Multi-station ISAR imaging method, device and equipment with overlapping observation angles
By constructing a substation observation model and performing l1 norm optimization, the resolution reduction problem caused by overlapping substation observation angles in multi-station ISAR imaging was solved, achieving high-resolution image reconstruction and improving imaging quality.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NAT UNIV OF DEFENSE TECH
- Filing Date
- 2023-07-14
- Publication Date
- 2026-05-19
AI Technical Summary
In multi-station ISAR imaging, overlapping observation angles at substations reduce imaging resolution, making it difficult to acquire high-resolution images in a short time.
By constructing a substation observation model, the multi-station ISAR imaging problem is transformed into an l1 norm optimization problem, and the high-resolution target ISAR image is reconstructed by using the Lagrangian function and the alternating direction multiplier model for iterative solution.
Under conditions of overlapping observation angles, high-resolution multi-station ISAR images were reconstructed, improving imaging quality, and maintaining good imaging performance even in low signal-to-noise ratio environments.
Smart Images
Figure CN116908847B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of radar imaging technology, and in particular to a multi-station ISAR imaging method, apparatus and equipment with overlapping observation angles. Background Technology
[0002] Inverse synthetic aperture radar (ISAR) imaging technology has the ability to acquire high-resolution images of moving targets in all weather conditions and at all times. It is an important means of space observation and target identification and has been widely used in military and civilian fields.
[0003] ISAR achieves high-resolution azimuth imaging by accumulating the relative rotation angle between the target and the radar. To obtain high-resolution images, the radar needs to observe the target for a relatively long time to acquire a large accumulated rotation angle. However, due to the non-cooperative motion of the target, long-term observation inevitably leads to difficulties in motion compensation.
[0004] Multi-station ISAR imaging is an imaging technique that integrates spatial and temporal observations. It utilizes multiple array elements at different locations in space to observe the target and jointly processes the echo data from different elements to achieve high-resolution imaging. Generally, multi-station ISAR can acquire a larger accumulated rotation angle in a shorter accumulation time, thus avoiding the trade-off between azimuth resolution and motion compensation inherent in single-station ISAR. However, when multiple substations are close together, there is significant overlap in the observation angles of adjacent substations. In this case, the accumulated observation angles from multi-station ISAR are limited, leading to a decrease in ISAR image resolution. Summary of the Invention
[0005] Therefore, it is necessary to provide a multi-station ISAR imaging method, apparatus, and equipment that can perform high-resolution imaging when there is a large overlap in the observation angles of the substations in a multi-station ISAR system, addressing the aforementioned technical problems.
[0006] A multi-station ISAR imaging method with overlapping observation angles, the method comprising:
[0007] Acquire a target echo signal set, which includes substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles;
[0008] Translational compensation and fast Fourier transform are performed sequentially on the echo signals of each substation to obtain one-dimensional range image data;
[0009] Based on the one-dimensional range image data of each substation and the ISAR images of each substation to be reconstructed, a substation observation model is constructed. Based on the substation observation model, the problem of solving the target ISAR image is transformed into an l1 norm optimization problem, and the corresponding l1 norm optimization solution model is obtained.
[0010] A Lagrange function is constructed based on the l1 norm optimization solution model, and an alternating direction multiplier model is constructed based on the Lagrange function;
[0011] The target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained in the current iteration is taken as the final multistation ISAR imaging result.
[0012] In one embodiment, the substation observation model is represented as:
[0013] Y i =AX i +N=DFX i +N
[0014] In the above formula, This represents the one-dimensional distance image data of the i-th substation. This represents the ISAR image of the i-th substation to be reconstructed. Represents the Gaussian white noise matrix. Represents the observation matrix. Represents the Fourier transform matrix. This represents the short aperture observation matrix.
[0015] In one embodiment, the short aperture observation matrix is represented as:
[0016]
[0017] In the above formula, I M Describes an M×M dimensional identity matrix, 0 M×L-M Represents an M×LM dimensional all-zero matrix
[0018] In one embodiment, the l1 norm optimization solution model is expressed as:
[0019]
[0020] stX i =Z
[0021] In the above formula, ||·|| F Let ||·||1 represent the F-norm and l1-norm of the matrix, respectively, λ represent the regularization parameter, and K represent the number of substations. This represents the target ISAR image to be solved.
[0022] In one embodiment, the Lagrange function is expressed as:
[0023]
[0024] In the above formula, Let ρ represent the Lagrange multiplier matrix. i represents the penalty coefficient, ⊙ represents the Hadamard product of the matrix, and sum(·) is the summation operator, which sums all elements in the matrix.
[0025] In one embodiment, the alternating direction multiplier model is represented as:
[0026]
[0027] In the above formula, j represents the number of iterations. This represents the element-wise division operation of a matrix, 1 L×N This represents a matrix of size L×N consisting entirely of 1s. This represents the mask matrix.
[0028] In one embodiment, the mask matrix is represented as:
[0029]
[0030] A multi-station ISAR imaging device with overlapping observation angles, the device comprising:
[0031] The target echo signal set acquisition module is used to acquire the target echo signal set, which includes the substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles;
[0032] The echo signal processing module is used to sequentially perform translational compensation and fast Fourier transform on the echo signals of each of the substations to obtain one-dimensional range image data.
[0033] The norm optimization solution model construction module is used to construct a substation observation model based on the one-dimensional range image data of each substation and the ISAR image of each substation to be reconstructed, and to convert the problem of solving the target ISAR image into an l1 norm optimization problem based on the substation observation model, and to obtain the corresponding l1 norm optimization solution model.
[0034] An alternating direction multiplier model construction module is used to construct a Lagrangian function based on the l1 norm optimization solution model, and to construct an alternating direction multiplier model based on the Lagrangian function;
[0035] The target ISAR image solving module is used to iteratively solve the target ISAR image using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained by the current iteration is taken as the final multistation ISAR imaging result.
[0036] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:
[0037] Acquire a target echo signal set, which includes substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles;
[0038] Translational compensation and fast Fourier transform are performed sequentially on the echo signals of each substation to obtain one-dimensional range image data;
[0039] Based on the one-dimensional range image data of each substation and the ISAR images of each substation to be reconstructed, a substation observation model is constructed. Based on the substation observation model, the problem of solving the target ISAR image is transformed into an l1 norm optimization problem, and the corresponding l1 norm optimization solution model is obtained.
[0040] A Lagrange function is constructed based on the l1 norm optimization solution model, and an alternating direction multiplier model is constructed based on the Lagrange function;
[0041] The target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained in the current iteration is taken as the final multistation ISAR imaging result.
[0042] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:
[0043] Acquire a target echo signal set, which includes substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles;
[0044] Translational compensation and fast Fourier transform are performed sequentially on the echo signals of each substation to obtain one-dimensional range image data;
[0045] Based on the one-dimensional range image data of each substation and the ISAR images of each substation to be reconstructed, a substation observation model is constructed. Based on the substation observation model, the problem of solving the target ISAR image is transformed into an l1 norm optimization problem, and the corresponding l1 norm optimization solution model is obtained.
[0046] A Lagrange function is constructed based on the l1 norm optimization solution model, and an alternating direction multiplier model is constructed based on the Lagrange function;
[0047] The target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained in the current iteration is taken as the final multistation ISAR imaging result.
[0048] The aforementioned multi-station ISAR imaging method, apparatus, and equipment with overlapping observation angles obtain one-dimensional range image data by sequentially performing translational compensation and fast Fourier transform on the echo signals received by the multi-station ISAR radar system from each substation. Based on the one-dimensional range image data and the ISAR images of each substation to be reconstructed, a substation observation model is constructed. The problem of solving the target ISAR image is then transformed into an l1-norm optimization problem based on this model, yielding a corresponding l1-norm optimization solution model. A Lagrangian function is constructed based on this solution model, followed by an alternating direction multiplier model. Finally, the target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data from each substation until the number of iterations meets a preset condition. The target ISAR image obtained in the current iteration is then taken as the final multi-station ISAR imaging result. This method can reconstruct high-resolution target images. Attached Figure Description
[0049] Figure 1 This is a flowchart illustrating a multi-station ISAR imaging method with overlapping observation angles in one embodiment.
[0050] Figure 2 This is a schematic diagram of the iterative solution process for an alternating direction multiplier model in one embodiment;
[0051] Figure 3 This is a schematic diagram of one-dimensional range image data received by each substation of a multi-station ISAR system in an experiment.
[0052] Figure 4 The image shows the imaging results of different imaging algorithms under an experimental signal-to-noise ratio of -9dB. (a) represents the imaging result of the orthogonal matching pursuit algorithm, (b) represents the imaging result of the smoothing l0 algorithm, and (c) represents the imaging result of the proposed method.
[0053] Figure 5 This is a structural block diagram of a multi-station ISAR imaging device with overlapping observation angles in one embodiment.
[0054] Figure 6 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation
[0055] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0056] To address the issue of low imaging resolution in existing multi-station ISAR radar systems under conditions of overlapping substation observation angles, such as... Figure 1 As shown, a multi-station ISAR imaging method with overlapping observation angles is provided, including the following steps:
[0057] Step S100: Obtain the target echo signal set, which includes the substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles;
[0058] Step S110: Perform translational compensation and fast Fourier transform on the echo signals of each substation in sequence to obtain one-dimensional range image data;
[0059] Step S120: Construct a substation observation model based on the one-dimensional range image data of each substation and the ISAR images of each substation to be reconstructed, and transform the problem of solving the target ISAR image into an l1 norm optimization problem based on the substation observation model, and obtain the corresponding l1 norm optimization solution model.
[0060] Step S130: Construct the Lagrangian function based on the l1 norm optimization solution model, and construct the alternating direction multiplier model based on the Lagrangian function;
[0061] Step S140: The target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained in the current iteration is taken as the final multistation ISAR imaging result.
[0062] In this method, a sub-observation model is first established. Based on this model, the multi-station ISAR imaging problem under the condition of overlapping observation angles is modeled as an l1-number optimization file. For the condition of overlapping observation angles, the similarity of the ISAR images of each sub-station is used as a constraint. For this optimization problem, C-ADMM is further used for solution. Through iterative calculation, high-resolution multi-station ISAR images can be reconstructed.
[0063] In step S110, translational compensation is performed on the echo signals of multiple substations in the target echo signal set before imaging. The translational compensation method used is a relatively mature technology. Therefore, the existing translational compensation method can be used to process the substation echo signals in this method.
[0064] Specifically, for the i-th substation in a multi-station ISAR system, the received two-dimensional echo (substation echo signal) can be modeled as follows:
[0065]
[0066] In formula (1), t m f c γ, c represent fast time, slow time, signal carrier frequency, signal modulation frequency, and speed of light in vacuum, respectively. q,i (t m ) represents the distance from the q-th scattering point to the i-th substation, σ q,i This represents the scattering coefficient of the q-th scattering point when observed at the i-th substation.
[0067] After demodulating the substation echo signal shown in formula (1), the echo expression is obtained as follows:
[0068]
[0069] In formula (2), the instantaneous distance R q,i (t m This can be expressed as the sum of the rotational distance component and the translational distance component:
[0070]
[0071] In formula (3), and Let these represent the translational and rotational components of the time-space distance, respectively. ω represents the position coordinates of the q-th scattering point in the observation scene of the i-th substation. i This represents the rotational speed of the target under the observation conditions of the i-th substation.
[0072] Substituting formula (3) into formula (2) and performing translational compensation, the expression for the received echo of the i-th substation is obtained as follows:
[0073]
[0074] In formula (4),
[0075] Next, regarding the relationship in formula (4) Performing a Fast Fourier Transform (FFT) yields the one-dimensional range image data of the i-th substation.
[0076] In step S120, when constructing the substation observation model, it is set that... The substation observation model consists of N distance units and M slow-time pulses, and is constructed as follows:
[0077] Y i =AX i +N=DFX i +N (5)
[0078] In formula (5), This represents the one-dimensional distance image data of the i-th substation. This represents the ISAR image of the i-th substation to be reconstructed. Represents the Gaussian white noise matrix. Represents the observation matrix. Represents the Fourier transform matrix. This represents the short aperture observation matrix.
[0079] Furthermore, short aperture observation matrix Represented as:
[0080]
[0081] In formula (6), I M Describes an M×M dimensional identity matrix, 0 M×L-M This represents an M×LM dimensional matrix of all zeros.
[0082] Next, based on the substation observation model, the multi-station ISAR imaging problem can be modeled as the following optimization problem, that is, the l1 norm optimization solution model is expressed as:
[0083]
[0084] In formula (7), ||·|| F Let ||·||1 represent the F-norm and l1-norm of the matrix, respectively, λ represent the regularization parameter, and K represent the number of substations. Let X represent the target ISAR image to be solved. Here, the similarity of the ISAR images of each substation is used as a constraint condition, that is, the ISAR images of each substation to be reconstructed X... i It is equal to the target ISAR image to be solved.
[0085] Next, in step S130, the Lagrange function can be constructed using formula (7) as follows:
[0086]
[0087] In formula (8), Let ρ represent the Lagrange multiplier matrix. i represents the penalty coefficient, ⊙ represents the Hadamard product of the matrix, and sum(·) is the summation operator, which sums all elements in the matrix.
[0088] In one embodiment, ρ is taken i =1, λ=0.2.
[0089] Using formula (8), the solution to formula (7) can be transformed into the following iterative operation:
[0090]
[0091] In formula (9), j represents the number of iterations. Substituting formula (8) into formula (9), the iterative operation of formula (9) can be further expressed as:
[0092]
[0093] In formula (10), This represents the element-wise division operation of a matrix, 1 L×N This represents a matrix of size L×N consisting entirely of 1s. This represents the mask matrix.
[0094] The mask matrix is represented as follows:
[0095]
[0096] In step S140, when performing iterative calculations on formula (10), Z is initialized. (0) =0 L×N , The one-dimensional distance image data obtained from each substation is used as... The initial value is determined, and then iterative calculations are performed until the number of iterations j meets the preset number. Then, the Z obtained in the current iteration is... (J+1) To reconstruct the high-resolution multi-station ISAR target image, the iterative calculation process of formula (10) is as follows: Figure 2 As shown.
[0097] In other embodiments, Z can also be obtained based on the current iteration. (J+1) Z obtained from the previous iteration (J) If the difference between the two iterations meets the preset threshold, it indicates that the calculation results have converged. If the changes between the two iterations are small, then the Z obtained in the current iteration is... (J+1) The high-resolution multi-station ISAR target image obtained through reconstruction.
[0098] In this paper, the effectiveness of the proposed method is also demonstrated through experiments.
[0099] This experiment uses an aircraft as the target and simulates multi-station ISAR measured data based on single-station radar measured data. The original data contains 256 pulses, each containing 256 sampling points. Assuming that the multi-station ISAR includes 4 substations, the 10*i+1 to 10*i+64th pulses of the original echo can be used as the simulated received echo of the i-th substation. At this time, there are 54 overlapping pulses in the echoes of adjacent substations, which satisfies the condition of observation angle overlap.
[0100] like Figure 3 As shown, this is one-dimensional range image data from four substations in a multi-station ISAR system. Figure 5 As shown, under the condition of a data signal-to-noise ratio of -9dB, Figure 4 (a) shows the results of orthogonal matching tracking imaging. Figure 4 (b) shows the imaging results of the smoothed l0 algorithm. Figure 4 (c) shows the imaging results of this invention. Due to the low signal-to-noise ratio, the main structure of the target is masked by noise in the imaging results of orthogonal matching pursuit and smoothing 10 algorithm, resulting in low imaging quality. However, the multi-station ISAR image reconstructed according to this method has high image quality.
[0101] The experiment demonstrates that this method can effectively solve the problem of low imaging quality under the condition of overlapping observation angles of multi-station ISAR substations. It can still achieve good imaging quality under low signal-to-noise ratio and has high engineering application value.
[0102] The aforementioned multi-station ISAR imaging method with overlapping observation angles obtains one-dimensional range image data by sequentially performing translational compensation and fast Fourier transform on the echo signals received by the multi-station ISAR radar system from each sub-station. Based on the one-dimensional range image data and the ISAR images of each sub-station to be reconstructed, a sub-station observation model is constructed. Then, based on this model, the problem of solving the target ISAR image is transformed into an l1-norm optimization problem, yielding a corresponding l1-norm optimization solution model. A Lagrangian function is constructed based on this model, followed by an alternating direction multiplier model. Finally, the target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data from each sub-station until the number of iterations meets a preset condition. The target ISAR image obtained in the current iteration is then used as the final multi-station ISAR imaging result. This method can reconstruct high-resolution target images.
[0103] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.
[0104] In one embodiment, such as Figure 5 As shown, a multi-station ISAR imaging device with overlapping observation angles is provided, including: a target echo signal set acquisition module 200, an echo signal processing module 210, a norm optimization solution model construction module 220, an alternating direction multiplier model construction module 230, and a target ISAR image solution module 240, wherein:
[0105] The target echo signal set acquisition module 200 is used to acquire the target echo signal set, which includes the substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles.
[0106] The echo signal processing module 210 is used to sequentially perform translational compensation and fast Fourier transform on the echo signals of each of the substations to obtain one-dimensional range image data.
[0107] The norm optimization solution model construction module 220 is used to construct a substation observation model based on the one-dimensional range image data of each substation and the ISAR image of each substation to be reconstructed, and to convert the problem of solving the target ISAR image into an l1 norm optimization problem based on the substation observation model, and to obtain the corresponding l1 norm optimization solution model.
[0108] Alternating direction multiplier model construction module 230 is used to construct a Lagrangian function based on the l1 norm optimization solution model, and to construct an alternating direction multiplier model based on the Lagrangian function;
[0109] The target ISAR image solving module 240 is used to iteratively solve the target ISAR image using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition, and then the target ISAR image obtained by the current iteration is taken as the final multi-station ISAR imaging result.
[0110] Specific limitations regarding multi-station ISAR imaging devices with overlapping observation angles can be found in the limitations of multi-station ISAR imaging methods with overlapping observation angles mentioned above, and will not be repeated here. Each module in the aforementioned multi-station ISAR imaging device with overlapping observation angles can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.
[0111] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 6 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a multi-station ISAR imaging method with overlapping observation angles. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.
[0112] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.
[0113] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:
[0114] Acquire a target echo signal set, which includes substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles;
[0115] Translational compensation and fast Fourier transform are performed sequentially on the echo signals of each substation to obtain one-dimensional range image data;
[0116] Based on the one-dimensional range image data of each substation and the ISAR images of each substation to be reconstructed, a substation observation model is constructed. Based on the substation observation model, the problem of solving the target ISAR image is transformed into an l1 norm optimization problem, and the corresponding l1 norm optimization solution model is obtained.
[0117] A Lagrange function is constructed based on the l1 norm optimization solution model, and an alternating direction multiplier model is constructed based on the Lagrange function;
[0118] The target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained in the current iteration is taken as the final multistation ISAR imaging result.
[0119] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:
[0120] Acquire a target echo signal set, which includes substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles;
[0121] Translational compensation and fast Fourier transform are performed sequentially on the echo signals of each substation to obtain one-dimensional range image data;
[0122] Based on the one-dimensional range image data of each substation and the ISAR images of each substation to be reconstructed, a substation observation model is constructed. Based on the substation observation model, the problem of solving the target ISAR image is transformed into an l1 norm optimization problem, and the corresponding l1 norm optimization solution model is obtained.
[0123] A Lagrange function is constructed based on the l1 norm optimization solution model, and an alternating direction multiplier model is constructed based on the Lagrange function;
[0124] The target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained in the current iteration is taken as the final multistation ISAR imaging result.
[0125] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.
[0126] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0127] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A multi-station ISAR imaging method with overlapping observation angles, characterized in that, The method includes: Acquire a target echo signal set, which includes substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles; Translational compensation and fast Fourier transform are performed sequentially on the echo signals of each substation to obtain one-dimensional range image data; Based on the one-dimensional range image data of each substation and the ISAR images of each substation to be reconstructed, a substation observation model is constructed, and based on this substation observation model, the problem of solving the target ISAR image is transformed into... Norm optimization problem, and obtain the corresponding Norm optimization solution model, wherein, the The norm optimization solution model is expressed as: In the above formula, and Let F norm and represent the matrix norm and respectively. Norm, This represents the regularization parameter, and K represents the number of substations. This represents the ISAR image of the target to be solved. Indicates the first i One-dimensional distance image data of each substation Indicates the first to be reconstructed i ISAR images from individual stations, Represents the observation matrix; According to the above The norm optimization solution model constructs a Lagrange function, and based on the Lagrange function, constructs an alternating direction multiplier model, wherein the alternating direction multiplier model is expressed as: In the above formula, j Indicates the number of iterations. This represents the element-wise division operation of a matrix. Indicates the size is A matrix of all 1s Represents the mask matrix. Represents the Lagrange multiplier matrix. The penalty coefficient is represented as follows: ； The target ISAR image is iteratively solved using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained in the current iteration is taken as the final multistation ISAR imaging result.
2. The multi-station ISAR imaging method according to claim 1, characterized in that, The substation observation model is represented as follows: In the above formula, Indicates the first i One-dimensional distance image data of each substation Indicates the first to be reconstructed i ISAR images from individual stations, Represents the Gaussian white noise matrix. Represents the observation matrix. Represents the Fourier transform matrix. This represents the short aperture observation matrix.
3. The multi-station ISAR imaging method according to claim 2, characterized in that, The short-aperture observation matrix is represented as follows: In the above formula, express 3D identity matrix express A matrix consisting entirely of zeros.
4. The multi-station ISAR imaging method according to claim 3, characterized in that, The Lagrange function is expressed as: In the above formula, Represents the Lagrange multiplier matrix. Indicates the penalty coefficient. Represents the Hadamard product of matrices. The summation operator represents summing over all elements in a matrix.
5. A multi-station ISAR imaging device with overlapping observation angles, characterized in that, The apparatus implements the multi-station ISAR imaging method with overlapping observation angles as described in any one of claims 1-4, and the apparatus comprises: The target echo signal set acquisition module is used to acquire the target echo signal set, which includes the substation echo signals obtained by each substation of the multi-station ISAR radar detecting the target from different observation angles; The echo signal processing module is used to sequentially perform translational compensation and fast Fourier transform on the echo signals of each of the substations to obtain one-dimensional range image data. The norm optimization solution model construction module is used to construct a sub-station observation model based on the one-dimensional range image data of each sub-station and the ISAR images of each sub-station to be reconstructed, and to transform the problem of solving the target ISAR image into a function based on the sub-station observation model. Norm optimization problem, and obtain the corresponding Norm optimization solution model; The alternating direction multiplier model construction module is used to construct the model based on the following: The norm optimization solution model is constructed using a Lagrange function, and an alternating direction multiplier model is constructed based on the Lagrange function. The target ISAR image solving module is used to iteratively solve the target ISAR image using the alternating direction multiplier model and the one-dimensional range image data of each substation until the number of iterations meets the preset condition. Then, the target ISAR image obtained by the current iteration is taken as the final multistation ISAR imaging result.
6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 4.