0088] Figure 13 This is a graph showing the relationship between slope displacement and regularized weight parameters (where group 1, group 2, and group 3 represent three repeated experiments);

[0089] Figure 14 It is a graph showing the relationship between lateral horizontal displacement and regularization weight parameters (where group 1, group 2, and group 3 represent three repeated experiments);

[0090] Figure 15 It is a graph showing the relationship between vertical slope surface displacement and regularized weight parameters (where group 1, group 2, and group 3 represent three repeated experiments);

[0091] Figure 16 This is a graph showing the relationship between regularization weight parameters and the system condition number (the condition number is used to measure the ill-conditioning of the coefficient matrix A; the smaller the condition number, the less severe the ill-conditioning). Detailed Implementation

[0092] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0093] Example:

[0094] See Figure 1 A slope displacement estimation method based on ground-based interferometric radar includes:

[0095] Step S1, see Figure 2 Three stations (station 1, station 2, and station 3) were selected around the perimeter of the slope area (slope width 10m, slope length 10m). Four artificial corner reflectors (labeled CR1, CR2, CR3, and CR4) were deployed on the slope area. A single GPRI-II ground-based interferometric radar (GPRI-II ground-based interferometric radar equipment parameters are shown in Table 1) was used to observe the radar images of the slope area before deformation and after deformation at each of the stations. The slope gradient and aspect angle data of the slope area, as well as the incident angle and azimuth angle of the ground-based interferometric radar at different stations, were recorded. The results are shown in Table 2.

[0096] The deformation of the slope area is formed by moving the two artificial corner reflectors (specifically CR3 and CR4) to a preset deformation, the specific preset deformation is shown in Table 3; step S1 is repeated twice, namely test 1 and test 2;

[0097] Step S2: Perform pixel-by-pixel complex multiplication on the radar images before and after deformation corresponding to each station to form an interferogram; extract phase information from the interferograms of each station to obtain a phase map; perform filtering and phase unwrapping on the phase maps of each station in sequence to obtain a phase image with continuous real phase; extract the unwrapped phase from the pixel positions of each artificial corner reflector in the phase image of each station, and perform transformation processing to obtain the deformation in the radar line-of-sight direction of the corresponding station.

[0098] Step S3, see Figure 3 The deformation along the radar line of sight at each of the aforementioned stations is decomposed into three components in the geographic coordinate system, and a three-dimensional deformation observation equation function model in the geographic coordinate system containing a coefficient matrix B is constructed. The coefficient matrix B is a coefficient matrix after singular value decomposition and regularization. Subsequently, the least squares method is used to process the three-dimensional deformation observation equation function model in the geographic coordinate system to obtain the best estimate of the three-dimensional surface deformation in the geographic coordinate system.

[0099] Step S4, see Figure 4 The three-dimensional components in the geographic coordinate system are rotated to obtain the three-dimensional components in the slope coordinate system of the slope area. Combined with the best estimate of the three-dimensional surface deformation in the geographic coordinate system, a three-dimensional deformation observation equation function model in the slope coordinate system containing the coefficient matrix A is obtained. The coefficient matrix A is the coefficient matrix after singular value decomposition and regularization. Subsequently, the least squares method is used to process the three-dimensional deformation observation equation function model in the slope coordinate system to obtain the best estimate of the three-dimensional surface deformation in the slope coordinate system. The three-dimensional displacement of the slope is obtained by constructing an objective function and solving it.

[0100] Table 1. Parameters of GPRI-II Ground-Based Interferometric Radar Equipment

[0101] category Parameter value Frequency range 17.1~17.3GHZ GPRI measurement range 50 meters to 10 kilometers Range sampling interval / resolution 0.75 / 0.95 meters Position-to-resolution 6.8 meters (1 km location) accuracy 0.1 mm accuracy 1 mm / km

[0102] Table 2. Geometric and radar parameters of the slope (unit: degrees)

[0103]

[0104] Table 3. Preset deformations of each artificial corner reflector in three directions under the slope coordinate system (unit: mm)

[0105]

[0106] In step S1, the baseline length between any two adjacent stations is greater than 10m, and the stations are not collinear; each station has a line of sight to the slope area.

[0107] The observation time interval between any two adjacent stations of the ground-based interferometric radar is no greater than 2 minutes.

[0108] The deformation direction of the preset deformation includes the direction along the slope, the direction perpendicular to the slope, and the horizontal direction; wherein, the horizontal direction is the direction perpendicular to the road direction.

[0109] In step S2, the phase diagram is expressed using equation (1):

[0110]

[0111] In equation (1), The original interference phase of the phase diagram is represented by arg; arg represents the complex phase function; I(x, y) represents the complex value of the interference diagram.

[0112] The phase image is represented by equation (2):

[0113]

[0114] In equation (2), Represents the interference phase after unwrapping, in radians; Unwrap represents the phase unwrapping algorithm function, used to remove 2π jumps and restore phase continuity;

[0115] The conversion process is represented by equation (3):

[0116]

[0117] In equation (3), D LOS λ0 represents the deformation along the radar line of sight at a certain station; λ0 represents the radar wavelength of the ground-based interferometric radar. This represents the unwrapped phase difference between the radar image before and after deformation at a certain station. Equation (3) yields the following... Figure 5 , Figure 6 , Figure 7 and Figure 8 D shown LOS result.

[0118] In step S3, the three-dimensional deformation observation equation function model in the geographic coordinate system is represented by equation (4):

[0119]

[0120] In equation (4), These represent the deformation along the radar line-of-sight direction obtained from station 1, station 2 to station i, respectively; the value of i is greater than or equal to 3; D E D Nand D U These represent the east-west, north-south, and vertical deformations in the geographic coordinate system, respectively; B represents the coefficient matrix B after the singular value decomposition and regularization processes.

[0121] The coefficient matrix B before the singular value decomposition and regularization processes is B0, which is represented by equation (5):

[0122]

[0123] In equation (5), θ 1 θ 2 ...θ i α represents the incident angle of the ground-based interferometric radar at stations 1, 2, and i, respectively; 1 α 2 ...α i These represent the azimuth angles of the ground-based interferometric radar at points 1 and 2 to 1, respectively.

[0124] From equation (4), we obtain the matrix expression (6):

[0125] D LOS =B*D ENU (6);

[0126] In equation (6), D LOS It is by The transpose of a single-column matrix formed by combination; D ENU This represents the three-dimensional surface deformation in a geographic coordinate system, which is caused by D E D N and D U The transpose of a single-column matrix formed by combination;

[0127] The least squares method is used to process equation (6) to obtain the optimal estimate of three-dimensional surface deformation in the geographic coordinate system shown in equation (7):

[0128] D ENU =[D E D N D U ]=(B T B) -1 B T D LOS (7).

[0129] In step S4, the three-dimensional components in the geographic coordinate system are rotated using equation (8) to obtain the three-dimensional components in the slope coordinate system of the slope area:

[0130]

[0131] In equation (8), D K D T and D I These represent the slope direction displacement in the slope coordinate system (i.e., Figure 4 Slope displacement), vertical displacement (i.e.) Figure 4 The vertical slope displacement and normal displacement are represented by μ; μ represents the slope of the slope region; β represents the slope angle of the slope region.

[0132] The three-dimensional deformation observation equation function model in the slope coordinate system is represented by matrix expression (9):

[0133] D LOS =A*D KTI (9);

[0134] In equation (9), D KTI D represents K D T and D I The transpose of the single-column matrix formed by the combination; A represents the coefficient matrix A after the singular value decomposition and regularization processes;

[0135] The coefficient matrix A before the singular value decomposition and regularization processes is A0, which is represented by equation (10):

[0136]

[0137] The least squares method is used to process equation (9) to obtain the optimal estimate of the three-dimensional surface deformation in the slope coordinate system shown in equation (11):

[0138] D KTI =(A T A) -1 A T D LOS (11);

[0139] D is obtained from equation (11) K D T and D I Regularization;

[0140] Using D K and D I The horizontal displacement D is obtained by regularization from equation (12). H (Right now Figure 4 (Horizontal displacement in the middle):

[0141] D H =D K cosμ-D I sinμ (12);

[0142] By D U D K and D H The displacements of the slope in three directions are obtained.

[0143] In step S4, the singular value decomposition process is performed on the coefficient matrix A0 using equation (13):

[0144] A0=U∑V T (13);

[0145] In equation (13), U and V are orthogonal matrices, i.e., satisfying U T U=I and V T V = I; I represents the identity matrix; U represents the set of left singular vectors; V represents the set of right singular vectors; ∑ is a diagonal matrix whose diagonal elements are the singular values ​​of A0;

[0146] From equation (13), it can be seen that after the singular value decomposition, the pseudo-inverse matrix of the coefficient matrix A0 is V∑ as shown in equation (14). + U T ;∑ + It is a pseudo-inverse matrix of ∑;

[0147] The pseudo-inverse matrix V∑ of the coefficient matrix A0 after the singular value decomposition is... + U T Substituting into equation (9), we obtain equation (15):

[0148] D KTI =V∑ + U T D LOS (15):

[0149] The singular value decomposition and regularization methods used to obtain the coefficient matrix B are the same as those used to obtain the coefficient matrix A.

[0150] In step S4, the method for constructing the objective function includes:

[0151] By introducing a regularization term into equation (15), we obtain the objective function shown in equation (16):

[0152] J(D KTI )=||A·D KTI -D LOS || 2 +λ·(L·D KTI ) 2 (16);

[0153] In equation (16), J(D) KTIA·D represents the total error of three-dimensional deformation in the slope coordinate system; KTI -D LOS || 2 λ·(L·D) represents the square of the difference between the inverted value and the observed value of the deformation along the radar line of sight. KTI ) 2 is the regularization term, representing the regularization constraint; λ represents the regularization weight parameter, with a value range of 0 to 0.2; L represents the regularization matrix, which is taken as the identity matrix;

[0154] In the objective function shown in equation (16), D KTI Taking the partial derivative and setting it to zero, we obtain the regularized solution expression shown in equation (17):

[0155] D KTI =(A T A+λ·L T L) -1 ·A T D LOS (17);

[0156] At the preset deformation point, D calculated by equation (17) KTI Preset true values ​​of three-directional displacements in the known slope coordinate system (See Table 4) Compare the two, and use Equation (18) to calculate the error term e(λ):

[0157]

[0158] By combining equations (17) and (18), multiple values ​​of λ are input into equation (17), and equation (18) is repeatedly solved until the error term e(λ) in equation (18) converges to a minimum, thereby determining the optimal value of λ. The relationship between the slope three-dimensional deformation estimation results and the regularization weight parameters involved in this convergence process is described in [reference missing]. Figure 13 , Figure 14 , Figure 15 and Figure 16 .

[0159] Substituting the optimal value of λ into equation (17), the optimal three-dimensional surface deformation result D in the slope coordinate system is then calculated. KTI ; to make the optimal D KTI Substituting into equation (11), we obtain the optimal D. K D T and D I Regularization; to achieve optimal D K and D I Substituting the regularized solution into equation (12) yields the optimal lateral horizontal displacement D. H Finally, by D U Optimal DK and D H For details on obtaining the three-directional displacement of the slope, please refer to [link / reference]. Figure 9 , Figure 10 , Figure 11 and Figure 12 .

[0160] Table 4 shows the preset true values ​​of the three-directional displacements of CR3 and CR4 at different stations. (Unit: mm)

[0161]

[0162] The accuracy of the slope displacements in three directions obtained from step S4 was verified using the root mean square error. The verification results are shown in Table 5.

[0163] Table 5 Verification Results (Unit: mm)

[0164]

[0165]

[0166] As shown in Table 5, the slope displacement estimation method based on ground-based interferometric radar proposed in this embodiment achieves deformation monitoring accuracies of 0.4 mm, 0.4 mm, and 1.8 mm in the slope aspect, vertical direction, and lateral displacement, respectively. This method can provide new observation technologies and means for stability monitoring and disaster early warning of small and medium-sized slope projects, and improve the accuracy and reliability of ground-based SAR observation results for unstable slopes.

[0167] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A slope displacement estimation method based on ground-based interferometric radar, characterized in that, include: Step S1: Select at least three stations around the outer perimeter of the slope area and deploy multiple artificial corner reflectors on the slope area; A single ground-based interferometric radar was used to sequentially observe radar images of the slope area before and after deformation at each of the aforementioned stations. The deformation of the slope area is formed by moving at least two of the artificial corner reflectors to a preset deformation. Step S2: Perform pixel-by-pixel complex multiplication on the radar images before and after deformation corresponding to each station to form an interferogram; extract phase information from the interferograms of each station to obtain a phase map; perform filtering and phase unwrapping on the phase maps of each station in sequence to obtain a phase image with continuous real phase; extract the unwrapped phase from the pixel positions of each artificial corner reflector in the phase image of each station, and convert it to obtain the deformation in the radar line-of-sight direction of the corresponding station. Step S3: Decompose the deformation of the radar line-of-sight direction at each of the aforementioned stations into three-dimensional components in the geographic coordinate system, and construct a coefficient matrix. B A three-dimensional deformation observation equation function model in a geographic coordinate system; wherein, the coefficient matrix B The coefficient matrix is ​​obtained after singular value decomposition and regularization. Subsequently, the least squares method is used to process the three-dimensional deformation observation equation function model in the geographic coordinate system to obtain the best estimate of the three-dimensional surface deformation in the geographic coordinate system. Step S4: Rotate the three-dimensional components in the geographic coordinate system to obtain the three-dimensional components in the slope coordinate system of the slope area, and combine them with the best estimate of the three-dimensional surface deformation in the geographic coordinate system to obtain a coefficient matrix. A The three-dimensional deformation observation equation function model in the slope coordinate system; wherein, the coefficient matrix A The coefficient matrix is ​​obtained after singular value decomposition and regularization. Then, the least squares method is used to process the three-dimensional deformation observation equation function model in the slope coordinate system to obtain the best estimate of the three-dimensional surface deformation in the slope coordinate system. The three-dimensional displacement of the slope is obtained by constructing the objective function and solving it. In step S4, the three-dimensional components in the geographic coordinate system are rotated using equation (8) to obtain the three-dimensional components in the slope coordinate system of the slope area: （8）； In equation (8), , and These represent the slope direction displacement, perpendicular slope direction displacement, and normal displacement in the slope coordinate system, respectively. Indicates the slope of the slope area; Indicates the aspect angle of the slope area; The three-dimensional deformation observation equation function model in the slope coordinate system is represented by matrix expression (9): （9）； In equation (9), express , and The transpose of a single-column matrix formed by combination; A This represents the coefficient matrix after the singular value decomposition and regularization processes. A ; The coefficient matrix A The coefficient matrix before the singular value decomposition and regularization processes is: A 0, which is represented by equation (10): （10）； The least squares method is used to process equation (9) to obtain the optimal estimate of the three-dimensional surface deformation in the slope coordinate system shown in equation (11): （11）； From equation (11) we get , and Regularization; use and The horizontal displacement is obtained by regularization from equation (12). : （12）； Depend on , and The three-directional displacements of the slope were obtained; In step S4, equation (13) is used to modify the coefficient matrix. A 0. Perform the singular value decomposition process as described above: （13）； In equation (13), U and V It is an orthogonal matrix, that is, it satisfies U T U=I and V T V=I ; I Represents the identity matrix; U The set of left singular vectors; V The set of right singular vectors; It is a diagonal matrix with diagonal elements as follows: A Singular values ​​of 0; From equation (13), we know that the coefficient matrix A After the singular value decomposition process, the pseudo-inverse matrix of 0 is shown in equation (14). ; yes The pseudo-inverse matrix; The coefficient matrix A 0. The pseudo-inverse matrix after the singular value decomposition process Substituting into equation (9), we obtain equation (15): （15）： Obtain the coefficient matrix B The singular value decomposition and regularization methods used to obtain the coefficient matrix are described above. A The singular value decomposition and regularization processes used are the same. In step S4, the method for constructing the objective function includes: Introducing a regularization term into equation (15) yields the objective function shown in equation (16): （16）； In equation (16), This represents the total error of three-dimensional deformation in the slope coordinate system; This represents the square of the difference between the inverted value and the observed value of the deformation along the radar line of sight. is the regularization term, representing the regularization constraint; λ represents the regularization weight parameter, whose value ranges from 0 to 0.2; L This represents the regularization matrix, which is taken as the identity matrix. In the objective function shown in equation (16), for Taking the partial derivative and setting it to zero, we obtain the regularized solution expression shown in equation (17): （17）； At the preset deformation point, the solution obtained from equation (17) Preset true values ​​of three-directional displacements in the known slope coordinate system Compare the two and use equation (18) to calculate the error term. : （18）； By combining equations (17) and (18), inputting multiple different values ​​of λ into equation (17), and repeatedly solving through equation (18) until the error term in equation (18) is reached. The convergence to the minimum is used to determine the optimal value of λ. Substituting the optimal value of λ into equation (17), the optimal three-dimensional surface deformation result in the slope coordinate system is then calculated. ; will be optimal Substituting into equation (11), we obtain the optimal result. , and Regularization; optimizing and Substituting the regularized solution into equation (12) yields the optimal lateral horizontal displacement. Finally, by Optimal and The displacements of the slope in three directions are obtained.

2. The slope displacement estimation method based on ground-based interferometric radar according to claim 1, characterized in that, In step S1, the baseline length between any two adjacent stations is greater than 10m, and the stations are not collinear; each station has a line of sight to the slope area. The observation time interval between any two adjacent stations of the ground-based interferometric radar is no greater than 2 minutes. The deformation direction of the preset deformation includes the direction along the slope, the direction perpendicular to the slope, and the horizontal direction; wherein, the horizontal direction is the direction perpendicular to the road direction.

3. The slope displacement estimation method based on ground-based interferometric radar according to claim 1, characterized in that, In step S2, the phase diagram is expressed by equation (1): （1）； In equation (1), This represents the original interference phase of the phase diagram; This represents the phase function of a complex number; Represents the complex values ​​of the interferogram; The phase image is represented by equation (2): （2）； In equation (2), This indicates the interference phase after unwrapping, expressed in radians. This represents the phase unwrapping algorithm function, used to remove 2π jumps and restore phase continuity; The conversion process is represented by equation (3): （3）； In equation (3), λ represents the deformation along the radar line of sight at a certain station; λ0 represents the radar wavelength of the ground-based interferometric radar; This represents the unwrapped phase difference between the radar image before deformation and the radar image after deformation at a certain station.

4. The slope displacement estimation method based on ground-based interferometric radar according to claim 1, characterized in that, In step S3, the three-dimensional deformation observation equation function model in the geographic coordinate system is represented by equation (4): （4）； In equation (4), , ... These respectively represent the locations at station 1, station 2, and station 3. i Deformation along the radar line-of-sight direction obtained at the location; i The value of is greater than or equal to 3; , and These represent the east-west deformation, north-south deformation, and vertical deformation in the geographic coordinate system, respectively. B This represents the coefficient matrix after the singular value decomposition and regularization processes. B ; The coefficient matrix B The coefficient matrix before the singular value decomposition and regularization processes is: B 0, which is represented by equation (5): （5）； In equation (5), , ... These represent the ground-based interferometric radars at stations 1, 2, and 3 respectively. i Angle of incidence at the point; , ... These represent the ground-based interferometric radars at stations 1, 2, and 3 respectively. i The direction angle at the location; From equation (4), we obtain the matrix expression (6): （6）； In equation (6), It is by , ... The transpose of a single-column matrix formed by combination; This represents the three-dimensional surface deformation in a geographic coordinate system, which is caused by... , and The transpose of a single-column matrix formed by combination; The least squares method is used to process equation (6) to obtain the optimal estimate of three-dimensional surface deformation in the geographic coordinate system shown in equation (7): （7）。 5. The slope displacement estimation method based on ground-based interferometric radar according to claim 1, characterized in that, The slope area has a width of 10-500m and a length of 10-500m.

6. A storage medium, characterized in that, The storage medium stores a computer program, which includes program instructions that, when executed by a processor, cause the processor to perform the slope displacement estimation method based on ground-based interferometric radar as described in any one of claims 1 to 5.

7. An electronic device, characterized in that, The device includes a processor and a memory, the processor being interconnected with the memory, wherein the memory is used to store a computer program supporting the electronic device, the computer program including program instructions, and the processor is configured to invoke the program instructions to execute the slope displacement estimation method based on ground-based interferometric radar as described in any one of claims 1 to 5.

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