A long-distance and high-precision deformation measurement method based on corner reflector SAR phase information

Abstract

The present invention belongs to the field of synthetic aperture radar (SAR) and discloses a long-distance, high-precision deformation measurement method based on corner reflector (SAR) phase information. The method comprises the following steps: S1, filtering a SAR image using an improved Lee filter algorithm to obtain a filtered SAR image; S2, performing registration processing on the filtered SAR image; S3, obtaining the position of each corner reflector in the registered SAR image; S4, estimating the elevation of the corner reflector; S5, compensating for the ground phase and the elevation phase to obtain an initial deformation phase; S6, unwrapping the initial deformation phase to obtain the true deformation phase of each corner reflector; and S7, obtaining the deformation amount based on the true deformation phase. By improving the existing Lee filter algorithm and filtering the SAR image based on an adaptive filter value, the present invention can effectively filter while avoiding oversmoothing, thereby facilitating the acquisition of more accurate deformation measurement results.

Description

Technical Field

[0001] The present invention relates to the field of synthetic aperture radar (SAR), and in particular to a long-distance high-precision deformation measurement method based on corner reflector SAR phase information. Background Art

[0002] SAR, or synthetic aperture radar, is an active Earth observation system that can be installed on platforms such as aircraft, satellites, and spacecraft. It provides 24 / 7, all-weather Earth observation and possesses a certain degree of surface penetration. Therefore, SAR systems offer unique advantages in disaster monitoring, environmental monitoring, oceanographic surveillance, resource exploration, crop yield estimation, surveying and mapping, and military applications, enabling them to perform functions that are difficult to achieve with other remote sensing methods.

[0003] When measuring deformation of a device based on SAR images, it is usually necessary to filter the SAR images first. In the existing technology, the Lee filter algorithm is generally used for filtering. However, the Lee filter algorithm requires the size of the filter window to be specified in advance during the noise reduction process. If the filter window is too large, it is easy to over-smooth the image, resulting in loss of details or blurring. If the filter window is too small, it is more affected by local noise, resulting in poor noise reduction effect. Summary of the Invention

[0004] The purpose of the present invention is to disclose a long-distance high-precision deformation measurement method based on corner reflector SAR phase information to solve the technical problems pointed out in the background technology.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] The present invention provides a long-distance high-precision deformation measurement method based on corner reflector SAR phase information, comprising:

[0007] S1, filtering the SAR image using an improved Lee filtering algorithm to obtain a filtered SAR image;

[0008] S2, performing registration processing on the filtered SAR image;

[0009] S3, obtaining the position of each corner reflector in the registered SAR image;

[0010] S4, estimate the elevation of the corner reflector;

[0011] S5, compensating the flat ground phase and the elevation phase to obtain the initial deformation phase;

[0012] S6, unwrapping the initial deformation phase to obtain the true deformation phase of each corner reflector;

[0013] S7, obtaining the deformation amount based on the true deformation phase;

[0014] Among them, S1 includes:

[0015] Each pixel in the SAR image is filtered in the following way to obtain a filtered SAR image:

[0016] For pixel point p in the SAR image, calculate the adaptive filtering value of p;

[0017] Filter p based on the adaptive filter value to obtain a pixel value of p after filtering.

[0018] Preferably, the calculation formula of the adaptive filtering value is:

[0019]

[0020] adpw p represents the adaptive filter value, pres represents the preset logarithmic parameter, wp represents the set of pixels in a 5×5 window centered on p, nwp represents the total number of pixels in wp, pxl i Represents the pixel value of pixel i, pxl p Represents the pixel value of pixel point p.

[0021] Preferably, S2 includes:

[0022] During the registration process, one SAR image is selected from multiple SAR images as a reference image, and the remaining images are registered to the grid where the reference image is located.

[0023] Preferably, S3 includes:

[0024] Perform interpolation processing on the registered SAR image to obtain an interpolated image;

[0025] Get the position of each corner reflector in the interpolated image.

[0026] Preferably, S4 includes:

[0027] Generate an interferogram based on two SAR images taken adjacently in time;

[0028] The correlation formula between the phase difference ΔΦ and the elevation in the interferogram is obtained:

[0029]

[0030] h represents the elevation, λ is the wavelength of the SAR signal, and θ is the angle between the SAR signal and the ground;

[0031] Calculate h:

[0032]

[0033] Preferably, S5 includes:

[0034] Use the following formula to calculate the flat ground phase difference:

[0035] ΔΦflat=Φactual-Φflat

[0036] ΔΦflat is the flat-ground phase difference; Φactual is the actual phase of the corner reflector; Φflat is the theoretical flat-ground phase of the corner reflector when the ground is completely flat;

[0037] Calculate the elevation phase difference:

[0038]

[0039] ΔΦheight is the elevation phase difference; hcorner is the actual elevation of the corner reflector; hflat is the assumed elevation of an ideal flat ground; λ is the wavelength of the SAR signal;

[0040] Calculate the atmospheric delay phase:

[0041]

[0042] represents the atmospheric delay phase, Δd represents the atmospheric delay from the zenith;

[0043] The initial deformation phase is obtained by subtracting the ground phase difference, elevation phase difference and atmospheric delay phase from the interference phase of the corner reflector.

[0044] Preferably, S6 includes:

[0045]

[0046] n is an integer representing the integer ambiguity, represents the true deformation phase, represents the initial deformation phase.

[0047] Preferably, S7 includes:

[0048]

[0049] wd represents the deformation variable.

[0050] Beneficial effects:

[0051] Compared with the existing technology, the present invention improves the existing Lee filtering algorithm and filters the SAR image based on the adaptive filtering value. It can effectively filter while avoiding over-smoothing. It can not only effectively reduce the probability of events where the filtering window is too large or too small, but also effectively improve the quality of filtering, which is conducive to obtaining more accurate deformation measurement results. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0053] Figure 1 This is a schematic diagram of a long-distance, high-precision deformation measurement method based on corner reflector SAR phase information of the present invention.

[0054] Figure 2 This is the optical image distribution diagram of the corner reflector.

[0055] Figure 3 Schematic diagram of corner reflector signal in SAR image.

[0056] Figure 4 This is the distribution map of corner reflector SAR images.

[0057] Figure 5 This is the distribution map of SAR images of power tower corner reflectors.

[0058] Figure 6 This is a schematic diagram of GACOS atmospheric data.

[0059] Figure 7 It is a Delaunay triangulation diagram.

[0060] Figure 8a Schematic diagram of the time-series deformation of the corner reflector of Tower 1.

[0061] Figure 8b Schematic diagram of the time-series deformation of the corner reflector of Tower 2.

[0062] Figure 8c Schematic diagram of the time-series deformation of the corner reflector of Tower 3. DETAILED DESCRIPTION

[0063] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0064] like Figure 1 In one embodiment shown, the present invention provides a long-distance, high-precision deformation measurement method based on corner reflector SAR phase information, comprising:

[0065] S1, filtering the SAR image using an improved Lee filtering algorithm to obtain a filtered SAR image;

[0066] S2, performing registration processing on the filtered SAR image;

[0067] S3, obtaining the position of each corner reflector in the registered SAR image;

[0068] S4, estimate the elevation of the corner reflector;

[0069] S5, compensating the flat ground phase and the elevation phase to obtain the initial deformation phase;

[0070] S6, unwrapping the initial deformation phase to obtain the true deformation phase of each corner reflector;

[0071] S7, obtaining the deformation amount based on the true deformation phase;

[0072] Among them, S1 includes:

[0073] Each pixel in the SAR image is filtered in the following way to obtain a filtered SAR image:

[0074] For pixel point p in the SAR image, calculate the adaptive filtering value of p;

[0075] Filter p based on the adaptive filter value to obtain a pixel value of p after filtering.

[0076] The present invention improves the existing Lee filtering algorithm and filters SAR images based on adaptive filtering values. It can effectively filter while avoiding over-smoothing. It can not only effectively reduce the probability of events where the filter window is too large or too small, but also effectively improve the quality of filtering, which is conducive to obtaining more accurate deformation measurement results.

[0077] Preferably, the calculation formula of the adaptive filtering value is:

[0078]

[0079] adpw p represents the adaptive filter value, pres represents the preset logarithmic parameter, wp represents the set of pixels in a 5×5 window centered on p, nwp represents the total number of pixels in wp, pxl i Represents the pixel value of pixel i, pxl p Represents the pixel value of pixel point p.

[0080] The adaptive filtering value of the present invention is calculated from the ratio between the pixel value of a pixel point and the variance of the pixel values of pixels in the neighborhood. When the local signal-to-noise ratio of the neighborhood is higher and the image noise level is lower, the adaptive filtering value is larger.

[0081] Specifically, the pixel value of a pixel point may be an amplitude.

[0082] Specifically, the set logarithm parameter may be 10.

[0083] Preferably, filtering p based on the adaptive filter value to obtain the pixel value of p after filtering includes:

[0084] Using apxl p Indicates the pixel value of p after filtering p, apxl p The calculation formula is:

[0085]

[0086] pxl ave represents the average value of the pixel values in sp, σ represents the noise standard deviation, u represents the noise mean, and sp represents the side length L centered on p. p The set of pixels within the range, pxl i is the pixel value of pixel i, pxl p The pixel value nsp of pixel p represents the number of pixels in sp;

[0087]

[0088] adpwm represents the maximum value of the adaptive filtering value of the pixel in the SAR image, and Lstd represents the preset length.

[0089] When filtering p, the present invention calculates the size of the filter window based on the adaptive filter value. Therefore, when the adaptive filter value is larger, the filter window length is smaller, and when the adaptive filter value is smaller, the filter window length is larger, thereby achieving adaptive variation of the filter window length. When the noise level is higher, a larger window can be used for effective noise reduction; when the noise level is lower, filtering efficiency can be improved by reducing the filter window.

[0090] Specifically, the preset length is 10.

[0091] Preferably, S2 includes:

[0092] During the registration process, one SAR image is selected from multiple SAR images as a reference image, and the remaining images are registered to the grid where the reference image is located.

[0093] Preferably, S3 includes:

[0094] Perform interpolation processing on the registered SAR image to obtain an interpolated image;

[0095] Get the position of each corner reflector in the interpolated image.

[0096] Preferably, S4 includes:

[0097] Generate an interferogram based on two SAR images taken adjacently in time;

[0098] The correlation formula between the phase difference ΔΦ and the elevation in the interferogram is obtained:

[0099]

[0100] h represents the elevation, λ is the wavelength of the SAR signal, and θ is the angle between the SAR signal and the ground;

[0101] Calculate h:

[0102]

[0103] InSAR technology uses interferometric phase information to invert target deformation characteristics. However, according to the InSAR principle, the interferometric phase includes not only the phase introduced by target deformation but also the phase introduced by various other factors. To achieve high-precision deformation measurement, the key is to accurately compensate for the phase introduced by these various factors.

[0104] Preferably, S5 includes:

[0105] Use the following formula to calculate the flat ground phase difference:

[0106] ΔΦflat=Φactual-Φflat

[0107] ΔΦflat is the flat-ground phase difference; Φactual is the actual phase of the corner reflector; Φflat is the theoretical flat-ground phase of the corner reflector when the ground is completely flat;

[0108] Calculate the elevation phase difference:

[0109]

[0110] ΔΦheight is the elevation phase difference; hcorner is the actual elevation of the corner reflector; hflat is the assumed elevation of an ideal flat ground; λ is the wavelength of the SAR signal;

[0111] When there's a lack of experience processing InSAR data or the amount of SAR data is small, conventional linear atmospheric phase simulation methods struggle to accurately estimate the atmospheric delay phase. While these methods can reduce the standard deviation of the interferogram, they don't significantly improve the deformation time series. Deformation measurement methods based on corner reflector SAR phase signals often require limited SAR data. Directly utilizing the GACOS external atmosphere model can, to a certain extent, mitigate the effects of atmospheric delay, thereby obtaining the surface deformation phase.

[0112] Calculate the atmospheric delay phase:

[0113]

[0114] represents the atmospheric delay phase, Δd represents the atmospheric delay from the zenith;

[0115] Since GACOS is a zenith distance measurement, the GACOS data must first be geocoded based on the satellite orbit and the intensity image simulated by the DEM. Then, the GACOS data is temporally differentiated based on the baseline interferometry set generated previously to obtain an atmospheric delay differential pair at the same time as the interferometry pair. During spatial differentiation, the set reference point is used as the atmospheric delay spatial differential point.

[0116] The initial deformation phase is obtained by subtracting the ground phase difference, elevation phase difference and atmospheric delay phase from the interference phase of the corner reflector.

[0117] In the present invention, an interferometer pair can first be constructed based on temporally adjacent SAR images. Within adjacent time periods, the deformation of the corner reflector is relatively small, resulting in a relatively small deformation phase, allowing for more accurate elevation estimation based on the interferometric phase. Subsequently, an interferogram is reconstructed using one image as the primary image and the other images as secondary images. Based on the high-precision row and column position data and high-precision elevation data h of the corner reflector in the primary image, combined with the Doppler equation, slant range equation, and ellipsoid equation, the spatial position coordinates of each corner reflector in WGS84 are calculated. Because the corner reflector's position and elevation data are very precise, the calculated reference phase is highly accurate, effectively compensating for the two phase terms in the interferometric phase.

[0118] Preferably, S6 includes:

[0119] After the above steps, after compensating the flat ground phase and elevation phase, the deformation phase is obtained Wrapped in the interval [-π, π). In order to restore the true deformation phase of the target point The phase data needs to be unwrapped:

[0120]

[0121] n is an integer representing the integer ambiguity, represents the true deformation phase, represents the initial deformation phase.

[0122] In the actual data error optimization process, the reference corner reflector and the other corner reflectors are connected by Delaunay triangulation. However, the distance between individual corner reflectors is far, and the deformation phase after unwrapping may contain abnormal values.

[0123] The use of least squares estimation in the error optimization process is easily affected by outliers and may produce a certain degree of deviation from the actual deformation phase. To improve the reliability of the relative deformation estimation of the corner reflector, the present invention uses a robust M-estimator to optimize the deformation phase change between each arc segment. Utilizing the idea of weighted least squares, points with large residuals are given lower weights during the iterative process, while the weights of points with normal residuals remain unchanged. This can suppress the impact of outliers on the optimization results to a certain extent, making the final estimate more stable and reliable.

[0124] The optimization process is as follows:

[0125] a) First, the deformation phase between corner reflectors can be expressed as follows:

[0126] Δφ=Vα+e (4)

[0127] Where V is the correction factor, α is the unknown parameter, and Δφ is the actual observation value.

[0128] b) In robust estimation, Equation (4) can be converted into a least squares problem, where l represents the number of observations, as shown in Equation (5). As a traditional robust estimation method, when the observations follow a normal distribution, the least squares estimate is the optimal linear unbiased estimate with optimal statistical properties. However, when the observations contain outliers, the assumption that the observations come from a specific normal distribution does not hold. The least squares estimate naturally no longer has the properties of an optimal estimate, and the parameter estimates are often corrupted by a few outliers.

[0129]

[0130] In practice, observational data do not follow a specific distribution. Least squares is only an ideal estimation method and cannot produce reliable results when faced with unknown distribution patterns. Robust estimation theory addresses this issue by minimizing the impact of unavoidable outliers on the overall results, resulting in optimal or near-optimal deformation observations.

[0131] c) There are many estimation methods for M estimation. The easiest one to implement is based on the weighted iteration method, which uses the iterative reweighted least squares algorithm to solve the position parameters. In this case, Equation (5) can be expressed as where e l =Δφ l -v l α, the specific formula is as follows:

[0132] α i+1 =(V T W i V) (-1) V T W i Δφ (6)

[0133] α i+1 Represents the iterative solution, i represents the number of iterations. It is not difficult to find that when the number of iterations is 0, Equation (6) is the same as the most primitive unweighted least squares algorithm. Set the initial weight matrix to the unit matrix:

[0134] W i＝0 =I M (7)

[0135] Then, the unknown parameter α is obtained by solving i+1 , calculate the residual of each observation value, and use the HuBer loss function to update the weights of different observation results during the iteration process, as shown in formula (8)

[0136]

[0137] Where,

[0138] e i is the residual value after the i-th iteration, and k is a pre-given threshold used to limit the normal range of residual variation. Residuals greater than the threshold are considered outliers, and the absolute value loss is used to reduce the weight of outliers in the estimation; otherwise, they are considered normal values, and the square loss is used to obtain an unbiased estimate of the parameters.

[0139] Finally, the iterative reweighted least squares process is performed until the residual value meets the set requirements to obtain the final optimization result.

[0140] Usually k can be taken as 2σ. In this case, taking the first-order derivative of equation (8) yields:

[0141]

[0142] The corresponding weight function can be solved:

[0143]

[0144] The Huber weight function shows that when all residual values are between -2σ and 2σ, the Huber estimate is the same as the classical least squares estimate. However, when the absolute value of the residual value of some observations is greater than 2σ, the corresponding weight decreases, which means that these observations have little influence on the parameter estimate. When the absolute value of the residual value of an observation is much greater than 2σ, the corresponding weight approaches zero, and the influence of these observations on the parameter estimate is almost negligible.

[0145] In summary, the use of Huber loss function when updating weights has a certain weakening effect on outliers, which enables it to better adapt to the overall distribution of data and provide a more robust model for the optimization of corner reflector shape.

[0146] Preferably, S7 includes:

[0147]

[0148] wd represents the deformation variable.

[0149] For X-band data, when the wavelength λ is 3.1 cm, in order to achieve a deformation measurement accuracy of 1 mm, The accuracy must reach 0.4rad.

[0150] Based on high-resolution time-series SAR data, the present invention first accurately extracts the position and phase data of the corner reflectors in each image. Subsequently, interferometric pairs are formed using temporally adjacent SAR images. Based on the known rough elevation of the corner reflectors, the elevation data of the corner reflectors is more accurately estimated. Next, a SAR image is selected as the primary image to construct the interferometric pair. The accurate position and elevation data of the corner reflectors are used to precisely compensate for the flat ground phase and elevation phase. This is then compensated for using the external atmospheric delay model GACOS to obtain a highly accurate deformation phase. Phase unwrapping is then performed to obtain the unwrapped deformation phase of each corner reflector. Based on this, the M-estimator proposed by Huber is used to optimize the observed values for error, thereby improving the stability of the observation results. Finally, deformation inversion processing is performed to extract the deformation information of each corner reflector. This method utilizes remote sensing non-contact measurement technology, achieving a deformation measurement accuracy of 1 mm. It can accurately obtain deformation data at key points, providing efficient technical support for deformation monitoring of key points in infrastructure such as power towers, reservoir dams, and bridges. The present invention improves the applicability of corner reflector deformation monitoring technology in long-interval monitoring equipment scenarios and provides technical support for the engineering application of this technology.

[0151] The following is a more specific example:

[0152] In this embodiment, 12 corner reflectors are installed on three power towers. In addition, a corner reflector is set up around the tower as a reference point to measure the relative deformation of the tower. The distribution of the corner reflectors is as follows: Figure 2 In the experiment, 3m resolution COSMO-SkyMed data was used to monitor the deformation of the corner reflector. The SAR data parameters are shown in Table 1.

[0153] Table 1 Basic information of COSMO-SkyMed data used in the experiment

[0154] parameter Numerical Satellite type COSMO-SkyMed track Lowering orbit Spatial resolution 3m×3m Polarization HH Number of images 10 Monitoring start time 20230814 Monitoring end time 20231227

[0155] Step 1:

[0156] First, Sinc interpolation is performed on the signals around the corner reflector, and the interpolation multipliers in the range and azimuth directions are set to 100. The interpolation of the GCP points in the SAR image is as follows: Figure 3 As shown, the precise position coordinates of the corner reflector are then found based on each interpolated image. Figure 4 is the distribution map of corner reflector SAR images, Figure 5The precise position distribution of the corner reflectors installed on Tower 1 in the SAR image. Since the satellite adopts a descending right-looking shooting method, P1 is blocked, resulting in a weak signal. Three corner reflectors were monitored this time, namely P2, P3, and P4. P10 and P11 were monitored on Tower 2, and P5, P6, and P7 were monitored on Tower 3. The corner reflectors not monitored above are not included in the deformation solution.

[0157] Step 2:

[0158] Based on the 10 images in this case study, we combined images from two adjacent dates into interferometric pairs to obtain the interferometric phase and perform a high-precision estimation of the corner reflector's elevation phase. We then selected the 20231102 image as the primary image to construct the interferometric pair. We then obtained the interferometric phase at the corner reflector's location and used the high-precision elevation data and corner reflector position data to compensate for the elevation and flat ground phases.

[0159] GACOS data based on weather models, due to its high temporal and spatial resolution and integration with GNSS observation data, can directly estimate the delay phase and has unique advantages in tropospheric delay correction. First, external atmospheric correction data GACOS is obtained based on the date and accurate time of image shooting. Figure 6 This is the GACOS atmospheric data for August 14, 2023. The GACOS data are temporally differentiated based on the baseline interferometric set to obtain atmospheric delay differential pairs with the same time as the interferometric image pairs. During spatial differentiation, a pre-set reference point is used as the atmospheric delay spatial differential point. The zenith distance atmospheric delay data is then converted into the atmospheric delay phase for InSAR processing. Finally, the deformation phases of all corner reflectors are obtained. Phase unwrapping is performed using the minimum cost flow method based on the reference point to obtain the deformation phase of each corner reflector relative to the reference corner reflector.

[0160] Step 3:

[0161] Connect each corner reflector through the Delaunay triangulation, such as Figure 7 Then, based on the unwrapped deformation phase, the M-estimator proposed by Huber is used to optimize the error of the observation value to improve the stability of the observation results. Finally, the deformation results of the corner reflectors on the three towers that can be monitored are obtained, as shown in Figures 8a-8c From the eight corner reflectors monitored, the maximum cumulative settlements of Tower 1, Tower 2, and Tower 3 from August to December 2023 were 13.2 mm, 20.9 mm, and 6.8 mm, respectively. The overall situation is relatively stable, but further observation is needed to see if there is uneven settlement at the tower bases. Figure 8a For the electric tower, Figure 8b For the second tower, Figure 8c It is the third electric tower.

[0162] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A long-distance high-precision deformation measurement method based on corner reflector SAR phase information, characterized in that: include: S1, filtering the SAR image using an improved Lee filtering algorithm to obtain a filtered SAR image; S2, performing registration processing on the filtered SAR image; S3, obtaining the position of each corner reflector in the registered SAR image; S4, estimate the elevation of the corner reflector; S5, using the interference phase of the corner reflector to subtract the ground phase difference, elevation phase difference and atmospheric delay phase to obtain the initial deformation phase; S6, unwrapping the initial deformation phase to obtain the true deformation phase of each corner reflector; S7, obtaining the deformation amount based on the true deformation phase; Among them, S1 includes: Each pixel in the SAR image is filtered in the following way to obtain a filtered SAR image: For pixel point p in the SAR image, calculate the adaptive filtering value of p; Filtering p based on the adaptive filter value to obtain a pixel value of p after filtering; The calculation formula of the adaptive filter value is: adpw p represents the adaptive filter value, pres represents the preset logarithmic parameter, wp represents the set of pixels in a 5×5 window centered on p, nwp represents the total number of pixels in wp, pxl i Represents the pixel value of pixel i, pxl p Represents the pixel value of pixel p; Filtering p based on the adaptive filter value to obtain a pixel value of p after filtering includes: Using apxl p Indicates the pixel value of p after filtering p, apxl p The calculation formula is: pxl ave represents the average value of the pixel values in sp, σ represents the noise standard deviation, u represents the noise mean, and sp represents the side length L centered on p. p The set of pixels within the range, pxl i is the pixel value of pixel i, pxl p The pixel value nsp of pixel p represents the number of pixels in sp; adpwm represents the maximum value of the adaptive filtering value of the pixel in the SAR image, and Lstd represents the preset length.

2. The long-distance high-precision deformation measurement method based on corner reflector SAR phase information according to claim 1 is characterized in that S2 include: During the registration process, one SAR image is selected from multiple SAR images as a reference image, and the remaining images are registered to the grid where the reference image is located.

3. The long-distance high-precision deformation measurement method based on corner reflector SAR phase information according to claim 1 is characterized in that: S3 includes: Perform interpolation processing on the registered SAR image to obtain an interpolated image; Get the position of each corner reflector in the interpolated image.

4. The long-distance high-precision deformation measurement method based on corner reflector SAR phase information according to claim 1, characterized in that S4 include: Generate an interferogram based on two SAR images taken adjacently in time; The correlation formula between the phase difference ΔΦ and the elevation in the interferogram is obtained: h represents the elevation, λ is the wavelength of the SAR signal, and θ is the angle between the SAR signal and the ground; Calculate h:

5. The long-distance high-precision deformation measurement method based on corner reflector SAR phase information according to claim 1, characterized in that S5 include: Use the following formula to calculate the flat ground phase difference: ΔΦflat=Φactual-Φflat ΔΦflat is the flat-ground phase difference; Φactual is the actual phase of the corner reflector; Φflat is the theoretical flat-ground phase of the corner reflector when the ground is completely flat; Calculate the elevation phase difference: ΔΦheight is the elevation phase difference; hcorner is the actual elevation of the corner reflector; hflat is the assumed elevation of an ideal flat ground; λ is the wavelength of the SAR signal; Calculate the atmospheric delay phase: represents the atmospheric delay phase, Δd represents the atmospheric delay from the zenith; The initial deformation phase is obtained by subtracting the ground phase difference, elevation phase difference and atmospheric delay phase from the interference phase of the corner reflector.

6. The long-distance high-precision deformation measurement method based on corner reflector SAR phase information according to claim 5 is characterized in that S6 include: n is an integer representing the integer ambiguity, represents the true deformation phase, represents the initial deformation phase.

7. The long-distance high-precision deformation measurement method based on corner reflector SAR phase information according to claim 6, characterized in that S7 include: wd represents the deformation variable.

Images