A distributed tomoSAR baseline design method fusing elevation prior and fold separation constraints

Abstract

This invention discloses a distributed TomoSAR baseline design method that integrates elevation prior and overlay separation constraints, belonging to the field of distributed synthetic aperture radar tomography and baseline design. Specifically, the method involves: first, acquiring the distributed TomoSAR formation system parameters and mission indicators, and constructing a baseline design constraint model; then, constructing an objective function for the information content of the subspace of interest based on elevation prior, an objective function for overlay separation based on mutual interference constraints, and auxiliary imaging performance evaluation indicators; finally, using the baseline design constraint model, constructing and solving a multi-criteria joint objective function based on the information content objective function, the overlay separation objective function, and the performance evaluation indicators, and outputting the final distributed TomoSAR baseline design result. This invention improves the effective observation capability of the target elevation subspace and the efficiency of space observation resource utilization.

Description

Technical Field

[0001] This invention belongs to the field of distributed synthetic aperture radar tomography (TomoSAR) and baseline design, specifically a distributed TomoSAR baseline design method that integrates elevation priors and overlay separation constraints. Background Technology

[0002] TomoSAR is a three-dimensional imaging technology developed on the basis of traditional SAR imaging. By observing multiple tracks or angles, it forms an equivalent aperture in the height direction, thereby realizing the separation and three-dimensional positioning of multiple scatterers within the same range-azimuth resolution cell. Therefore, it has important application value in the separation of overlapping scatterers in urban scenes, three-dimensional reconstruction of buildings, and elevation inversion in complex scenes.

[0003] Distributed SAR systems, which consist of multiple platforms working collaboratively, can provide a designable spatial baseline distribution, offering a new approach to TomoSAR 3D imaging. In distributed TomoSAR systems, baseline design directly affects height-axis sampling characteristics, elevation resolution, sidelobe level, and the ability to suppress blurred targets, making it a crucial factor determining tomographic imaging performance.

[0004] Existing TomoSAR baseline design methods mainly fall into the following categories: one category is uniform or near-uniform baseline design methods, which pursue relatively uniform height sampling under a given total aperture condition, so as to balance the stability of height imaging and the unambiguous height range to a certain extent; another category is sparse baseline design methods such as Minimum Redundancy Array (MRA), which attempt to obtain a larger equivalent aperture with fewer observation nodes, thereby improving the height resolution and aperture utilization efficiency under limited observation conditions.

[0005] However, existing technologies still have several shortcomings when dealing with complex urban environments, especially overlapping scenarios with small elevation intervals and significant differences in scattering intensity:

[0006] First, existing methods typically focus more on the resolution performance or error index of the overall baseline design, and do not adequately consider the separation capability in scenarios where strong and weak scatterers coexist. When the total aperture is limited, uniform or near-uniform baselines may not be able to achieve the resolution of closely spaced scatterers, while partially sparse baseline designs may result in higher grating lobe or side lobe responses, thus affecting the stable detection and reconstruction quality of weak scatterers.

[0007] Secondly, existing baseline design methods do not fully utilize prior elevation information, making it difficult to optimize baseline configuration around elevation regions where target scatterers are likely to be concentrated. This, in turn, affects the separation capability and reconstruction effect of overlapping scatterers in complex scenes. In real-world urban scenes, scatterers are typically not uniformly distributed across the entire elevation range, but rather concentrated on the ground, rooftops, or several characteristic elevation intervals. If such prior information is not effectively utilized during the baseline design phase, observation resources may be evenly distributed across non-priority elevation intervals, hindering the targeted separation of overlapping scatterers within the elevation intervals of interest. Existing research indicates that utilizing scene priors, structural sparsity, or semantic information can help improve reconstruction and parameter estimation performance.

[0008] Furthermore, existing methods often focus on imaging performance indicators themselves, lacking a unified design mechanism that simultaneously considers engineering feasibility. For real-world distributed spaceborne SAR formations, baseline design must not only meet altitude imaging requirements but also comprehensively consider factors such as inter-platform safety spacing, formation configuration feasibility, baseline accuracy, critical baseline constraints, and coherence preservation. If mathematical optimization is performed independently of these engineering conditions, the resulting baseline design may be difficult to deploy in a practical system or may cause a decrease in coherence and affect tomographic imaging results.

[0009] Therefore, there is an urgent need for a distributed TomoSAR baseline design method that can simultaneously integrate scene elevation priors, overlay separation requirements, and engineering physical constraints to improve the separation capability of overlay scatterers in complex urban scenes, while also taking into account the engineering feasibility of the system. Summary of the Invention

[0010] To address the problems in existing distributed TomoSAR baseline design technologies, such as difficulty in simultaneously considering the ability to separate near-spaced scatterers at elevation, the distinguishability of weak scatterers in scenarios where strong and weak scatterers coexist, and insufficient utilization of prior elevation data, this invention provides a distributed TomoSAR baseline design method that integrates prior elevation data with overlay separation constraints.

[0011] Includes the following steps:

[0012] Step 1: Obtain the parameters and mission indicators of the distributed TomoSAR formation system, and construct a baseline design constraint model;

[0013] System parameters and mission indicators include radar wavelength Reference slope distance Radar downward view Satellite flight speed azimuth processing bandwidth Total number of distributed satellite formations Target elevation resolution requirements and minimum permissible azimuth to coherence baseline .

[0014] The baseline design constraint model is as follows:

[0015]

[0016] in, For the penalty weighting coefficient, Number of satellites;

[0017] Each penalty sub-item is defined as follows:

[0018]

[0019]

[0020]

[0021]

[0022] The platform's collision avoidance safety distance threshold, the first satellite and the first The three-dimensional spatial distance between satellites is denoted as The baseline difference along the track is denoted as ; The upper limit of the allowable baseline difference along the track, This is the minimum interval threshold along the track. The minimum vertical baseline interval threshold is denoted as . .

[0023] Step 2: Construct an objective function for the information content of the interest subspace based on elevation priors. ;

[0024]

[0025] in, Indicates taking the real part, For numerically stable terms, It is an identity matrix. In the elevation subspace of interest The focused observation guidance matrix Let be the diagonal prior probability weight matrix. det(⋅) denotes the matrix determinant, and H denotes the conjugate transpose.

[0026] Step 3: Construct an overlay separation objective function based on mutual coherence constraints. ;

[0027]

[0028] in, and These are the weighting coefficients. To smooth out correlation indicators, This refers to the mutual coherence between the ground guide vector and the guide vectors of each roof.

[0029] Step 4: Construct auxiliary imaging performance evaluation indicators;

[0030] Imaging performance evaluation metrics include sidelobe suppression metrics and azimuth coherence loss metrics. Differential co-array structured sampling index and the along-track equilibrium regularization term .

[0031] (1) Sidelobe suppression indices include peak sidelobe ratio indices Integral sidelobe ratio index

[0032] Peak sidelobe ratio :

[0033]

[0034] Integral sidelobe ratio index :

[0035]

[0036] For full elevation search space Within this framework, the normalized point spread function magnitude response of the baseline array is constructed; Main lobe region; This refers to the side lobe region;

[0037] (2) Construction of azimuth coherence loss index

[0038] Based on the along-orbit baseline difference between any two satellites, an azimuth coherence loss index is constructed. :

[0039]

[0040] Among them, satellites are the total number .

[0041] (3) Differential co-array structured sampling index

[0042]

[0043] in, This is the redundancy penalty coefficient. The effective coverage of the differential co-array characterizes the effective coverage range of the vertical baseline differential set at a preset quantization step size. The redundancy of the differential co-array characterizes the degree of resampling in the vertical baseline differential set.

[0044] (4) Orbital equilibrium regularity term

[0045] Based on the baseline vector along the track The mean of the terms is used to construct a balanced regularization term. :

[0046]

[0047] Step 5: Using the baseline design constraint model, construct and solve a multi-criteria joint objective function based on the information content objective function, the overlay separation objective function, and the performance evaluation index, and output the distributed TomoSAR baseline design results.

[0048] First, the information content objective function Overlay separation objective function Differential co-array structured sampling index Peak-to-sidelobe ratio index Integral sidelobe ratio index Azimuth coherence loss index and the along-track equilibrium regularization term Normalization is performed.

[0049] Then, the normalized indicators are dimensionless and homogenized to be uniformly converted into a minimum form.

[0050] Finally, combined with the preset weight vector Construct a joint objective function based on multiple criteria. :

[0051]

[0052]

[0053] in, , , , , , and These represent the evaluation indicators after normalization and uniform conversion to their minimum form.

[0054] A hybrid genetic algorithm and pattern search algorithm are used to evaluate the joint objective function. Solve the following:

[0055] First, a genetic algorithm is used to perform a global search on the baseline variables to be optimized in order to obtain candidate baseline schemes that satisfy multiple constraints. After the genetic algorithm converges, the excellent candidate baseline schemes output by the genetic algorithm are used as the initial points of the pattern search algorithm to further perform local optimization. Finally, the vertical baseline vector and the orbital baseline vector that satisfy the optimization requirements of the joint objective function are output, thus completing the baseline design of distributed TomoSAR.

[0056] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0057] (1) This invention introduces prior information on scene elevation into the distributed TomoSAR baseline design process. By constructing an objective function for the amount of information in the subspace of interest based on prior probability weights, the spatial sampling resources of limited observation nodes are preferentially allocated to the elevation regions where targets are likely to exist, thereby improving the effective observation capability of the target elevation subspace and the utilization efficiency of spatial observation resources.

[0058] (2) This invention addresses the overlapping scenarios in sparse urban areas where strong and weak scatterers such as the ground and buildings coexist, and constructs a method based on mutual interference constraints and higher order... The objective function of norm-aggregated stacking separation can enhance the suppression of highly correlated combinations, reduce the shading effect of strong scatterer sidelobes on weak scatterers, and improve the separation capability in near-elevation spaced dual scatterer scenarios.

[0059] (3) In the process of baseline optimization, the present invention simultaneously introduces three-dimensional anti-collision safety distance constraints, upper limit constraints of baseline difference along the track, minimum interval constraints along the track and minimum interval constraints of vertical baseline, and combines azimuth coherence loss assessment to realize unified modeling of imaging performance indicators and engineering physical constraints, thereby improving the engineering feasibility and system application reliability of the output baseline design scheme. Attached Figure Description

[0060] Figure 1 This is a flowchart of a distributed TomoSAR baseline design method that integrates elevation priors and overlay separation constraints according to the present invention.

[0061] Figure 2 This is a schematic diagram of the baseline design scheme optimized by the present invention.

[0062] Figure 3 This is a comparison diagram of the vertical differential coarray distribution and repeatability of the present invention and different baseline design schemes.

[0063] Figure 4 This is a comparison chart of the elevation-direction point extension function response of the present invention and different baseline design schemes.

[0064] Figure 5 This is a comparison chart of the theoretical performance lower bounds of the present invention and different baseline design schemes.

[0065] Figure 6 This is a comparison chart of the separation performance of the present invention and different baseline design schemes in a two-scatterer scenario.

[0066] Figure 7 This is a comparison chart of the reconstruction results of the present invention and different baseline design schemes in a complex urban profile overlay scenario. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. All equivalent substitutions, improvements, and modifications made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0068] This invention presents a distributed TomoSAR baseline design method that integrates elevation priors and overlay separation constraints. Taking a distributed spaceborne TomoSAR system as the target, it designs the baseline for elevation-oriented overlay scatterer separation in sparse urban scenarios. Due to the geometric characteristics of side-looking imaging by spaceborne radar, the same range-azimuth resolution cell may simultaneously contain ground scatterers and building roof scatterers, thus forming a typical dual-scatterer overlay situation, and the scattering intensities of the two may differ significantly.

[0069] To improve the 3D reconstruction capability and weak scatterer separation capability in such overlapping scenarios, this invention utilizes the digital elevation model of the observation scenario and statistical information on the typical height of buildings to construct prior elevation constraints. Based on this, and combined with the security constraints and coherence constraints of the distributed satellite constellation, the vertical baseline and along-orbit baseline of each satellite node are jointly optimized.

[0070] like Figure 1 As shown, the specific steps include:

[0071] Step 1: Initialize the parameters and mission indicators of the distributed TomoSAR formation system, and construct the baseline design constraint model;

[0072] Input the physical parameters and mission specifications of the distributed spaceborne TomoSAR system, including radar wavelength. Center reference slope distance Radar downward view Satellite flight speed azimuth processing bandwidth Total number of distributed satellite formations Target elevation resolution requirements and minimum permissible azimuth to coherence baseline .

[0073] Based on the target elevation resolution requirements, calculate the total vertical baseline aperture requirement to meet the elevation resolution requirements. :

[0074]

[0075] To reduce the optimization dimensionality and determine the reference baseline, a fixed-length real-number encoding method is used to parameterize the baseline variables in a dimensionality-reduced manner: the vertical baseline and the along-orbit baseline of the first satellite are fixed at zero, i.e. Fixed number The vertical baseline of each satellite is the total vertical baseline aperture requirement, i.e. The rest Internal vertical baselines and If each baseline along the track is used as a variable to be optimized, then the total optimization dimension is: .

[0076] According to the minimum permissible azimuth to the coherence baseline Calculate the upper limit of the allowable baseline difference along the track. :

[0077]

[0078] Based on this, the upper and lower bounds of the search space along the baseline are set as follows: .

[0079] For any candidate baseline scheme, based on the vertical baseline vector and baseline vector along the track Calculate any two satellites and Vertical baseline difference and along-track baseline difference: , At the same time, the first satellite was calculated based on its spatial position within the satellite formation. satellite and the first Three-dimensional spatial distance between satellites .

[0080] Then, , and Substituting the baseline design constraint model into equation (1), we obtain the engineering constraint penalty term. The aforementioned engineering constraint penalty items This is used to constrain candidate baseline schemes to meet requirements such as platform anti-collision safety distance, upper limit of baseline difference along the track, minimum spacing along the track, and minimum spacing of vertical baselines.

[0081] In this embodiment, the collision avoidance safety distance threshold of the three-dimensional platform Minimum interval threshold along the track and the minimum vertical baseline interval threshold It can be configured according to the constellation platform configuration and engineering deployment requirements.

[0082] The baseline design constraint model is as follows:

[0083]

[0084] in, For the penalty weighting coefficient, Number of satellites;

[0085] Each penalty sub-item is defined as follows:

[0086]

[0087]

[0088]

[0089]

[0090] Each penalty sub-item constrains candidate baseline schemes that do not meet the requirements for platform security, along-track coherence, and baseline sampling interval.

[0091] Step 2: Input the prior elevation information of the scene and construct an objective function for the information content of the subspace of interest based on the prior elevation information. ;

[0092]

[0093] in, Indicates taking the real part, For numerically stable terms, It is an identity matrix. In the elevation subspace of interest The focused observation guidance matrix This is a diagonal prior probability weight matrix.

[0094] First, construct the elevation subspace of concern based on the prior information of the scene. Specifically, the ground elevation undulation zone is defined as... Typical building height zone is The two elevation intervals mentioned above are discretely sampled and then merged to form the elevation subspace of interest. Among them, the ground elevation undulation zone is used to characterize the elevation range where ground scatterers may occur, and the typical building height zone is used to characterize the elevation range where roofs or strong scattering structures of buildings may occur.

[0095] For the Vertical baselines Calculate the corresponding elevation wave number. :

[0096]

[0097] set up For each The wavenumber vector formed, To focus on the elevation sampling vector corresponding to the elevation subspace, then in the elevation subspace... Constructing a focused observation guidance matrix :

[0098]

[0099] Based on the prior occurrence probabilities of ground elevation zones and building height zones in the task scenario, a diagonal prior probability weight matrix is ​​constructed. For example, in the reconstruction of features in sparse urban areas, different weights can be assigned to ground elevation zones and building height zones based on digital elevation models, building height statistics, or existing feature category information.

[0100] Subsequently, the focus will be on the observation guidance matrix. and diagonal prior probability weight matrix Substituting the objective function for the information content of the subspace of interest, i.e., equation (2), the information content of the subspace of interest corresponding to the candidate baseline scheme is calculated. .

[0101] The amount of information in the subspace of concern This is used to measure the effective observation capability of candidate baseline schemes for the target elevation subspace. The objective function for the amount of information in the subspace of interest is described below. This guides the observation degrees of freedom to be concentrated in the elevation intervals where targets are likely to exist, thereby improving the effective observation capability of candidate baseline schemes for the target elevation subspace.

[0102] Step 3: Construct an overlay separation objective function based on mutual coherence constraints. ;

[0103]

[0104] in, and These are the weighting coefficients. To smooth out correlation indicators, This refers to the mutual coherence between the ground guide vector and the guide vectors of each roof.

[0105] For dual-target overlay scenarios where ground scatterers and roof scatterers coexist, extract the steering vector corresponding to the ground reference elevation. It then iterates through candidate elevation points within typical building height zones and extracts the corresponding roof guide vectors for each. .in, Numbering of candidate elevation points within the typical height zone of the building. For the first Candidate elevations for each roof.

[0106] Calculate the intercoherence between the ground guidance vector and the guidance vectors of each roof. :

[0107]

[0108] To enhance the suppression of locally highly correlated combinations while maintaining necessary continuity and searchability during the optimization process, a higher-order method is employed. The norm is used to aggregate the mutually coherent sequences to obtain a smoothed correlation index. :

[0109]

[0110] In this embodiment, the norm order The preferred values ​​are 4 or 6, representing the mutual cohesion weighting coefficient. and mean weighting coefficient The setting can be adjusted based on the level of concern regarding the worst-case correlation peak and the overall average correlation level. Subsequently, the correlation smoothing index will be applied. and mutual compatibility Substituting the overlay separation objective function described in the invention, i.e., equation (3), the overlay separation capability evaluation value corresponding to the candidate baseline scheme is calculated. .

[0111] The overlapping separation objective function This is used to suppress the high correlation response between ground and roof candidate heights, thereby reducing the shading effect of strong scatterer sidelobes on weak scatterers and improving the separation capability in near-elevation spaced dual scatterer scenarios.

[0112] Step 4: Input engineering physical constraints and construct auxiliary imaging performance evaluation indicators based on candidate baseline schemes;

[0113] To further balance sidelobe suppression, azimuth coherence, differential co-array sampling structure, and along-track formation balance, an auxiliary imaging performance evaluation index set is constructed. This auxiliary imaging performance evaluation index includes sidelobe suppression indices and azimuth coherence loss indices. Differential co-array structured sampling index and the along-track equilibrium regularization term .

[0114] (1) Sidelobe suppression indices include peak sidelobe ratio indices Integral sidelobe ratio index

[0115] Peak sidelobe ratio :

[0116]

[0117] Integral sidelobe ratio index :

[0118]

[0119] For full elevation search space Within this framework, the normalized point spread function magnitude response of the baseline array is constructed; Main lobe region; This refers to the side lobe region;

[0120] In full elevation search space Within, construct the normalized point spread function magnitude response of the baseline array. :

[0121]

[0122] Define the main lobe region and side lobe region They are respectively:

[0123]

[0124]

[0125] in, The main lobe expansion tolerance coefficient can be set according to the system's resolution requirements, with an optimal value range of [value range missing]. to .

[0126] Subsequently, the normalized point spread function magnitude response was... Main lobe region and side lobe region Substitute the peak-to-sidelobe ratio index Integral sidelobe ratio index Equations (4) and (5) are used to calculate the sidelobe suppression performance of the candidate baseline scheme. The peak-to-sidelobe ratio is an important indicator. The integral sidelobe ratio is used to characterize the degree of suppression of the maximum sidelobe peak outside the main lobe region relative to the main lobe peak. Used to characterize the ratio of total energy in the sidelobe region to total energy in the mainlobe region.

[0127] (2) Construction of azimuth coherence loss index

[0128] For candidate baseline schemes, the baseline difference along the orbit between any two satellites is used. Construct an azimuth coherence loss index :

[0129]

[0130] Among them, satellites are the total number .

[0131] The azimuth coherence loss index Used to evaluate the overall azimuth coherence loss caused by baseline differences along the track.

[0132] (3) Differential co-array structured sampling index

[0133]

[0134] in, This is the redundancy penalty coefficient. The effective coverage of the differential co-array characterizes the effective coverage range of the vertical baseline differential set at a preset quantization step size. The redundancy of the differential co-array characterizes the degree of resampling in the vertical baseline differential set.

[0135] First, extract the vertical baseline vector. Construct a nonnegative difference coarray set based on the absolute difference of the vertical baseline between any two satellites. :

[0136]

[0137] To statistically analyze the effective coverage of the differential comatrix, a differential quantization step size is introduced. Perform step-size operations on each element in the set of difference comatrixes. Discrete mappings, constructing a quantization index set :

[0138]

[0139] in, This indicates rounding to the nearest integer.

[0140] Extract the quantization index set The effective coverage of the difference comatrix is ​​defined as the number of unique elements in the matrix. :

[0141]

[0142] in, This indicates that you need to extract unique elements from the set.

[0143] The difference between the total number of difference pairs and the effective coverage is defined as the differential co-array redundancy. :

[0144]

[0145] Then, and Substituting the differential co-array structured sampling index into equation (7), the differential sampling structure evaluation value corresponding to the candidate baseline scheme is calculated. .

[0146] Among them, the effective coverage of the differential co-array Used to characterize the effective number of vertical differential cells occupied under a given differential quantization step size; differential co-array redundancy. This characterizes the degree of resampling caused by multiple difference pairs falling into the same quantization unit. By increasing... And inhibit This improves the effective utilization rate of the elevation-oriented virtual aperture under conditions of limited observation nodes. Preferably, the differential quantization step size... The elevation resolution can be set according to the scene's requirements, with a range of 1m to 5m.

[0147] (4) Orbital equilibrium regularity term

[0148] Based on the baseline vector along the track The mean of the values ​​is used to construct the along-track balance regularization term for candidate baseline schemes. :

[0149]

[0150] The along-track balance regularization term Used to prevent the satellite formation from drifting as a whole along the orbit.

[0151] Step 5: Using the baseline design constraint model, construct and solve a multi-criteria joint objective function based on the information content objective function, the overlay separation objective function, and the performance evaluation index, and output the distributed TomoSAR baseline design results that integrate the elevation prior and the overlay separation constraint.

[0152] First, the information content objective function Overlay separation objective function Differential co-array structured sampling index Peak-to-sidelobe ratio index Integral sidelobe ratio index Azimuth coherence loss index and the along-track equilibrium regularization term Normalization is performed.

[0153] Among them, the objective function focusing on the information content of subspaces Overlay separation objective function Sum of differential co-matrix structured sampling index This is a benefit-oriented indicator; a higher value indicates better performance of the candidate baseline scheme. Peak-sidelobe ratio is also an indicator. Integral sidelobe ratio index Azimuth coherence loss index and the equilibrium regularization term along the track As a cost-based metric, the smaller the value, the better the performance of the candidate baseline scheme.

[0154] Then, the normalized indicators are dimensionless and homogenized to be uniformly converted into a minimum form.

[0155] Finally, combined with the preset weight vector Construct a joint objective function based on multiple criteria. :

[0156]

[0157]

[0158] in, , , , , , and These represent the evaluation indicators after normalization and uniform conversion to their minimum form.

[0159] The normalized and homogenized evaluation indicators and the preset weight vector are combined. and engineering constraints and penalties Substituting the multi-criteria joint objective function, i.e., equation (9), we obtain the comprehensive objective function value corresponding to the candidate baseline scheme. .

[0160] In the solution process, this embodiment adopts a hybrid heuristic search architecture for optimization.

[0161] First, a genetic algorithm is used to perform a global search on the baseline variables to be optimized in order to obtain candidate baseline schemes that satisfy multiple constraints. After the genetic algorithm converges, the excellent candidate baseline schemes output by the genetic algorithm are used as the starting point of the pattern search algorithm to further perform local optimization in the local neighborhood. Finally, the distributed TomoSAR baseline design results are output.

[0162] The baseline design results include the vertical baseline vector. baseline vector along the track And the distributed TomoSAR two-dimensional baseline topology layout determined by the two, thus completing the distributed TomoSAR baseline design that integrates elevation priors and overlay separation constraints.

[0163] Experimental results

[0164] To verify the effectiveness of the distributed TomoSAR baseline design method proposed in this invention, which integrates elevation priors and overlay separation constraints, simulation experiments were conducted on a typical ground-roof dual scatterer overlay scenario in sparse urban areas. The experiments comprehensively considered system imaging parameters, formation physical constraints, and optimization solution parameters, and employed the method of this invention to jointly optimize the vertical baseline and along-track baseline of the distributed formation.

[0165] The system parameters, constraint parameters, and optimization parameters used in this embodiment are shown in Table 1.

[0166] Table 1

[0167]

[0168] Under the parameter conditions shown in Table 1, the method of this invention is used to optimize the design of distributed TomoSAR formation baselines and is compared with traditional uniform baselines, near-uniform baselines, and minimum redundancy array (MRA) baselines.

[0169] The effectiveness of the method of the present invention will be explained from three aspects: baseline design and theoretical-aided evaluation, two-scatterer separation performance, and reconstruction results of complex urban profile overlay scenes.

[0170] 1. Baseline Design Scheme and Theoretical-Assisted Evaluation and Analysis

[0171] like Figure 2 The figure shows the baseline design obtained after optimization using this method. Among them, Figure 2 (a) gives the vertical baseline sequence, Figure 2 (b) The two-dimensional baseline topology layout is given. As can be seen from the figure, the baseline design obtained by this method not only meets the vertical aperture requirements but also takes into account the distribution requirements along the track direction, and each satellite node can meet the preset engineering constraints.

[0172] like Figure 3 The figure shows a comparison of the vertical difference coarray distribution and repeatability of different baseline design schemes. Among them, Figure 3 (a) is a uniform baseline scheme. Figure 3 (b) is a near-uniform baseline scheme. Figure 3 (c) is the minimum redundancy array scheme. Figure 3(d) represents the method of the present invention. Compared with the uniform baseline scheme, the differential co-array of the present invention has higher effective coverage and lower resampling degree, which is beneficial to improving the virtual aperture utilization under the condition of limited observation nodes. In particular, the vertical difference set corresponding to the method of the present invention has a unique difference score of 21 and a maximum resampling degree of 1, indicating that it has a better differential sampling structure under the condition of limited satellite node number.

[0173] like Figure 4 As shown, the comparison results of the elevation-to-point spread function response of different baseline design schemes are presented. Among them, Figure 4 (a) is a uniform baseline scheme. Figure 4 (b) is a near-uniform baseline scheme. Figure 4 (c) is the minimum redundancy array scheme. Figure 4 (d) is the method of the present invention. It can be seen that although the minimum redundancy array scheme has a narrower main lobe, its sidelobe level is relatively high; in contrast, the method of the present invention, while maintaining good resolution, reduces the strong sidelobe response outside the main lobe, further reducing its peak-to-sidelobe ratio to [missing value]. This helps to reduce the shielding effect of the side lobes of strong scatterers on weak scatterers.

[0174] 2. Two-scatterer separation performance experiment

[0175] To quantify the dual-scatterer separation capability of the method of the present invention in a noisy environment, this embodiment further designs... Monte Carlo simulation experiment in a two-scatterer overlay scenario. In the experiment, the actual elevations of the two scatterers are set as follows: and The corresponding elevation interval is The scattering amplitudes are respectively and Set the number of quick photos to [number]. The signal-to-noise ratio scanning range is .

[0176] In each experiment, the MUSIC spectral estimation algorithm is first used to perform an initial peak search on a preset elevation scanning grid. Then, using the detected peak positions as initial values, a local nonlinear least squares method is employed to perform a fine estimation of the scatterer elevation. When the estimation errors of both scatterers are less than [a certain value], [the experiment continues]. When the separation is successful, the test is considered to be successful. In the successfully separated samples, the root mean square error of the scatterers with higher elevations is further statistically analyzed.

[0177] Figure 5A comparison chart of the theoretical performance lower bounds of different baseline design schemes is shown. The theoretical lower bound is characterized by the Cramér-Rao Lower Bound (CRLB). The results show that the theoretical lower bound of the elevation reconstruction error corresponding to the method of the present invention is lower than that of the uniform baseline scheme, the near-uniform baseline scheme, and the minimum redundancy array scheme, indicating that the baseline design obtained by the method of the present invention has good theoretical height measurement potential in the two-scatterer scenario.

[0178] Figure 6 The graph shows a comparison of the separation performance of different baseline designs in a two-scatterer scenario. Figure 6 (a) Design schemes for different baselines , The comparison chart of separation success rates in the dual-scatterer scenario shows that, under low signal-to-noise ratio conditions, the method of this invention maintains a high dual-peak detection capability, and its overall separation performance is better than that of the uniform baseline scheme, the near-uniform baseline scheme, and the minimum redundancy array scheme. Figure 6 (b) Comparison of root mean square errors in weak scatterer elevation reconstruction under different baseline design schemes. The results show that the method of the present invention has a lower weak scatterer elevation reconstruction error in the medium-to-high signal-to-noise ratio range, and is superior to the uniform baseline scheme, near-uniform baseline scheme, and minimum redundancy array scheme overall. This indicates that the method of the present invention not only has good separation capability in dual scatterer scenarios, but also improves the height measurement accuracy of weak scatterers.

[0179] 3. Experiment on the reconstruction of complex urban cross-section overlay scenes

[0180] To further verify the reconstruction performance of the method of this invention in complex and sparse urban overlapping scenarios, this embodiment designed a two-dimensional urban street profile simulation experiment. The signal-to-noise ratio was set to [value missing] in the experiment. The number of quick shots is The near-uniform baseline scheme, the minimum redundancy array scheme, and the method of this invention were compared.

[0181] The constructed urban profile contains 85 distance gates, within which three typical building areas are defined:

[0182] (1) Near-elevation interval area, corresponding to distances of 10 to 25, with ground elevation of The roof elevation is The two scattering amplitudes are similar, which can be used to examine the resolving power of closely spaced two scatterers;

[0183] (2) Medium-height areas with varying degrees of overlap, corresponding to distances of 35 to 50 from the door, with ground elevations of... The roof elevation is A significant difference in the amplitude of strong and weak scattering was set to examine the ability of weak scatterers to be retained at locations with high sidelobe risk.

[0184] (3) The area sheltered by taller buildings, corresponding to a distance of 60 to 75 from the door, with a ground elevation of The roof elevation is Similarly, a significant difference in the amplitude of strong and weak scattering was set to examine the overall reconstruction stability in complex overlay scenarios.

[0185] At each distance gate, multi-channel echo data is first generated based on a given baseline. Then, the MUSIC algorithm is used to perform an initial peak search on a high-precision scanning grid, combined with a local nonlinear least squares method for fine estimation of the scatterer elevation. To suppress spurious scattering points caused by noise, a threshold is set to filter the estimated complex amplitudes, retaining only reconstructed points with amplitudes higher than the preset threshold.

[0186] like Figure 7 The image shows a comparison of reconstruction results for different baseline design schemes in the aforementioned complex urban profile overlay scenario. Among them, Figure 7 (a) is a near-uniform baseline scheme. Figure 7 (b) is the minimum redundancy array scheme. Figure 7 (c) shows the method of the present invention. In the figure, gray blocks represent the actual location of the scattering layer, and scattered dots represent the reconstruction results. As can be seen from the figure, all three schemes can recover the main scattering layer structure in the scene to a certain extent, but there are significant differences in the reconstruction integrity and stray point control capabilities.

[0187] for Figure 7 (a) shows a near-uniform baseline scheme that can generate a certain reconstruction response in the low-rise, mid-rise, and high-rise roof areas. However, in the mid-rise and high-rise areas, there are many discrete points that deviate from the actual scattering layer position, indicating that its ability to suppress false alarms under complex overlay conditions is limited.

[0188] for Figure 7 (b) shows the minimum redundancy array scheme. The scatterers of the middle and upper roofs can be recovered relatively well, but the scatterers of the bottom ground are not stable enough. Furthermore, abnormal scattering points that deviate from the true positions still appear at some distance gate positions. This indicates that the scheme is easily affected by the high sidelobe and grating lobe responses under the condition of coexistence of strong and weak scatterers.

[0189] for Figure 7 (c) As shown in the present invention, the three main scattering layers—low-rise, mid-rise, and high-rise roofs—can be recovered relatively continuously, and the reconstructed points are generally closer to the actual scattering layer locations. Compared to the near-uniform baseline scheme and the minimum redundancy array scheme, the present invention's method performs better in maintaining ground layer continuity, restoring the main roof layer structure, and suppressing stray points, indicating that the present invention has better structural adaptability and reconstruction robustness in complex urban profile overlay scenarios.

[0190] The results of this embodiment demonstrate that the distributed TomoSAR baseline design method proposed in this invention, which integrates elevation priors and overlay separation constraints, can simultaneously address the utilization of elevation subspace information, overlay separation capability, and sidelobe suppression performance while satisfying formation safety and coherence constraints. Compared with traditional uniform baseline, near-uniform baseline, and minimum redundancy array schemes, the baseline design obtained using the method of this invention can improve scatterer separation capability in complex and sparse urban overlay scenarios and enhance the stability of tomographic 3D reconstruction results.

Claims

1. A distributed TomoSAR baseline design method integrating elevation priors and overlay separation constraints, characterized in that, The specific steps are as follows: Step 1: Obtain the parameters and mission indicators of the distributed TomoSAR formation system, and construct a baseline design constraint model; The baseline design constraint model is as follows: ； in, For the penalty weighting coefficient, Number of satellites; , , and These are the various penalty factors, and Number the satellite; Step 2: Construct an objective function for the information content of the interest subspace based on elevation priors. ; ； in, Indicates taking the real part, For numerically stable terms, It is the identity matrix. In the elevation subspace of interest The focused observation guidance matrix This is a diagonal prior probability weight matrix; Step 3: Construct an overlay separation objective function based on mutual coherence constraints. ; ； in, and These are the weighting coefficients. To smooth out correlation indicators, The mutual coherence between the ground guide vector and the guide vectors of each roof; Step 4: Construct auxiliary imaging performance evaluation indicators; Imaging performance evaluation metrics include sidelobe suppression metrics and azimuth coherence loss metrics. Differential co-array structured sampling index and the along-track equilibrium regularization term Among them, the sidelobe suppression index includes the peak sidelobe ratio index. Integral sidelobe ratio index ; Step 5: Using the baseline design constraint model, construct and solve a multi-criteria joint objective function based on the information content objective function, the overlay separation objective function, and the performance evaluation index, and output the distributed TomoSAR baseline design results.

2. The method as described in claim 1, characterized in that, In step one, the system parameters and task indicators include radar wavelength. Reference slope distance Radar downward view Satellite flight speed azimuth processing bandwidth Total number of distributed satellite formations Target elevation resolution requirements and minimum permissible azimuth to coherence baseline .

3. The method as described in claim 1, characterized in that, In step two, ground elevation undulation zones and typical building height zones are constructed based on prior elevation information of the scene. The ground elevation undulation zones and typical building height zones are then sampled discretely and merged to form a subspace of elevation of interest. A focused observation guidance matrix is ​​constructed on the subspace of elevation of interest, and a diagonal prior probability weight matrix is ​​constructed based on the prior occurrence probabilities of ground elevation zones and building height zones in the task scene.

4. The method as described in claim 2, characterized in that, In step one, each penalty sub-item is defined as follows: ； ； ； ； This refers to the platform's collision avoidance safety distance threshold. For the first satellite and the first The three-dimensional spatial distance between satellites The difference in baseline along the track, The upper limit of the allowable baseline difference along the track, This is the minimum interval threshold along the track. The minimum interval threshold for the vertical baseline. This represents the vertical baseline difference.

5. The method as described in claim 4, characterized in that, In step four, (1) Sidelobe suppression indices include peak sidelobe ratio indices Integral sidelobe ratio index Peak-to-sidelobe ratio index : ； Integral sidelobe ratio index : ； For full elevation search space Within this framework, the normalized point spread function magnitude response of the baseline array is constructed; Main lobe region; This refers to the side lobe region; (2) Construction of azimuth coherence loss index ; Based on the along-orbit baseline difference between any two satellites, an azimuth coherence loss index is constructed. : ； Among them, satellites are the total number ; (3) Differential co-array structured sampling index ; ； in, This is the redundancy penalty coefficient; The effective coverage of the differential co-array characterizes the effective coverage range of the vertical baseline differential set at a preset quantization step size. The redundancy of the differential co-array characterizes the degree of resampling in the vertical baseline differential set. (4) Orbital equilibrium regularity term , Based on the baseline vector along the track The mean of the terms is used to construct a balanced regularization term. :

6. The method as described in claim 5, characterized in that, Step five involves constructing a joint objective function based on multiple criteria, specifically as follows: First, the information content objective function Overlay separation objective function Differential co-array structured sampling index Peak-to-sidelobe ratio index Integral sidelobe ratio index Azimuth coherence loss index and the along-track equilibrium regularization term Perform normalization processing; Then, the normalized indicators are dimensionless and homogenized to be uniformly converted into a minimum form. Finally, combined with the preset weight vector Construct a joint objective function based on multiple criteria. : ； ； in, , , , , , and These represent the evaluation indicators after normalization and uniform conversion to their minimum form.

7. The method as described in claim 6, characterized in that, Step five employs a hybrid genetic algorithm and a pattern search algorithm to evaluate the multi-criteria joint objective function. Solve the following: First, a genetic algorithm is used to perform a global search on the baseline variables to be optimized in order to obtain candidate baseline schemes that satisfy multiple constraints. After the genetic algorithm converges, the excellent candidate baseline schemes output by the genetic algorithm are used as the initial points of the pattern search algorithm to further perform local optimization. Finally, the vertical baseline vector and the orbital baseline vector that satisfy the optimization requirements of the joint objective function are output, thus completing the baseline design of distributed TomoSAR.

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