A Large Gradient Phase Optimization Method for Mining Areas Based on Probabilistic Integral Model

Abstract

This invention discloses a method for optimizing the phase of a mining area with a large gradient based on a probabilistic integral model, comprising: estimating the prior deformation variables of the mining area at different time periods by combining SAR image dates and prior probabilistic integral model parameters; converting the prior temporal deformation variables into radar line-of-sight deformation variables by combining satellite image parameters, and then converting the deformation variables into prior deformation phase values; constructing a full interferometric pair network based on SAR image data, removing the prior deformation phase from the differential interferometric phase to obtain the residual interferometric phase; selecting a homogeneous pixel set based on temporal amplitude values, calculating the coherence value of the residual phase, and constructing a complex coherence matrix; constructing a phase optimization model based on a coherence power weighting strategy to estimate the phase optimization estimate corresponding to the residual phase; and constructing a short-spatial-temporal baseline interferometric pair network to combine the interferometric phase calculated by the phase optimization estimate with the prior deformation phase of the same period to obtain the final optimized interferometric phase.

Description

Technical Field

[0001] This invention belongs to the field of time-series SAR data processing technology for monitoring large gradient time-series deformation in mining areas, and particularly relates to a phase optimization method for large gradient time-series deformation in mining areas based on a probability integral model. Background Technology

[0002] Temporal synthetic aperture radar interferometry (TSInSAR) technology, through long-term sequence analysis of multiple SAR images, effectively compensates for the shortcomings of differential InSAR technology affected by spatiotemporal decoherence, further improving deformation monitoring accuracy from centimeter-level to millimeter-level, thus demonstrating broader application prospects in fields such as earthquakes, landslides, mining subsidence, and urban health monitoring. However, since permanent scatterers are mostly distributed in artificial surface areas with strong ground reflection, such as buildings and bridges, monitoring in non-artificial surface areas such as farmland and forests suffers from insufficient monitoring point density and limited monitoring accuracy. To address this, TSInSAR technology based on distributed scatterers has been widely developed. Its widespread distribution in non-artificial surface areas such as rural and mountainous regions effectively compensates for the lack of permanent scatterers, improving the effectiveness and reliability of non-artificial surface deformation monitoring. Unlike permanent scatterer points with a dominant scatterer, DS point-resolution cells consist of multiple sub-scatterers with similar characteristics and no dominant scatterer. This makes DS points susceptible to temporal and geometric decoherence, resulting in poor phase quality and severely limiting the interpretation accuracy of phase information. Therefore, phase optimization processing, aimed at improving the phase signal-to-noise ratio, is an indispensable key step in time-series monitoring applications based on DS-based TSInSAR technology. Based on the analysis of the general function model for phase optimization, current research on phase optimization methods mainly focuses on unbiased coherence estimation, weight factor setting, and efficient model solution. However, research on the phase ambiguity problem at dense fringes corresponding to large-gradient deformation is still lacking. When estimating the covariance matrix, homogeneous filtering based on homogeneous pixel sets is commonly used to obtain interferometric phase information. However, homogeneous pixel identification usually only considers image amplitude information and does not consider phase fringe variation information. Therefore, homogeneous filtering based on this method easily leads to the loss of phase information at dense fringes. Especially for large-gradient deformation fields caused by mining in mining areas, existing phase optimization methods still cannot effectively balance the protection of phase information at dense fringes and the improvement of the phase signal-to-noise ratio, severely limiting the interpretation accuracy of surface deformation information in mining areas. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a large gradient phase optimization method for mining areas based on a probability integral model. The method uses a probability integral model to estimate prior deformation information in the mining area, and combines the correlation model between the estimated quantity and the deformation along the radar line of sight to obtain prior phase information and residual phase. By performing coherence estimation and covariance matrix construction on the residual phase, and combining a coherence power-weighted strategy, the phase optimization process of the residual phase is completed. Finally, by compensating for the prior phase, the optimized interference phase is obtained.

[0004] To achieve the above objectives, this invention provides a method for optimizing the phase of a mining area with a large gradient based on a probability integral model, comprising the following steps:

[0005] Based on SAR image data of the mining area, the image dates are obtained; the time intervals between different dates are calculated, and the prior deformation variables of the mining area under different time periods are estimated by combining the probability integral model.

[0006] By combining SAR image data, the prior deformation variables of the mining area are converted into radar line-of-sight deformation variables, and the radar line-of-sight deformation variables are converted into prior deformation phase.

[0007] A full interferometric pair network is constructed based on the SAR image data, the differential interferometric phase of the full interferometric pair is obtained, the prior deformation phase is removed from the differential interferometric phase, and the residual phase of the full interferometric pair is obtained.

[0008] Based on the confidence interval hypothesis testing method, a homogeneous set of pixels is selected in combination with the temporal amplitude values ​​of the SAR image data; the coherence value of the residual phase is obtained based on the homogeneous set of pixels, and a complex coherence matrix is ​​constructed by combining the residual phase and the corresponding coherence value.

[0009] A phase optimization model based on a coherence power-weighted strategy is constructed, and the phase optimization estimate corresponding to the residual phase is obtained by combining the complex coherence matrix.

[0010] A short-spatial baseline interferometric pair network is constructed based on the SAR image data. The differential interferometric phase of the corresponding interferometric pair is obtained through the phase optimization estimate. Combined with the prior deformation phase of the same period, the optimized interferometric phase is obtained.

[0011] Optional methods for estimating prior deformations of the mining area at different time periods include:

[0012] Based on the probability integral model, combined with the subsidence of surface points caused by coal seam mining in the mining area and the Knothe time function, the deformation variables under different time intervals are obtained;

[0013] Based on the image dates obtained from the SAR image data, the time intervals for different dates are calculated, and combined with the probability integral model, the prior deformation variables of the mining area under different time periods are estimated.

[0014] Optionally, the method for determining the subsidence of surface points caused by coal seam mining in a mining area is as follows:

[0015]

[0016] W0=mqcosα

[0017] l = D3 - S4

[0018] L=(D1-S2)cosα

[0019] Where W(x,y) is the settlement, x and y are the x-coordinates and y-coordinates of the surface point, respectively, W0 is the maximum subsidence of the surface point, m is the normal mining thickness of the coal seam, q is the subsidence coefficient, α is the dip angle of the coal seam, l is the equivalent integral strike length of the working face, D3 and D1 are the strike length and dip length of the working face, respectively, S1, S2, S3 and S4 are the inflection point offset distances in the downhill direction, uphill direction, left strike direction and right strike direction, respectively, and L is the equivalent integral dip width of the working face.

[0020] Optionally, the method for converting the prior deformation variables of the mining area into radar line-of-sight deformation variables by combining SAR image data is as follows:

[0021]

[0022] Where x and y are the x-coordinate and y-coordinate of a SAR image pixel, respectively. LOS For radar line-of-sight deformation, Def PIM-W Def PIM-UN Def PIM-UE θ represents the vertical, north-south, and east-west deformations estimated by the probability integral model, α represents the radar incident angle, α represents the satellite heading angle, N represents the north-south direction, and E represents the east-west direction.

[0023] Optionally, the method for converting the radar line-of-sight deformation into a priori deformation phase is as follows:

[0024]

[0025] Among them, Def LOS For the radar line-of-sight deformation, ψ prior λ represents the a priori deformation phase, and λ is the radar wavelength.

[0026] Optionally, the method for constructing a full interferometric pair network based on the SAR image data and obtaining the differential interferometric phase of the full interferometric pair includes:

[0027]

[0028]

[0029]

[0030] φ'=φ defo +φ ε

[0031] Where, φ flat For flat ground phase, B is the standard baseline, θ is the radar incident angle, and η is the angle between the baseline and the horizontal direction. || For parallel baselines, φ topo R is the terrain phase, R is the slant distance, h is the elevation of the ground point, and B is the elevation of the terrain phase. ⊥ For the vertical baseline, φ ε The error phase represents the phase component with a relatively small proportion of deformation. These represent the residual flatland and terrain phase errors, φ. atmo For atmospheric phase, φ scat For the scattering phase, φ noise For noise phase, φ defo φ' is the deformation phase, and φ' is the differential interference phase of the full interference pair.

[0032] Optionally, the method for removing the prior deformation phase from the differential interference phase to obtain the residual phase of the complete interference pair is as follows:

[0033] φ' res =angle(exp(j·φ')·conj(exp(j·ψ prior )))

[0034] Where, φ' res For the residual phase of the complete interference pair, ψ prior φ' represents the a priori deformed phase, j is the imaginary unit of the complex number, φ' is the differential interference phase of the full interference pair, angle() is the phase angle operation, and conj() is the conjugate operation.

[0035] Optionally, the method for obtaining the coherence value of the residual phase based on the homogeneous pixel set, and constructing a complex coherence matrix by combining the residual phase and the corresponding coherence value, is as follows:

[0036]

[0037]

[0038] in, φ' represents the coherence value corresponding to the residual phase, Ω is the homogeneous pixel set, and φ' is the coherence value. res The residual phase of the complete interference pair. For single-view complex images in t m The complex value at pixel i at time i. Single-view complex image in tn The complex value at pixel i at time i, where j is the imaginary unit of the complex number. For t m t n The residual phase at pixel i over the time interval, Φ res ' is the time-dimensional residual phase matrix, The time-dimensional coherence matrix, This is a dot product operation. It is a complex coherence matrix.

[0039] Optionally, constructing the phase optimization model based on the coherence power-weighted strategy includes:

[0040] A general mathematical function model for phase optimization is constructed, and a coherence power weighting factor is constructed based on the coherence value.

[0041] Substituting the coherence power-weighted factor into the general mathematical function model for phase optimization, the phase optimization model based on the coherence power-weighted strategy is obtained.

[0042] Optionally, the method for obtaining the optimized interference phase is as follows:

[0043]

[0044] in, The optimized interference phase is given by j, where j is the imaginary unit of the complex number. The interference phase of the corresponding interference pair obtained from the residual optimization estimator, ψ prior For the a priori deformed phase, angle() is the phase angle operation.

[0045] Technical advantages of this invention: This invention discloses a phase optimization method for large gradient areas in mining areas based on a probability integral model. It fully utilizes the probability integral model unique to mining subsidence to obtain prior deformation information. By performing phase optimization processing on the residual phase after removing the prior deformation phase, it helps reduce the density of initial phase fringes and minimizes phase loss caused by homogeneous filtering during phase optimization. Furthermore, the use of a coherence power-weighted phase optimization model facilitates the allocation of reasonable weight information, improving the signal-to-noise ratio (SNR) performance of phase optimization. Compared with conventional phase optimization methods, this invention effectively balances the protection of phase information at dense fringes corresponding to large gradient deformation and the improvement of the phase SNR in high-noise areas, exhibiting higher phase optimization performance and contributing to improved monitoring point density and subsequent phase information interpretation accuracy. Attached Figure Description

[0046] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0047] Figure 1 This is a flowchart illustrating a large gradient phase optimization method for mining areas based on a probability integral model, according to an embodiment of the present invention.

[0048] Figure 2 This is a schematic diagram of the a priori deformation phase in the mining area according to an embodiment of the present invention;

[0049] Figure 3 This is a schematic diagram of the original differential interference phase in an embodiment of the present invention;

[0050] Figure 4 This is a schematic diagram of the residual phase in an embodiment of the present invention;

[0051] Figure 5 This is a schematic diagram of the phase optimization estimate corresponding to the residual phase in an embodiment of the present invention;

[0052] Figure 6 This is a schematic diagram of the final optimized interference phase in an embodiment of the present invention. Detailed Implementation

[0053] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0054] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0055] like Figure 1 As shown, this embodiment provides a method for optimizing the phase of a mining area with a large gradient based on a probability integral model, including the following steps:

[0056] S1. Based on the acquisition date of SAR image data, calculate the time interval for different dates, and estimate the prior deformation variables of the mining area for different time periods according to the parameters of the prior probability integral model; the specific operation is as follows:

[0057] Based on the probability integral model, the subsidence W(x,y) of surface point P(x,y) caused by coal seam mining in the mining area can be expressed as:

[0058]

[0059] Where x and y are the x-coordinates and y-coordinates of the surface point, respectively; W0 is the maximum subsidence of the surface point; m is the normal mining thickness of the coal seam; q is the subsidence coefficient; α is the dip angle of the coal seam; l is the equivalent integral strike length of the working face; D3 and D1 are the strike length and dip length of the working face, respectively; S1, S2, S3, and S4 are the inflection point offsets in the downhill, uphill, left-hand, and right-hand directions, respectively; L is the equivalent integral dip width of the working face; W e (x,y) represents the subsidence at point P(x,y) on the surface caused by any mining unit O(u,v) in the coal seam, expressed as:

[0060]

[0061] Where r is the main influence radius of the mining unit, H is the mining depth at the mining unit, β is the main influence angle, and θ is the mining influence propagation angle.

[0062] Combined with the Knothe time function, obtain t m t s Deformation under time intervals,

[0063]

[0064] Among them, W max Let c represent the maximum settlement, and c be the lithological parameter of the overlying rock in the mining area. By combining mining data from the mining area, the parameter information required for the above probabilistic integral model can be obtained.

[0065] Based on the acquisition date of the SAR time series dataset, different time intervals are calculated, and combined with the above probability integral model, the prior deformation variables of the mining area under different time periods are obtained.

[0066] S2. Combining satellite imagery parameters, the prior time-series deformation variables obtained in S1 are converted into radar line-of-sight deformation variables. Based on the conversion relationship between deformation variables and phase, the radar line-of-sight deformation variables are converted into prior deformation phase values. The specific operation steps are as follows:

[0067] S2.1. Establish the correlation function model between the InSAR radar line-of-sight (LOS) deformation variable and the prior deformation variable estimated by the probability integral model (PIM), expressed as:

[0068]

[0069] Where x and y are the x-coordinates and y-coordinates of a SAR image pixel, respectively, θ is the radar incident angle, and α is the satellite heading angle. LOS For radar line-of-sight deformation, Def PIM-W Def PIM-UN Def PIM-UEThese represent the vertical, north-south, and east-west deformation variables estimated by the probability integral model, where N represents the north-south direction and E represents the east-west direction.

[0070] Based on the SAR image parameters and the prior deformation variables of the mining area obtained in step S1, the prior deformation variables of the mining area are converted into radar line-of-sight deformation variables Def. LOS .

[0071] S2.2 Based on the conversion relationship between radar line-of-sight deformation and phase, the radar line-of-sight is converted to the prior deformation Def. LOS Convert to prior deformation phase value ψ prior , is represented as:

[0072]

[0073] Where λ is the radar wavelength. Taking a 24-day time interval as an example, the prior deformation phase of the study area is as follows: Figure 2 As shown.

[0074] S3. Construct a full interferometric pair network based on SAR image data, and calculate the differential interferometric phase under the full interferometric pair. Remove the prior deformation phase obtained in S2 from the differential interferometric phase to obtain the residual phase under the full interferometric pair. The specific operation steps are as follows:

[0075] S3.1 Based on the SAR time series dataset, construct an initial full interferometric pair network containing all possible interferometric pairs, and perform main and sub-image interferometric processing based on the initial network to obtain the interferometric phase φ, which mainly includes the following phase components:

[0076] φ=φ flat +φ topo +φ defo +φ atmo +φ scat +φ noise (6)

[0077] Where, φ flat For flat-ground phase, φ topo For terrain phase, φ defo For the deformation phase, φ atmo For atmospheric phase, φ scat For the scattering phase, φ noise noise phase

[0078] S3.2 Based on the basic characteristics of each phase component, phase interference components other than the deformation phase are removed and suppressed to obtain the differential interference phase φ' which is mainly composed of deformation phase information.

[0079] The flat-ground phase can be approximated as:

[0080]

[0081] Where B is the standard baseline, θ is the radar incident angle, and η is the angle between the baseline and the horizontal direction. || The baseline is parallel. The flat phase can be calculated and removed based on the orbit and reference surface parameters.

[0082] Terrain phase can be approximated as:

[0083]

[0084] Where R is the slant distance, h is the elevation of the ground point, and B ⊥ The vertical baseline is used. Topographic phase can be estimated and removed by combining image parameters and external DEM data.

[0085] After removing the flat terrain and topographic phases, the differential interference phase φ' is obtained.

[0086]

[0087] Where, φ ε The error phase represents the phase component with a relatively small proportion of deformation. These are the residual flatland and terrain phase errors, respectively. Figure 2 The original differential interference phases corresponding to the same time intervals are shown as follows: Figure 3 As shown.

[0088] S3.3, combined with the prior deformation phase ψ obtained from S2 prior The residual phase φ' is obtained by subtracting the differential interference phase from the prior deformation phase. res , is represented as:

[0089] φ' res =angle(exp(j·φ')·conj(exp(j·ψ prior ))) (10)

[0090] Where j is the imaginary unit of the complex number, angle() is the phase angle operation, and conj() is the conjugate operation.

[0091] Traverse all interference pairs in the network and obtain the residual phase under all interference pairs. Figure 3 The residual phase corresponding to the differential interference phase shown is as follows: Figure 4 As shown.

[0092] S4. Using the confidence interval hypothesis testing algorithm, and combining the temporal amplitude values ​​of the SAR image dataset, a homogeneous pixel set is selected. Based on the homogeneous pixel set, the coherence value corresponding to the residual phase obtained in S3 is calculated. The complex coherence matrix is ​​constructed by combining the residual phase under the full interferometric pair and the corresponding coherence value. The specific operation steps are as follows:

[0093] S4.1. Based on the temporal SAR dataset, obtain the temporal amplitude value A = [A1 A2 … A N N represents the number of time-series images. Then, assuming a reference pixel, an initial rectangular window is selected with that pixel as the center, and the initial window is divided into strip sub-windows in different directions. Based on the time-series amplitude value, the local variance in different sub-windows is calculated, and the sub-window with the smallest local variance is selected as the candidate window.

[0094] S4.2. Perform a two-sample test between the reference pixel and all sub-pixels within the selected candidate window to filter out acceptable pixels, and use the average amplitude of the acceptable pixels as the time average value μ of the reference pixel. A .

[0095] S4.3, Perform a logarithmic transformation on the amplitude variable, i.e., A i '=lnA i A' follows a log-Rayleigh distribution. Using the confidence interval hypothesis testing algorithm, the interval estimator of A' under L looks can be expressed as:

[0096]

[0097] Where, μ A' To find the expected value of the probability density function corresponding to the logarithmic Rayleigh distribution, we directly use the time mean of acceptable pixels within the candidate window obtained in S4.2, i.e., μ. A' =μ A , z 1-α / 2 is the percentile of the 1-α / 2 standard normal distribution.

[0098] Traverse all pixels within the initial rectangular window, define pixels that satisfy the interval shown in the above formula as homogeneous pixels of the reference pixel, and then construct a set of homogeneous pixels Ω.

[0099] Repeat steps S4.1-S4.3 to obtain a set of homogeneous pixels for all pixels.

[0100] S4.4, Based on homogeneous pixel set Ω and residual phase φ' res Calculate the coherence value corresponding to the residual phase. It can be represented as:

[0101]

[0102] in, For single-view complex images in t m The complex value at pixel i at time i. For single-view complex images in t n The complex value at pixel i at time i, where j is the imaginary unit of the complex number. For t m tn The residual phase at pixel i over the time interval.

[0103] Iterate through all pixels and calculate the coherence map corresponding to the residual phase map. Iterate through all interference pairs in the full interferometric pair network and obtain the full interferometric pair coherence map corresponding to the residual phase map of the full interferometric pair.

[0104] S4.5. Convert the residual phase matrix and coherence matrix of the full interferometer pair into the time-dimensional residual phase matrix and time-dimensional coherence matrix for a single pixel.

[0105] Suppose that for any pixel i, the time-dimensional residual phase matrix at that pixel can be expressed as:

[0106]

[0107] Where j is the imaginary unit of the complex number, For t m t n The complex residual phase at pixel i over the time interval. Iterate through all pixels to obtain the time-dimensional residual phase matrix Φ. res '.

[0108] The temporal coherence matrix corresponding to pixel i can be expressed as:

[0109]

[0110] in, For t m t n The coherence value corresponding to the residual phase at pixel i over the time interval. Iterate through all pixels to obtain the temporal coherence matrix.

[0111] S4.6, Based on the time-dimensional residual phase matrix Φ obtained above res 'and time-dimensional coherence matrix Constructing a complex coherence matrix Represented as:

[0112]

[0113] in, This is a dot product operation.

[0114] S5. Construct a phase optimization model based on a coherence power-weighted strategy, and estimate the phase optimization estimator corresponding to the residual phase using the covariance matrix obtained in S4. The specific steps are as follows:

[0115] S5.1. Derive the general mathematical function model for phase optimization, which can be expressed as:

[0116]

[0117] in, Let ω be the residual optimization phase to be solved, and let ω be the weighting factor of the phase optimization model.

[0118] S5.2. Based on the coherence value, construct a coherence power-weighted factor, expressed as:

[0119]

[0120] Where n is a power, usually taking the value 1 to 3.

[0121] By substituting the coherence power weights into the general mathematical function model for phase optimization, a phase optimization model based on the coherence power weighting strategy is derived, namely:

[0122]

[0123] By combining nonlinear optimization algorithms, the above optimization model is solved, and the phase optimization estimate corresponding to the residual phase is estimated. Figure 4 The phase optimization estimate corresponding to the residual phase shown is as follows: Figure 5 As shown.

[0124] S6. Reconstruct the short-spatial-temporal baseline interferometric pair network for time-series monitoring based on SAR image data. Calculate the differential interferometric phase for the corresponding interferometric pair based on the phase optimization estimate obtained in S5, and combine it with the prior deformation phase value obtained in S2 at the same time interval to obtain the final optimized interferometric phase. The specific operation steps are as follows:

[0125] S6.1 Based on the SAR time-series image dataset, a short-spatial baseline interferometric pair network for subsequent time-series monitoring and analysis is reconstructed. Based on the interferometric pair combination information, the phase optimization estimate obtained in S5 is used. Perform SAR main and secondary image interferometry to obtain the interferometric phase of the corresponding interferometry pair.

[0126] S6.2. Combining the prior deformation phase information of the mining area obtained in S2, extract the prior deformation phase ψ of the mining area under the same time interval corresponding to different interferometric pairs. prior , will ψ prior The final optimized interference phase, obtained by adding the residual optimized phase estimate to the interference phase, can be represented as follows:

[0127]

[0128] in, This is the final optimized interference phase. Figure 3 The final optimized interference phase corresponding to the original differential interference phase is shown below. Figure 6 As shown.

[0129] This invention makes full use of the probability integral model unique to mining deformation, and uses the deformation value estimated by the probability integral model as the prior deformation phase information to reduce the density of stripes caused by large gradient deformation in the mining area. By optimizing the residual phase of sparse stripes, the phase ambiguity phenomenon at dense stripes with large gradient is avoided. It can take into account both the protection of phase information and the improvement of phase quality at large gradients in the mining area, and improve the phase optimization performance.

[0130] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for optimizing the phase of a mining area with a large gradient based on a probability integral model, characterized in that, Includes the following steps: Based on SAR image data of the mining area, the image dates are obtained; the time intervals between different dates are calculated, and the prior deformation variables of the mining area under different time periods are estimated by combining the probability integral model. By combining SAR image data, the prior deformation variables of the mining area are converted into radar line-of-sight deformation variables, and the radar line-of-sight deformation variables are converted into prior deformation phase. Based on the SAR image data, a full interferometric pair network is constructed to obtain the differential interferometric phase of the full interferometric pair. The prior deformation phase is removed from the differential interferometric phase to obtain the residual phase of the full interferometric pair, specifically including: in, The residual phase of the complete interference pair. Let be the a priori deformation phase, and j be the imaginary unit of the complex number. The differential interference phase of the full interference pair For phase angle operations, This is a conjugate operation; Based on the confidence interval hypothesis testing method, a homogeneous set of pixels is selected in combination with the temporal amplitude values ​​of the SAR image data; the coherence value of the residual phase is obtained based on the homogeneous set of pixels, and a complex coherence matrix is ​​constructed by combining the residual phase and the corresponding coherence value. A phase optimization model based on a coherence power-weighted strategy is constructed, and the phase optimization estimate corresponding to the residual phase is obtained by combining the complex coherence matrix. A short-spatial baseline interferometric pair network is constructed based on the SAR image data. The differential interferometric phase of the corresponding interferometric pair is obtained through the phase optimization estimate. Combined with the prior deformation phase of the same period, the optimized interferometric phase is obtained.

2. The method for large gradient phase optimization in mining areas based on a probability integral model as described in claim 1, characterized in that, Methods for estimating prior deformation variables of mining areas at different time periods include: Based on the probability integral model, combined with the subsidence of surface points caused by coal seam mining in the mining area and the Knothe time function, the deformation variables under different time intervals are obtained; Based on the image dates obtained from the SAR image data, the time intervals for different dates are calculated, and combined with the probability integral model, the prior deformation variables of the mining area under different time periods are estimated.

3. The method for large gradient phase optimization in mining areas based on a probability integral model as described in claim 2, characterized in that, The method for measuring the subsidence of surface points caused by coal seam mining in a mining area is as follows: in, Let x represent the settlement, and y represent the x-coordinate and y-coordinate of the point on the ground surface, respectively. ρ represents the maximum subsidence at the surface point, m represents the normal mining thickness of the coal seam, and q represents the subsidence coefficient. Let be the dip angle of the coal seam, and l be the equivalent integral strike length of the working face. and These are the strike length and dip length of the working face, respectively. , , and These represent the inflection point offsets in the downhill, uphill, leftward, and rightward directions, respectively, while L is the equivalent integral dip width of the working face. Represents any mining unit in a coal seam The amount of subsidence caused at point P(x, y) on the ground surface.

4. The method for large gradient phase optimization in mining areas based on a probability integral model as described in claim 1, characterized in that, The method for converting the prior deformation variables of the mining area into radar line-of-sight deformation variables by combining SAR image data is as follows: Where x and y are the x-coordinates and y-coordinates of a SAR image pixel, respectively. For radar line-of-sight deformation, , , These represent the vertical, north-south, and east-west deformation variables estimated by the probability integral model, respectively. For radar incident angle, Here, N represents the satellite's heading angle, and E represents the north-south direction.

5. The method for large gradient phase optimization in mining areas based on a probability integral model as described in claim 1, characterized in that, The method for converting the radar line-of-sight deformation into a priori deformation phase is as follows: in, For radar line-of-sight deformation, For the a priori deformation phase, This is the radar wavelength.

6. The method for large gradient phase optimization in mining areas based on a probability integral model as described in claim 1, characterized in that, The method for constructing a full interferometric pair network based on the SAR image data and obtaining the differential interferometric phase of the full interferometric pair includes: in, It is a flat phase. B is the radar wavelength, and B is the standard baseline. For radar incident angle, The angle between the baseline and the horizontal direction. For parallel baselines, R represents the terrain phase, R represents the slant distance, and h represents the elevation of the ground point. For vertical baseline, The error phase represents the phase component with a relatively small proportion of deformation. , These represent the residual flatland and terrain phase errors, respectively. Atmospheric phase, For the scattering phase, For noise phase, For deformation phase, The differential interference phase of the full interference pair.

7. The method for large gradient phase optimization in mining areas based on a probability integral model as described in claim 1, characterized in that, The method for obtaining the coherence value of the residual phase based on the homogeneous pixel set, and constructing a complex coherence matrix by combining the residual phase and the corresponding coherence value, is as follows: in, This represents the coherence value corresponding to the residual phase. A set of homogeneous pixels The residual phase of the complete interference pair. For single-view complex images in t m The complex value at pixel i at time i. Single-view complex image in t n The complex value at pixel i at time i, where j is the imaginary unit of the complex number. For t m t n The residual phase at pixel i over the time interval. The time-dimensional residual phase matrix, The time-dimensional coherence matrix, This is a dot product operation. It is a complex coherence matrix.

8. The method for large gradient phase optimization in mining areas based on a probability integral model as described in claim 1, characterized in that, The phase optimization model based on the coherence power-weighted strategy includes: A general mathematical function model for phase optimization is constructed, and a coherence power weighting factor is constructed based on the coherence value. Substituting the coherence power-weighted factor into the general mathematical function model for phase optimization, the phase optimization model based on the coherence power-weighted strategy is obtained.

9. The method for large gradient phase optimization in mining areas based on a probability integral model as described in claim 1, characterized in that, The method for obtaining the optimized interference phase is as follows: in, The optimized interference phase is given by j, where j is the imaginary unit of the complex number. The interference phase of the corresponding interference pair is obtained for the residual optimization estimator. For the a priori deformation phase, This is for phase angle operations.

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