Nested three-dimensional sar antenna array design method and application

Abstract

The application discloses a kind of based on nesting three-dimensional SAR antenna array design method and application.For the problem of low resolution of small unmanned aerial three-dimensional SAR imaging, a design method of small three-dimensional SAR sparse antenna array configuration based on nesting is proposed;At the same time, based on the design method of three-dimensional SAR sparse antenna array, using the characteristics of slow flight speed of small unmanned aerial SAR, low azimuth doppler frequency, it is proposed to use azimuth decimation to obtain azimuth multi-shot data.Compared with the traditional method, the aperture length of the virtual antenna array formed by difference is twice that of the real antenna array by designing the sparse antenna array configuration, so as to improve the resolution in height direction;At the same time, the problem of distance-azimuth resolution reduction caused by traditional spatial averaging method is solved, and the resolution of three-dimensional SAR imaging result is improved.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture radar array antenna configuration design and three-dimensional imaging, and specifically relates to a nested three-dimensional SAR antenna array design method and application. Background Technology

[0002] UAV-borne array interferometric 3D SAR can acquire multi-channel coherent data in a single flight, enabling 3D imaging of the target scene. Compared to traditional multi-flight tomography and conventional airborne array interferometric 3D SAR, UAV-borne array interferometric 3D SAR offers advantages such as high efficiency, low cost, and high mobility, making it a promising and practical technology.

[0003] According to SAR 3D imaging theory, a longer maximum vertical baseline is needed to obtain better 3D resolution, and a shorter minimum element spacing is needed to ensure a sufficiently large maximum unambiguous height. Therefore, antenna arrays are generally designed in a uniformly distributed form, requiring a relatively large number of elements to simultaneously meet the above two requirements (usually more than 10). However, due to the limited payload of small UAV platforms, only a small number of antenna elements can be carried (usually no more than 5). 3D imaging can only be achieved by designing miniaturized sparse antenna arrays, thus significantly affecting the 3D resolution.

[0004] To address these issues, improvements are needed in areas such as antenna array configuration design and 3D imaging algorithms. However, there are relatively few reports on 3D SAR carried by small UAVs. Some scholars have used spherical wave models to study 3D SAR imaging of small UAVs flying at low altitudes, aiming to eliminate approximation errors caused by the traditional plane wave assumption and improve 3D imaging accuracy. However, this method does not directly solve the problem of low third-dimensional resolution caused by the small number of antennas and short apertures. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a nested three-dimensional SAR antenna array design method and application. The method increases the aperture length of the virtual antenna array to twice that of the actual antenna array, and uses azimuth downsampling to extract azimuth multi-shot data from a single-flight three-dimensional array SAR.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] On the one hand, the present invention provides a nested three-dimensional SAR antenna array design method, the method comprising the following steps:

[0008] Step 1: Determine the nesting level K of the nested 3D SAR antenna array to be designed, the minimum spacing d between antenna elements, and the number of elements in each level of uniformly distributed linear array. The above parameters must satisfy:

[0009]

[0010]

[0011]

[0012] In the formula, This represents the total number of all antenna elements. ∑ represents the total length of the antenna array, both of which are limited by the UAV's payload; ∑ represents the accumulation operation, ∏ represents the accumulation multiplication, and i is the counter used for the accumulation operation; It is the radar wavelength. It is the radar's downward view. Indicates the radar's flight altitude. This represents the maximum unambiguous height required by the system, i.e., the imaging range in the height dimension;

[0013] Step 2: Arrange all array elements according to the following formula:

[0014]

[0015]

[0016]

[0017] In the formula, Let D represent the set of antenna element locations of the k-th uniformly distributed linear array, where k represents the number of the uniformly distributed linear array, and D represents the entire nested three-dimensional SAR antenna array designed.

[0018] On the other hand, this invention provides an application of a nested three-dimensional SAR antenna array design method. The method utilizes the aforementioned nested three-dimensional SAR antenna array design method to design a three-dimensional SAR antenna array for SAR three-dimensional imaging, specifically including the following steps:

[0019] Step 1: Design a nested 3D SAR antenna array and install it on the UAV;

[0020] Step 2: Use a drone to fly and capture raw SAR echo data of the target scene;

[0021] Step 3: Perform azimuth descent sampling on the raw SAR echo data to obtain azimuth multi-shot two-dimensional imaging results;

[0022] Step 4: Perform interferometric image registration on the azimuth multi-shot 2D imaging results;

[0023] Step 5: Establish a new observation matrix pixel by pixel based on the registration results;

[0024] Step 6: Use the OMP algorithm to perform sparse 3D imaging to obtain the initial 3D point cloud of the target scene;

[0025] Step 7: Post-process the initial 3D point cloud to obtain the complete 3D imaging point cloud of the target area.

[0026] The beneficial effects of this invention are as follows:

[0027] This invention is based on a nested design of a miniaturized 3D SAR sparse antenna array configuration, which makes the aperture length of the virtual antenna array formed by differential array twice that of the real antenna array, thereby improving the altitude resolution. Taking advantage of the slow flight speed and low azimuth Doppler frequency of small UAV-borne SAR, this invention proposes to use azimuth downsampling to extract azimuth multi-shot data from a single-flight 3D array SAR, thus solving the problem of reduced range-azimuth resolution caused by the traditional spatial averaging method. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of a two-level nested array;

[0029] Figure 2 This is a flowchart illustrating the application of the nested three-dimensional SAR antenna array design method of the present invention.

[0030] Figure 3 This is a schematic diagram illustrating the acquisition of multi-shot data based on azimuth descent sampling.

[0031] Figure 4 This is a schematic diagram of the baseline design scheme of an embodiment of the present invention;

[0032] Figure 5 The images show a comparison between the three-dimensional imaging point cloud results and the optical oblique photography, where (a) is the optical oblique photography image and (b) is the three-dimensional imaging point cloud result image.

[0033] Figure 6 The images show a comparison of 3D imaging results from different methods on the ground, where (a) is a slice of the original SAR image, (b) is a slice of the traditional BOMP method on the ground, and (c) is a slice of the method of the present invention on the ground. Detailed Implementation

[0034] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0035] This invention provides a nested three-dimensional SAR antenna array design method, comprising:

[0036] Step 1: Determine the nesting level K of the nested 3D SAR antenna array to be designed, the minimum spacing d between antenna elements, and the number of elements in each level of uniformly distributed linear array. The above parameters must satisfy:

[0037]

[0038]

[0039]

[0040] In the formula, This indicates the total number of antenna elements. This indicates the total length of the antenna array, both of which are limited by the drone's payload. This indicates an accumulation operation. This indicates cumulative multiplication, where i is the counter used for the cumulative operation; It is the radar wavelength. It is the radar's downward view. Indicates the radar's flight altitude. This represents the maximum unambiguous height required by the system, i.e., the height-dimensional imaging range.

[0041] Step 2: Arrange all array elements according to the following formula:

[0042]

[0043]

[0044]

[0045] In the formula, This represents the set of antenna element positions for the k-th uniformly distributed linear array, where k represents the array number and the element spacing is . The number of array elements in the first k-1 uniformly distributed linear arrays and The spacing d is determined by both; This represents the entire nested array obtained from the design. Figure 1 A schematic diagram of a two-level nested array is given. As shown in the figure, each level of the nested array is a uniformly distributed linear array, and the previous level subarray is contained within the first array interval of the next level subarray, forming a nested structure.

[0046] On the other hand, this invention also provides an application of a nested three-dimensional SAR antenna array design method, such as... Figure 2 As shown, it includes the following steps:

[0047] Step 1: Based on the aforementioned design method, design a nested three-dimensional SAR antenna array and install it on the UAV;

[0048] Step 2: Obtain raw SAR echo data of the target scene by drone flight photography:

[0049] Based on the antenna array built in step 1, aerial photography is carried out on the target scene to obtain the raw SAR echo data of the target scene.

[0050] Step 3: Perform azimuth descent sampling on the raw SAR echo data to obtain azimuth multi-shot two-dimensional imaging results:

[0051] Because the UAV payload platform flies at a relatively slow speed, the azimuth sampling rate is much higher than the Doppler frequency, resulting in oversampled SAR echo data. The echo signal of each channel of the raw SAR echo data is divided into q groups, and downsampled by a factor of q to obtain q sub-echo data. The value of q is determined by the ratio of the azimuth sampling rate to the Doppler frequency. Finally, each of these q sub-echo data groups undergoes independent two-dimensional imaging processing.

[0052] ;

[0053] in, The azimuth sampling rate is... For Doppler frequency, This indicates rounding down to the nearest integer.

[0054] Step 4: Perform interferometric image registration on the azimuth multi-shot 2D imaging results:

[0055] Identify a main channel and use the maximum spectrum method or existing mature interferometric image registration methods to register the images of other channels with the main channel image;

[0056] Step 5: Establish a new observation matrix pixel by pixel:

[0057] Select a pixel from the registration results obtained in step 4, extract the observation values ​​of each channel at that pixel, and merge them into an observation vector. Under q-fold downsampling conditions, the observation vector There are q samples in total. Observation vector With observation matrix A and solution space target signal vector Gaussian white noise The relationship between them satisfies:

[0058] ;

[0059] ;

[0060] in, is the l-th column vector of the observation matrix A, representing the signal's observation of the target at the l-th grid point; exp represents the exponential function, and j represents the imaginary unit. It is the baseline length corresponding to the nth antenna element, where n represents the antenna element number; It is the slant range length corresponding to the main antenna of this pixel; It is the slant height corresponding to the l-th grid in the 3D imaging model.

[0061] Calculate the observation vector autocorrelation matrix The following formula is given:

[0062] ;

[0063] in, This represents the expected value of a random variable, where I represents the identity matrix. This represents the energy of Gaussian white noise, and the superscript H indicates the vector conjugate transpose. Let represent the autocorrelation matrix of the target signal vector x. If the target signal vector x is uncorrelated, then... , where L is the length of the target signal vector x; Let represent the energy of the target signal vector x corresponding to the l-th grid, where l represents the index of the component of the target vector, and is related to the grid and the column elements of the observation matrix A. One-to-one correspondence; diag represents a diagonal matrix. The observation vector... autocorrelation matrix Straighten, and obtain the straightened observation vector. :

[0064] ;

[0065] in, It is the autocorrelation matrix of the target signal vector x. The new target signal vector obtained after straightening; Represents the Khatri-Rao product. To indicate conjugate, the last character in the above equation is... This represents a column vector where all components are 1.

[0066] An intermediate matrix is ​​set up separately. Then the intermediate matrix The l-th column vector Represented as:

[0067] ;

[0068] In the formula, This represents the Kronecker product of matrices. At this point, and They are homographs; therefore, they can be... It can be viewed as a new observation matrix generated by a virtual array, the positions of which are obtained by the mutual difference of the elements of the actual antenna.

[0069] Step 6: Perform sparse 3D imaging using the OMP algorithm;

[0070] Based on the straightened observation vector calculated in step 5 and intermediate matrix The OMP algorithm is used to estimate the third-dimensional height at the two-dimensional position corresponding to the pixel; the height of each pixel in the registration result obtained in step 4 is estimated to obtain the three-dimensional point cloud of the target scene.

[0071] Step 7: Obtain the 3D point cloud and perform post-processing such as filtering on the point cloud:

[0072] After obtaining the initial 3D point cloud, thresholds are set according to the scattering intensity of each pixel, the inversion residual value, etc., and point cloud filtering is performed to remove noise and dark spots, thus obtaining the final 3D point cloud.

[0073] Example

[0074] This embodiment uses a miniature Ku-band SAR system mounted on a UAV to conduct a sparse array 3D imaging processing experiment in the Binhai New Area of ​​Tianjin. To balance maximum unambiguous altitude, elevation resolution, and the integrity of the final 3D imaging results, the antenna array designed for this experiment adopts the two-level nested array proposed in this invention. Figure 4 As shown, R4 forms a first-order subarray. The element spacing d = 0.107; R3, R2, and R1 form a two-level subarray. The spacing between array elements is Subsequently, aerial photography was conducted on the target scene to acquire raw SAR echo data of the target scene;

[0075] like Figure 3 As shown, let the initial sampling time be... The sampling time interval is ○, □, ◇, etc., represent downsampled subsamples, denoted as sample 1 to sample q. The SAR system's azimuth sampling rate is approximately 500Hz, and the Doppler frequency is approximately 42.7Hz. Using the method proposed in this invention, the echo signal is downsampled 8 times in the azimuth direction, acquiring one downsampled 2D SAR image in each channel. The first downsampled result of the first channel is used as the master image for interferometric image registration. Subsequently, according to step 5 above, the observation matrix is ​​established and solved pixel by pixel, and the obtained 3D point cloud is post-processed to obtain... Figure 5The point cloud shown is (a) an optical oblique photograph and (b) a three-dimensional imaging point cloud result. The three-dimensional imaging point cloud of the target area is complete and the structure is distinguishable.

[0076] By classifying points in a 3D point cloud and reprojecting them onto a 2D image grid, three slice images corresponding to the original 2D image—the ground, rooftop, and building—were obtained. Since building scattering is much stronger than ground scattering, the ability to reproduce scene details on the ground becomes an important indicator for evaluating the algorithm's performance. Figure 6 This paper presents a comparison of the results of the processing method proposed in this invention and the general BOMP algorithm. (a) is a slice of the original SAR image, (b) is a slice of the traditional BOMP method at the ground location, and (c) is a slice of the proposed method at the ground location. It is evident that for the four continuous vertical lines on the left side of the image representing scattering from the ground-level billboards, the proposed algorithm produces a more complete and continuous inversion result, while the BOMP algorithm's result is significantly affected by the scattering and overlay from the building. Regarding the inversion results for vehicles on the ground in front of the building, the BOMP algorithm incorrectly inverts some scattering points from the building onto the ground location, affecting the observation of ground targets. The multi-shot differential array algorithm avoids these problems and clearly shows the vehicle targets in front of the building.

[0077] As can be seen, the nested 3D SAR antenna array design method and application proposed in this invention possess the capability for 3D information inversion under conditions of few observations and single-flyover operation. Compared with existing methods, it has higher resolution, which is beneficial for further information mining of the imaging results.

[0078] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A nested three-dimensional SAR antenna array design method, characterized in that, The method includes the following steps: Step 1: Determine the nesting level K of the nested 3D SAR antenna array to be designed, the minimum spacing d between antenna elements, and the number of elements in each level of uniformly distributed linear array. ; The above parameters are required to satisfy: In the formula, This represents the total number of all antenna elements. ∑ represents the total length of the antenna array, both of which are limited by the UAV's payload; ∑ represents the accumulation operation, ∏ represents the accumulation multiplication, and i is the counter used for the accumulation operation; It is the radar wavelength. It is the radar's downward view. Indicates the radar's flight altitude. This represents the maximum unambiguous height required by the system, i.e., the imaging range in the height dimension; Step 2: Arrange all array elements according to the following formula: In the formula, Let represent the set of antenna element locations of the k-th uniformly distributed linear array, where k represents the number of the uniformly distributed linear array. This represents the entire nested three-dimensional SAR antenna array designed.

2. An application of a nested three-dimensional SAR antenna array design method, characterized in that, The method for designing a three-dimensional SAR antenna array based on nesting, as described in claim 1, for SAR three-dimensional imaging specifically includes the following steps: Step 1: Design a nested 3D SAR antenna array and install it on the UAV; Step 2: Use a drone to fly and capture raw SAR echo data of the target scene; Step 3: Perform azimuth descent sampling on the raw SAR echo data to obtain azimuth multi-shot two-dimensional imaging results; Step 4: Perform interferometric image registration on the azimuth multi-shot 2D imaging results; Step 5: Establish a new observation matrix pixel by pixel based on the registration results; Step 6: Use the OMP algorithm to perform sparse 3D imaging to obtain the initial 3D point cloud of the target scene; Step 7: Post-process the initial 3D point cloud to obtain the complete 3D imaging point cloud of the target area.

3. The application of the nested three-dimensional SAR antenna array design method according to claim 2, characterized in that, Step 3 includes: The echo data of each channel of the raw SAR echo data is divided into q groups, and q-fold downsampling is performed to obtain q sub-echo data. The q value is determined by the ratio of the azimuth sampling rate to the Doppler frequency. The q sub-echo data are then processed independently for two-dimensional imaging. ； in, The azimuth sampling rate is... For Doppler frequency, This indicates rounding down to the nearest integer.

4. The application of the nested three-dimensional SAR antenna array design method according to claim 2, characterized in that, Step 5 includes: Based on the obtained registration results, arbitrarily select a pixel, extract the observation values ​​of each channel of the pixel, and merge them into an observation vector. Under the condition of q-fold downsampling, the observation vector There are q samples in total, and the observation vector is... With observation matrix A and solution space target signal vector Gaussian white noise The relationship between them satisfies: ； ； in, is the l-th column vector of the observation matrix A, representing the signal's observation of the target at the l-th grid point; exp represents the exponential function, and j represents the imaginary unit. It is the baseline length corresponding to the nth antenna element, where n represents the antenna element number. ; It is the slant range length corresponding to the main antenna of this pixel; It is the slant height of the l-th grid in the 3D imaging model; Calculate the observation vector autocorrelation matrix The following formula is given: ； in, This represents the expected value of a random variable, where I represents the identity matrix. This represents the energy of Gaussian white noise, and the superscript H indicates the vector conjugate transpose. Let represent the autocorrelation matrix of the target signal vector x. If the target signal x is uncorrelated, then... , where L is the length of the target signal x; Let represent the energy of the target signal vector x corresponding to the l-th grid, where l represents the index of the component of the target vector, and is related to the grid and the column vectors in the observation matrix A. One-to-one correspondence, diag represents a diagonal matrix, which stores the observed signals. autocorrelation matrix Straighten, and obtain the straightened observation vector. : ； in, It is the new target vector obtained by straightening the autocorrelation matrix of the target signal x; Represents the Khatri-Rao product. To indicate conjugate, the last character in the above equation is... This represents a column vector where all components are 1. An intermediate matrix is ​​set up separately. Then the l-th column vector of the intermediate matrix HH Represented as: ； in, This represents the Kronecker product of matrices, where... and They are homographs. It is considered to be a new observation matrix generated by a virtual array, the positions of which are obtained by differentiating the elements of the actual antenna.

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