Slope radar deformation monitoring method based on multi-frequency-point phase unwrapping

Abstract

The invention belongs to the technical field of slope deformation monitoring, and relates to a slope radar deformation monitoring method based on multi-frequency-point phase unwrapping. According to the method, a dynamic synthesis wavelength extension and terrain constraint combined unwrapping technology is utilized, the unwrapping bottleneck of large gradient deformation is effectively overcome, the synthesis wavelength is generated through multi-frequency combination, and in combination with terrain-guided network flow optimization, the path breakage risk and jump point error transmission of traditional single-frequency-point unwrapping are avoided; secondly, on the basis of a frequency difference physical model, an equation set is constructed through the physical property difference between the deformation phase and the atmospheric phase to directly invert the atmospheric retardation, self-elimination of atmospheric interference is achieved, and a physically pure deformation signal is output through closed-loop phase purification; and finally, through lightweight unwrapping and multi-frequency result weighted fusion, a closed-loop framework from unwrapping, correction to re-unwrapping is constructed, the precision and reliability of deformation monitoring in a complex scene are remarkably improved, and a universal solution is provided for deformation early warning of abrupt slopes and complex terrains.

Description

Technical Field

[0001] This application belongs to the field of slope deformation monitoring technology, and more specifically, relates to a slope radar deformation monitoring method based on multi-frequency phase unwrapping. Background Technology

[0002] Ground-based slope radar utilizes differential interferometry to achieve high-precision, large-area, and non-contact slope deformation monitoring by analyzing the phase difference of radar images. Its core technology is phase unwrapping to overcome phase wrapping limitations and obtain true displacement. Traditional unwrapping algorithms rely on the key assumption that the phase difference between adjacent pixels is less than π. However, in extreme scenarios with steep and complex terrain and rapid, non-uniform large gradient deformation, this assumption is severely violated. This causes traditional unwrapping algorithms to easily select incorrect paths, resulting in significant jump point errors. Moreover, these errors accumulate and propagate, ultimately causing severe distortion of deformation results and rendering them ineffective for monitoring and early warning. On the other hand, for the need for long-term, high-frequency continuous monitoring, atmospheric disturbances along the radar signal propagation path accumulate significantly over monitoring time. This atmospheric phase screen exhibits low-pass characteristics in space and changes dynamically over time, easily becoming confused with the true signal, severely contaminating long-baseline monitoring results, and significantly reducing accuracy and reliability. Summary of the Invention

[0003] This invention provides a slope radar deformation monitoring method based on multi-frequency phase unwrapping, which aims to solve the technical problems of jump point error in traditional methods and the influence of atmospheric disturbance on monitoring results.

[0004] The slope radar deformation monitoring method based on multi-frequency phase unwrapping includes the following steps: S1. Deploy a slope radar system capable of transmitting multiple discrete frequency signals, synchronously collect echo data at different frequency points under the same spatiotemporal reference, preprocess each frequency point, and generate a time-series complex interferogram stack; S2. Based on the complex interferogram stack, calculate the synthetic wavelength between any two frequency points, dynamically select the optimal combination of synthetic wavelengths according to the real-time deformation gradient prediction, and generate the corresponding differential interferometric phase diagram. S3. A high-precision digital elevation model is introduced to calculate the terrain gradient map. Combined with the phase quality map, a composite weight is generated. The network flow optimization algorithm is used to unwrap multiple differential interferometric phase maps with the terrain weight as a constraint, and the absolute differential phase map is output. S4. Based on the absolute differential phase map, a physical model of atmospheric delay and frequency difference is established using absolute phase difference data of different frequency combinations. The atmospheric phase is separated by least squares inversion. The estimated value is subtracted from the original single-frequency phase to obtain the corrected single-frequency interference phase. S5. Perform lightweight unwrapping on the corrected single-frequency interference phase, invert the line-of-sight deformation at each frequency, and weight average the multi-frequency results based on physical consistency to output the final deformation field and early warning analysis.

[0005] This invention utilizes a combined unwrapping technique of dynamic synthetic wavelength extension and terrain constraints to effectively overcome the unwrapping bottleneck of large gradient deformation. By generating synthetic wavelengths through multi-frequency combination and combining them with terrain-guided network flow optimization, the path breakage risk and jump point error propagation of traditional single-frequency unwrapping are avoided. Secondly, based on the frequency difference physical model, the atmospheric delay is directly inverted by constructing an equation system based on the difference in physical characteristics between the deformation phase and the atmospheric phase, realizing the self-elimination of atmospheric interference. Physically pure deformation signals are output through closed-loop phase purification. Finally, a closed-loop framework from unwrapping, correction to re-unwrapping is constructed through lightweight unwrapping and weighted fusion of multi-frequency results, which significantly improves the accuracy and reliability of deformation monitoring in complex scenarios and provides a universal solution for deformation early warning of steep slopes and complex terrains.

[0006] Preferably, the preprocessing includes motion compensation, radar imaging, and multi-frequency image registration; Motion compensation: Based on the ideal trajectory of the platform at each frequency point, the vibration displacement is projected onto the radar line of sight, the vibration phase component is estimated, the vibration phase component is then subtracted from the original echo signal, and phase correction is achieved through complex exponential multiplication to obtain the corrected echo data; Radar imaging: The corrected echo data is converted into a high-resolution image, and then a back projection algorithm is used for focusing: In the range term, the echoes of different targets are separated by pulse compression technology; in the azimuth term, the platform motion trajectory is used to synthesize the aperture, the actual slant range is calculated for each scene pixel, and the signal phases of all slow time points are aggregated to generate a complex image with three frequency points. Multi-frequency image registration: Based on the generated complex images of three frequencies, an affine transformation model is adopted, including translation, rotation and scaling parameters. The amplitude difference between the X-band image, C-band image and Ku-band image is minimized by an optimization algorithm to obtain the registered image set.

[0007] Preferably, generating a stack of complex interferograms for a time series includes the following steps: Based on the registered image set, a master image at a reference time point is selected, and complex conjugate multiplication is performed on the slave images at other time points to extract phase difference information. This process is performed independently at each frequency point, generating three stacks. Each stack includes interferograms at K time points, and each interferogram is stored in complex form. Based on this, a stack of complex interferograms for the time series is obtained.

[0008] Preferably, step S2 includes the following steps: All frequency points are paired up, the absolute value of the frequency difference between each pair of frequency points is calculated, and then the combined wavelength of each pair of frequency points is calculated by combining the speed of light. The optimal synthetic wavelength is dynamically selected based on the synthetic wavelength of each pair of frequency points calculated by the basis and the maximum expected deformation gradient determined by historical data, resulting in a list of synthetic wavelength combinations and corresponding synthetic wavelengths. For each selected combination of synthetic wavelengths, calculate the corresponding differential interferometric phase diagram, where the value of the differential interferometric phase diagram is in the range of [-π, π). The coherence coefficient map of the differential interferogram for each selected combination is calculated as the phase quality map, where the coherence coefficient map is obtained based on the complex conjugate operation of the complex interferogram stack and the averaging operation within the local window.

[0009] Preferably, the dynamic selection of the optimal synthesis wavelength includes the following steps: If half of the synthetic wavelengths corresponding to all combinations is greater than or equal to the maximum expected deformation gradient, then the shortest synthetic wavelength is selected. If half of the synthetic wavelengths corresponding to all combinations are less than the maximum expected deformation gradient, then increase the number of frequency points and recalculate the synthetic wavelengths for each pair of frequency points until there is a synthetic wavelength that is greater than or equal to the maximum expected deformation gradient. If half of the synthesized wavelength corresponding to a certain combination is greater than or equal to the maximum expected deformation gradient, then at least two combinations that satisfy the condition that half of the synthesized wavelength is greater than or equal to the maximum expected deformation gradient shall be selected.

[0010] Preferably, step S3 includes the following steps: Based on a high-precision digital elevation model, the horizontal gradients in the x and y directions are calculated. Based on the horizontal gradients in the x and y directions, the square root of the sum of squares is calculated to obtain the slope value. Then, the arctangent function is used to calculate the ratio of the gradient in the y direction to the gradient in the x direction to obtain the slope aspect of the terrain. The composite weight is calculated by combining the slope of the terrain and the phase quality, where the phase quality is obtained based on the coherence coefficient diagram of the differential interferogram; Then, each pixel is treated as an independent node, and adjacent nodes are connected. The weights of the edges are composite weights, and the network flow model is obtained based on this. The minimum cost flow algorithm is adopted to find the flow with the minimum total cost under the condition of satisfying the constraints, and obtain the optimal phase unwrapping path. Phase unwrapping is performed based on the optimal phase unwrapping path to obtain the absolute difference phase map. The constraints include ensuring that the change in phase gradient does not exceed a set threshold and that the slope aspect is guided by the terrain.

[0011] Preferably, step S4 includes the following steps: For each pair of frequencies, calculate the frequency difference between them, extract the atmospheric delay phase part from the unwrapped absolute difference phase diagram, and obtain the decomposed atmospheric delay phase part. A model is established to relate atmospheric phase to frequency difference, linking atmospheric phase delay to refractive index change rate. The model expresses the proportional relationship between atmospheric phase delay and frequency difference, slant range, and refractive index change, thus obtaining a model of atmospheric phase and refractive index change. A system of equations was established to relate the atmospheric delay phase of different frequency pairs to the rate of refractive index change. The least squares method was used to solve for the refractive index change, and a spatial smoothing constraint was introduced in the solution process to obtain an estimate of the refractive index change. Based on the estimated value of the refractive index change, the atmospheric phase at a single frequency point is calculated. The atmospheric phase is then subtracted from the original phase diagram to obtain the corrected single-frequency interference phase.

[0012] Preferably, step S5 includes the following steps: A lightweight unwrapping operation is performed on the interference phase at each frequency point, and then the unwrapped absolute phase value is converted into physical deformation based on the characteristics of the radar wavelength to obtain an independent line-of-sight deformation map for each frequency point. For each frequency point, a fusion weight is calculated at each pixel location. The weight is determined by the coherence coefficient of the frequency point. The larger the coherence coefficient, the larger the weight. For each pixel location, the deformation of each frequency point is multiplied by the corresponding weight and summed. Then, it is divided by the sum of all weights to obtain the final deformation of the corresponding pixel. Based on this, the time series deformation field is obtained, and an early warning is given based on the deformation rate threshold.

[0013] The beneficial effects of this invention include: This invention utilizes a combined unwrapping technique of dynamic synthetic wavelength extension and terrain constraints to effectively overcome the unwrapping bottleneck of large gradient deformation. By generating synthetic wavelengths through multi-frequency combination and combining them with terrain-guided network flow optimization, the path breakage risk and jump point error propagation of traditional single-frequency unwrapping are avoided. Secondly, based on the frequency difference physical model, the atmospheric delay is directly inverted by constructing an equation system based on the difference in physical characteristics between the deformation phase and the atmospheric phase, realizing the self-elimination of atmospheric interference. Physically pure deformation signals are output through closed-loop phase purification. Finally, a closed-loop framework from unwrapping, correction to re-unwrapping is constructed through lightweight unwrapping and weighted fusion of multi-frequency results, which significantly improves the accuracy and reliability of deformation monitoring in complex scenarios and provides a universal solution for deformation early warning of steep slopes and complex terrains. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a schematic diagram of the system structure provided in an embodiment of the present invention.

[0016] Figure 2 A simplified flowchart provided for embodiments of the present invention.

[0017] Figure 3 This is a simplified structural diagram of the network flow model provided in an embodiment of the present invention. Detailed Implementation

[0018] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.

[0019] See Figure 1 As shown, the preferred embodiment of the present invention will be further described; The slope radar deformation monitoring method based on multi-frequency phase unwrapping includes the following steps: S1. Deploy a slope radar system capable of transmitting multiple discrete frequency signals, synchronously collect echo data at different frequency points under the same spatiotemporal reference, preprocess each frequency point, and generate a time-series complex interferogram stack; Before data acquisition in this embodiment, the transmitter uses a bandwidth frequency synthesizer to support rapid switching between three frequency points: Ku-band (approximately 17.2 GHz), X-band (approximately 9.6 GHz), and C-band (approximately 5.3 GHz), with a dwell time of approximately 10 milliseconds for each frequency point. The receiver is designed with a multi-channel parallel architecture, and the sampling clock synchronization accuracy of each channel is controlled within 1 ps to ensure that the echo signals at different frequencies are consistent in time and space. At the same time, the spatiotemporal reference module (GNSS timing and IMU) continuously records the platform's position and attitude data. GNSS provides time synchronization, and the IMU measures the three-dimensional attitude. The acquired data is aligned with the radar pulse in real time through a hardware interface. Within a single scan cycle, the transmitter transmits signals at three frequencies in a fixed sequence: first, it transmits a Ku-band signal for 10 milliseconds, then switches to the X-band for 10 milliseconds, and finally switches to the C-band for 10 milliseconds. This ensures that the transmission at each frequency is quasi-synchronous (due to the extremely small interval), i.e., completed within a timescale much smaller than deformation or atmospheric changes (within 1 second), thereby preventing additional errors introduced by dynamic scene changes. The receiver synchronously captures the echo signals at each frequency, while the IMU and GNSS record the platform's real-time position and attitude data. The echo signals include: target reflection information, terrain phase, deformation phase, atmospheric phase delay, and thermal noise.

[0020] Motion compensation: Since platform micro-vibrations can contaminate the echo signal, at each frequency point, based on the platform's ideal trajectory (slant range when there is no vibration), the vibration displacement is projected onto the radar line-of-sight direction to estimate the vibration phase component. This vibration phase component is then subtracted from the original echo signal, and phase correction is achieved through complex exponential multiplication to obtain the corrected echo data. The specific expression is as follows: ; In the formula: This represents the corrected echo data; This represents the original echo signal; Indicates the vibration phase correction amount; Represents the imaginary unit; The vibration phase correction amount is obtained based on the following formula: ; In the formula: Represents the platform displacement vector. These represent the platform's displacements in the x, y, and z directions, respectively. Represents frequency Relevant constants; Represents the ideal slant range vector; It represents the speed of light.

[0021] Radar imaging: The vibration-corrected echo data is converted into a high-resolution image, and then a back-projection algorithm is used for focusing. Specifically, in the range term, pulse compression technology is used to separate the echoes of different targets; in the azimuth term, the platform's motion trajectory is used to synthesize the aperture, the actual slant range is calculated for each scene pixel, and the signal phases of all slow time points are aggregated to generate a complex image with three frequency points. The specific expression is as follows: ; In the formula: Indicates at pixel point The imaging result at the i-th frequency point, i.e., the complex image at the i-th frequency point; This represents the corrected received signal, corresponding to the pixel at time t. echo delay The value at; This indicates the platform's position from time t to pixel. The actual distance.

[0022] Multi-frequency image registration: Feature points are extracted from the Ku band (reference image) and X and C bands (images to be registered) using feature detection algorithms (such as SIFT). Corresponding point pairs between the two images are found using matching algorithms (such as FLANN). A system of equations is then established, and the affine transformation parameters are solved using the corresponding point pairs. HORN's algorithm is applied to transform the problem into solving for the eigenvalues ​​of a matrix to minimize the reprojection error, where the corresponding point pairs satisfy the following: ; ; In the formula: and Indicates the translation amount; k represents the scale factor; Indicates the rotation angle; and Indicates the coordinates of feature points in the reference image; and Indicates the coordinates of the corresponding feature point in the image to be registered; The parameters are solved using the least squares method, which minimizes the objective function, as follows: ; In the formula: n represents the corresponding feature point; Solve for the parameters k using the least squares method. , as well as This minimizes the objective function; based on this, the registered image set is obtained.

[0023] Finally, based on the registered image set, a master image at a reference time point (such as the initial time) is selected, and complex conjugate multiplication is performed on the slave images at other time points to extract phase difference information (i.e., interference phase). Each frequency point is executed independently to generate three stacks. Each stack includes interferograms at K time points, and each interferogram is stored in complex form. Based on this, the complex interferogram stack of the time series is obtained.

[0024] In this embodiment, a multi-frequency slope radar system is deployed to simultaneously collect echo data from different frequency points, which can effectively cover a wider frequency band, thereby improving the accuracy and stability of monitoring. Furthermore, vibration phase components are eliminated through motion compensation to reduce noise interference, and high-resolution images are generated through radar imaging to ensure data quality. Image matching criteria further reduce geometric deviations between different frequency points, providing a reliable foundation for subsequent interferogram generation.

[0025] S2. Based on the complex interferogram stack, calculate the synthetic wavelength between any two frequency points, dynamically select the optimal combination of synthetic wavelengths according to the real-time deformation gradient prediction, and generate the corresponding differential interferometric phase diagram. All frequency points are paired up, the absolute value of the frequency difference between each pair of frequency points is calculated, and then the combined wavelength of each pair of frequency points is calculated by combining the speed of light. ; In the formula: This represents the combined wavelength of frequency points i and j; and Let i represent the carrier frequencies of two different frequency points, where i ≠ j; Represents the speed of light; based on this step, all possible combinations are generated. List; The optimal synthetic wavelength is dynamically selected based on the synthesized wavelength of each pair of frequency points calculated from the baseline and the maximum expected deformation gradient determined from historical data, resulting in a list of synthetic wavelength combinations and their corresponding synthetic wavelengths. The strategy for dynamically selecting the optimal synthetic wavelength is as follows: If half of the synthetic wavelengths corresponding to all combinations are greater than or equal to the maximum expected deformation gradient, then the shortest synthetic wavelength is selected. If half of the synthetic wavelengths corresponding to all combinations are less than the maximum expected deformation gradient, then increase the number of frequency points and recalculate the synthetic wavelengths for each pair of frequency points until there is a synthetic wavelength that is greater than or equal to the maximum expected deformation gradient. If half of the synthesized wavelength corresponding to a certain combination is greater than or equal to the maximum expected deformation gradient, then at least two combinations that satisfy the condition that half of the synthesized wavelength is greater than or equal to the maximum expected deformation gradient shall be selected.

[0026] For each selected combination of synthetic wavelengths, calculate the corresponding differential interferometric phase diagram, where the value of the differential interferometric phase diagram is in the range of [-π, π). ; In the formula: and The original entangled interference phase diagrams for frequency points i and j are shown respectively. This represents the differential interferometric phase diagram for frequencies i and j.

[0027] The coherence coefficient map of the differential interferogram for each selected combination is calculated as the phase quality map, where the coherence coefficient map is obtained based on the complex conjugate operation of the complex interferogram stack and the averaging operation within the local window: ; In the formula: and A complex interferogram representing frequency points i and j; Represents the complex conjugate operation; This represents the desired spatial or temporal computation, performed within a local window. This represents the coherence coefficient map. The closer the value is to 1, the better the pixel phase quality and the higher the reliability.

[0028] In this embodiment, dynamically selecting the synthesis wavelength can effectively adapt to different deformation gradients and avoid phase ambiguity problems, thereby improving the accuracy and reliability of phase unwrapping. The selection of the optimal synthesis wavelength combination can not only reduce errors, but also improve the quality of the differential interferometric phase map.

[0029] S3. A high-precision digital elevation model is introduced to calculate the terrain gradient map. Combined with the phase quality map, a composite weight is generated. The network flow optimization algorithm is used to unwrap multiple differential interferometric phase maps with the terrain weight as a constraint, and the absolute differential phase map is output. See Figure 2 As shown, step S3 includes the following steps: Based on a high-precision digital elevation model, the horizontal gradients in the x and y directions are calculated. Based on the horizontal gradients in the x and y directions, the square root of the sum of squares is calculated to obtain the slope value. Then, the arctangent function is used to calculate the ratio of the gradient in the y direction to the gradient in the x direction to obtain the slope aspect of the terrain. The composite weight is calculated by combining the slope of the terrain and the phase quality, where the phase quality is obtained based on the coherence coefficient diagram of the differential interferogram; ; In the formula: and This represents the weight parameters, and their sum is 1. This indicates the maximum slope value of the terrain; Indicates the location The slope at that location; Represents a composite weighted graph; See Figure 3 As shown, each pixel point As an independent node, the edges connecting to adjacent nodes have composite weights. Based on this, a network flow model is obtained; The minimum cost flow algorithm is adopted to find the flow with the minimum total cost under the condition of satisfying the constraints, and obtain the optimal phase unwrapping path. Phase unwrapping is performed based on the optimal phase unwrapping path to obtain the absolute difference phase map. The constraints include that the change in phase gradient does not exceed a set threshold and that the slope aspect guided by the terrain is satisfied. In this embodiment, the total cost is the sum of all weights traversed by the unwrapping path. Given the network flow model, the objective (finding the flow with the minimum total cost), and the constraints, finding the optimal phase unwrapping path using the minimum cost flow algorithm is a conventional technique in this field, and therefore will not be elaborated upon in this embodiment. The steps for phase unwrapping based on the optimal phase unwrapping path are as follows: Choose a reference point (source node or sink node) and set its absolute value to a known value (such as 0). Based on the edge weights on the optimal path, gradually adjust the phase value of each node. Assuming that the edge weights on the path are the phase adjustment amount, the phase value of the source node can be propagated to other nodes along the path. The absolute phase value of each node is equal to its relative phase value plus the phase adjustment amount propagated along the path. Combine the absolute phase values ​​of all nodes into an absolute phase difference graph.

[0030] In this embodiment, the terrain information provided by the high-precision DEM can effectively constrain the phase unwrapping process and reduce the error caused by terrain. The network flow optimization algorithm can efficiently process large-scale data by constructing a network flow model, ensuring the global optimality of phase unwrapping. By introducing composite weights, it can better adapt to terrain changes, thereby generating a high-precision absolute differential phase map.

[0031] S4. Based on the absolute differential phase map, a physical model of atmospheric delay and frequency difference is established using absolute phase difference data of different frequency combinations. The atmospheric phase is separated by least squares inversion. The estimated value is subtracted from the original single-frequency phase to obtain the corrected single-frequency interference phase. Step S4 includes the following steps: For each pair of frequencies and Calculate the frequency difference between the two. The atmospheric delay phase component is extracted from the unwrapped absolute difference phase diagram to obtain the decomposed atmospheric delay phase component. ; In the formula: Indicates the deformation phase; Indicates atmospheric delay phase; Indicates residual orbital error; Indicates noise; This represents the absolute differential phase diagram.

[0032] A model is established to relate atmospheric phase to frequency difference, linking atmospheric phase delay to refractive index change rate. The model expresses the proportional relationship between atmospheric phase delay and frequency difference, slant range, and refractive index change, thus obtaining a model of atmospheric phase and refractive index change. ; In the formula: Indicates the slant distance; Indicates the change in refractive index; Represents the speed of light; A system of equations was established to relate the atmospheric delay phase of different frequency pairs to the rate of refractive index change. The least squares method was used to solve for the refractive index change, and a spatial smoothing constraint was introduced in the solution process to obtain an estimate of the refractive index change. ; In the formula: Indicates the smoothing constraint parameters; Indicates the smoothing term; Based on the estimated value of the refractive index change, the atmospheric phase at a single frequency point is calculated. The atmospheric phase is then subtracted from the original phase diagram to obtain the corrected single-frequency interference phase. ; In the formula: This represents the estimated atmospheric phase (i.e., the calculated atmospheric phase at a single frequency point). Corrected phase diagram This represents the original phase diagram.

[0033] In this embodiment, atmospheric phase is one of the main sources of error in deformation monitoring. By establishing a physical model and introducing spatial smoothing constraints, the influence of atmospheric delay can be effectively eliminated, improving the accuracy of phase measurement. The corrected single-frequency interferometric phase provides a more reliable data basis for subsequent deformation response, thereby further improving the accuracy of monitoring results.

[0034] S5. Perform lightweight unwrapping on the corrected single-frequency interference phase, invert the line-of-sight deformation at each frequency, and weight average the multi-frequency results based on physical consistency to output the final deformation field and early warning analysis.

[0035] A lightweight unwrapping operation is performed on the interference phase of each frequency point (using the region growth method or the fast minimum cost flow method), and then the unwrapped absolute phase value is converted into physical deformation based on the radar wavelength characteristics to obtain an independent line-of-sight deformation map for each frequency point. ; In the formula: This represents the line-of-sight deformation inverted at frequency point i; The radar wavelength represents frequency point i; This represents the absolute phase value of frequency point i after unwrapping; For each frequency point, a fusion weight is calculated at each pixel location. The weight is determined by the coherence coefficient of the frequency point; the larger the coherence coefficient, the larger the weight. ; In the formula: This represents the coherence coefficient of frequency point i at the current pixel; This represents the fusion weight of frequency point i in the current pixel; For each pixel location, multiply the deformation of each frequency point by its corresponding weight, sum the results, and then divide by the sum of all weights to obtain the final deformation of the corresponding pixel. ; In the formula: This indicates the total number of frequency points participating in the fusion. Indicates the final shape variable; Step S5 is repeated at each time point to generate a time-series deformation field, and an early warning is triggered based on a deformation rate threshold; Example: Based on the obtained time-series deformation field, a time-series model can be used to model the deformation data and calculate the deformation rate of each monitoring point, such as calculating the rate of change of deformation with time t using a linear regression model. Then, based on geological conditions, engineering requirements, and historical data, different levels of deformation rate thresholds are set, for example: Yellow alert: Deformation rate between 0.1 and 0.5 mm / day; Orange alert: Deformation rate between 0.5 and 1.0 mm / day; Red alert: Deformation rate greater than 1.0 mm / day; Early warning is provided based on the set deformation rate threshold and the calculated deformation rate.

[0036] In this embodiment, a technical logic of unwrapping, correction, and re-unwrapping is adopted. First, a high-precision digital elevation model is introduced in the initial unwrapping, allowing terrain information to constrain the phase unwrapping process. The terrain gradient map effectively reflects the impact of terrain undulations on the phase, helping the algorithm identify phase changes caused by terrain, thereby reducing the impact of atmospheric phase interference on the unwrapping results. Second, by establishing a physical model of atmospheric delay and frequency difference, the relationship between multi-frequency interferometric phases can be used to separate and estimate the atmospheric phase. Combined with the absolute phase map generated in the initial unwrapping, the atmospheric phase can be accurately inverted. Lightweight unwrapping is then performed on the corrected single-frequency interferometric phase, further eliminating phase ambiguity and improving the accuracy of deformation inversion. Simultaneously, the weighted average of the multi-frequency results can further integrate the advantages of each frequency point, reducing the influence of errors from a single frequency point.

[0037] The above are merely preferred embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A slope radar deformation monitoring method based on multi-frequency phase unwrapping, characterized in that, Includes the following steps: S1. Deploy a slope radar system capable of transmitting multiple discrete frequency signals, synchronously collect echo data at different frequency points under the same spatiotemporal reference, preprocess each frequency point, and generate a time-series complex interferogram stack; S2. Based on the complex interferogram stack, calculate the synthetic wavelength between any two frequency points, dynamically select the optimal combination of synthetic wavelengths according to the real-time deformation gradient prediction, and generate the corresponding differential interferometric phase diagram. S3. A high-precision digital elevation model is introduced to calculate the terrain gradient map. Combined with the phase quality map, a composite weight is generated. The network flow optimization algorithm is used to unwrap multiple differential interferometric phase maps with the terrain weight as a constraint, and the absolute differential phase map is output. S4. Based on the absolute differential phase map, a physical model of atmospheric delay and frequency difference is established using absolute phase difference data of different frequency combinations. The atmospheric phase is separated by least squares inversion. The estimated value is subtracted from the original single-frequency phase to obtain the corrected single-frequency interference phase. S5. Perform lightweight unwrapping on the corrected single-frequency interference phase, invert the line-of-sight deformation at each frequency, and weight average the multi-frequency results based on physical consistency to output the final deformation field and early warning analysis.

2. The slope radar deformation monitoring method based on multi-frequency phase unwrapping according to claim 1, characterized in that, The preprocessing includes motion compensation, radar imaging, and multi-frequency image registration. Motion compensation: Based on the ideal trajectory of the platform at each frequency point, the vibration displacement is projected onto the radar line of sight, the vibration phase component is estimated, the vibration phase component is then subtracted from the original echo signal, and phase correction is achieved through complex exponential multiplication to obtain the corrected echo data; Radar imaging: The corrected echo data is converted into a high-resolution image, and then a back projection algorithm is used for focusing: In the range term, the echoes of different targets are separated by pulse compression technology; in the azimuth term, the platform motion trajectory is used to synthesize the aperture, the actual slant range is calculated for each scene pixel, and the signal phases of all slow time points are aggregated to generate a complex image with three frequency points. Multi-frequency image registration: Based on the generated complex images of three frequencies, an affine transformation model is adopted, including translation, rotation and scaling parameters. The amplitude difference between the X-band image, C-band image and Ku-band image is minimized by an optimization algorithm to obtain the registered image set.

3. The slope radar deformation monitoring method based on multi-frequency phase unwrapping according to claim 2, characterized in that, The process of generating a complex interferogram stack for a time series includes the following steps: Based on the registered image set, a master image at a reference time point is selected, and complex conjugate multiplication is performed on the slave images at other time points to extract phase difference information. This process is performed independently at each frequency point, generating three stacks. Each stack includes interferograms at K time points, and each interferogram is stored in complex form. Based on this, a stack of complex interferograms for the time series is obtained.

4. The slope radar deformation monitoring method based on multi-frequency phase unwrapping according to claim 1, characterized in that, Step S2 includes the following steps: All frequency points are paired up, the absolute value of the frequency difference between each pair of frequency points is calculated, and then the combined wavelength of each pair of frequency points is calculated by combining the speed of light. The optimal synthetic wavelength is dynamically selected based on the synthetic wavelength of each pair of frequency points calculated by the basis and the maximum expected deformation gradient determined by historical data, resulting in a list of synthetic wavelength combinations and corresponding synthetic wavelengths. For each selected combination of synthetic wavelengths, calculate the corresponding differential interferometric phase diagram, where the value of the differential interferometric phase diagram is in the range of [-π, π). The coherence coefficient map of the differential interferogram for each selected combination is calculated as the phase quality map, where the coherence coefficient map is obtained based on the complex conjugate operation of the complex interferogram stack and the averaging operation within the local window.

5. The slope radar deformation monitoring method based on multi-frequency phase unwrapping according to claim 4, characterized in that, The dynamic selection of the optimal synthesis wavelength includes the following steps: If half of the synthetic wavelengths corresponding to all combinations is greater than or equal to the maximum expected deformation gradient, then the shortest synthetic wavelength is selected. If half of the synthetic wavelengths corresponding to all combinations are less than the maximum expected deformation gradient, then increase the number of frequency points and recalculate the synthetic wavelengths for each pair of frequency points until there is a synthetic wavelength that is greater than or equal to the maximum expected deformation gradient. If half of the synthesized wavelength corresponding to a certain combination is greater than or equal to the maximum expected deformation gradient, then at least two combinations that satisfy the condition that half of the synthesized wavelength is greater than or equal to the maximum expected deformation gradient shall be selected.

6. The slope radar deformation monitoring method based on multi-frequency phase unwrapping according to claim 1, characterized in that, Step S3 includes the following steps: Based on a high-precision digital elevation model, the horizontal gradients in the x and y directions are calculated. Based on the horizontal gradients in the x and y directions, the square root of the sum of squares is calculated to obtain the slope value. Then, the arctangent function is used to calculate the ratio of the gradient in the y direction to the gradient in the x direction to obtain the slope aspect of the terrain. The composite weight is calculated by combining the slope of the terrain and the phase quality, where the phase quality is obtained based on the coherence coefficient diagram of the differential interferogram; Then, each pixel is treated as an independent node, and adjacent nodes are connected. The weights of the edges are composite weights, and the network flow model is obtained based on this. The minimum cost flow algorithm is adopted to find the flow with the minimum total cost under the condition of satisfying the constraints, and obtain the optimal phase unwrapping path. Phase unwrapping is performed based on the optimal phase unwrapping path to obtain the absolute difference phase map. The constraints include ensuring that the change in phase gradient does not exceed a set threshold and that the slope aspect is guided by the terrain.

7. The slope radar deformation monitoring method based on multi-frequency phase unwrapping according to claim 1, characterized in that, Step S4 includes the following steps: For each pair of frequencies, calculate the frequency difference between them, extract the atmospheric delay phase part from the unwrapped absolute difference phase diagram, and obtain the decomposed atmospheric delay phase part. A model is established to relate atmospheric phase to frequency difference, linking atmospheric phase delay to refractive index change rate. The model expresses the proportional relationship between atmospheric phase delay and frequency difference, slant range, and refractive index change, thus obtaining a model of atmospheric phase and refractive index change. A system of equations was established to relate the atmospheric delay phase of different frequency pairs to the rate of refractive index change. The least squares method was used to solve for the refractive index change, and a spatial smoothing constraint was introduced in the solution process to obtain an estimate of the refractive index change. Based on the estimated value of the refractive index change, the atmospheric phase at a single frequency point is calculated. The atmospheric phase is then subtracted from the original phase diagram to obtain the corrected single-frequency interference phase.

8. The slope radar deformation monitoring method based on multi-frequency phase unwrapping according to claim 1, characterized in that, Step S5 includes the following steps: A lightweight unwrapping operation is performed on the interference phase at each frequency point, and then the unwrapped absolute phase value is converted into physical deformation based on the characteristics of the radar wavelength to obtain an independent line-of-sight deformation map for each frequency point. For each frequency point, a fusion weight is calculated at each pixel location. The weight is determined by the coherence coefficient of the frequency point. The larger the coherence coefficient, the larger the weight. For each pixel location, the deformation of each frequency point is multiplied by the corresponding weight and summed. Then, it is divided by the sum of all weights to obtain the final deformation of the corresponding pixel. Based on this, the time series deformation field is obtained, and an early warning is given based on the deformation rate threshold.

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