A SAR time-domain fast echo simulation method suitable for a terrain undulating scene

Abstract

This invention belongs to the field of radar imaging technology and discloses a fast time-domain echo simulation method for SAR systems in terrain-undulating scenarios. The method involves establishing a signal model, projecting the height information of the imaging scene onto a Cartesian coordinate grid through sampling, compressing the wavenumber spectrum of the SAR complex image in the Cartesian coordinate system, and then transforming it to the two-dimensional frequency domain. Based on the sub-aperture size of the previous level, the image is segmented along the azimuth frequency domain in the two-dimensional frequency domain, resulting in two frequency domain signals. Two-dimensional inverse Fourier transforms are performed on each of the two signals to compensate for the conjugate function of the wavenumber spectrum compression kernel. New wavenumber spectrum compression functions are then compensated for on each of the two signals, and the images are transformed back to the two-dimensional frequency domain. Zeroing operations are then performed on both ends of each signal, and the scene height is reprojected onto the imaging grid with doubled azimuth sampling intervals. This process is recursively repeated to obtain SAR complex images with progressively decreasing azimuth resolution until the SAR echo signal for each transmitted pulse is obtained, at which point the loop ends. This invention can save significant manpower and resources and can be used to evaluate various performance indicators of SAR systems.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, and in particular relates to a SAR time-domain fast echo simulation method suitable for terrain undulation scenarios. Background Technology

[0002] Radar can detect long-range targets around the clock, unaffected by fog, clouds, or rain, possessing all-weather, all-time characteristics and a certain degree of penetration capability. Therefore, it has become an indispensable electronic equipment in the military and is widely used in socio-economic development and scientific research. Synthetic Aperture Radar (SAR), a new type of radar system developed in the 1950s, meets the demands for imaging and high resolution, and has broad application prospects. When designing new radar system schemes, researching algorithms, and verifying systems, raw echo data meeting specific parameter requirements is needed, which cannot all be obtained through actual flight tests. Obtaining the required raw echo signals through simulation is an important solution and research direction. Radar fast echo simulation technology efficiently obtains large amounts of echo data under various conditions through simulation, which is used for the development and verification of SAR imaging algorithms and the determination of SAR system parameters. This can greatly accelerate the system research progress, mitigate development risks, and save development funds and reduce costs by requiring fewer flight tests.

[0003] There are many methods for SAR echo simulation, the basic ones being the concentric circle-based time-domain (TDA) generation method and the frequency-domain (FDA) data generation method. The TDA method is the most traditional and easiest to understand. Compared to the FDA method, the TDA method has higher accuracy and is easier to compensate for motion errors, making it widely used in area target simulation. During the working time, the TDA method needs to calculate the distance between the flight platform and the ground target at each pulse transmission moment, calculate the raw echo data of each point target, and then superimpose them to obtain the area target echo data for the entire region. The TDA algorithm has a clear physical concept, high simulation accuracy, and is easy to add motion error models, but it has high computational complexity and slow simulation speed. The computational load is acceptable for simulating single point targets or array targets, but it is not suitable for echo simulation of large-scale area targets with high computational complexity. SAR echo frequency domain simulation algorithms primarily transform the target's scattering coefficients to the frequency domain, multiply the target scattering function in the frequency domain by the radar system's impulse response, and achieve a time-domain convolution effect to obtain echo data. However, methods based on azimuth frequency domain processing typically require the assumption of azimuth invariance for the echo signal. In many SAR applications with non-uniform linear trajectories and complex geometric configurations, the echo signal no longer satisfies this assumption, introducing challenges to azimuth frequency domain processing-based simulation methods. Furthermore, for 3D scenes with terrain undulations, images prone to geometric distortions such as overlay, perspective contraction, and shadows due to elevation variations increase the difficulty of SAR image interpretation. In conclusion, echo simulation technology in 3D scenes with terrain undulations must not only address the modeling of ground scenes and the rapid implementation of large-scale echo simulation, but also overcome the shortcomings of the two aforementioned data generation methods. It is necessary to research new, efficient, accurate, and widely applicable SAR data simulation methods to meet the needs of developing and evaluating SAR imaging systems for arbitrary estimation and configuration applications.

[0004] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0005] (1) In the existing echo signal simulation methods, the computational load of the time-domain echo simulation method increases rapidly with the increase of the number of point targets, and its computational efficiency is low for large-scale echo simulation.

[0006] (2) In SAR application modes with complex geometric configurations of non-uniform linear trajectories, the echo signal no longer satisfies the assumption of azimuth invariance, which introduces difficulties to the simulation method based on azimuth frequency domain processing.

[0007] (3) For three-dimensional scenes with terrain undulations, geometric distortions such as overlay, perspective contraction, and shadows are prone to occur in the elevation undulation images, which will increase the difficulty of interpreting SAR images. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides a fast time-domain echo simulation method for SAR in terrain undulation scenarios, and particularly relates to an echo simulation method, system, medium, device and terminal based on CFBP inverse processing for analyzing terrain undulation.

[0009] This invention is implemented as follows: a fast time-domain echo simulation method for SAR in terrain-undulating scenarios. The echo simulation method for analyzing terrain undulations includes: establishing a signal model; projecting the height information of the imaging scene onto the rectangular coordinate grid of the imaging through sampling; compressing the wavenumber spectrum of the SAR complex image in the rectangular coordinate system and then transforming it to the two-dimensional frequency domain; dividing the image along the azimuth frequency domain in the two-dimensional frequency domain according to the sub-aperture size of the previous level, obtaining two frequency domain signals; performing two-dimensional inverse Fourier transform on the two signals respectively to compensate for the conjugate function of the wavenumber spectrum compression kernel; compressing the two signals respectively with a new wavenumber spectrum compression function, transforming them again to the two-dimensional frequency domain, and then performing zero-removal operations at both ends to reproject the scene height onto the imaging grid with doubled azimuth sampling interval; and continuously obtaining SAR complex images with progressively decreasing azimuth resolution through recursive processing until the SAR echo signal under each transmission pulse is obtained, ending the loop.

[0010] Furthermore, the SAR time-domain fast echo simulation method suitable for terrain undulation scenarios includes the following steps:

[0011] Step 1: Establish a signal model, projecting the height information of the imaging scene onto the Cartesian coordinate grid of the image through sampling. Transform the complex image expression of the scene in Cartesian coordinates to the two-dimensional frequency domain. Use the established signal model and wavenumber vector decomposition to derive the width of the wavenumber spectrum, and obtain the sampling rate limit in the image domain from the wavenumber spectrum width. By analyzing the sampling rate limit, azimuth wavenumber spectrum compression kernel is derived, so that the sampling rate of the compressed azimuth image is only related to the aperture length. Derive the full-aperture wavenumber spectrum compression kernel to compress the image domain signal, and perform a two-dimensional FFT transformation to the spectrum, at which point the spectrum is located in the middle position.

[0012] Step two: Divide the signal in the two-dimensional spectrum into two parts along the azimuth direction. Perform two-dimensional inverse Fourier transform on each part, and then compensate the conjugate function of the wavenumber spectrum compression function in the previous step to preserve the phase.

[0013] Step 3: Establish a new wavenumber spectrum compression function based on the aperture center of the segmented sub-apertures, compensate the segmented signal, so that the spectrum after the cut is in the middle position, transform it to the two-dimensional frequency domain again, and then perform zero removal operations at both ends. At this time, the azimuth resolution of the signal in the image domain is reduced by half, and the scene height is reprojected into the imaging grid with the azimuth sampling interval doubled.

[0014] Step 4: Repeat steps 2 to 3 to continuously obtain SAR complex images with progressively decreasing azimuth resolution until the SAR echo signal under each transmission pulse is obtained; perform three-dimensional calculation using the height information on the imaging grid to obtain the range data of the echo signal.

[0015] Furthermore, in step one, the radar is mounted on a moving flight platform, following an arbitrary curve. The beam is in flight with a total aperture length of L, and it always points towards the center of the scene during platform operation; P is any scattering point in the radar-illuminated scene, and its position in Cartesian coordinates is represented by P(x). p ,y p ,z p If ), then the slant range history over the entire aperture time is expressed as . Where (x,y,z) represents the instantaneous position of the platform, (x...y...z) i ,y i Let be any point on the imaging grid, and project the scene's elevation information onto the imaging grid. Imaging employs a back-projection algorithm. In Cartesian coordinates, the SAR complex image containing the point is represented as:

[0016]

[0017] In the formula, K B =K max -K min The minimum and maximum values ​​of the wavenumber spectrum width in the range direction of the transmitted signal are K. max and K min ; It is the central wavenumber, K = K c +K r K r ∈(-K B / 2,K B / 2); It is the slant distance history between the scene point and the platform location, z i It is the height information projected onto the grid, and (x,y,z) is the instantaneous orientation position of the platform.

[0018] Convert the image to x i and y i In the corresponding 2D inverse transform domain The variable K is obtained through the stationary phase method.x and K y The range of K sinθ min ≤K x ≤K sinθ max K min cosθ≤K y ≤K max cosθ, where θ min and θ max These are the antenna viewpoints. The maximum and minimum values; the sampling rate of the image domain is limited to... The results utilize the properties of small oblique angles: sinθ = θ and cosθ = 1.

[0019] The sampling interval in the azimuth direction is limited by the azimuth beam angle range. Under focused conditions, the beam angle range is affected by both the scene width and the synthetic aperture length. In contrast, the sampling interval in the range direction is only affected by the transmit signal bandwidth. Where x i / r i and x / r i These represent the wavenumber spectral components represented by the scene width and the sub-aperture length, respectively. Starting from the slant range, under frontal side-view conditions, the slant range is expanded as follows: In the expanded configuration, the aperture length is much smaller than the scene distance. Construct an azimuth wavenumber spectrum compression kernel. The first term is used for azimuth wavenumber spectrum compression, and the second term is the phase preservation factor. After compression kernel compensation, the wavenumber spectrum width in Cartesian coordinates depends only on the length of the sub-aperture. The azimuth image domain sampling interval Δx only needs to satisfy... Where l is the length of the sub-aperture. The sampling interval in the azimuth image domain is proportional to the aperture length. By decomposing the full aperture image into sub-aperture images and reducing the sampling interval by multiples until the echo signal is obtained, the wavenumber spectrum compression kernel of the full aperture is derived to compress the image domain signal. The two-dimensional FFT transform is then applied to the spectrum, at which point the spectrum is located in the middle position.

[0020] Furthermore, in step two, the full-aperture signal is divided into two equal-length sub-aperture signals. The full-aperture signal corresponds to the full-aperture SAR image, and the full-aperture SAR image corresponds to the full-aperture image spectrum. The full-aperture image spectrum is then divided into K... x Centered on 0, the image is divided into two parts along the azimuth frequency direction, resulting in sub-aperture image spectrum 1 and sub-aperture image spectrum 2. Sub-aperture image spectrum 1 corresponds to the spectrum of sub-image 1, and sub-image 1 corresponds to the echo signal of sub-aperture 1. Sub-aperture image spectrum 2 corresponds to the spectrum of sub-image 2, and sub-image 2 corresponds to the echo signal of sub-aperture 2. Two-dimensional inverse Fourier transforms are performed on both parts of the signal, and the conjugate function of the wavenumber spectrum compression function from the previous step is compensated to maintain phase.

[0021] Furthermore, in step three, a new wavenumber spectrum compression function is established based on the aperture centers of the segmented sub-aperture 1 and sub-aperture 2, and the segmented signals are compensated respectively, so that the cut spectrum 1 and spectrum 2 are both located in the middle position. The signal is then transformed to the two-dimensional frequency domain and zeroing is performed at both ends. At this time, the azimuth resolution of the image domain of the signal is reduced by half, and the scene height is reprojected onto the imaging grid with the azimuth sampling interval doubled.

[0022] Furthermore, in step four, a Cartesian coordinate complex image with progressively decreasing resolution is obtained through recursive processing until the SAR echo signal under each pulse is obtained, at which point the recursive processing ends.

[0023] Another objective of this invention is to provide an echo simulation system for analyzing terrain undulations using the aforementioned SAR time-domain fast echo simulation method suitable for terrain undulation scenarios. The echo simulation system for analyzing terrain undulations includes:

[0024] The image transformation module is used to establish a signal model, project the height information of the imaging scene onto the rectangular coordinate grid of the imaging through sampling, and transform the SAR complex image to the two-dimensional frequency domain;

[0025] The image segmentation module is used to segment the image in the two-dimensional frequency domain according to the sub-aperture size of the previous level, shift the spectrum to the middle position, and then perform zero removal operation at both ends to obtain the frequency domain signal and perform two-dimensional inverse Fourier transform to obtain two SAR complex images.

[0026] The wavenumber spectrum compression module is used to compress the wavenumber spectrum of SAR complex images so that the azimuth resolution is only related to the aperture length and the spectrum of the image is also moved to the middle position.

[0027] The sampling projection module is used to transform the signal to the image domain to obtain a SAR complex image with a lower azimuth resolution, and to project the height information of the imaging scene onto the Cartesian coordinate grid of the imaging through sampling.

[0028] The echo simulation module is used to obtain SAR complex images with progressively decreasing azimuth resolution through recursive processing. The loop ends when the SAR echo signal under each transmitted pulse is obtained, thus realizing echo simulation.

[0029] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, causing the processor to perform the steps of the SAR time-domain fast echo simulation method applicable to terrain undulation scenarios.

[0030] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the SAR time-domain fast echo simulation method applicable to terrain undulation scenarios.

[0031] Another objective of this invention is to provide an information data processing terminal for implementing the aforementioned echo simulation system for analyzing terrain undulations.

[0032] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0033] First, addressing the technical problems existing in the prior art and the difficulty in solving them, this paper closely analyzes, in conjunction with the technical solution to be protected by this invention and the results and data obtained during the research and development process, how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about by solving these problems. The specific description is as follows:

[0034] This invention provides a fast simulation method for SAR (Synthetic aperture radar) echo signals based on CFBP (Cartesian factorized backprojection) inverse processing for analyzing terrain undulations. A signal model is established, and the height information of the imaging scene is sampled and projected onto a Cartesian coordinate grid. The SAR complex image in the Cartesian coordinate system is then compressed in wavenumber spectrum and transformed to the two-dimensional frequency domain. According to the sub-aperture size of the previous level, the image is segmented along the azimuth frequency domain in the two-dimensional frequency domain, resulting in two frequency domain signals. Two-dimensional inverse Fourier transforms are performed on each of the two signals to compensate for the conjugate function of the wavenumber spectrum compression kernel. The two signals are then compressed using a new wavenumber spectrum compression function, transformed again to the two-dimensional frequency domain, and zero-removal operations are performed at both ends to reproject the scene height onto the imaging grid with doubled azimuth sampling intervals. Through recursive processing, SAR complex images with progressively decreasing azimuth resolution are continuously obtained until the SAR echo signal for each transmitted pulse is obtained, at which point the loop ends.

[0035] To further improve the computational efficiency of the TDA algorithm, this invention is based on the Cartesian factorized backprojection (CFBP) algorithm. This algorithm achieves coarse image fusion by upsampling and coherent synthesis of the image spectrum in Cartesian coordinates. By avoiding extensive two-dimensional interpolation, this algorithm significantly improves both accuracy and efficiency. This invention reverse-engineers the CFBP algorithm, improving the efficiency and accuracy of the echo signal simulation method. Simultaneously, it incorporates height information into the imaging grid, resolving the problem caused by radar image geometric distortion in SAR echo simulation.

[0036] The echo simulation framework provided by this invention, applicable to terrain undulations, significantly reduces the number of interpolation operations used for image segmentation compared to traditional time-domain echo simulation algorithms, thereby greatly improving the algorithm's computational efficiency. Furthermore, the efficiency improvement becomes more pronounced as the number of transmit and receive pulses increases across the full aperture. This invention effectively solves the problem of geometric distortion of radar images caused by scene altitude in the SAR echo simulation process. Simultaneously, this invention can simulate SAR echo signals from aircraft under various complex application conditions with minimal manpower and resources, enabling the evaluation of various performance indicators of SAR systems and the improvement and optimization of real-time imaging processing hardware systems.

[0037] Second, considering the technical solution as a whole or from a product perspective, the technical effects and advantages of the technical solution to be protected by this invention are specifically described as follows:

[0038] The SAR time-domain fast echo simulation method provided by this invention, suitable for terrain-undulating scenarios, leverages the high accuracy of time-domain algorithms. Improvements to the time-domain algorithm significantly enhance computational efficiency, making it suitable for large-scale echo generation. It also eliminates the need for the assumption of azimuth invariance and addresses the impact of terrain undulations. This invention saves substantial human and material resources for evaluating various performance indicators of SAR systems and for improving and optimizing real-time imaging processing hardware systems.

[0039] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0040] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0041] The biggest advantage of SAR echo simulation technology is that it can efficiently obtain a large amount of echo data under various conditions through simulation, without the need for actual flight testing, making it convenient and fast. This can greatly accelerate the research progress of SAR systems, mitigate development risks, and save research and development funds and reduce costs by requiring fewer flight tests.

[0042] (2) The technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully:

[0043] The technical solution of this invention is an echo simulation algorithm based on the time-domain CFBP algorithm, which has the characteristics of high precision. Compared with the traditional concentric circle echo generation method, it greatly improves the computational efficiency, and can also process the height information of the scene. The obtained echo has high quality, and the difference between the obtained echo and the original image is very small. Attached Figure Description

[0044] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart of a SAR time-domain fast echo simulation method for terrain undulation scenarios provided in this embodiment of the invention;

[0046] Figure 2 This is a schematic diagram of the SAR time-domain fast echo simulation method for terrain undulation scenarios provided in this embodiment of the invention;

[0047] Figure 3 This is a signal model diagram provided in an embodiment of the present invention;

[0048] Figure 4 This is a schematic diagram of the height information of the experimental scene provided in the embodiment of the present invention;

[0049] Figure 5 This is a schematic diagram of the spectrum segmentation steps provided in an embodiment of the present invention;

[0050] Figure 6 This is a schematic diagram of a scene SAR complex image provided in an embodiment of the present invention. The scene size is approximately 150m × 300m (X direction × Y direction), and the pixel array is 512 × 1024 (X direction × Y direction).

[0051] Figure 7 This is a schematic diagram of the SAR image result obtained by performing SAR imaging processing on the SAR simulation echo signal obtained by the algorithm provided in this invention, as provided in an embodiment of the invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0053] To address the problems existing in the prior art, this invention provides a fast time-domain echo simulation method for SAR in terrain undulation scenarios. The invention will be described in detail below with reference to the accompanying drawings.

[0054] like Figure 1 As shown, the echo simulation method for analyzing terrain undulations provided in this embodiment of the invention includes the following steps:

[0055] S101, establish a signal model and project the height information of the imaging scene onto the Cartesian coordinate grid of the image through sampling. Transform the complex image expression of the scene in Cartesian coordinates to the two-dimensional frequency domain. Use the established signal model and wavenumber vector decomposition to derive the width of the wavenumber spectrum, and obtain the sampling rate limit of the image domain from the wavenumber spectrum width. By analyzing the sampling rate limit, azimuth wavenumber spectrum compression kernel is derived, so that the sampling rate of the compressed azimuth image is only related to the aperture length. Derive the full-aperture wavenumber spectrum compression kernel to compress the image domain signal, and perform a two-dimensional FFT transformation to the spectrum, at which point the spectrum is located in the middle position.

[0056] S102, the signal in the two-dimensional spectrum is divided into two parts along the azimuth direction. Two-dimensional inverse Fourier transforms are performed on each part, and then the conjugate function of the wavenumber spectral compression function from the previous step is compensated to preserve phase.

[0057] S103, a new wavenumber spectrum compression function is established based on the aperture center of the segmented sub-apertures to compensate the segmented signal so that the spectrum after the cut is in the middle position. The signal is then transformed to the two-dimensional frequency domain and zeroing is performed at both ends. At this time, the azimuth resolution of the image domain of the signal is reduced by half. The scene height is then reprojected onto the imaging grid with the azimuth sampling interval doubled.

[0058] S104 continuously obtains SAR complex images with progressively decreasing azimuth resolution through recursive processing until the SAR echo signal under each transmitted pulse is obtained, thus ending the loop and realizing echo simulation.

[0059] As a preferred embodiment, such as Figure 2 As shown, the echo simulation method for analyzing terrain undulations provided in this embodiment of the invention specifically includes the following steps:

[0060] (1) Establish a signal model and project the height information of the imaging scene onto the rectangular coordinate grid of the image through sampling; then transform the complex image expression of the scene in the Cartesian coordinate system to the two-dimensional frequency domain, derive the width of the wavenumber spectrum using the established signal model and wavenumber vector decomposition, and obtain the sampling rate limit of the image domain through the width of the wavenumber spectrum; by analyzing the sampling rate limit, derive the azimuth wavenumber spectrum compression kernel so that the sampling rate of the compressed azimuth image is only related to the aperture length, specifically including:

[0061] The radar is mounted on a moving flight platform, following arbitrary curves. The beam is in flight with a total aperture length of L, and it always points towards the center of the scene during platform operation; P is any scattering point in the radar-illuminated scene, and its position in Cartesian coordinates is represented by P(x). p ,y p ,z p If ), then the slant range history over the entire aperture time can be expressed as: Where (x,y,z) represents the instantaneous position of the platform, (x...y...z) i ,y i Let be any point on the imaging grid, and project the scene's elevation information onto the imaging grid. Imaging uses the backprojection (BP) algorithm. In Cartesian coordinates, the SAR complex image containing this point is represented as:

[0062]

[0063] In the formula, K B =K max -K min The range-direction wavenumber spectral width of the transmitted signal is given by K, whose minimum and maximum values ​​are respectively K. max and K min , It is the central wavenumber, K = K c +K r K r ∈(-K B / 2,K B / 2), It is the slant distance history between the scene point and the platform location, z i It is the height information projected onto the grid, and (x,y,z) is the instantaneous orientation position of the platform.

[0064] Convert the image to x i and y i In the corresponding 2D inverse transform domain The variable K is obtained through the stationary phase method. x and K y The range of K sinθ min ≤K x≤K sinθ max K min cosθ≤K y ≤K max cosθ, where θ min and θ max These are the antenna viewpoints. The maximum and minimum values. This range determines the sampling rate limit required for the image domain: The above results utilize the properties of small oblique angles: sinθ = θ and cosθ = 1.

[0065] As can be seen from the sampling rate limit required in the image domain, the sampling interval in the azimuth direction is limited by the azimuth beam angle range. Under spotting conditions, the beam angle range is affected by both the scene width and the synthetic aperture length. The sampling interval in the range direction is the same as that in the full aperture and is only affected by the transmit signal bandwidth. Where x i / r i and x / r i These represent the wavenumber spectral components, namely the scene width and the sub-aperture length. Within a relatively short sub-aperture time, the former has a small range, while the latter occupies the majority of the wavenumber spectrum, resulting in a high azimuth sampling rate in sub-aperture imaging.

[0066] To solve this problem, x i / r i The term is derived from x in the slope distance expression. i The quadratic term leads to this problem, so this invention first starts with the slant range to seek a solution. Under frontal side view conditions, the slant range is expanded as... The expansion uses the assumption that the aperture length is much smaller than the scene distance. Since the second term only contains x... i The first-order term, after differentiation, no longer contains x. i Therefore, the broadening of the wavenumber spectrum is only related to the first term. That is, the first term is the reason for the larger wavenumber spectrum. Therefore, this invention constructs an azimuth wavenumber spectrum compression kernel. The first term is used for azimuth wavenumber spectrum compression, and the second term is the phase preservation factor. After compression kernel compensation, the wavenumber spectrum width in Cartesian coordinates is the same as that in polar coordinates, and is only related to the length of the sub-aperture, no longer affected by the scene size. At this point, the azimuth image domain sampling interval Δx only needs to satisfy... Where l is the length of the sub-aperture. Thus, it can be seen that the sampling interval in the azimuth image domain is proportional to the aperture length. By decomposing the full aperture image into sub-aperture images, the sampling interval is reduced by a factor until the echo signal is obtained. The wavenumber spectral compression kernel of the full aperture is derived to compress the image domain signal, and a two-dimensional FFT transform is performed to obtain the spectrum, which is now located in the middle position.

[0067] (2) The signal in the two-dimensional spectrum is divided into two parts along the azimuth direction. Two-dimensional inverse Fourier transforms are performed on each part, and then the conjugate function of the wavenumber spectral compression function from the previous step is compensated to preserve the phase. Specifically, this includes:

[0068] The full aperture signal was divided into two equal-length sub-aperture signals. The full aperture signal corresponds to the full aperture SAR image, and the full aperture SAR image corresponds to the full aperture image spectrum. The full aperture image spectrum is then divided into K... x Centered on 0, the image is divided into two parts along the azimuth frequency direction, resulting in sub-aperture image spectrum 1 and sub-aperture image spectrum 2. Two-dimensional inverse Fourier transforms are performed on both parts of the signal, and the conjugate function of the wavenumber spectrum compression function from the previous step is compensated to preserve phase. Sub-aperture image spectrum 1 corresponds to the spectrum of sub-image 1, and sub-image 1 corresponds to the echo signal of sub-aperture 1. Simultaneously, sub-aperture image spectrum 2 corresponds to the spectrum of sub-image 2, and sub-image 2 corresponds to the echo signal of sub-aperture 2.

[0069] (3) Compensate the two parts of the signal with new wavenumber spectrum compression functions, transform them to the two-dimensional frequency domain again, and then perform zero removal operations at both ends to reproject the scene height onto the imaging grid with doubled azimuth sampling interval;

[0070] Specifically, this includes: establishing a new wavenumber spectrum compression function based on the aperture center of the segmented sub-apertures, compensating the segmented signal so that the cut spectrum is in the middle position, transforming it to the two-dimensional frequency domain again, and then performing zero removal operations at both ends. At this time, the azimuth resolution of the signal in the image domain is reduced by half, and the scene height is reprojected onto the imaging grid with the azimuth sampling interval doubled.

[0071] (4) Repeat steps (2) to (3) to continuously obtain SAR complex images with progressively decreasing azimuth resolution until the SAR echo signal under each transmission pulse is obtained. Perform three-dimensional calculation using the height information on the imaging grid to obtain the range data of the echo signal, specifically including:

[0072] Repeat steps (2) to (3) to perform recursive processing to obtain Cartesian coordinate complex images with progressively decreasing resolution until the SAR echo signal under each pulse is obtained, at which point the recursive processing ends.

[0073] The echo simulation system for analyzing terrain undulations provided in this embodiment of the invention includes:

[0074] The image transformation module is used to establish a signal model, project the height information of the imaging scene onto the rectangular coordinate grid of the imaging through sampling, and transform the SAR complex image to the two-dimensional frequency domain;

[0075] The image segmentation module is used to segment the image in the two-dimensional frequency domain according to the sub-aperture size of the previous level, shift the spectrum to the middle position, and then perform zero removal operation at both ends to obtain the frequency domain signal and perform two-dimensional inverse Fourier transform to obtain two SAR complex images.

[0076] The wavenumber spectrum compression module is used to compress the wavenumber spectrum of SAR complex images so that the azimuth resolution is only related to the aperture length and the spectrum of the image is also moved to the middle position.

[0077] The sampling projection module is used to transform the signal to the image domain to obtain a SAR complex image with a lower azimuth resolution, and to project the height information of the imaging scene onto the Cartesian coordinate grid of the imaging through sampling.

[0078] The echo simulation module is used to obtain SAR complex images with progressively decreasing azimuth resolution through recursive processing. The loop ends when the SAR echo signal under each transmitted pulse is obtained, thus realizing echo simulation.

[0079] like Figure 3 As shown, the radar is mounted on a moving flight platform, along an arbitrary curve. The beam is in flight with a total aperture length of L, and it always points towards the center of the scene during platform operation; P is any scattering point in the radar-illuminated scene, and its position in Cartesian coordinates is represented by P(x). p ,y p ,z p If ), then the slant range history over the entire aperture time can be expressed as: Where (x,y,z) represents the instantaneous position of the platform, (x...y...z) i ,y i Let be any point on the imaging grid, and project the scene's elevation information onto the imaging grid. Imaging uses the back projection (BP) algorithm. In Cartesian coordinates, the SAR complex image containing this point is represented as:

[0080]

[0081] In the formula, K B =K max -K min The range-direction wavenumber spectral width of the transmitted signal is given by K, whose minimum and maximum values ​​are respectively K. max and K min , It is the central wavenumber, K = K c +K r K r ∈(-K B / 2,K B / 2), It is the slant distance history between the scene point and the platform location, zi It is the height information projected onto the grid, and (x,y,z) is the instantaneous orientation position of the platform.

[0082] By analyzing the relationship between wavenumber vectors and image domain sampling rate, it can be concluded that the azimuth sampling interval is determined by the scene width and the synthetic aperture length, and the scene width is the main reason for the high azimuth sampling rate in sub-aperture imaging. Therefore, this invention constructs an azimuth wavenumber spectrum compression kernel. The first term is used for azimuth wavenumber spectrum compression, and the second term is the phase preservation factor. After compression kernel compensation, the sampling interval of the azimuth image domain in the Cartesian coordinate system is only related to the length of the sub-aperture and is no longer affected by the scene size. As can be seen from the above analysis, by constructing an azimuth wavenumber spectrum compression kernel, the azimuth image domain sampling interval can be made to be only related to the aperture length. Therefore, by continuously reducing the sampling interval of the azimuth image through aperture division, sub-images with progressively decreasing azimuth resolution can be obtained until the SAR echo signal under each transmitted pulse is obtained.

[0083] like Figure 5 As shown, the sub-image partitioning process was analyzed in the frequency domain. The full aperture signal was divided into two equal-length sub-aperture signals. The full aperture signal corresponds to the full aperture SAR image, and the full aperture SAR image corresponds to the full aperture image spectrum; 2, the full aperture image spectrum is divided into K... x Centered on 0, the spectrum is divided into two parts along the azimuth frequency direction, resulting in sub-aperture image spectrum 1 and sub-aperture image spectrum 2. Sub-aperture image spectrum 1 corresponds to the spectrum of sub-image 1, and sub-image 1 corresponds to the echo signal of sub-aperture 1. Sub-aperture image spectrum 2 corresponds to the spectrum of sub-image 2, and sub-image 2 corresponds to the echo signal of sub-aperture 2. The full aperture spectrum is divided into two sub-aperture spectra.

[0084] pass Figure 5 Analysis shows that after azimuth wavenumber spectrum kernel compression, the frequency domain behavior is to shift the segmented spectrum to the middle position. Therefore, further zeroing at both ends will not remove the sub-aperture spectrum and cause information loss, thus preserving the echo signal information intact. Zeroing at both ends of the segmented sub-aperture image spectrum 1 and sub-aperture image spectrum 2 yields the reduced resolution spectra of sub-image 1 and sub-image 2.

[0085] like Figure 2As shown, segmentation begins with the complex image obtained from the backpropagation (BP) algorithm. Scene height information is projected onto the imaging grid, and the signal is compressed using a wavenumber spectrum compression function. The frequency spectrum is then segmented to obtain spectrum 1 corresponding to sub-aperture 1 and spectrum 2 corresponding to sub-aperture 2. Two-dimensional IFFT is performed on the sub-aperture image spectrum 1 and sub-aperture image spectrum 2 obtained after segmentation. Aspectral wavenumber spectrum compression kernel conjugate function compensation is then applied to each to preserve phase. A new wavenumber spectrum compression function is constructed using the aperture center of the sub-apertures for compression, followed by two-dimensional FFT. Zeros are removed from both ends of the frequency domain to obtain the reduced resolution spectra of sub-image 1 and sub-image 2 corresponding to sub-aperture 1 and sub-image 2. The height information is then reprojected onto the new imaging grid. Steps 2 to 3 are repeated recursively to obtain Cartesian coordinate SAR complex images with progressively decreasing resolution until the SAR echo signal for each pulse is obtained, at which point the recursive processing ends.

[0086] To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides specific product or related technology application examples of the technical solution claimed.

[0087] 1) Development and verification of SAR imaging algorithms

[0088] SAR echo simulation technology can quickly and accurately simulate a large amount of echo data under different conditions (such as large squint, special configuration dual-station, etc.) using a computer, which can greatly improve the development efficiency of imaging algorithms. At the same time, the advantages and disadvantages and applicable scope of SAR imaging algorithms can also be analyzed and verified through simulated echoes.

[0089] 2) Determination of SAR system parameters

[0090] Computer simulation can quickly generate a large amount of echo data under different parameters. By inputting this echo data into the SAR system and analyzing the results, suitable SAR system parameters can be determined efficiently, thus avoiding the development risks of synthetic aperture radar.

[0091] 3) Revealing the mechanism of SAR imaging

[0092] SAR echo simulation technology is based on the actual echo generation process or basic principles of SAR. It uses computer-generated echoes and compares them with measured SAR echoes to reveal the process and mechanism of the interaction between electromagnetic waves and ground objects. This can improve the scattering models of ground targets such as trees, houses and the ground, and provide theoretical support for the development of synthetic aperture radar.

[0093] 4) Verification of SAR system performance

[0094] Before a synthetic aperture radar system can be used in practice, it must undergo multi-directional and multi-angle testing to ensure its stability and effectiveness. Obtaining echo data under different conditions required for testing through computer simulation is the most efficient and convenient method. Therefore, SAR echo simulation technology can provide a guarantee for the verification of its system performance.

[0095] 5) Provides data sources for SAR imaging correction algorithms

[0096] SAR uses pulse compression technology for two-dimensional imaging. Due to the influence of squinting or motion errors, the images exhibit geometric distortion. Correction algorithms are needed to correct the images to obtain normal scene images. SAR echo simulation technology can add various squinting angles and distortions caused by motion errors to the echoes, providing raw imaging data for the study of correction algorithms.

[0097] 6) Shorten the system development cycle and reduce development costs and risks.

[0098] The biggest advantage of SAR echo simulation technology is that it can efficiently obtain a large amount of echo data under various conditions through simulation, without the need for actual flight testing, making it convenient and fast. This can greatly accelerate the system research process, mitigate development risks, and save research and development funds by requiring fewer flight experiments, thus reducing costs.

[0099] The parameters used in the simulation of this invention are shown in Table 1, and the SAR imaging geometry is as follows: Figure 3 As shown.

[0100] Table 1 Simulation Experiment Parameters

[0101]

[0102] That is: Ka band, bandwidth 200MHz, sampling frequency 350MHz, pulse repetition frequency 500Hz, radar platform according to Figure 3 The flight path shown is a curved trajectory, with a flight altitude of approximately 650m and a center-of-effect distance of approximately 1274m. The radar platform's speed in both the X and Y directions is 100m / s. The set imaging scene size is approximately 150m × 300m (X × Y direction), with a pixel density of 512 × 1024 (X × Y direction). The corresponding SAR complex image is shown below. Figure 6 As shown, the height of the scene is as follows: Figure 4 As shown.

[0103] Based on the radar parameters shown in Table 1 and as shown in Table 2 Figure 6The SAR complex image shown is simulated using the echo signal simulation method for analyzing terrain undulations provided in this embodiment of the invention. The simulation conditions are a 64-bit Windows 10 system MATLAB environment, a PC hardware platform of i5 9400f CPU, and 16G memory. Using the method of this invention, the entire echo signal generation and processing time is 60.5s. In contrast, under the same test environment and platform, the traditional time-domain concentric circle method requires approximately 3600s of processing time, and the FFBP (Fast Factorized Back Projection) based echo simulation method takes only 230s (without considering scene height).

[0104] As can be seen from the comparison, the echo simulation method of this invention significantly shortens the processing time and has higher efficiency compared to the traditional concentric circle method. Compared to the improved FFBP-based echo generation method, this invention not only greatly improves the computation speed but also can process scene height. SAR imaging processing is performed on the echo signal generated using the echo simulation method of this invention. The SAR image obtained using the most accurate BP algorithm is shown below. Figure 7 As shown. Through the original image Figure 6 and Figure 7 The comparison shows that the differences between the two SAR complex images are very small, and the structural similarity between the two images reaches 0.99989, which is very close to 1. Therefore, it can be considered that the echo simulation method of the present invention obtains high signal quality even in the presence of complex scene heights, while significantly shortening the echo generation time and improving processing efficiency.

[0105] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0106] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A fast time-domain echo simulation method for SAR suitable for terrain undulation scenarios, characterized in that, A fast time-domain echo simulation method for SAR in terrain-undulating scenarios includes: establishing a signal model; projecting the height information of the imaging scene onto the Cartesian coordinate grid through sampling; compressing the wavenumber spectrum of the SAR complex image in the Cartesian coordinate system and then transforming it to the two-dimensional frequency domain; segmenting the image along the azimuth frequency domain in the two-dimensional frequency domain according to the sub-aperture size of the previous level, obtaining two frequency domain signals; performing two-dimensional inverse Fourier transform on the two signals respectively to compensate for the conjugate function of the wavenumber spectrum compression kernel; compensating the two signals with the new wavenumber spectrum compression function, transforming them again to the two-dimensional frequency domain, and then performing zero-removal operations at both ends to reproject the scene height onto the imaging grid with doubled azimuth sampling intervals; continuously obtaining SAR complex images with progressively decreasing azimuth resolution through recursive processing until the SAR echo signal under each transmission pulse is obtained, ending the loop; and finally, achieving echo simulation.

2. The SAR time-domain fast echo simulation method applicable to terrain undulation scenarios as described in claim 1, characterized in that, The SAR time-domain fast echo simulation method applicable to terrain undulation scenarios includes the following steps: Step 1: Establish a signal model and project the height information of the imaging scene onto the Cartesian coordinate grid of the image through sampling. Transform the complex image expression of the scene in the Cartesian coordinate system to the two-dimensional frequency domain. Use the established signal model and wavenumber vector decomposition to derive the width of the wavenumber spectrum. Obtain the sampling rate limit of the image domain from the width of the wavenumber spectrum. By analyzing the sampling rate limit, derive the azimuth wavenumber spectrum compression kernel so that the sampling rate of the compressed azimuth image is only related to the aperture length. Derive the full aperture wavenumber spectrum compression kernel to compress the image domain signal. Perform a two-dimensional FFT transformation to the spectrum, at which point the spectrum is located in the middle position. Step 2: Divide the signal in the two-dimensional spectrum into two parts along the azimuth direction; perform two-dimensional inverse Fourier transform on the two parts respectively, and then compensate the conjugate function of the wavenumber spectrum compression function in the previous step to maintain the phase. Step 3: Establish a new wavenumber spectrum compression function based on the aperture center of the segmented sub-apertures, compensate the segmented signal, so that the spectrum after the cut is in the middle position, transform it to the two-dimensional frequency domain again, and then perform zero removal operations at both ends. At this time, the azimuth resolution of the signal in the image domain is reduced by half, and the scene height is reprojected into the imaging grid with the azimuth sampling interval doubled. Step 4: Repeat steps 2 to 3 to continuously obtain SAR complex images with progressively decreasing azimuth resolution until the SAR echo signal under each transmission pulse is obtained; perform three-dimensional calculation using the height information on the imaging grid to obtain the range data of the echo signal.

3. The SAR time-domain fast echo simulation method applicable to terrain undulation scenarios as described in claim 2, characterized in that, In step one, the radar is mounted on a moving flight platform, following an arbitrary curve. During flight, with a full aperture length of L, the beam always points towards the center of the scene during platform operation; For any scattering point in the radar-illuminated scene, in the Cartesian coordinate system, Location ( , , If ), then the slant range history over the entire aperture time is expressed as . ;in, The instantaneous location of the platform. For any point on the imaging grid, the elevation information of the scene is projected onto the imaging grid; the imaging uses a back projection algorithm, and in the Cartesian coordinate system, the SAR complex image containing the point is represented as: ； In the formula, The minimum and maximum values ​​of the wavenumber spectrum width in the range direction of the transmitted signal are respectively. and ; It is the central wavenumber. , ; It is the slant distance journey between the scene point and the platform location. It is the height information projected onto the grid. This refers to the platform's instantaneous location. Convert the image to and In the corresponding 2D inverse transform domain The variables are obtained through the stationary phase method. and Scope , ,in and These are the antenna viewpoints. The maximum and minimum values; the sampling rate of the image domain is limited to... , The result utilizes the property of small oblique angles and ; The sampling interval in the azimuth direction is limited by the azimuth beam angle range. Under focused conditions, the beam angle range is affected by both the scene width and the synthetic aperture length. In contrast, the sampling interval in the range direction is only affected by the transmit signal bandwidth. ,in and These represent the wavenumber spectral components represented by the scene width and the sub-aperture length, respectively; starting from the slant range, under frontal side-view conditions, the slant range is expanded as follows: In the expanded form, the aperture length is much smaller than the scene distance; construct an azimuth wavenumber spectrum compression kernel. The first term is used for azimuth wavenumber spectrum compression, and the second term is the phase preservation factor; after compression kernel compensation, the wavenumber spectrum width in Cartesian coordinates depends only on the length of the sub-aperture; azimuth image domain sampling interval Only need to meet ,in It is the length of the sub-aperture; the sampling interval in the azimuth image domain is proportional to the aperture length. By decomposing the full aperture image into sub-aperture images, the sampling interval is reduced by multiples until the echo signal is obtained.

4. The SAR time-domain fast echo simulation method applicable to terrain undulation scenarios as described in claim 2, characterized in that, In step two, the full aperture signal is divided into two equal-length sub-aperture signals. The full aperture signal corresponds to the full aperture SAR image, and the full aperture SAR image corresponds to the full aperture image spectrum. The full aperture image spectrum is divided into two parts along the azimuth frequency direction, centered on the full aperture image spectrum, to obtain sub-aperture image spectrum 1 and sub-aperture image spectrum 2. Two-dimensional inverse Fourier transforms are performed on the two parts of the signal respectively, and the conjugate function of the wavenumber spectrum compression function in the previous step is compensated to maintain the phase. Among them, the spectrum of sub-aperture image spectrum 1 corresponds to the spectrum of sub-image 1, and sub-image 1 corresponds to the echo signal of sub-aperture 1. At the same time, the spectrum of sub-aperture image spectrum 2 corresponds to the spectrum of sub-image 2, and sub-image 2 corresponds to the echo signal of sub-aperture 2.

5. The SAR time-domain fast echo simulation method applicable to terrain undulation scenarios as described in claim 2, characterized in that, In step three, a new wavenumber spectrum compression function is established based on the aperture center of the segmented sub-apertures to compensate the segmented signal, so that the spectrum after the cut is located in the middle position. It is then transformed to the two-dimensional frequency domain and zeroing operations are performed at both ends. At this time, the azimuth resolution of the signal in the image domain is reduced by half, and the scene height is reprojected into the imaging grid with the azimuth sampling interval doubled.

6. The SAR time-domain fast echo simulation method applicable to terrain undulation scenarios as described in claim 2, characterized in that, In step four, through recursive processing, Cartesian coordinate complex images with progressively decreasing resolution are obtained until the SAR echo signal under each pulse is obtained, at which point the recursive processing ends.

7. An echo simulation system for analyzing terrain undulations using the SAR time-domain fast echo simulation method as described in any one of claims 1 to 6, characterized in that, Echo simulation systems for analyzing terrain undulations include: The image transformation module is used to establish a signal model, project the height information of the imaging scene onto the rectangular coordinate grid of the imaging through sampling, and transform the SAR complex image to the two-dimensional frequency domain; The image segmentation module is used to segment the image in the two-dimensional frequency domain according to the sub-aperture size of the previous level, shift the spectrum to the middle position, and then perform zero removal operation at both ends to obtain the frequency domain signal and perform two-dimensional inverse Fourier transform to obtain two SAR complex images. The wavenumber spectrum compression module is used to compress the wavenumber spectrum of SAR complex images so that the azimuth resolution is only related to the aperture length and the spectrum of the image is also moved to the middle position. The sampling projection module is used to transform the signal to the image domain to obtain a SAR complex image with a lower azimuth resolution, and to project the height information of the imaging scene onto the Cartesian coordinate grid of the imaging through sampling. The echo simulation module is used to obtain SAR complex images with progressively decreasing azimuth resolution through recursive processing. The loop ends when the SAR echo signal under each transmitted pulse is obtained, thus realizing echo simulation.

8. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform the steps of the SAR time-domain fast echo simulation method for terrain undulation scenarios as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the SAR time-domain fast echo simulation method for terrain undulation scenarios as described in any one of claims 1 to 6.

10. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the echo simulation system for analyzing terrain undulations as described in claim 7.

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