An optimal configuration design method for atmospheric tomography of distributed spaceborne SAR

Abstract

This invention provides an optimal atmospheric tomography configuration design method for distributed spaceborne SAR. This method can obtain the optimal distributed spaceborne SAR configuration design under the joint optimization of atmospheric tomography inversion scale and inversion error at multiple altitude levels. This method accurately models the atmospheric tomography measurement error of distributed spaceborne SAR and establishes an objective function for configuration optimization design based on this. It uses a multi-parameter joint optimization method under the framework of non-dominated sorting genetic algorithm (NSGA-II) to optimize the atmospheric tomography configuration design of distributed spaceborne SAR, thereby improving the accuracy of atmospheric tomography of distributed spaceborne SAR.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture radar technology, and particularly relates to an optimal atmospheric tomography configuration design method for distributed spaceborne synthetic aperture radar. Background Technology

[0002] Spaceborne synthetic aperture radar (SAR) offers advantages such as high precision, high resolution, and wide coverage, enabling effective implementation of various Earth observation applications. Generally, spaceborne SAR differential interferometry (D-InSAR) can be used for measuring surface deformation such as earthquakes and landslides via double-orbit differential interferometry. When scene deformation is negligible, the phase changes in the differential interferogram primarily originate from the differential atmospheric delay signal caused by water vapor distribution in the lower troposphere, since the permanent dipole moment of water molecules dominates the change in atmospheric refractive index. By assimilating these differential atmospheric delays with a meteorological model, the absolute atmospheric delay and water vapor parameters can be retrieved.

[0003] With the rapid advancement of aerospace technology, distributed spaceborne SAR systems have gradually become mainstream. Leading aerospace research institutions and companies worldwide, including NASA, the European Space Agency (ESA), the German Aerospace Center (DLR), Capella Space (USA), and Synspective (Japan), have planned to launch distributed spaceborne SAR systems for next-generation Earth observation missions, including the TanDEM-L and Harmony systems. my country has also begun constructing its own distributed spaceborne SAR system. The dual L-band SAR system outlined in the "National Civil Space Infrastructure Medium and Long-Term Development Plan (2015-2025)" was successfully launched in early 2022. Commercial satellite companies such as CAS Remote Sensing and Aerospace Hongtu also plan to launch multi-satellite, high-capacity, heavy-orbit distributed spaceborne SAR systems. Compared to traditional single-satellite SAR, distributed spaceborne SAR possesses strong collaborative capabilities and flexible configurations, offering the potential for multi-dimensional dynamic and static atmospheric observation.

[0004] However, due to the strong time-varying nature of the atmosphere, distributed systems still face the following challenges. On the one hand, the system requires sufficient spatial observation angle differences to achieve good tomographic inversion sensitivity; on the other hand, the scale of the tomographic inversion parameters is constrained by observation sensitivity and measurement errors. Therefore, optimizing the configuration design requires solving the joint optimization problem of multiple configuration parameters under multi-objective function constraints. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides an optimal atmospheric tomography configuration design method for distributed spaceborne SAR. This method can obtain a distributed spaceborne SAR configuration design with the joint optimal atmospheric tomography inversion scale and inversion error at multiple altitude levels, thereby improving the accuracy of atmospheric tomography inversion for distributed spaceborne SAR and obtaining more accurate atmospheric refractive index and water vapor distribution.

[0006] The optimal atmospheric tomography configuration design method for distributed spaceborne SAR of the present invention includes:

[0007] Step 1: Model the signal model for atmospheric tomography measurements of distributed spaceborne SAR and determine the measurement error model.

[0008] Step 2: Determine the objective function and the parameters to be optimized in the configuration design of the distributed spaceborne SAR based on the measurement error model.

[0009] Step 3: Based on the multi-parameter joint optimization method under the framework of non-dominated sorting genetic algorithm, the design of distributed spaceborne SAR atmospheric tomography configuration is optimized to obtain the optimal configuration.

[0010] Furthermore, step 1 includes:

[0011] Using X satellites to obtain the observational interferometric phase, solve for the altitude upwards. The differential atmospheric refractive index, the signal model of atmospheric tomography measurement is expressed as follows:

[0012] (1)

[0013] in, It is a vector composed of the differential interferometric phases of X satellites. and It is the number of pixels in the interferogram. It is the differential atmospheric refractive index. It is the atmospheric refractive index. and These represent the acquisition times of the main and auxiliary interferogram images, respectively. and The number of pixels representing the inverted atmospheric refractive index map.

[0014] (2)

[0015] It is the observation matrix of differential atmospheric delay for each star. It is the radar wavelength. It is a scene deformation vector.

[0016] (3)

[0017] The observation matrix representing the deformation of each star, It is the error vector of the observation.

[0018] Ignoring the deformation effects between the double-track interferences, the covariance matrix of the measured interference phase is used. Least square solution of atmospheric tomography and accuracy Represented as

[0019] (4)

[0020] Assuming the phase errors between each star and each observation point in the interferometry are independent, Represented as

[0021] (5)

[0022] Among them, observation error Defined as follows

[0023] (6)

[0024] in, The interferogram coherence coefficient, Indicates the number of layers in the height direction. For scene length, To achieve the horizontal resolution of the atmospheric grid for 3D tomographic inversion, The variance of the refractive index distribution in the current atmospheric layer. The error coefficient of the current layer. This represents the distance the ray path travels through the current layer. This represents the total distance traversed by the ray path.

[0025] For the error coefficient of the grid The definition is expressed as

[0026] (7)

[0027] in It is the sub-distance of the ray path across the inversion grid. This represents the maximum distance in the inverted grid.

[0028] For each valid interferometric point on the ground, i.e., the observation point whose ray path originates from the top of the inversion grid, its ray path passes through a certain layer. Each grid. Error coefficients in the current layer. , represented as

[0029] (8)

[0030] in The sub-distance of the ray across the grid. The error coefficients for the current grid. This represents the distance the ray path travels through the current layer.

[0031] Step 2 includes:

[0032] The objective function for the optimized design of distributed spaceborne SAR configurations consists of two parts, expressed as follows:

[0033] (9)

[0034] in, The number of grid cells the ray passes through. This represents the total number of grid cells used for overall atmospheric inversion. Represents a geometric parameter vector. The angle between the main star and the center of the scene and the orbital direction. For bistatic angles between satellites, The change in right ascension of the ascending node indicates the distance between the various orbital planes. This is the perspective from below the main star. It is the size of the atmospheric refraction three-dimensional tomography grid. It is the optimization space for geometric parameter vectors.

[0035] Step 3 includes:

[0036] Step 3.1: First, under a coarse-resolution atmospheric inversion grid, determine the variation range and step size of the parameters to be optimized, and encode them in decimal. Then, initialize the parameters to be optimized using a random method to form an initialization population. .

[0037] Step 3.2, for The offspring population obtained by selecting, crossing over, and mutating individuals using the binary tournament method Integrating parental populations and offspring population ,get A fast non-dominated sorting strategy is adopted. Individuals are sequentially added to the parent population according to their sorting rank. Until the facility reaches full capacity.

[0038] Step 3.3, This process is repeated for the next iteration of the parent population, continuing step 3.2 until the optimal solution is found under the coarse-resolution atmospheric inversion grid.

[0039] Step 3.4: Based on the optimal solution under the coarse-resolution atmospheric inversion grid, further determine the variation range and step size of the parameters to be optimized. Repeat steps 3.1, 3.2, and 3.3 to perform more detailed optimization under the fine-resolution atmospheric inversion grid.

[0040] The beneficial effects of this invention are as follows:

[0041] This invention achieves the optimization of the configuration design of distributed spaceborne SAR atmospheric tomography by accurately modeling the measurement error of distributed spaceborne SAR and establishing an objective function based on this. It then utilizes a multi-parameter joint optimization method under the framework of non-dominated sorting genetic algorithm to improve the accuracy of distributed spaceborne SAR atmospheric tomography configuration design. Attached Figure Description

[0042] Figure 1 A schematic diagram of the atmospheric configuration of a distributed spaceborne SAR;

[0043] Figure 2 This is a schematic diagram of tropospheric tomography based on distributed spaceborne SAR.

[0044] Figure 3 This is a schematic diagram of the multi-parameter joint optimization steps;

[0045] Figure 4 This is a schematic diagram of the optimization results at coarse resolution;

[0046] Figure 5 This is a schematic diagram of the optimization results at high resolution;

[0047] Figure 6 To optimize the inversion results of the previous configuration and the true value;

[0048] Figure 7 The inversion results and true values ​​of the configuration optimized using the method proposed in this invention are shown. Detailed Implementation

[0049] A schematic diagram of the atmospheric configuration of a distributed spaceborne SAR is shown below. Figure 1 As shown, a "one master, multiple slaves" SAR satellite formation is constructed using multiple orbital planes. Only the master satellite in the reference orbit contains active SAR payloads and has transmission capabilities; the remaining satellites are lightweight, passive receivers. Operating in a multi-site mode reduces complexity and cost. Each satellite in the system can perform heavy orbit D-InSAR measurements, enabling simultaneous multi-angle observations. The satellite orbits are planned to use short return period orbits (e.g., 1-4 days) or can be expanded into a distributed multi-temporal system to ensure high coherence of heavy orbit interferometry and reduce the impact of cumulative deformation in the scene on atmospheric measurements.

[0050] In conducting three-dimensional atmospheric refractive index measurements, the primary satellite and satellites orbiting and along its orbits together form a tomographic measurement group. Simultaneous imaging of the same scene is achieved through beam-synchronized spatiotemporal observations, and three-dimensional tomographic measurements of the differential atmospheric refractive index are realized through double-orbit interferometry phase analysis from different perspectives. The tomographic group requires both signal-level and information-level collaborative processing.

[0051] The invention will now be described in detail with reference to the accompanying drawings. The optimal atmospheric tomography configuration design method for distributed spaceborne SAR of the present invention includes:

[0052] Step 1, the basic schematic diagram of its tropospheric chromatography measurement is as follows: Figure 2 As shown. Using the X satellites in the tomographic array of the above configuration to obtain the observational interferometric phase, the altitude-upward phase is solved. The differential atmospheric refractive index, the signal model of atmospheric tomography measurement is expressed as follows:

[0053] (10)

[0054] in, It is a vector composed of the differential interferometric phases of X satellites. and It is the number of pixels in the interferogram. It is the differential atmospheric refractive index. It is the atmospheric refractive index. and These represent the acquisition times of the main and auxiliary interferogram images, respectively. and The number of pixels representing the inverted atmospheric refractive index map.

[0055] (11)

[0056] It is the observation matrix of differential atmospheric delay for each star. It is the radar wavelength. It is a scene deformation vector.

[0057] (12)

[0058] The observation matrix representing the deformation of each star, It is the error vector of the observation.

[0059] Ignoring the deformation effects between the double-track interferences, the covariance matrix of the measured interference phase is used. Least square solution of atmospheric tomography and accuracy Represented as

[0060] (13)

[0061] Assuming the phase errors between each star and each observation point in the interferometry are independent, Represented as

[0062] (14)

[0063] Among them, observation error Defined as follows

[0064] (15)

[0065] in, The interferogram coherence coefficient, Indicates the number of layers in the height direction. For scene length, To achieve the horizontal resolution of the atmospheric grid for 3D tomographic inversion, The variance of the refractive index distribution in the current atmospheric layer. The error coefficient of the current layer. This represents the distance the ray path travels through the current layer. This represents the total distance traversed by the ray path.

[0066] For the error coefficient of the grid The definition is expressed as

[0067] (16)

[0068] in It is the sub-distance of the ray path across the inversion grid. This represents the maximum distance in the inverted grid.

[0069] For each valid interferometric point on the ground, i.e., the observation point whose ray path originates from the top of the inversion grid, its ray path passes through a certain layer. Each grid. Error coefficients in the current layer. , represented as

[0070] (17)

[0071] in The sub-distance of the ray across the grid. The error coefficients for the current grid. This represents the distance the ray path travels through the current layer.

[0072] In equation (15), the first part represents the differential interferometry measurement error, and the second part represents the quantization error during three-dimensional tomography inversion. Thus, the modeling of the objective function is complete.

[0073] Step 2, regarding the optimization design problem of the above-mentioned distributed spaceborne SAR atmospheric spherical configuration, the overall optimization process is as follows: Figure 3 As shown, the objective function of this joint optimization problem consists of two parts, expressed as follows:

[0074] (18)

[0075] in, The number of grid cells the ray passes through. This represents the total number of grid cells used for overall atmospheric inversion. Represents a geometric parameter vector. The angle between the main star and the center of the scene and the orbital direction. For bistatic angles between satellites, The change in right ascension of the ascending node indicates the distance between the various orbital planes. This is the perspective from below the main star. It is the size of the atmospheric refraction three-dimensional tomography grid. It is the optimization space for geometric parameter vectors.

[0076] Step 3: After modeling, begin the multi-parameter joint optimization step based on the non-dominated sorting genetic algorithm framework. The specific steps are as follows:

[0077] Step 3.1: First, set the atmospheric inversion grid to coarse resolution. At coarse resolution, determine the parameters to be optimized. The range and step size of the parameters to be optimized are determined, and the parameters are encoded in decimal. The index of each parameter within its range is used as its gene, and all encoded parameters form a chromosome. The chromosome and the objective function under the current parameters together constitute an individual. Then, the parameters to be optimized are initialized using a random method to form an initial population. .

[0078] Step 3.2, for The offspring population obtained by selecting, crossing over, and mutating individuals using the binary tournament method Integrating parental populations and offspring population ,get A fast non-dominated sorting strategy is adopted to sort the population. All individuals are stratified into non-dominated sets, and the total local crowding of each non-dominated set is calculated and sorted. Next, individuals from the non-dominated sets are added to the parent population according to their non-dominated levels. Until the facility is fully staffed. Thus, upon obtaining... In addition to the offspring population There are excellent solutions in the parent population. Solutions with higher fitness will also be retained, thus achieving an elite retention strategy.

[0079] Step 3.3, put This process is repeated for the next iteration of the parent population, continuing step 3.2 until the optimal solution is found under the coarse-resolution atmospheric inversion grid.

[0080] Step 3.4: Based on the optimal solution under the coarse-resolution atmospheric inversion grid, further determine the parameters to be optimized. Adjust the range and step size of the changes. Repeat steps 3.1, 3.2, and 3.3 for more detailed optimization using a high-resolution atmospheric inversion grid.

[0081] Using the optimal satellite configuration under the high-resolution atmospheric inversion grid obtained in step 3.4, the three-dimensional measurement of atmospheric refractive index is obtained by the least squares method.

[0082] This completes all the steps.

[0083] The following provides an implementation example with specific parameters.

[0084] In this example, the scene center is set at 106°E, 29°N, and the atmospheric inversion grid range is set to 10km. 10km The altitude is 4500m, with a coarse horizontal resolution of 2km and a fine horizontal resolution of 400m. Vertically, it is divided into 10 layers: 400m for the altitude range of 0-2000m and 500m for the altitude range of 2000m-4500m. A basic configuration of one primary satellite and two secondary satellites, operating in two orbital planes, was used for subsequent inversion verification experiments. The overall orbital plane altitude of the formation is 645km, and its initial configuration satellite parameters are shown in Table 1.

[0085] Table 1 Initial Configuration Parameters

[0086]

[0087] The initial configuration is then optimized. Under a coarse-resolution atmospheric inversion grid, the range and step size of the optimization parameters for the formation are shown in Table 2. The optimal configuration is obtained using the multi-parameter joint optimization steps based on the non-dominated sorting genetic algorithm framework described above. After 50 iterations, the solution group with the lowest non-dominated level in the population is as follows: Figure 4 As shown, the horizontal axis is The vertical axis is The midpoint of the diagram is selected as the optimal configuration at coarse resolution. Based on the optimal configuration parameters at coarse resolution, the formation parameters and step size to be optimized at fine resolution are determined, as shown in Table 3. The configuration is then optimized at fine resolution. After 50 iterations, the solution group with the lowest non-dominant level in the population is shown below. Figure 5 As shown, the horizontal axis is The vertical axis is The midpoint of the diagram is selected as the optimal configuration at the highest resolution. At this point... , , , Its optimized configuration parameters are shown in Table 4.

[0088] Table 2 Formation parameters to be optimized at coarse resolution

[0089]

[0090] Table 3 Formation parameters to be optimized at high resolution

[0091]

[0092] Table 4 Optimized configuration parameters at high resolution

[0093]

[0094] To verify the effectiveness of the optimization method, the initial configuration before optimization was used. , The values ​​are 0.236640 and 0.01725702 respectively, and the optimized configurations are... , The values ​​are 0.218880 and 0.00461559 respectively. , The values ​​decreased by 7.5% and 73.26% respectively. The differential atmospheric refractive index was solved using the configurations before and after optimization, respectively, on a high-resolution grid. Figure 6 The inversion results and actual values ​​of the configuration before optimization are shown. Figure 7 The inversion results and true values ​​of the configuration optimized using the method proposed in this invention are shown. The zenith delay error of the configuration inversion before optimization is 0.0025m, and the zenith delay error of the configuration inversion after optimization is 0.0017m, which is a decrease of 32%. The simulation results demonstrate the effectiveness of the multi-parameter joint optimization method based on the non-dominated sorting genetic algorithm framework in satellite configuration optimization design under atmospheric tomography applications.

[0095] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for optimal configuration design of distributed space-borne SAR tomography, characterized in that, The steps of the method comprise: Firstly, modeling the signal model of the atmospheric tomography of the distributed spaceborne SAR, and determining a measurement error model; Specifically, the signal model of atmospheric tomography measurement is that the observation interference phase is obtained by using X satellites, and the height is solved upwards The differential atmospheric refraction index is solved, and the signal model of atmospheric tomography is represented ； wherein, is a vector composed of X satellite differential interferometric phases, and is the number of pixels of the interferogram, is the differential atmospheric refractive index, is the atmospheric refractive index, and respectively represent the acquisition time of the primary and secondary images of the interferogram, and represents the number of pixels of the inverted atmospheric refractive index map, ； is the observation matrix of the differential atmospheric delays of the stars, is the radar wavelength, is the scene deformation vector, ； is the observation matrix representing each star variation, is the error vector of the observation; Ignoring the deformation between the heavy rail interference, using the measurement of the covariance matrix of the interference phase least squares solution of atmospheric tomography and accuracy is expressed as ； Assume that the phase errors between stars and observation points in the interferometric measurement are independent, is represented as ； where the observation error is defined as follows ； wherein, is the interferogram coherence factor, denotes the number of height layers, is the scene length, is the horizontal resolution of the atmospheric grid for the three-dimensional tomography, is the variance of the atmospheric refractive index distribution for the current layer, is the error factor for the current layer, is the distance covered by the ray path in the current layer, is the total distance covered by the ray path; For the error coefficient of a grid is defined as ； wherein is a sub-distance of the ray path through the inversion grid, is the maximum distance in the inversion grid; For each valid point on the ground, i.e. an observation point whose ray path goes out from the top of the inversion grid, its ray path goes through a certain layer at a certain point in the grid; the error coefficient at the current layer is denoted as ​ ； wherein is a sub-distance of the ray passing through the grid, is an error coefficient of the current grid, is a distance of the ray path passing through the current layer; Secondly, determining a target function of the configuration optimization design of the distributed spaceborne SAR and parameters to be optimized in the configuration design based on the measurement error model; Specifically, the target function of the configuration optimization design of the distributed spaceborne SAR is expressed as ； wherein, is the number of grids crossed by the ray, is the total number of atmospheric tomography grids, denotes the parameters to be optimized, is the angle between the main star to the scene center and the intersection orbit, is the bistatic angle between satellites, is the change of the ascending node right ascension, indicating the distance between the orbit planes, is the main star's angle of view, is the size of the atmospheric refraction three-dimensional tomography grid, is the optimization space of the geometric parameter vector; Thirdly, based on a multi-parameter joint optimization method under a non-dominated sorting genetic algorithm framework, the atmospheric tomography configuration design of the distributed spaceborne SAR is optimized to obtain an optimal configuration.

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