Optimal configuration design method for distributed spaceborne D-InSAR surface deformation and convective atmosphere multi-dimensional measurement
Patent Information
- Application Number
- CN202510505273.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-21
- Publication Date
- 2025-08-19
AI Technical Summary
由于SAR观测几何的约束，传统的单星SAR无法测量大气折射率的空间三维分布，而分布式系统通过多个视角的协同观测，能够通过大气层析恢复其三维信息
[0062]1.对分布式星载D-InSAR的三维形变测量精度和大气层析测量精度进行分析，得到精确的测量精度函数；
Smart Images
Figure CN120507751A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of synthetic aperture radar, and in particular relates to an optimal configuration design method for distributed spaceborne D-InSAR (D-InSAR) for multi-dimensional measurement of surface deformation and convective atmosphere. Background Art
[0002] Distributed spaceborne synthetic aperture radar (SAR) systems hold great promise for Earth observation and are crucial for improving our understanding of the Earth's environment and our ability to respond to natural disasters. Compared to a single satellite, distributed SAR systems leverage the collaborative capabilities of multiple satellites to achieve high-precision, high-resolution observations of the Earth's surface. Furthermore, by leveraging the perspective differences between satellites, distributed SAR systems can acquire stereoscopic observation data, providing richer information for multi-dimensional surface deformation monitoring and three-dimensional tomographic inversion of the convective atmosphere.
[0003] Traditional single-satellite SAR technology measures surface deformation information through differential interferometry (D-InSAR), while distributed SAR systems can provide observation data from multiple angles. Through re-orbit interferometry, they provide more accurate three-dimensional deformation inversion capabilities in the east-west, north-south, and vertical directions. They can be applied to disaster monitoring such as earthquakes and landslides, and perform outstandingly in complex terrain and urban environments.
[0004] On this basis, if the effects of deformation during short-duration re-orbit interferometry can be neglected, distributed SAR systems can also monitor atmospheric refractive index variations through differential interferometry, particularly the atmospheric delay effect caused by water vapor variations in the lower troposphere. Due to the constraints of SAR observation geometry, traditional single-satellite SAR cannot measure the spatial three-dimensional distribution of atmospheric refractive index. However, distributed systems, through coordinated observations from multiple perspectives, can recover this three-dimensional information through atmospheric tomography.
[0005] However, distributed spaceborne D-InSAR multidimensional measurements of surface deformation and convective atmospheres face the following challenges. On the one hand, it is necessary to design appropriate satellite orbits and observation configurations to ensure that the system achieves both high atmospheric tomography inversion sensitivity and three-dimensional deformation measurement accuracy. On the other hand, there are contradictions and constraints between atmospheric tomography and three-dimensional deformation inversion. The system requires sufficient spatial observation angle differences to achieve higher three-dimensional deformation measurement accuracy, while excessive angle differences affect the number of spatial grids required for atmospheric tomography inversion. Therefore, to perform distributed spaceborne D-InSAR multidimensional measurements of surface deformation and convective atmospheres, it is necessary to design configuration optimization methods to solve the problem of joint optimization of dual-mission configurations and multiple parameters under the constraints of multiple objective functions, thus achieving multi-functionality of a single system. Summary of the Invention
[0006] To solve the above problems, the present invention provides a design method for the optimal configuration of distributed spaceborne D-InSAR for multi-dimensional measurement of surface deformation and convective atmosphere. This method can obtain the distributed spaceborne D-InSAR configuration design under the joint optimization of three-dimensional deformation inversion accuracy and multi-layer atmospheric tomography inversion accuracy, thereby simultaneously improving the accuracy of distributed spaceborne D-InSAR three-dimensional deformation measurement and atmospheric tomography measurement, and realizing multiple functions of one system.
[0007] The optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere of the present invention includes:
[0008] Step 1: Model the three-dimensional deformation measurement signal and error of distributed space-borne D-InSAR to determine the inversion result and measurement accuracy of the three-dimensional deformation.
[0009] Step 1. Model the 3D deformation measurement signal and error of the distributed spaceborne D-InSAR to determine the inversion results and measurement accuracy of the 3D deformation;
[0010] Step 2. Model the distributed spaceborne D-InSAR atmospheric tomography measurement signals and errors to determine the inversion results and measurement accuracy of atmospheric tomography;
[0011] Step 3. Based on the three-dimensional deformation and atmospheric tomography accuracy, determine the objective function and parameters to be optimized for the distributed spaceborne D-InSAR configuration optimization design;
[0012] Step 4. Based on the multi-parameter joint optimization method under the framework of fast non-dominated sorting genetic algorithm (NSGA-Ⅱ), the configuration design of distributed spaceborne D-InSAR for multi-dimensional measurement of surface deformation and convective atmosphere is optimized to obtain the optimal configuration.
[0013] Furthermore, the step 1 includes:
[0014] For a typical one-transmitter, two-receiver, three-satellite multi-base system, we denote the equivalent aperture center position corresponding to the three different observation angles as S An , the corresponding bistatic angle at the aperture center is β n , the deformation interference phase obtained by differential interferometry is Φ n The observation target is P0, and d=(d N ,d E ,d U ) T Represents the three-dimensional surface deformation information of the target in the geodetic coordinate system. N, E, and U are unit vectors in the north, east, and vertical directions respectively. The three-dimensional deformation inversion model based on multi-angle observation is expressed as
[0015] Φ=Θd (1)
[0016] Where Φ = (Φ1, Φ2, Φ3) T is the phase measurement vector.
[0017] The three-dimensional deformation model coefficient matrix Θ can be expressed as
[0018]
[0019] Among them, <·,·> represents the vector inner product, S An ,P0,n=1,2,3 is the unit vector of the line of sight direction between the equivalent aperture center position of the multi-base D-InSAR and the target under three different observation angles.
[0020] The least squares method is used to solve the deformation inversion expression, and the estimated three-dimensional deformation variable d is expressed as
[0021]
[0022] Among them, C Φ is the covariance matrix of the phase error.
[0023] In order to evaluate the comprehensive performance of the three-dimensional deformation measurement accuracy of scene targets under different angle data combinations, we introduce the concept of geometric dilution of precision (GDOP) in the GNSS system. Generally, GDOP consists of two parts: PDOP and clock deviation precision coefficient (TDOP). Since there is no clock error in the SAR system, we only need to consider the measurement based on PDOP. According to the classic PDOP definition, we define the measurement precision coefficient PDOP of three-dimensional deformation as d Expressed as
[0024]
[0025] in,
[0026]
[0027] It represents the square root of the three-dimensional deformation variance and characterizes the comprehensive accuracy of 3D deformation inversion.
[0028] When using the multi-angle observation method for three-dimensional deformation inversion, since the phase errors of the three orbital positions of the distributed satellite can be assumed to be consistent, the variance vector expression of the three-dimensional deformation obtained by the multi-angle observation method is:
[0029]
[0030] Formula (4) can also be simplified as
[0031]
[0032] where tr(·) represents the trace of the matrix.
[0033] Furthermore, the step 2 includes:
[0034] Assume that the number of effective observations obtained by the distributed D-InSAR system satellites is n e , then the tropospheric observation equation can be written as
[0035]
[0036] in, is a column vector consisting of all effective observed interference phases, with dimension [n e ×1], ΔN=N t2 -N t1 is the differential refractive index at two moments. We divide the voxels into p, q, and k according to longitude, latitude, and altitude, respectively. Then the dimension of ΔN is [pqk×1]. L is [n e ×pqk]-dimensional observation matrix can be written as
[0037]
[0038] Where l is the distance the radar signal passes through the voxel. d is the scene deformation vector,
[0039]
[0040] is the deformation observation matrix, n is the noise error vector, which can be written as the superposition of coherent noise, ionospheric residual noise, orbit error, synchronization error and thermal noise, that is,
[0041] n=n coh +n iono +n orbit +n sys +n t (11)
[0042] Assuming that there is no sudden deformation caused by volcanic eruptions or earthquakes during the D-InSAR acquisition time, the deformation effect during the short-time re-orbit interferometry period can be ignored. At this time, the atmospheric tomography result ΔN can be obtained by measuring the interferometry phase, which is expressed as
[0043]
[0044] Here, inv(L) represents the calculation of the generalized inverse matrix of L, because L is usually not a square matrix.
[0045] Chromatographic precision can be expressed as
[0046] A=diag{C ΔN} (13)
[0047] in, is the covariance matrix of the measured interferometric phase.
[0048] Furthermore, the step 3 includes:
[0049] Consider a multistatic D-InSAR system consisting of three X-band satellites operating in two different orbital planes. The reference satellite (S0) and slave satellite 1 (S1) operate in the same orbital plane, while the second slave satellite (S2) operates in another orbital plane.
[0050] parameter vector The geometric configuration of the system is determined, where α is the azimuth between S0 and the scene center, β1 is the double base angle between S0 and S1, β2 is the double base angle between S0 and S2, ΔLon represents the differential longitude between the two orbital planes, ΔLon and ε = I dis / ΔLon together determine the trajectory of the orbit, where I dis is the differential longitude from the scene center to the reference orbit ground track.
[0051] The objective function of the distributed spaceborne D-InSAR configuration optimization design consists of two parts:
[0052] Expressed as
[0053]
[0054] Among them, PDOP d That is, the measurement accuracy coefficient of the three-dimensional deformation we defined in step 1. The smaller the value of f1, the higher the measurement accuracy of the three-dimensional deformation; is the atmospheric tomography accuracy expression obtained in step 2. Similarly, the smaller the value of f2, the higher the measurement accuracy of atmospheric tomography.
[0055] Furthermore, the step 4 includes:
[0056] Step 4.1: Determine the range and step size of the geometric parameter vector to be optimized in the configuration and encode it accordingly.
[0057] Step 4.2, initialize the parameters of population P1.
[0058] Step 4.3, design the objective function according to step 3, calculate the individual fitness, perform selection, crossover, and mutation operations, and generate the offspring population Q.
[0059] In step 4.4, use fast non-dominated sorting and crowding calculation to select the next generation parent population P. Repeat step 4.3 to iteratively search for the optimal solution.
[0060] In step 4.5, when the set number of iterations is reached, the optimal solution is selected from the first Paleto front.
[0061] Beneficial effects:
[0062] 1. Analyze the 3D deformation measurement accuracy and atmospheric tomography measurement accuracy of distributed spaceborne D-InSAR to obtain an accurate measurement accuracy function;
[0063] 2. Based on the measurement accuracy function, the objective function of the configuration optimization design is established. Using the multi-parameter joint optimization method under the framework of the fast non-dominated sorting genetic algorithm (NSGA-II), a configuration design optimization method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere is proposed.
[0064] 3. According to the above configuration design optimization method, the configuration design is optimized to obtain the optimal design configuration, realizing multiple functions of one system, and at the same time improving the accuracy of the joint measurement of three-dimensional deformation and atmospheric tomography of distributed spaceborne SAR. BRIEF DESCRIPTION OF THE DRAWINGS
[0065] Figure 1 Schematic diagram of the distributed spaceborne D-InSAR configuration for multi-dimensional measurement of surface deformation and convective atmosphere;
[0066] Figure 2 Schematic diagram of 3D deformation inversion accuracy under PDOP;
[0067] Figure 3 Schematic diagram of tropospheric tomography measurement;
[0068] Figure 4 Schematic diagram of the multi-parameter joint optimization steps of NSGA-Ⅱ;
[0069] Figure 5 Comparison diagram of the three-dimensional deformation inversion results and true values before and after configuration optimization; (a) three-dimensional deformation inversion results before optimization, (b) three-dimensional deformation inversion results after optimization, (c) true value of three-dimensional deformation results;
[0070] Figure 6 Comparison diagram of tropospheric tomography results and true values before and after configuration optimization; (a) atmospheric tomography inversion result before optimization, (b) atmospheric tomography inversion result after optimization, (c) true value of atmospheric tomography result;
[0071] Figure 7 Comparison of the tropospheric tomography results and the true value errors before and after configuration optimization; (a) error before optimization, (b) error after optimization. DETAILED DESCRIPTION
[0072] The distributed spaceborne D-InSAR (D-InSAR) satellite fleet for multi-dimensional measurements of surface deformation and convective atmosphere uses multiple orbital planes to form a "one primary, multiple secondary" SAR satellite formation. Only the primary satellite, located in a reference orbit, contains the active SAR payload and has transmitting capabilities. The remaining satellites are lightweight, passive receivers. This multi-base operation reduces complexity and costs. Each satellite in the system can perform D-InSAR measurements in multiple orbits, enabling simultaneous multi-angle observations.
[0073] The present invention is discussed in detail below with reference to the accompanying drawings. The optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere of the present invention includes:
[0074] Step 1, for Figure 1 The typical one-transmitter, two-receiver, three-star distributed D-InSAR system shown in the figure is denoted by S. An , the corresponding bistatic angle at the aperture center is β n , the deformation interference phase obtained by differential interferometry is Φ n , where n = 1, 2, 3. Let the observed target be P0, and use d = (d N ,d E ,d U ) T Represents the three-dimensional deformation information of the target surface in the geodetic coordinate system, where d N is the deformation in the north-south direction, d E is the deformation in the east-west direction, d U is the vertical deformation variable. N, E, and U are unit vectors in the north, east, and vertical directions, respectively. The three-dimensional deformation inversion model based on multi-angle observation is expressed as
[0075] Φ=Θd (15)
[0076] Where Φ = (Φ1, Φ2, Φ3) T is the phase measurement vector.
[0077] The three-dimensional deformation model coefficient matrix Θ can be expressed as
[0078]
[0079] Among them, <·,·> represents the vector inner product, S An ,P0,n=1,2,3 is the unit vector of the line of sight direction between the equivalent aperture center position of the multi-base D-InSAR and the target under three different observation angles.
[0080] The least squares method is used to solve the deformation inversion expression, and the estimated three-dimensional deformation variable d is expressed as
[0081]
[0082] Among them, C Φ is the covariance matrix of the phase error.
[0083] In order to evaluate the comprehensive performance of the three-dimensional deformation measurement accuracy of scene targets under different angle data combinations, we introduce the concept of geometric dilution of precision (GDOP) in the GNSS system. Generally, GDOP consists of two parts: PDOP and clock deviation precision coefficient (TDOP). Since there is no clock error in the SAR system, we only need to consider the measurement based on PDOP. According to the classic PDOP definition, it is assumed that the phase error size of the interferogram generated at different angles is not distinguished (the phase variance is ), we define the measurement accuracy coefficient of three-dimensional deformation PDOP d Expressed as
[0084]
[0085] in,
[0086]
[0087] It represents the square root of the three-dimensional deformation variance and characterizes the comprehensive accuracy of the three-dimensional deformation inversion. The geometric diagram of the error sphere under the PDOP is as follows: Figure 2 shown.
[0088] When using the multi-angle observation method for 3D deformation inversion, since the phase errors of the three orbital positions can be assumed to be consistent, the variance vector expression of the 3D deformation obtained by the multi-angle observation method is:
[0089]
[0090] Formula (18) can also be simplified as
[0091]
[0092] where tr(·) represents the trace of the matrix.
[0093] Step 2, the basic schematic diagram of tropospheric tomography measurement is as follows Figure 3 shown.
[0094] Assume that the number of effective observations obtained by the distributed D-InSAR system satellites is n e , then the tropospheric observation equation can be written as
[0095]
[0096] in, is a column vector consisting of all effective observed interference phases, with dimension [n e ×1], ΔN=N t2 -N t1 is the differential refractive index at two moments. We divide the voxels into p, q, and k according to longitude, latitude, and altitude, respectively. Then the dimension of ΔN is [pqk×1]. L is [n e ×pqk]-dimensional observation matrix can be written as
[0097]
[0098] Where l is the distance the radar signal passes through the voxel. d is the scene deformation vector,
[0099]
[0100] is the deformation observation matrix, n is the noise error vector, which can be written as the superposition of coherent noise, ionospheric residual noise, orbit error, synchronization error and thermal noise, that is,
[0101] n=n coh +n iono +n orbit +n sys +n t (25)
[0102] Assuming that there is no sudden deformation caused by volcanic eruptions or earthquakes during the D-InSAR acquisition time, the deformation effect during the short-time re-orbit interferometry period can be ignored. At this time, the atmospheric tomography result ΔN can be obtained by measuring the interferometry phase, which is expressed as
[0103]
[0104] Here, inv(L) represents the calculation of the generalized inverse matrix of L, because L is usually not a square matrix.
[0105] Chromatographic precision can be expressed as
[0106] A=diag{C ΔN} (27)
[0107] in, is the covariance matrix of the measured interferometric phase.
[0108] In step 3, to address the configuration optimization design problem for the distributed spaceborne D-InSAR multidimensional measurement of surface deformation and convective atmosphere, a multistatic D-InSAR system with one transmitter and two receivers is considered. The system consists of three X-band satellites distributed in two different orbital planes. The reference satellite (S0) and slave satellite 1 (S1) operate in the same orbital plane, while the second slave satellite (S2) operates in a different orbital plane.
[0109] parameter vector The geometric configuration of the system is determined, where α is the azimuth between S0 and the scene center, β1 is the double base angle between S0 and S1, β2 is the double base angle between S0 and S2, ΔLon represents the differential longitude between the two orbital planes, ΔLon and ε = I dis / ΔLon together determine the trajectory of the orbit, where I dis is the differential longitude from the scene center to the reference orbit ground track.
[0110] The optimization process of distributed spaceborne D-InSAR configuration design is as follows: Figure 4 As shown, the objective function consists of two parts and can be expressed as
[0111]
[0112] Among them, PDOP d That is, the measurement accuracy coefficient of the three-dimensional deformation we defined in step 1. The smaller the value of f1, the higher the measurement accuracy of the three-dimensional deformation; is the atmospheric tomography accuracy expression obtained in step 2. Similarly, the smaller the value of f2, the higher the atmospheric tomography measurement accuracy. At this point, the modeling of the configuration parameters and objective function is completed.
[0113] Step 4: After modeling, the multi-parameter joint optimization step based on the fast non-dominated sorting genetic algorithm (NSGA-Ⅱ) framework is started. The specific steps are as follows:
[0114] Step 4.1: Determine the geometric parameter vector to be optimized in the configuration The range and step size of the parameters to be optimized are encoded in decimal.
[0115] Step 4.2: Initialize the population and use the random method to initialize the parameters to be optimized to form the initialized population P1.
[0116] Step 4.3, design the objective function according to step 3, calculate the individual fitness, perform selection, crossover, and mutation operations, and generate the offspring population Q.
[0117] In step 4.4, use fast non-dominated sorting and crowding calculation, and use the elite retention strategy to select the next generation parent population P. Repeat step 4.3 to iteratively search for the optimal solution.
[0118] In step 4.5, after reaching the set number of iterations, due to the multiple constraints in the objective function, there may be multiple possible solutions (the first Paleto front). Normalize the two objective functions of each individual and calculate the Euclidean distance to the origin. Select the solution with the smallest Euclidean distance as the optimal solution.
[0119] Using the optimized optimal satellite configuration obtained in step 4.5, the least squares method is used to calculate the inversion results of the three-dimensional deformation; ignoring the influence of the deformation, the three-dimensional tomography results of the atmospheric refractive index are calculated according to formula (26) to obtain the results.
[0120] At this point, all steps are completed.
[0121] Next, an implementation example is given with specific parameters.
[0122] In this example, 106°E and 29°N were used as the scene center for 3D deformation inversion and atmospheric tomography inversion. The 3D deformation inversion reference data was obtained from a local GNSS station and did not undergo deformation during the sampling period. The atmospheric tomography grid was set to 10 km × 10 km × 10 km, and the DALES model was used to generate simulations of different tropospheric conditions. The satellite configuration employed a primary satellite and two secondary satellites operating in two basic orbital planes for subsequent verification experiments. The overall formation orbital altitude was 512 km. The initial configuration satellite parameters are shown in Table 1.
[0123] Table 1 Initial configuration parameters
[0124]
[0125]
[0126] The following configuration optimization is carried out, The ranges corresponding to the elements used for optimization are [30, 90°], [0, 90°], [0, 90°], [1, 10°], and [-0.4, 0.4]. For more accurate optimization, a smaller step size is set, with the step sizes corresponding to the five parameters being 1, 1, 1, 0.2, and 0.01, respectively. To balance simulation time and optimization effect, the population size is set to 20 and the number of iterations is set to 100.
[0127] After all the iterative optimizations, the five parameters of the optimal individual are as follows: the master satellite azimuth angle α is 76°, the double base angle between the master satellite and slave satellite 1 is 36°, the double base angle between the master satellite and slave satellite 2 is 55°, ΔLon is 4.6°, and ε is 0.01. The optimized satellite configuration parameters are shown in Table 2. Furthermore, the initial configuration F1 and F2 before optimization were 595.13 and 10.85, respectively, while the optimized configuration F1 and F2 were 0.34 and 5.55, respectively, indicating significant optimization results.
[0128] Table 2 Optimized configuration parameters
[0129]
[0130] In order to verify the effectiveness of the optimization method, we used the configurations before and after optimization to invert the three-dimensional deformation results and atmospheric tomography results respectively. Figure 5 The comparison between the three-dimensional deformation inversion results and the true value before and after configuration optimization is shown. Figure 6 The comparison between the atmospheric tomography inversion results and the true values before and after configuration optimization is shown. According to calculations, the RMSE of the three-dimensional deformation inversion before optimization were 5.7mm, 7.8mm, and 3.2mm, respectively. After optimization, the RMSE of the three-dimensional deformation inversion were 1.4mm, 5.8mm, and 2.8mm, respectively, which were improved by about 75%, 26%, and 13%, respectively. The RMSE of the central differential refractive index ΔN of the atmospheric tomography inversion was also reduced from 5.29 to 3.28, and the accuracy was improved by about 40%. In addition, Figure 7 A comparison chart of the difference between the atmospheric tomography inversion results and the true values before and after configuration optimization is shown. It can be seen from the figure that the inversion error of the optimized configuration is significantly smaller and the optimization effect is significant.
[0131] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.
Claims
1. An optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere, characterized by , including the following steps: Step 1. Model the 3D deformation measurement signal and error of the distributed spaceborne D-InSAR to determine the inversion results and measurement accuracy of the 3D deformation; Step 2. Model the distributed spaceborne D-InSAR atmospheric tomography measurement signals and errors to determine the inversion results and measurement accuracy of atmospheric tomography; Step 3. Based on the three-dimensional deformation and atmospheric tomography accuracy, determine the objective function and parameters to be optimized for the distributed spaceborne D-InSAR configuration optimization design; Step 4. Based on the multi-parameter joint optimization method under the framework of fast non-dominated sorting genetic algorithm (NSGA-Ⅱ), the configuration design of distributed spaceborne D-InSAR for multi-dimensional measurement of surface deformation and convective atmosphere is optimized to obtain the optimal configuration.
2. The optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere according to claim 1, characterized in that: In step 1, the concept of geometric dilution of precision (GDOP) in the GNSS system is introduced. GDOP consists of two parts: PDOP and clock deviation coefficient of precision (TDOP).
3. The optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere according to claim 1, characterized in that: In step 1, the measurement accuracy coefficient of the three-dimensional deformation PDOP d Expressed as in, It represents the square root of the three-dimensional deformation variance and characterizes the comprehensive accuracy of 3D deformation inversion.
4. The optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere according to claim 1, characterized in that: In step 1, when the multi-angle observation method is used for three-dimensional deformation inversion, the variance vector expression of the three-dimensional deformation variable obtained by the multi-angle observation method is Mode Simplified expression: where tr(·) represents the trace of the matrix.
5. The optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere according to claim 1, characterized in that: In step 2, the atmospheric tomography result ΔN is obtained by measuring the interferometric phase and is expressed as Where inv(L) represents the generalized inverse matrix calculation of L; the tomographic accuracy is expressed as A=diag{C ΔN } in, is the covariance matrix of the measured interferometric phase.
6. The optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere according to claim 1, characterized in that: In step 3, the objective function of the distributed spaceborne D-InSAR configuration optimization design consists of two parts, which are expressed as Among them, PDOP d That is, the measurement accuracy coefficient of the three-dimensional deformation defined in step 1. The smaller the value of f1, the higher the measurement accuracy of the three-dimensional deformation; is the atmospheric tomography accuracy expression obtained from the analysis in step 2. The smaller the value of f2, the higher the measurement accuracy of atmospheric tomography.
7. The optimal configuration design method for distributed spaceborne D-InSAR multi-dimensional measurement of surface deformation and convective atmosphere according to claim 1, characterized in that: The step 4 comprises: Step 4.1, determine the range and step size of the geometric parameter vector to be optimized in the configuration and encode it accordingly; Step 4.2, initialize the parameters of population P1; Step 4.3: Design the objective function according to step 3, calculate the individual fitness, perform selection, crossover, and mutation operations, and generate the offspring population Q; In step 4.4, use fast non-dominated sorting and crowding calculation to select the next generation parent population P; repeat step 4.3 to iteratively search for the optimal solution; In step 4.5, when the set number of iterations is reached, the optimal solution is selected from the first Paleto front.