InSAR calibration technology combining KAPU algorithm and Radar Altimeter data

Abstract

The invention discloses an InSAR (Interferometric Synthetic Aperture Radar) calibration technology in combination with a KAPU (Kernel-to-Average Power Unit) algorithm and Radar Altimeter data. The method comprises the following steps: firstly, constructing an irregular triangular network based on Radar Altimeter data, and constructing a regular grid based on an interferogram; then, according to the triangular irregular network and the regular grid, a phase unwrapping result is obtained by using a KAPU algorithm; then, obtaining surface elevation information of the InSAR through phase-elevation conversion; and finally, a difference value is calculated by using the Radar Altimeter absolute elevation and the InSAR relative elevation, and linear calibration relation fitting is realized. According to the irregular triangular network construction method provided by the invention, complex surface information can be represented with different resolutions, and the method can be used for a sparse point data generation network; according to the method, the InSAR signal processing and calibration robustness can be enhanced by using the irregular grid gradient information of the exogenous auxiliary data; by combining exogenous auxiliary data, the KAPU algorithm provided by the invention can break through a phase continuity hypothesis, maintain the full-unit modularity of a phase unwrapping model constraint matrix, and obtain an accurate and reliable InSAR calibration result.

Description

Technical Field

[0001] The invention relates to the field of microwave remote sensing technology, in particular to an integrated InSAR signal processing and calibration technology based on KAPU algorithm and Radar Altimetry data. Background Art

[0002] The InSAR technique measures the relative quantity of a certain point or certain points in space; therefore, in order to obtain the final shape variable or elevation value of each pixel, deformation inversion and elevation calibration are required; InSAR calibration can be divided into two categories: calibration without external data assistance and calibration with external data assistance;In the absence of external data, it is necessary to select stable ground control points (GCPs) that theoretically meet the "zero deformation" requirement based on certain standards (such as high coherence, phase continuity, etc.) according to phase interference maps or interference quality maps (such as coherence coefficient maps, pseudo-coherence coefficient maps, and phase derivative variance maps) through visual interpretation, and calibrate the InSAR measurement results with reference to these GCP control points; the advantage of this calibration method is that only InSAR data is needed throughout the process, and the operation is easy, but the robustness is poor; InSAR calibration based on reference GCP control points can obtain effective However, even if the GCP control points are selected based on the same standard, when their spatial positions change, the InSAR calibration results will be different, and even the calibration will be invalid. This shows that 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 set of results to use as the InSAR calibration results. Therefore, when conditions permit, external data can be used to assist InSAR calibration. External auxiliary data can be divided into radar altimeters in glacier and ocean scenarios according to the usage scenarios. The other external auxiliary data in the single-satellite application scenario include but are not limited to the global positioning system (GPS) data, laser radar (LiDAR) data and deformation models, etc.; Radar Altimetry altimetry can be converted into the problem of determining the sea surface height through the half-power point. The sea surface height can be calculated based on the gate tracking method, Brown-Hayne model and least squares algorithm. 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 the point and the InSAR measurement height of a certain point in the regular grid of the InSAR measurement result as the overall offset to compensate and calibrate the InSAR measurement result; the other method is based on n high-quality points in the interference quality map, and counts its Radar The mean of the Altimetry measurement value and the mean of the InSAR measurement value are used, and the difference between the two is used as the overall offset of the InSAR measurement result for compensation calibration; both methods are based on the InSAR signal processing results for calibration, which has the advantages of simple calculation and strong operability; however, when the InSAR signal processing results are incorrect, such as in the presence of steep terrain, severe deformation or spatiotemporal incoherence in actual applications, the phase continuity assumption fails, and an erroneous unwrapping result will be obtained, and the calibration result obtained thereby becomes unreliable; in other words, the errors in InSAR signal processing will accumulate to the calibration results, resulting in error transmission, thus causing erroneous InSAR calibration results. ; Summary of the invention

[0003] In view of this, the present invention aims at the deficiencies of existing InSAR calibration methods and proposes an integrated InSAR phase unwrapping and calibration technology for realizing calibration in the process of InSAR signal processing. By utilizing the gradient signal in the irregular triangular network of exogenous auxiliary data, the exogenous data is integrated into the InSAR phase unwrapping process, thereby realizing the integration of InSAR phase unwrapping and calibration. Experiments show that the KAPU algorithm can obtain more accurate and reliable InSAR calibration results.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data provided by the present invention comprises the following steps:

[0006] S1: Acquire Radar Altimetry data and interferogram;

[0007] S2: Construction of irregular triangulated network based on Radar Altimetry data;

[0008] S3: construct a regular grid based on the interference pattern;

[0009] S4: Obtain phase unwrapping results using KAPU algorithm: Based on regular grid and irregular triangular network, the phase unwrapping results are calculated using KAPU algorithm;

[0010] S5: Obtain InSAR surface elevation through phase-elevation conversion relationship;

[0011] S6: Calculate the elevation difference and then fit the linear calibration relationship: Calculate the difference based on the Radar Altimetry absolute elevation and the InSAR relative elevation to get the elevation difference, and then fit the linear calibration relationship.

[0012] Furthermore, the calibration technology uses a Delaunay triangulation algorithm to achieve triangulation and construct a triangulated network; the construction of the triangulated network is a process of generating a set of triangles based on a given point set; the Delaunay triangulation meets the evaluation criteria of excellent irregular triangulated networks such as empty circle properties and maximizing minimum angles, and its generation is unique, making it the best performing triangulation algorithm.

[0013] Furthermore, the KAPU algorithm is composed of two layers of networks, namely an irregular triangular network constructed based on Radar Altimetry data and a regular grid constructed based on interference patterns.

[0014] Furthermore, in the regular grid, assuming that s represents a point in the grid, (s - 1) is the adjacent point of s in the horizontal or vertical direction; in the irregular grid In the above example, we assume that u and v are The objective function of the KAPU algorithm is expressed as follows:

[0015] ;

[0016] in, 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 (such as correlation coefficients and pseudo correlation coefficients).

[0017] Furthermore, the constraint condition of the regular grid in the KAPU algorithm is expressed according to the following formula:

[0018] ;

[0019] Where k(s) and k(s - 1) represent the fuzzy numbers to be calculated for pixels s and (s - 1), respectively. represents the estimated fuzzy number gradient between pixels s and (s - 1), φ(s) and φ(s - 1) represent the winding phases of pixels s and (s - 1), respectively, and k(s) is an integer.

[0020] Furthermore, the constraints of the irregular triangular network in the KAPU algorithm are determined according to the following formula:

[0021] ;

[0022] Where k(u) and k(v) represent the desired fuzzy numbers of points u and v, k(u) and k(v) are integers, K(u) and K(v) represent the fuzzy numbers of points u and v estimated based on Radar Altimetry data and interferometric phase, and (K(u) - K(v)) represents the fuzzy number gradient between points u and v.

[0023] Furthermore, K(u) and K(v) are calculated according to the following formula:

[0024] ;

[0025] 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. is the vertical baseline, h is the height measurement value of Radar Altimetry; represents the wavelength of SAR data, R is the slant distance between the radar and the target, is the radar incident angle.

[0026] Furthermore, 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, which is an NP-hard problem, that is, it is impossible to find the optimal solution in polynomial time; assuming that points p, q and r are the three vertices of a triangle in the triangular network, the constraints of the irregular triangular network can be further expanded to a closed-loop gradient field represented by the following formula:

[0027] .

[0028] Furthermore, according to the closed-loop gradient field formula, the integer constraint can be removed, thereby converting 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. At this time, the fuzzy number gradients of the three vertices are calculated according to the following formula:

[0029] .

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

[0031] The irregular triangulated network method provided by the present invention can represent more complex surface information with 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 exogenous auxiliary data can enhance the robustness of InSAR signal processing and calibration.

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

[0033] Figure 1 This is the InSAR calibration flow chart presented by this technology;

[0034] Figure 2 It is a schematic diagram of the irregular triangulation network constructed by two intersecting Radar Altimetry tracks in this InSAR calibration technique;

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

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

[0037] Figure 5 It verifies the influence of triangular networks with different densities on the calibration results of the KAPU algorithm in the experiment;

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

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

[0040] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the specific implementation methods, structures, features and effects of the present invention are further described below in combination with the accompanying drawings and preferred embodiments, so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

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

[0042] S1: Acquire Radar Altimetry data and interferogram;

[0043] S2: Construction of irregular triangulated network based on Radar Altimetry data;

[0044] S3: construct a regular grid based on the interference pattern;

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

[0046] S5: Obtain InSAR surface elevation through phase-elevation conversion relationship;

[0047] S6: Calculate the elevation difference and then fit the linear calibration relationship: Calculate the difference based on the Radar Altimetry absolute elevation and the InSAR relative elevation to get the elevation difference, and then fit the linear calibration relationship.

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

[0049] First, a triangulated network is constructed based on Radar Altimetry data. According to the number of Radar Altimetry tracks, it can be divided into the following three basic cases: one Radar Altimetry track, two Radar Altimetry tracks, and three Radar Altimetry tracks. In the case of one Radar Altimetry track, since all points on the same Radar Altimetry track are collinear, it is impossible to generate a closed triangle or construct an irregular triangulated network. In this case, three arc segments can be used to connect three different discrete points into a closed loop, and the closed loop is treated as a special "triangle" for processing.

[0050] Then, using all the special closed loops, an irregular "triangulated network" can be formed, which is recorded as ; The "triangulated network" The shorter the arc segment of the adjacent vertices of the "triangle", the smaller the distance between the two points, and the higher the spatial correlation between the vertices; the high spatial correlation is similar to the high spatial correlation of the atmospheric phase, so the short arc segment can be used to avoid the introduction of atmospheric errors in the InSAR signal processing process, thereby obtaining more accurate phase unwrapping and calibration results; on the contrary, the long arc segment is prone to cause low spatial correlation of the "triangle" vertices, resulting in InSAR calibration failure;

[0051] When two Radar Altimetry tracks intersect, the following Figure 2 (b) Delaunay triangulation network shown; different from the case where there is only one Radar Altimetry track, in this case three non-collinear points can form a true closed triangle, in which the adjacent vertices of the triangle are connected to each other; irregular triangulation network is constructed based on all closed triangles ;according to Figure 2 (b) It can be found that the triangles formed by the points closer to the intersection of the two trajectories are more likely to meet the optimal triangulation standard, that is, the arc segments of the formed triangles are shorter and will not appear too "narrow and long", thereby avoiding the introduction of atmospheric errors in InSAR phase unwrapping; the proportion of "short arc segment" triangles constructed by the two intersecting Radar Altimetry trajectories is higher than that of the case with only one Radar Altimetry trajectory, so it is more conducive to obtaining accurate InSAR calibration results;

[0052] When there are three Radar Altimetry tracks intersecting, the following can be generated: Figure 3 (b) The Delaunay triangulation network shown ; Different from the previous two cases, as the number of Radar Altimetry trajectories increases, the number of measured data points increases, and the number of trajectory intersections increases, so more adjacent high spatial correlation points are found through the triangulated network. The number of “short arc segment” triangles is increased, which is more conducive to obtaining accurate phase unwrapping and calibration results.

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

[0054] The study area is located in Weinan, Shanxi Province, with high mountains and valleys as the main terrain. The single-track dual-antenna TanDEM-X SAR image on October 21, 2012 is used as the research data. Figure 4 (a) The interference fringe pattern shown; according to Figure 4 (a) It can be seen that due to the dramatic terrain undulations, 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 wrong unwrapping results will inevitably lead to wrong InSAR calibration results; Figure 4 (b) is based on Figure 4 (a) The interference fringes and the reference terrain phase simulated by SRTM DEM data can be used as external auxiliary data and also to measure the error of InSAR calibration results; Figure 4 (c) is the InSAR calibration result based on the traditional calibration method; Figure 4 (b) An irregular triangular network is constructed by randomly selecting points in the corresponding regular grid, and the closed-loop gradient field formula of the irregular triangular network is embedded in the KAPU algorithm to obtain the following: Figure 4 (d) KAPU calibration results shown; Figure 4 (e) is the calibration error of the InSAR calibration result based on the traditional calibration method relative to the reference terrain phase, such as Figure 4 As shown in (e), the root mean square error (RMSE) value of the whole image is 20.74, and there are a lot of block errors in the image; Figure 4 (f) is the calibration error of the KAPU calibration result relative to the reference terrain phase, such as Figure 4 As shown in (f), the RMSE value of the whole image is 1.37, which is about Figure 4 (e) is 1 / 15 of the RMSE, and there is almost no blocking error in the figure; this shows that with the assistance of external data, the KAPU algorithm can achieve effective InSAR phase unwrapping and calibration, and the calibration results are significantly improved compared with traditional InSAR calibration results.

[0055] In this embodiment, the influence of triangulated networks with different densities on the KAPU calibration results is determined in the following manner:

[0056] Isolation Peak in Colorado, USA, which is dominated by mountainous, rugged and steep terrain, was selected as the research area to analyze the impact of the increase in the amount of external auxiliary data, the increase in the density of triangles in the irregular triangulated network, and the increase in the proportion of high-quality triangles on the calibration of KAPU InSAR; Figure 5 (a) shows the reference terrain phase simulated based on the SRTM DEM. Figure 5 (b) represents the winding phase corresponding to the reference terrain phase; based on Figure 5 (a) Corresponding to the regular grid, randomly select points from the regular grid with probabilities of 1 / 500, 1 / 100 and 1 / 50, and construct an irregular triangulated network based on the random point selection results, and embed the constructed irregular triangulated network into the KAPU calibration algorithm; based on the probability of 1 / 500, construct the following Figure 5 (c) shows a low-density triangular network based on Figure 5 (c) The triangular network is obtained with the KAPU algorithm as shown in Figure 5 (d) shows the KAPU calibration result, and Figure 5 The calibration error between the KAPU calibration result and the reference terrain phase in (d) is shown in Figure 5 As shown in (e), it can be found that Figure 5 The RMSE value in (e) is 1.67, and there are some error blocks in the upper part and the middle left of the error graph; based on the probability of 1 / 100, the following Figure 5 (f) shows a higher density triangulated network, and Figure 5 The calibration error between the KAPU calibration result and the reference terrain phase in (f) is shown in Figure 5 (g) As shown, Figure 5 The RMSE value in (g) is 1.4, compared with Figure 5 (e) is reduced, and the error block of this result is compared with Figure 5 (e) Significantly reduced; based on a probability of 1 / 50, the following Figure 5 (i) shows a high-density triangulated network, and Figure 5 The calibration error between the KAPU calibration result and the reference terrain phase in (i) is as follows: Figure 5 (j) As shown, Figure 5 The RMSE value in (j) is 1.09, compared with Figure 5 (g) is further reduced, and the error block in the result is further reduced. Figure 5 From the analysis of the KAPU calibration results, it can be found that with the increase of exogenous auxiliary data, the density of the irregular triangulated network continues to increase, and the accuracy of the calibration results of the KAPU algorithm steadily improves.

[0057] In this embodiment, the KAPU algorithm is used in conjunction with Radar Altimetry data to calibrate the InSAR of the glacier ocean scene in the following manner:

[0058] In terms of SAR data preparation, two scenes of SAR data from the Sentinel-1 satellite dated January 25, 2021 and January 31, 2021 were downloaded, covering a glacial area in southern Greenland; in terms of Radar Altimetry data preparation, 11 scenes of Radar Altimetry data from the Sentinel-6 satellite in the above-mentioned area from January 16, 2021 to February 12, 2021 were downloaded, including 4 scenes of ascending orbit data and 7 scenes of descending orbit data, which provided data support for the construction of a high-density triangulated network; an irregular triangulated network was constructed based on the Radar Altimetry data, and the KAPU algorithm was embedded for phase unwrapping, and the InSAR surface elevation information was obtained through phase-elevation conversion; in order to determine the relationship between the InSAR relative elevation and the Radar Altimetry absolute elevation, the Radar Altimetry absolute elevation was subtracted from the InSAR relative elevation, and the InSAR relative elevation was used as the horizontal axis and the elevation difference as the vertical axis to fit a straight line to obtain a linear calibration relationship; Figure 6 The figure shows the linear fitting results of relative elevation and elevation difference obtained by using the traditional MCF method and the InSAR calibration method combined with Radar Altimetry data; Figure 6 (a) It can be seen that some scattered points converge into a new straight line below the scatter plot fitted by the MCF method, which greatly reduces the accuracy of linear fitting. Figure 6 (b) The scatter plot fitted by the method has a good linear fitting result, which is significantly better than the fitting result of the MCF method, proving the superiority of the KAPU algorithm using RadarAltimetry data in linear fitting in calibration; Figure 6 As shown, the mathematical relationship of the fitted straight line can be obtained, where the linear relationship between the relative elevation and the elevation difference fitted using the MCF method is: , and the linear relationship between relative elevation and elevation difference fitted by the method is ; Based on the above linear relationship, the relationship between the absolute elevation and the elevation difference fitted by the two methods can be further obtained as follows: and , thus completing the InSAR calibration.

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

[0060] Depend on Figure 6 The results shown have proved that the method can be used for calibration of glacier ocean scenes. In the single-satellite application scenario, KAPUInSAR calibration can still be achieved by combining other external data, including but not limited to LiDAR data, GPS data and deformation models. Similar to the Radar Altimetry data in the glacier ocean scene, the above external data can be used to construct an irregular triangulated network and embed the KAPU algorithm. However, the fuzzy number gradient formula of the three vertices of the triangle K(p), K(q) and K(v) are obtained differently from the glacier ocean scene and can be calculated according to the following formula:

[0061] ;

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

[0063] The landslide neck (less than 200 meters in width) of the Slumgullion landslide in Colorado, USA, continues to deform at a rate of tens of millimeters per day. The deformation gradient has exceeded the applicable range of the phase continuity assumption, and traditional methods cannot obtain correct InSAR deformation calibration results. In terms of SAR data acquisition of the method, two Sentinel-1 satellite single-view complex images covering the above area on August 13, 2018 and August 25, 2018 were selected, with a radar wavelength of 0.0555m. After data preprocessing, a differential interferogram was obtained: In terms of exogenous auxiliary data acquisition of the method, NASA / JPL's airborne UAVSAR data was used. Based on the data and pixel offset tracking (POT) technology, the deformation rate of the landslide neck was obtained as follows: Figure 7 (a) as shown; Figure 7 (b) is the calibration result based on the traditional method; a deformation model is established based on the deformation rate, that is, absolute deformation phase = deformation rate × time interval × 4π / λ (λ is the radar wavelength); points are randomly selected for the exogenous deformation model with a probability of 1 / 100, and an irregular triangular network is constructed based on the point selection results, and the KAPU algorithm is embedded to obtain the following: Figure 7 (c) shows the calibration results based on the method; Figure 7 (c) It can be seen that with the help of the exogenous deformation model, the proposed method breaks through the limitation of the phase continuity assumption, so that its calibration results can successfully capture the large deformation of the landslide neck, and the deformation distribution is consistent with Figure 7The results shown in (a) are highly similar, while the calibration 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. This shows that when the traditional method fails under single-satellite application, the method described can still achieve relatively accurate and reliable InSAR calibration.

[0064] The above description is only the preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as the preferred embodiment as above, it is not used to limit the present invention. Any technical personnel in this field can make some more or modify the equivalent embodiments with equivalent changes by using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any brief modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. InSAR calibration technology combining KAPU algorithm and Radar Altimetry data, characterized by: The steps include: S1: Acquire Radar Altimetry data and interferogram; S2: Construction of irregular triangulated network based on Radar Altimetry data; S3: construct a regular grid based on the interference pattern; S4: Obtain phase unwrapping results using KAPU algorithm: Based on regular grid and irregular triangular network, the phase unwrapping results are calculated using KAPU algorithm; S5: Obtain InSAR surface elevation through phase-elevation conversion relationship; S6: Calculate the elevation difference and then fit the linear calibration relationship: Calculate the difference based on the Radar Altimetry absolute elevation and the InSAR relative elevation to get the elevation difference, and then fit the linear calibration relationship.

2. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: The calibration technology uses the Delaunay triangulation generation algorithm to achieve triangulation and construct a triangulated network; the construction of the triangulated network is the process of generating a set of triangles based on a given point set; the Delaunay triangulation meets the evaluation criteria of excellent irregular triangulated networks such as empty circle properties and maximizing minimum angles, and its generation is unique, making it the best performing triangulation algorithm.

3. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: The KAPU algorithm consists of two layers of networks, namely an irregular triangular network constructed based on Radar Altimetry data and a regular grid constructed based on interference patterns.

4. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: In the regular grid, assuming that s represents a point in the grid, (s - 1) is the adjacent point of s in the horizontal or vertical direction; in the irregular grid In the above example, we assume that u and v are The objective function of the KAPU algorithm is expressed as follows: ； in, 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 (such as correlation coefficients and pseudo correlation coefficients).

5. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: The constraints of the regular grid in the KAPU algorithm are expressed as follows: ； Where k(s) and k(s - 1) represent the fuzzy numbers to be calculated for pixels s and (s - 1), respectively. represents the estimated fuzzy number gradient between pixels s and (s - 1), φ(s) and φ(s - 1) represent the winding phases of pixels s and (s - 1), respectively, and k(s) is an integer.

6. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: The constraints of the irregular triangulated network in the KAPU algorithm are determined according to the following formula: ； Where k(u) and k(v) represent the desired fuzzy numbers of points u and v, k(u) and k(v) are integers, K(u) and K(v) represent the fuzzy numbers of points u and v estimated based on Radar Altimetry data and interferometric phase, and (K(u) - K(v)) represents the fuzzy number gradient between points u and v.

7. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: The K(u) and K(v) are calculated according to the following formula: ； The value of m depends on the signal transceiver 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. is the vertical baseline, h is the height measurement value of Radar Altimetry; represents the wavelength of SAR data, R is the slant distance between the radar and the target, is the radar incident angle.

8. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: 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, which is an NP-hard problem, that is, it is impossible to find the optimal solution in polynomial time; assuming that points p, q and r are the three vertices of a triangle in the triangular network, the constraints of the irregular triangular network can be further expanded to a closed-loop gradient field expressed by the following formula.

9.

10. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: According to the closed-loop gradient field formula, the integer constraints can be removed, thereby converting 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. At this time, the fuzzy number gradients of the three vertices are calculated according to the following formula.

11.

12. The InSAR calibration technology combining KAPU algorithm and Radar Altimetry data as claimed in claim 1, characterized in that: Due to the introduction of exogenous auxiliary data, the KAPU algorithm can break through the phase continuity assumption in the traditional InSAR signal processing process, and thus obtain more accurate and reliable unwrapping results; since the exogenous data is directly involved in the signal processing process, the KAPU algorithm can realize InSAR unwrapping and calibration in an integrated manner.

Images