InSAR calibration technique combined KAPU algorithm with radar altimetry data

Abstract

The application discloses an InSAR calibration technology combined with a KAPU algorithm and Radar Altimetry data; firstly, an irregular triangle network is constructed based on Radar Altimetry data, and a regular grid is constructed based on an interferogram; then, according to the irregular triangle network and the regular grid, a phase unwrapping result is obtained by using the KAPU algorithm; next, InSAR ground elevation information is obtained through phase-elevation conversion; finally, a difference value is calculated by using Radar Altimetry absolute elevation and InSAR relative elevation, and a linear calibration relationship fitting is realized. The irregular triangle network construction method provided by the application can represent complex ground information at different resolutions, and can be used for network generation of sparse point data; the application can enhance InSAR signal processing and calibration robustness by using gradient information of an irregular grid of exogenous auxiliary data; by combining exogenous auxiliary data, the KAPU algorithm provided by the application can break through the phase continuity assumption, maintain full unit modulus of a phase unwrapping model constraint matrix, and obtain accurate and reliable InSAR calibration results.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of microwave remote sensing, and particularly relates to an integrated InSAR signal processing and calibration technology based on a KAPU algorithm and Radar Altimetry data. BACKGROUND

[0002] The InSAR technology measures the relative quantity of some points in space; therefore, in order to obtain the final deformation quantity or height value of each pixel, deformation inversion and height calibration are needed. InSAR calibration can be divided into two categories: no external data assisted calibration and external data assisted calibration.In the absence of external data assistance, it is necessary to select stable ground control points (GCPs) that theoretically conform to "zero deformation" based on certain criteria (such as high coherence, phase continuity, etc.) through visual interpretation of phase interferograms or interference quality maps (such as coherence coefficient maps, pseudo-coherence coefficient maps, and phase derivative variance maps, etc.), and to calibrate the InSAR measurement results by referring to these GCP control points. The advantage of this calibration method is that only InSAR data is used in the entire process, and the operation is difficult, but the robustness is poor. Based on the reference GCP control points, the InSAR calibration can obtain effective calibration results, however, even if the GCP control points are selected based on the same criteria, when their spatial positions change, the InSAR calibration results will be different, and even the calibration will be invalid, thus the robustness of this method is poor. In the absence of prior information (such as geological disaster warning or polar DEM inversion), it is difficult for the experimenter to select and determine which group of results to use as the InSAR calibration results. Therefore, under the condition that the condition permits, external data can assist InSAR calibration. External auxiliary data can be divided into Radar Altimetry data in the ice and ocean scenarios and other external auxiliary data in the single-satellite application scenario according to the use scenario. Other external auxiliary data in the single-satellite application scenario includes but is not limited to Global Positioning System (GPS) data, LiDAR data, and deformation models, etc. Radar Altimetry height measurement can be converted into the problem of determining the sea surface height through the half-power point. Based on the gate tracking method, the Brown-Hayne model and the least squares algorithm, the sea surface height can be calculated. According to the height measurement value, the traditional method usually uses two methods to compensate the InSAR calibration height measurement value. One method is to use the offset between the absolute height of Radar Altimetry at a certain point in the regular grid of InSAR measurement results and the InSAR measurement height as the overall offset to compensate and calibrate the InSAR measurement results. Another method is to calculate the mean value of Radar Altimetry measurement value and the mean value of InSAR measurement value based on n high-quality points in the interference quality map, and the difference between the two is used as the overall offset of the InSAR measurement results for compensation and calibration. Both of these two methods are based on InSAR signal processing results for calibration, and have the advantages of simple calculation and strong operability. However, when the InSAR signal processing results are incorrect, for example, in actual application, when there are steep terrain, severe deformation or spatio-temporal incoherence, the phase continuity assumption fails, at this time, the unwrapping result will be wrong, and the calibration result obtained from it will also become unreliable. In other words, the error of InSAR signal processing will be accumulated to the calibration result, causing error propagation, and thus causing the wrong InSAR calibration result. SUMMARY

[0003] Therefore, the present application proposes an integrated InSAR phase unwrapping and scaling technology for realizing scaling in the InSAR signal processing process, by using the gradient signal in the irregular triangle network of the external source auxiliary data, fusing the external source data into the InSAR phase unwrapping process, and then realizing the integration of InSAR phase unwrapping and scaling; experiments show that the KAPU algorithm can obtain more accurate and reliable InSAR scaling results.

[0004] In order to achieve the above object, the present application provides the following technical scheme:

[0005] The InSAR scaling technology combined with the KAPU algorithm and Radar Altimetry data provided by the present application comprises the following steps:

[0006] S1: obtaining Radar Altimetry data and an interferogram;

[0007] S2: constructing an irregular triangle network based on the Radar Altimetry data;

[0008] S3: constructing a regular grid based on the interferogram;

[0009] S4: obtaining phase unwrapping results by using the KAPU algorithm: based on the regular grid and the irregular triangle network, the KAPU algorithm is used to calculate the phase unwrapping results;

[0010] S5: obtaining InSAR ground elevation through a phase-elevation conversion relationship;

[0011] S6: calculating the elevation difference and then fitting a linear scaling relationship: the difference is calculated based on the Radar Altimetry absolute elevation and the InSAR relative elevation, and then the linear scaling relationship is fitted.

[0012] Further, the scaling technology adopts a Delaunay triangle network generation algorithm to realize triangle partitioning and construct a triangle network; the construction of the triangle network is a process of generating a triangle set according to a given point set; the Delaunay triangle network satisfies the empty circle property, the maximum minimum angle and other excellent evaluation standards of irregular triangle networks, and its generation has uniqueness, which is the best triangle partitioning algorithm.

[0013] Further, the KAPU algorithm is composed of two networks, namely an irregular triangle network constructed based on the Radar Altimetry data and a regular grid constructed based on the interferogram.

[0014] Further, in the regular grid, assuming s represents a certain point in the grid, (s - 1) is the adjacent point of s in the horizontal direction or the vertical direction; in the irregular grid , assuming u, v are respectively two adjacent vertices of a triangle in , the objective function of the KAPU algorithm is expressed as follows:

[0015] ;

[0016] wherein, represents a phase unwrapping algorithm, when , it represents an L1 norm phase unwrapping; t(s, s - 1) and t(u, v) in the objective function represent auxiliary variables, and w(s, s - 1) and w(u, v) represent weighting coefficients (such as correlation coefficients, pseudo correlation coefficients).

[0017] Further, the constraint condition of the regular grid in the KAPU algorithm is expressed as follows:

[0018] ;

[0019] wherein, k(s) and k(s - 1) represent respectively the to-be-solved ambiguity number of the pixels s and (s - 1), represents the estimated ambiguity number gradient between the pixels s and (s - 1), φ(s) and φ(s - 1) represent respectively the wrapped phase of the pixels s and (s - 1), and k(s) is an integer.

[0020] Further, the constraint condition of the irregular triangle network in the KAPU algorithm is determined as follows:

[0021] ;

[0022] wherein, k(u) and k(v) represent the to-be-solved ambiguity number of the points u and v, k(u) and k(v) are integers, K(u) and K(v) represent the estimated ambiguity number of the points u and v according to Radar Altimetry data and interferometric phase, and (K(u) - K(v)) represents the ambiguity number gradient between the points u and v.

[0023] Further, the K(u) and K(v) are calculated as follows:

[0024] ;

[0025] wherein, the value of m depends on the signal transceiver mechanism of the SAR system, when the SAR system is a single-track double-antenna, m = 1, and when the SAR system is a single-antenna repeated orbit, m = 2. is the vertical baseline, h is the height measurement of Radar Altimetry; represents the wavelength of SAR data, R is the slant range between radar and target, is the radar incidence angle.

[0026] Further, since k(s), k(u) and k(v) are integers, the problem described by the above formula can be considered as an integer programming problem, and the integer programming problem is an NP-hard problem, that is, it is impossible to obtain an optimal solution in polynomial time; assuming that points p, q and r are three vertices of a triangle in a triangular network, the constraint condition of the irregular triangular network can be further extended to the closed loop gradient field represented by the following formula:

[0027] .

[0028] Further, according to the closed loop gradient field formula, the integer constraint can be removed, and the integer programming problem is converted into a linear programming problem, and the optimal integer solution is not affected, in other words, the constraint matrix has full unit modulus; at this time, the fuzzy number gradient of the three vertices is calculated according to the following formula:

[0029] .

[0030] The beneficial effects of the present application are:

[0031] The irregular triangular network method provided by the present application can represent more complex ground information at different resolutions, and is suitable for network generation of sparse point data (such as Radar Altimetry data); the gradient information in the irregular grid of the external auxiliary data can enhance the robustness of InSAR signal processing and calibration.

[0032] The KAPU algorithm provided by the present application can maintain the full unit modulus of the phase unwrapping model constraint matrix, thereby avoiding the generation of error propagation; by combining external auxiliary information, the KAPU algorithm can break through the phase continuity assumption, and obtain more accurate and reliable InSAR calibration results. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is the InSAR calibration flowchart presented by the present technology;

[0034] Figure 2 is a schematic diagram of constructing an irregular triangular network by two intersecting Radar Altimetry tracks in the present InSAR calibration technology;

[0035] Figure 3 is a schematic diagram of constructing an irregular triangular network by three intersecting Radar Altimetry tracks in the present InSAR calibration technology;

[0036] Figure 4 is the calibration result of KAPU algorithm in the verification experiment;

[0037] Figure 5 is the influence of different density triangular networks on the calibration result of KAPU algorithm in the verification experiment;

[0038] Figure 6 is a linear calibration relationship diagram of the InSAR calibration technology in the glacier ocean scene in the verification experiment;

[0039] Figure 7 is the calibration result of the InSAR calibration technology in the single satellite application scene in the verification experiment. DETAILED DESCRIPTION

[0040] In order to further illustrate the technical means and effects adopted by the present application to achieve the predetermined object of the application, the specific embodiments, structures, features and effects according to the present application are further described below in combination with the drawings and preferred embodiments, so that those skilled in the art can better understand the present application and implement it. The embodiments are not limiting to the present application.

[0041] As shown in Figure 1 , the InSAR calibration technology combining KAPU algorithm and Radar Altimetry data provided by the present embodiment comprises the following steps:

[0042] S1: obtaining Radar Altimetry data and an interferogram;

[0043] S2: constructing an irregular triangular network based on the Radar Altimetry data;

[0044] S3: constructing a regular grid based on the interferogram;

[0045] S4: obtaining phase unwrapping results by using KAPU algorithm: based on the regular grid and the irregular triangular network, the phase unwrapping results are calculated by using KAPU algorithm;

[0046] S5: obtaining InSAR ground elevation by phase-elevation conversion relationship;

[0047] S6: calculating the elevation difference and fitting the linear calibration relationship: the difference is calculated based on the Radar Altimetry absolute elevation and the InSAR relative elevation, and then the linear calibration relationship is fitted.

[0048] In the present embodiment, the irregular triangular network is constructed based on the Radar Altimetry data in the following manner:

[0049] Firstly, a triangular network is constructed based on Radar Altimetry data, which can be divided into the following three basic cases according to the number of Radar Altimetry tracks: one Radar Altimetry track, two Radar Altimetry tracks and three Radar Altimetry tracks; in the case of one Radar Altimetry track, all points on the same Radar Altimetry track are collinear, so that no closed triangle or irregular triangular network can be generated; at this time, three different discrete points can be connected into a closed loop by using three arc segments, and the closed loop is regarded as a special "triangle" for processing;

[0050] Then, all special closed loops can form an irregular "triangular network", which is denoted as ; the adjacent vertices of the "triangle" in the "triangular network" have a shorter arc segment and a smaller distance between two points, and the spatial correlation between the vertices is higher; the high spatial correlation is similar to the high spatial correlation of atmospheric phase, so the short arc segment can be used to avoid the introduction of atmospheric error in the InSAR signal processing process, thereby obtaining more accurate phase unwrapping and calibration results; on the contrary, the long arc segment is easy to cause low correlation of the "triangle" vertices in space, leading to InSAR calibration failure;

[0051] When two Radar Altimetry tracks intersect, a Delaunay triangular network as shown in Figure 2 (b) can be generated; unlike the case where there is only one Radar Altimetry track, three points that are not collinear can form a real closed triangle at this time, in which the adjacent vertices of the triangle are connected to each other; according to all closed triangles, an irregular triangular network is constructed; according to Figure 2 (b), it can be found that the triangle formed by the points closer to the intersection point of the two tracks is more likely to meet the optimal triangular partitioning standard, that is, the arc segment of the formed triangle is shorter and does not appear too "narrow", thereby avoiding the introduction of atmospheric error in InSAR phase unwrapping; the "short arc segment" triangle formed by the two intersecting Radar Altimetry tracks has a higher proportion than the case where there is only one Radar Altimetry track, so it is more conducive to obtaining accurate InSAR calibration results;

[0052] When there are three Radar Altimetry tracks intersecting, a Delaunay triangular network as shown in Figure 3 (b) can be generated ; Unlike the previous two cases, with the increase of the number of Radar Altimetry tracks, the number of measured data points and the number of track intersection points also increase, so more adjacent high spatial correlation points pass through the triangular network The number of "short arc" triangular networks increases, which is more conducive to obtaining accurate phase unwrapping and calibration results.

[0053] In this embodiment, the KAPU InSAR calibration based on the irregular triangular network is carried out in the following manner:

[0054] The Weinan region in Shanxi Province with high mountains and valleys as the main terrain is selected as the research region, and the single-track dual-antenna TanDEM-X SAR image on October 21, 2012 is used as the research data; based on the SAR data, the interference fringe pattern as shown in Figure 4 (a) is generated; according to Figure 4 (a), it can be seen that due to the severe terrain undulation, the interference fringes are dense and complex, which poses a challenge to the traditional single baseline phase unwrapping method based on the phase continuity assumption, and the incorrect unwrapping result will inevitably lead to incorrect InSAR calibration results; Figure 4 (b) is the reference terrain phase simulated based on the interference fringes in Figure 4 (a) and the SRTM DEM data, which can be used as exogenous auxiliary data or can be used to measure the error of the InSAR calibration result; Figure 4 (c) is the InSAR calibration result based on the traditional calibration method; according to the 1 / 100 probability in Figure 4 (b), the irregular triangular network is constructed by randomly selecting points in the corresponding regular grid, and the KAPU algorithm is embedded according to the closed loop gradient field formula of the irregular triangular network, to obtain the KAPU calibration result as shown in Figure 4 (d); Figure 4 (e) is the calibration error of the InSAR calibration result based on the traditional calibration method relative to the reference terrain phase, as shown in Figure 4 (e); the root mean square error (RMSE) value of the whole figure is 20.74, and there are a large number of block errors in the figure; Figure 4 (f) is the calibration error of the KAPU calibration result relative to the reference terrain phase, as shown in Figure 5 (f); the RMSE value of the whole figure is 1.37, which is about 1 / 15 of the RMSE in Figure 5 (e); there are almost no block errors in the figure; it can be seen that with the assistance of exogenous data, the KAPU algorithm can realize effective InSAR phase unwrapping and calibration, and the calibration result is significantly improved compared with the traditional InSAR calibration result.

[0055] In this embodiment, the impact of different density triangular networks on the KAPU calibration results is determined in the following manner:

[0056] Isolation Peak in Colorado, USA, characterized by rugged and steep mountainous terrain, was selected as the study area. The impact of increased triangle density and a higher proportion of high-quality triangles in the irregular triangular mesh on KAPU InSAR calibration was analyzed as the amount of external auxiliary data increased. Figure 5 As shown in (a), the reference terrain phase is represented by the simulation based on the SRTM DEM. Figure 5 (b) represents the winding phase corresponding to the reference terrain phase; based on Figure 5 (a) For the corresponding regular grid, points are randomly selected from the regular grid with probabilities of 1 / 500, 1 / 100, and 1 / 50, respectively. Based on the random point selection results, an irregular triangular network is constructed, and the constructed irregular triangular network is embedded into the KAPU calibration algorithm; based on a probability of 1 / 500, a network is constructed as follows: Figure 5 The low-density triangular network shown in (c) is based on Figure 5 (c) The triangular network and KAPU algorithm obtain as follows Figure 5 (d) shows the KAPU calibration results, and Figure 5 (d) The calibration error between the KAPU calibration results and the reference topographic phase is as follows: Figure 5 As shown in (e), it can be found that Figure 5 In (e), the RMSE value is 1.67, and there are some error blocks in the upper and middle left parts of the error plot; based on a probability of 1 / 100, a plot is constructed as follows: Figure 5 The higher-density triangular network shown in (f), and Figure 5 (f) The calibration error between the KAPU calibration results and the reference topographic phase is as follows: Figure 5 As shown in (g), Figure 5 (g) has an RMSE value of 1.4, compared to Figure 5 (e) is reduced, and the error block of this result is smaller compared to Figure 5 (e) Significantly reduced; constructing a model based on a probability of 1 / 50, such as Figure 5 The high-density triangular network shown in (i) and Figure 6 (i) The calibration error between the KAPU calibration results and the reference topographic phase is as follows: Figure 6 As shown in (j), Figure 6 The RMSE value in (j) is 1.09, compared to Figure 6 (g) is further reduced, and the error block in this result is further reduced. This is achieved through... Figure 6 Analysis of the KAPU calibration results reveals that as the amount of external auxiliary data increases, the density of the irregular triangular network continuously increases, and the accuracy of the KAPU algorithm's calibration results steadily improves.

[0057] InSAR calibration in the glacier-ocean scene in this embodiment is performed in the following manner by using the KAPU algorithm combined with Radar Altimetry data:

[0058] In terms of SAR data preparation, SAR data of two scenes of the Sentinel-1 satellite on January 25, 2021 and January 31, 2021 is downloaded, which covers an ice glacier area in the south of Greenland; in terms of Radar Altimetry data preparation, 11 scenes of Radar Altimetry data of the Sentinel-6 satellite from January 16, 2021 to February 12, 2021 are downloaded, which includes 4 ascending orbit scenes and 7 descending orbit scenes, providing data support for constructing a high-density triangular network; an irregular triangular network is constructed based on the Radar Altimetry data, and the KAPU algorithm is embedded for phase unwrapping, and InSAR ground elevation information is obtained through phase-elevation conversion; to determine the relationship between the InSAR relative elevation and the Radar Altimetry absolute elevation, the Radar Altimetry absolute elevation and the InSAR relative elevation are subtracted, and the InSAR relative elevation is taken as the horizontal axis and the elevation difference is taken as the vertical axis to fit a straight line, and a linear calibration relationship is obtained; as shown in Figure 7 , the linear fitting results of the relative elevation and the elevation difference obtained by using the traditional MCF method and the InSAR calibration method combined with Radar Altimetry data are shown; according to Figure 7 (a), it can be seen that part of the scattered points below the scatter plot fitted using the MCF method are gathered into a new straight line, which greatly reduces the accuracy of linear fitting, while Figure 7 (b) shows that the scatter plot fitted using the method has good linear fitting results, which are significantly better than the fitting results of the MCF method, proving the superiority of the KAPU algorithm using Radar Altimetry data in linear fitting in calibration; as shown in Figure 7 , the mathematical relationship of the fitted straight line can be obtained, wherein the linear relationship between the relative elevation and the elevation difference fitted using the MCF method is , and the linear relationship between the relative elevation and the elevation difference fitted using the method is ; according to the above linear relationship, the relationship between the absolute elevation and the elevation difference fitted by the two methods is and , thereby completing the InSAR calibration.

[0059] In this embodiment, the KAPU algorithm combined with Radar Altimetry data is used to perform InSAR calibration in a single-satellite application scene in the following manner:

[0060] The results shown in Figure 7 have proved that the method can be used for glacier-ocean scene calibration, and in single satellite application scenarios, combined with other exogenous data, including but not limited to LiDAR data, GPS data and deformation models, KAPUInSAR calibration can still be achieved. Similar to Radar Altimetry data in the glacier-ocean scene, at this time the above-mentioned exogenous data can be used to construct an irregular triangle network and embed the KAPU algorithm, but the K(p), K(q) and K(v) in the fuzzy number gradient formula of the three vertices of the triangle are different from the way of obtaining in the glacier-ocean scene, which can be calculated according to the following formula:

[0061] ;

[0062] Where d(p), d(q) and d(r) are deformation variables at points p, q and r along the radar slant range direction obtained according to exogenous auxiliary data; if the exogenous auxiliary data provides deformation rate, d(p), d(q) and d(r) can be obtained by multiplying the time interval by the deformation rate.

[0063] The landslide neck (width less than 200 meters) of Slumgullion landslide in Colorado, USA, is continuously deforming at a rate of tens of millimeters per day, and the deformation gradient has exceeded the applicable range of the phase continuity assumption, so the traditional method cannot obtain correct InSAR deformation calibration results; in terms of SAR data acquisition of the method, the dates selected are two scenes of Sentinel-1 satellite single-view complex images on August 13, 2018 and August 25, 2018, covering the above area, the radar wavelength is 0.0555m, and the differential interferogram is obtained after data preprocessing; in terms of exogenous auxiliary data acquisition of the method, NASA / JPL airborne UAVSAR data is used, and based on the data and pixel offset tracking (POT) technology, the deformation rate of the landslide neck is obtained as shown in ​ (a); ​ (b) is the calibration result based on the traditional method; based on the deformation rate, a deformation model is established, that is, absolute deformation phase = deformation rate × time interval × 4π / λ (λ is the radar wavelength); the exogenous deformation model is randomly selected according to a probability of 1 / 100, and an irregular triangle network is constructed based on the selected point results, and the KAPU algorithm is embedded, to obtain the calibration result based on the method as shown in ​ (c); ​ (c) can be seen that with the assistance of the exogenous deformation model, the method breaks through the limitation of the phase continuity assumption, so that its calibration result successfully captures the large deformation of the landslide neck, and the deformation distribution is consistent with ​(a) The results are similar, and the results based on the traditional method do not capture the significant deformation of the landslide neck due to the limitation of the phase continuity assumption; thus, the method can achieve more accurate and reliable InSAR calibration when the traditional method fails under single satellite application.

[0064] The above is only the preferred embodiment of the present application, and does not limit the present application in any form. Although the present application has been disclosed as above with the preferred embodiment, it is not intended to limit the present application. Any person skilled in the art can make some more or modified equivalent embodiments by using the disclosed technical content without departing from the technical solution of the present application. Any modification, equivalent change and modification of the above embodiments made according to the technical essence of the present application without departing from the technical solution of the present application still belong to the scope of the technical solution of the present application.

Claims

1. An InSAR calibration method combining the KAPU algorithm and Radar Altimetry data, characterized by: Includes the following steps: S1. Obtain Radar Altimetry data and interferograms; S2. Construct an irregular triangular network based on Radar Altimetry data: According to the number of Radar Altimetry trajectories, it is divided into the following three basic cases: one Radar Altimetry trajectory, two Radar Altimetry trajectories, and three Radar Altimetry trajectories; In the case of one Radar Altimetry trajectory, three different discrete points are connected into a closed loop using three arc segments, and the closed loop is regarded as a triangle. S3. Constructing a regular grid based on interferograms; S4. Obtaining phase unwrapping results using the KAPU algorithm: Based on regular grids and irregular triangular networks, the phase unwrapping results are calculated using the KAPU algorithm. S5. Obtain InSAR surface elevation through phase-elevation conversion relationship; S6. Calculate the elevation difference and then fit a linear calibration relationship: Calculate the elevation difference based on the difference between the absolute elevation of Radar Altimetry and the relative elevation of InSAR, and then fit a linear calibration relationship. The calibration method uses the Delaunay triangulation algorithm to perform triangulation and construct a triangular network. The construction of the triangular network is a process of generating a set of triangles based on a given set of points. The Delaunay triangulation satisfies the evaluation criteria of excellent irregular triangular networks, such as the empty circle property and maximizing the minimum angle, and its generation is unique, making it the best-performing triangulation algorithm. The KAPU algorithm consists of two layers: an irregular triangular network constructed based on Radar Altimetry data and a regular grid network constructed based on interferograms. In the regular grid, s represents a point in the grid, and s-1 is the adjacent point of s along the horizontal or vertical direction; in the irregular triangular network... In the middle, u and v are respectively Given two adjacent vertices of a triangle; the objective function of the KAPU algorithm is expressed by the following formula: ； in, This represents the phase unwrapping algorithm, when When, it represents the L1 norm phase solution; in the objective function, t(s, s-1) and t(u, v) represent auxiliary variables, and w(s, s-1) and w(u, v) represent weighting coefficients; The constraints of the regular grid in the KAPU algorithm are expressed by the following formula: ； Where k(s) and k(s-1) represent the undetermined fuzzy numbers of pixels s and s-1, respectively. This represents the estimated fuzzy number gradient between pixels s and s-1. Let k(s) represent the winding phases of pixels s and s-1, respectively, where k(s) is an integer. The constraint conditions of the irregular triangular network in the KAPU algorithm are determined according to the following formula: ； Where k(u) and k(v) represent the ambiguity numbers to be determined for points u and v, k(u) and k(v) are integers, K(u) and K(v) represent the ambiguity numbers of points u and v estimated based on Radar Altimetry data and interferometric phase, and (K(u) - K(v)) represents the ambiguity gradient between points u and v; K(u) and K(v) are calculated according to the following formula: ； The value of m depends on the signal transmission and reception mechanism of the SAR system. When the SAR system is a single-track dual-antenna system, m = 1. When the SAR system is a single-antenna repeating track system, m = 2. The vertical baseline is h, which is the elevation measurement value of Radar Altimetry. This represents the SAR data wavelength, where R is the slant range between the radar and the target. The radar incident angle; Since k(s), k(u), and k(v) are integers, the problem described by the above formula is an integer programming problem. Integer programming problems are NP-hard, meaning that the optimal solution cannot be found in polynomial time. Points p, q, and r are the three vertices of a triangle in a triangular network. The constraints of the irregular triangular network are further extended to the closed-loop gradient field expressed by the following formula: ； According to the closed-loop gradient field formula, removing the integer constraints transforms the integer programming problem into a linear programming problem without affecting the optimal integer solution; in other words, the constraint matrix has full unit modulus property. At this point, the fuzzy gradients of the three vertices are calculated using the following formula: 。 2. The InSAR calibration method using the combined KAPU algorithm and Radar Altimetry data as described in claim 1, characterized in that: By introducing external auxiliary data, the KAPU algorithm can break through the phase continuity assumption in the traditional InSAR signal processing process, thus obtaining more accurate and reliable unwrapping results. Since the external data directly participates in the signal processing process, the KAPU algorithm can integrate InSAR unwrapping and calibration.

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