A method for optimizing the tropospheric atmosphere inversion grid based on spaceborne multi-angle D-InSAR

Abstract

This invention discloses a method for optimizing the tropospheric atmospheric inversion grid based on spaceborne multi-angle D-InSAR. Firstly, based on a tomographic inversion model, this method quantitatively models the quantization noise and inversion performance constraints under the influence of grid division. Furthermore, by combining multi-angle observation configurations, the optimization parameters and objective function are constructed for the optimization design. Finally, a multi-objective optimization algorithm is used to jointly optimize the observation configuration and the inversion grid, achieving an optimal balance between observation information utilization efficiency and inversion accuracy.

Description

Technical Field

[0001] This invention belongs to the field of spaceborne synthetic aperture radar interferometry and atmospheric remote sensing technology. Specifically, it relates to a method for optimizing the grid design of tropospheric atmospheric inversion based on spaceborne multi-angle D-InSAR. Background Technology

[0002] The troposphere, as the most active and complex region of Earth's atmosphere, exhibits significant non-uniformity in its atmospheric conditions. Detailed observation and reconstruction of this region are crucial for understanding the formation mechanisms and evolution of severe weather events such as rainstorms and typhoons. Therefore, achieving high-precision three-dimensional observation of the troposphere is of great significance for meteorological disaster prevention and mitigation, refined weather forecasting, and meteorological scientific research.

[0003] Existing atmospheric observation methods still have certain limitations at different levels. Optical methods, such as visible light and infrared remote sensing, are easily affected by complex meteorological conditions such as clouds and rainfall, making it difficult to achieve stable observations. On the other hand, ground-based microwave measurement methods, such as radiosondes and Global Navigation Satellite Systems (GNSS), have sparse station distribution, limited spatial coverage and resolution, making it difficult to obtain continuous high-resolution three-dimensional atmospheric structure information.

[0004] In contrast, spaceborne differential synthetic aperture radar interferometry (D-InSAR) technology possesses all-weather, all-time observation capabilities and demonstrates great potential for high-precision atmospheric parameter inversion. Furthermore, spaceborne multi-angle D-InSAR, through multi-angle observations of the same region, can provide additional spatial constraint information. Combined with grid-based tomographic reconstruction methods, it enables three-dimensional inversion of the troposphere, providing a feasible approach for high-resolution atmospheric sounding.

[0005] However, the performance of spaceborne multi-angle D-InSAR tropospheric tomography inversion is directly affected by the grid division method. On the one hand, overly fine grid division significantly increases the size of the parameters to be estimated, thereby reducing the accuracy and solution stability of the inversion; on the other hand, overly sparse grid division introduces large quantization errors and makes it difficult to effectively characterize the fine-scale changes of the tropospheric atmosphere. In addition, the tropospheric atmosphere typically exhibits characteristics of dramatic changes in the lower layers and relatively gradual changes in the upper layers. A uniform-scale grid division cannot take into account the structural characteristics of different altitude layers, thus leading to a significant trade-off between accuracy and stability in the tomography problem.

[0006] Current research largely focuses on parameter inversion processes under fixed grid division conditions, lacking systematic analysis and modeling of the grid's impact on itself. To achieve high-precision three-dimensional tomographic inversion of the troposphere, it is necessary to quantitatively assess the impact of grid division and establish a collaborative optimization design mechanism based on multi-angle observation configurations. Summary of the Invention

[0007] In view of this, the present invention provides a method for optimizing the tropospheric atmospheric inversion grid based on spaceborne multi-angle D-InSAR. This method firstly, based on a tomographic inversion model, achieves quantitative modeling of quantization noise and inversion performance constraints under the influence of grid division. Furthermore, combining multi-angle observation configurations, it constructs the parameters to be optimized and the objective function in the optimization design, and performs joint optimization design of the observation configuration and inversion grid based on a multi-objective optimization algorithm to achieve the optimal balance between observation information utilization efficiency and inversion accuracy.

[0008] To achieve the above-mentioned objectives, the technical solution of this invention is as follows: This invention proposes a tropospheric atmosphere inversion grid optimization method based on spaceborne multi-angle D-InSAR, comprising the following steps: S1. Based on the observation geometry of spaceborne multi-angle D-InSAR, a three-dimensional tomographic inversion model of tropospheric atmospheric refractive index is established, and the quantization noise under the influence of grid division is quantitatively modeled and a quantization noise model is established. S2. Based on the tomographic inversion model and the quantitative noise model, the core performance constraints of the three-dimensional tomographic inversion of the troposphere atmosphere by spaceborne multi-angle D-InSAR are modeled, and the quantitative model of the tomographic inversion performance constraints is established. S3. Based on the quantitative model constrained by tomographic inversion performance, determine the optimization parameters and objective function of the spaceborne multi-angle D-InSAR tropospheric atmospheric inversion grid optimization. S4. Based on the multi-objective and multi-parameter joint optimization algorithm framework, the joint optimization of the spaceborne multi-angle D-InSAR tropospheric atmospheric inversion grid and system configuration is realized to obtain the joint optimal configuration of grid and configuration.

[0009] Furthermore, the refractive index tomography inversion model under the spaceborne multi-angle D-InSAR observation geometry in S1 is as follows: Assuming there is a total n From one observation angle, the troposphere above the scene is divided into... M For a three-dimensional grid, after removing flat land and topographic phases using an external digital elevation model, and assuming no significant deformation such as volcanoes or earthquakes occurred during the reorbit observation period, the tomographic inversion equation is expressed as follows: (1) in, Indicates the first iA column vector consisting of all effective observation phases from each observation angle. For the first m The relative refractive index corresponding to each grid Indicates the first i The observation matrix corresponding to each observation angle is represented as follows: (2) in, l This represents the sub-distance by which the radar signal passes through the grid.

[0010] Furthermore, the quantization noise model under the influence of mesh generation in S1 is as follows: In tomographic inversion, it is assumed that the refractive index is constant within each grid cell. However, the actual refractive index field exhibits continuous fluctuations. This introduces phase quantization noise, which can be expressed as: (3) in, This represents the true relative refractive index field of the grid. This represents the line integral along the radar signal. The average relative refractive index within the grid. l This represents the sub-distance the signal travels across the grid.

[0011] Through the grid center Perform a second-order Taylor expansion at that point. Further expressed as: (4) in, , Indicates the relative refractive index field at The vector gradient at point H, where H is the second-order mixed partial derivative matrix, is expressed as: (5) Substituting (4) into (3) and simplifying, we obtain the final phase quantization noise, expressed as: (6) Where u represents the unit direction vector of the signal path direction.

[0012] Furthermore, the quantitative model of inversion performance constraints in S2 consists of three parts, expressed as follows: (7) in, Indicates the accuracy of tomographic inversion. X For the total number of invertible grid cells, Represents the trace of a matrix. Let be the covariance matrix of the observation vectors, where the diagonal elements represent the variance of the effective observations; Δ represents the resolution of the tomographic inversion grid. x Δ y With Δ z These represent the 3D dimensions of the smallest mesh within the scene; This indicates the scale of the invertible grid.

[0013] Furthermore, the system parameters to be optimized in S3 are expressed as follows: (8) in, For the tomographic inversion mesh parameter vector, D l , D m and D u These correspond to the tropospheric atmospheric grid sizes of 0-2 km, 2-6 km, and 6-10 km, respectively. To determine the parameter vector of the system observation configuration.

[0014] Furthermore, the optimization objective function in S3 is expressed as: (9) in, J 1 indicates the precision of the tomographic inversion. J 2 indicates the inversion grid resolution. J 3 represents the scale of the non-reversible mesh; all three are system parameter vectors. The function.

[0015] Furthermore, the multi-objective, multi-parameter joint optimization in S4 employs the multi-parameter particle swarm optimization algorithm (MOPSO) as the framework optimization solution.

[0016] Beneficial effects: 1. This invention addresses the significant impact of mesh generation on tomographic inversion performance, particularly by providing a detailed model of the quantization noise introduced by mesh discretization. This enables a quantitative assessment of tomographic inversion accuracy and provides a theoretical basis for mesh optimization. 2. This invention introduces multi-objective and multi-parameter joint optimization to jointly design and optimize the system observation configuration and grid division, thereby obtaining the optimal configuration of the configuration and grid. This improves the efficiency of observation information utilization while ensuring inversion stability, and provides effective support for high-precision three-dimensional tropospheric atmospheric inversion. Attached Figure Description

[0017] Figure 1 A flowchart illustrating the implementation of this invention; Figure 2 Spaceborne multi-angle D-InSAR tropospheric tomography inversion geometric model; Figure 3 1. Schematic diagram of the Samsung system observation configuration in the embodiment; Figure 4 The simulation interferograms of angle 1 before and after optimization in the embodiments; Figure 5 The three-dimensional tomographic inversion results and true values ​​of the tropospheric atmosphere before and after optimization are shown in the examples. Detailed Implementation

[0018] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] like Figure 1 As shown, this invention provides a method for optimizing the tropospheric atmospheric inversion grid based on spaceborne multi-angle D-InSAR, specifically including the following steps: S1. Based on the spaceborne multi-angle D-InSAR observation geometry, a three-dimensional tomographic inversion model of the tropospheric atmospheric refractive index is established, and the quantization noise under the influence of grid division is quantitatively modeled, establishing a quantization noise model: For spaceborne multi-angle D-InSAR measurements, for any angle interferogram, after removing the flat terrain and topographic phase using an external digital elevation model, removing the ionospheric error phase using the spectral method, and removing the residual orbital error phase using the Chirp-Z transform, and assuming no significant deformation such as volcanoes or earthquakes during the re-orbit observation period, the interferometric phase mainly consists of the tropospheric atmospheric phase. Its composition reflects the changes in atmospheric delay along the signal propagation path and can be used to invert the differential refractive index of the troposphere and other important parameters.

[0020] like Figure 2 As shown, assuming there are a total of n From one observation angle, the troposphere above the scene is divided into... M A three-dimensional grid. Furthermore, pixels whose signal observation path enters from the top of the tomographic scene are considered valid observations, as shown in the figure, while those entering from the edge of the tomographic scene are discarded, as shown by the dashed lines in the figure, because their propagation paths are incomplete.

[0021] For any observation path, the relative refractive index integrated along its tropospheric atmospheric phase response path is expressed as: (10) in, This represents the true relative refractive index field of the grid.

[0022] By dividing the scene into several three-dimensional tomographic inversion grids, and assuming that the relative refractive index is consistent within each grid, the tropospheric atmospheric phase is further represented as follows: (11) in,L total This indicates the total number of grid cells traversed by the current signal path. and They represent passing through the first i Sub-distance of each grid.

[0023] Based on the above analysis, the tomographic inversion equation is expressed as: (12) in, Indicates the first i A column vector consisting of all effective observation phases from each observation angle. For the first m The relative refractive index corresponding to each grid Indicates the first i The observation matrix corresponding to each observation angle is represented as follows: (13) in, l This represents the sub-distance by which the radar signal passes through the grid.

[0024] Furthermore, considering that the tomographic inversion assumes a constant refractive index within each grid cell, while the actual refractive index field exhibits continuous fluctuations, the resulting phase quantization noise is expressed as: (14) in, This represents the line integral along the radar signal. The average relative refractive index within the grid.

[0025] Through the grid center Perform a second-order Taylor expansion at that point. Further expressed as: (15) in, , Indicates the relative refractive index field at The vector gradient at point H, where H is the second-order mixed partial derivative matrix, is expressed as: (16) Based on (15), the path integral refractive index in (14) is expressed as: (17) Where u represents the unit direction vector of the signal path direction.

[0026] Similarly, the grid-average relative refractive index in (14) is expressed as: (18) in,V Represents the mesh volume, Δ x Δ y With Δ z This indicates the three-dimensional dimensions of the current mesh.

[0027] Finally, the simplified phase quantization noise is expressed as: (19) S2. Based on the tomographic inversion model and the quantified noise model, the core performance constraints of the three-dimensional tomographic inversion of the troposphere by spaceborne multi-angle D-InSAR are modeled, and a quantitative model of the tomographic inversion performance constraints is established: The quantitative model for performance constraints in tomographic inversion consists of three parts, expressed as follows: (20) in, Indicates the accuracy of tomographic inversion. X For the total number of invertible grid cells, Represents the trace of a matrix. Let be the covariance matrix of the observation vectors; Δ represents the resolution of the tomographic inversion grid. x Δ y With Δ z These represent the 3D dimensions of the smallest mesh within the scene; This indicates the scale of the invertible grid.

[0028] Furthermore, The diagonal elements represent the variance of the effective observations. , is represented as: (twenty one) in, The variance of the interference phase noise is expressed as: (twenty two) in, The interferometric phase correlation coefficient, Indicates multiple views, The variance of the quantization noise introduced by the mesh, i.e., the variance of the phase quantization noise, is expressed as: (twenty three) In this embodiment, the phase quantization noise variance corresponding to various commonly used mesh sizes at different height layers was generated and calculated based on simulation for subsequent optimization. The results are shown in Table 1. Table 1. Statistical Table of Phase Quantization Noise Variance

[0029] S3. Based on the quantitative model constrained by tomographic inversion performance, determine the optimization parameters and objective function for the spaceborne multi-angle D-InSAR tropospheric atmospheric inversion grid optimization: To achieve the joint optimal design of mesh generation and system observation configuration, the parameters to be optimized are expressed as follows: (twenty four) in, For the tomographic inversion mesh parameter vector, D l , D m and D u These correspond to the tropospheric atmospheric grid sizes of 0-2 km, 2-6 km, and 6-10 km, respectively. To determine the parameter vector of the system observation configuration.

[0030] In this embodiment, as Figure 3 As shown, taking three satellites distributed across two orbital planes as an example, the system observation configuration parameter vector is represented as follows: ,in and These represent the downward and oblique angles of the primary star S0, respectively. and These represent the angles between S1 and S2 and the main star, respectively. This indicates the difference in longitude between the two orbital planes.

[0031] Based on the modeling and analysis in S2, the optimization objective function is expressed as: (25) in, J 1 indicates the precision of the tomographic inversion. J 2 indicates the inversion grid resolution. J 3 represents the scale of the non-reversible mesh; all three are system parameter vectors. The function.

[0032] S4. Based on a multi-objective, multi-parameter joint optimization algorithm framework, the joint optimization of the spaceborne multi-angle D-InSAR tropospheric atmospheric inversion grid and system configuration is achieved, resulting in the joint optimal configuration of the grid and configuration: Modeling based on S3, J 1- J All 3 are The function, the optimization goal is to find the function that makes J 1- J The three are all relatively small The optimization problem is expressed as: (26) The above is a typical multi-parameter, multi-objective joint optimization problem. This invention uses the Multi-parameter Particle Swarm Optimization (MOPSO) algorithm for framework optimization, and its specific steps are as follows: 1) Determine the range of values ​​and search step size of the geometric parameter vector to be optimized in the configuration, and encode the parameters to be optimized to form the position vector representation of the particles; 2) Initialize the particle swarm, generate the position and velocity of the particles in a random manner, construct the initial particle swarm P1, and initialize the individual optimal position of each particle and the external file set for storing non-dominated solutions; 3) Based on the objective function constructed in S3, calculate the fitness value of each particle, update the individual optimal position of the particle, and combine the non-dominated solutions in the external archive set to select the global guiding particle through crowding or grid partitioning strategy, and update the velocity and position of the particle accordingly. 4) Evaluate the fitness of the updated particle swarm, update the external archive set based on the non-dominated sorting criterion, remove dominated solutions and retain the current Pareto optimal solution set, and repeat step 3 for iterative search. 5) When the preset iteration termination condition is met, normalize each objective function from the Pareto front solution set corresponding to the final external archive set, calculate the Euclidean distance of each solution to the origin, and select the solution with the smallest distance as the optimal solution.

[0033] Next, we will provide implementation examples with specific parameters.

[0034] In this embodiment, 106°E, 29°N is taken as the central area of ​​the observation scene, and the following is adopted: Figure 3 Data acquisition was performed using the three-star multi-angle observation geometry shown. The atmospheric tomography inversion range was set to 10 km × 10 km × 10 km, and the satellite orbital altitude was 510 km.

[0035] Through multi-parameter, multi-objective joint optimization, the system parameter vectors before and after optimization are obtained. and The specific parameters are shown in Table 2, and the comparison of the objective functions before and after optimization is shown in Table 3. The mesh generation changes significantly after optimization, with the bottom layer becoming noticeably denser and the upper layer becoming sparser. This is because the refractive index of the bottom layer changes drastically, resulting in high quantization noise. Furthermore, the optimization improves the mesh by approximately 50% in all three objective dimensions.

[0036] Table 2 Statistical Table of System Parameter Vectors Before and After Optimization

[0037] Table 3. Statistical table of system parameter vectors before and after optimization

[0038] Furthermore, a differential convective atmospheric refractive index field is generated through simulation, and a simulated interferogram is constructed based on multi-angle ray tracing. Taking angle 1 as an example, the interferograms before and after optimization are shown below. Figure 4 As shown.

[0039] Based on the multi-angle interferograms before and after optimization, three-dimensional tomographic inversion of the tropospheric differential atmospheric refractive index was performed. The inversion results and true values ​​are as follows: Figure 5 As shown in the results, the optimized results are significantly closer to the true values, especially in the dense water vapor region at the bottom layer, and the outlier errors at the edges are also significantly reduced. Furthermore, 100 Monte Carlo simulations with random noise were performed to evaluate the inversion accuracy. The root mean square errors of the inversion before and after optimization were 8.9315 and 4.7737, respectively, showing that the accuracy is basically consistent with the theoretical evaluation and the optimization effect is significant.

[0040] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the tropospheric atmospheric inversion grid based on spaceborne multi-angle D-InSAR, characterized in that, Includes the following steps: S1. Based on the observation geometry of spaceborne multi-angle D-InSAR, a three-dimensional tomographic inversion model of tropospheric atmospheric refractive index is established, and the quantization noise under the influence of grid division is quantitatively modeled and a quantization noise model is established. S2. Based on the tomographic inversion model and the quantitative noise model, the core performance constraints of the three-dimensional tomographic inversion of the troposphere atmosphere by spaceborne multi-angle D-InSAR are modeled, and the quantitative model of the tomographic inversion performance constraints is established. S3. Based on the quantitative model constrained by tomographic inversion performance, determine the optimization parameters and objective function of the spaceborne multi-angle D-InSAR tropospheric atmospheric inversion grid optimization. S4. Based on the multi-objective and multi-parameter joint optimization algorithm framework, the joint optimization of the spaceborne multi-angle D-InSAR tropospheric atmospheric inversion grid and system configuration is realized to obtain the joint optimal configuration of grid and configuration.

2. The method as described in claim 1, characterized in that, The quantization noise model under the influence of mesh generation in step S1 is as follows: In tomographic inversion, it is assumed that the refractive index is constant within each grid cell. However, the actual refractive index field exhibits continuous fluctuations. This introduces phase quantization noise, which can be expressed as: (1)； in, This represents the true relative refractive index field of the grid. This represents the line integral along the radar signal. The average relative refractive index within the grid. l The sub-distance of the signal across the grid; Through the grid center Perform a second-order Taylor expansion at that point. Further expressed as: (2)； in, , Indicates the relative refractive index field at The vector gradient at point H, where H is the second-order mixed partial derivative matrix, is expressed as: (3)； Substituting (2) into (1) and simplifying, we obtain the final phase quantization noise, expressed as: (4)； Where u represents the unit direction vector of the signal path direction.

3. The method as described in claim 1, characterized in that, The quantitative model for inversion performance constraints in step S2 consists of three parts, expressed as follows: (5)； in, Indicates the accuracy of tomographic inversion. X For the total number of invertible grid cells, Represents the trace of a matrix. Let be the covariance matrix of the observation vectors, where the diagonal elements represent the variance of the effective observations; Δ represents the resolution of the tomographic inversion grid. x Δ y With Δ z These represent the 3D dimensions of the smallest mesh within the scene; This indicates the scale of the invertible grid.

4. The method as described in claim 1, characterized in that, The system parameters to be optimized in step 3 are represented as follows: (6)； in, For the tomographic inversion mesh parameter vector, D l , D m and D u These correspond to the tropospheric atmospheric grid sizes of 0-2 km, 2-6 km, and 6-10 km, respectively. To determine the parameter vector of the system observation configuration.

5. The method as described in claim 1, characterized in that, The modeling in step S4 is based on S3. J 1- J All 3 are The function, the optimization goal is to find the function that makes J 1- J The three are all relatively small The optimization problem is expressed as: (7)。 6. The method as described in claim 1, characterized in that, Step S4 employs the Multi-Parameter Particle Swarm Optimization (MOPSO) algorithm to solve the framework optimization problem. The specific steps are as follows:

1. Determine the range of values ​​and search step size of the geometric parameter vector to be optimized in the configuration, and encode the parameters to be optimized to form the position vector representation of the particles; 2. Initialize the particle swarm, generate the position and velocity of the particles in a random manner, construct the initial particle swarm P1, and initialize the individual optimal position of each particle and the external file set for storing non-dominated solutions; 3. Based on the objective function constructed in S3, calculate the fitness value of each particle, update the individual optimal position of the particle, and combine the non-dominated solutions in the external archive set to select the global guiding particle through crowding or grid partitioning strategy, and update the velocity and position of the particle accordingly.

4. Evaluate the fitness of the updated particle swarm, update the external archive set based on the non-dominated sorting criterion, remove dominated solutions and retain the current Pareto optimal solution set, and repeat step 3 for iterative search.

5. When the preset iteration termination condition is met, normalize each objective function from the Pareto front solution set corresponding to the final external archive set, calculate the Euclidean distance of each solution to the origin, and select the solution with the smallest distance as the optimal solution.

Images