A Sub-Aperture Autofocusing CSAR Imaging Method Incorporating Terrain Ripple Error Compensation

Abstract

This invention discloses a sub-aperture autofocusing CSAR imaging method combining terrain undulation error compensation, comprising the following steps: reading digital elevation model data of the observation scene, supplementing the grid points of the imaging area with height information to eliminate height errors; transforming the echo signal acquired by CSAR to the frequency domain, multiplying it by a reference signal, and then converting it to a time domain signal to complete range pulse compression; dividing the full-circumferential aperture into multiple non-overlapping sub-apertures, and using a back projection algorithm to image the sub-aperture data to obtain sub-aperture images; using an autofocusing algorithm based on the image sharpest criterion to process each sub-aperture image for motion error compensation, estimating phase errors, and performing multiple iterative estimations; and accumulating the autofocused sub-aperture images to obtain a high-precision full-aperture CSAR image. Compared with traditional technologies, this application can improve the accuracy and quality of CSAR imaging by combining terrain undulation error compensation and sub-aperture autofocusing processing.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and more specifically, to a sub-aperture autofocusing CSAR imaging method that incorporates terrain undulation error compensation. Background Technology

[0002] Synthetic Aperture Radar (SAR) achieves high resolution in the range direction by transmitting a wide-bandwidth signal, while the radar platform observes scene targets at a wide angle, enabling high resolution in the azimuth direction. As one of the new high-quality sensors in the fields of microwave remote sensing and advanced arrays, SAR technology has experienced rapid development and widespread attention. SAR imaging can obtain more electromagnetic scattering information of observed targets by reconstructing the target scattering function, which helps in the analysis, classification, and identification of target features. SAR can provide all-weather, all-time reconnaissance capabilities, offering significant advantages in remote sensing observation and having a wide range of applications.

[0003] Circular SAR (CSAR) refers to a radar platform that performs 360-degree surround observation of a scene target, with its antenna beam always pointing towards the target scene. Compared with traditional SAR, which uses a straight-line trajectory, CSAR can perform 360-degree observation, thus obtaining a more complete target outline and better background clutter suppression. Therefore, the omnidirectional scattering characteristics of scene targets obtained by CSAR can effectively improve target detection performance.

[0004] High-resolution CSAR images provide richer target feature information, facilitating high-precision identification, classification, localization, and tracking of different targets, thereby obtaining the target's position and trajectory. However, terrain undulation errors and CSAR platform motion errors can lead to blurred CSAR images, making it difficult to effectively obtain high-resolution CSAR images. Therefore, relevant processing methods are needed to further obtain high-quality CSAR images.

[0005] CSAR imaging processing is typically based on the flat-surface assumption, which assumes the imaging scene is an ideal plane where all targets are distributed. In reality, the observed scene inevitably has terrain undulations, making it impossible for the actual imaging area to perfectly satisfy the ideal plane assumption. Furthermore, CSAR typically uses slant-range imaging, recording the slant range rather than the vertical distance. During imaging, targets of equal scattering intensity are projected onto the imaging plane at equal distances. Therefore, when the observed scene has terrain undulations, the projected target positions in the imaging result will deviate from the actual imaging positions, causing geometric displacement in the CSAR image. This reduces CSAR's ability to resolve targets in the vertical slant range direction, preventing CSAR from obtaining high-precision images.

[0006] Furthermore, due to various factors such as airflow and actual flight control, an unavoidable deviation exists between the actual flight trajectory and the ideal circular trajectory of an airborne CSAR platform. However, the positioning accuracy provided by commercial-grade Inertial Navigation Systems (INS) and Global Positioning Systems (GPS) is generally only on the order of meters, which is insufficient for the requirements of high-resolution CSAR imaging. Due to limitations in physical space, weight, and cost of the platform, airborne CSAR often cannot use ultra-high-precision measurement sensors and typically relies on INS or GPS to record the flight trajectory. CSAR imaging is more sensitive to flight trajectory data, and excessive measurement errors in INS and GPS can lead to severe defocusing in CSAR images. Therefore, the application of autofocus algorithms is particularly crucial in high-resolution CSAR imaging processing. However, existing methods typically perform autofocus processing on full-aperture CSAR echo data, but the improvement in image quality is not significant because the poor quality of imaging data at certain sub-aperture angles leads to poor quality of the full-aperture image obtained through coherent accumulation.

[0007] Existing technology discloses a circular synthetic aperture radar (CSAR) imaging method, system, device, medium, and terminal. It involves aperture segmentation of complete CSAR data, followed by imaging of sub-aperture data using a fast algorithm to obtain sub-images. Registration is then performed using local images located at different elevation planes within the sub-aperture images as references to obtain a set of CSAR images with different depths of field. Finally, multi-focus fusion is performed on the obtained images with different depths of field to obtain a full-focus image. The drawback of this approach is that poor imaging data quality at certain sub-aperture angles can lead to poor quality of the full-aperture image obtained through coherent accumulation.

[0008] Therefore, in light of the above requirements and the shortcomings of existing technologies, this application proposes a sub-aperture autofocusing CSAR imaging method that incorporates terrain undulation error compensation. Summary of the Invention

[0009] This invention provides a sub-aperture autofocus CSAR imaging method that combines terrain undulation error compensation. By combining terrain undulation error compensation and sub-aperture autofocus processing, the accuracy and quality of CSAR imaging are improved.

[0010] The primary objective of this invention is to solve the aforementioned technical problems. The technical solution of this invention is as follows:

[0011] The first aspect of this invention provides a sub-aperture autofocusing CSAR imaging method that incorporates terrain undulation error compensation. This method includes the following steps:

[0012] S1. Read the digital elevation model data of the observation scene, supplement the grid points of the imaging area with height information, and eliminate height error.

[0013] S2. The echo signal acquired by CSAR is transformed into the frequency domain, multiplied by the reference signal, and then converted into a time domain signal to complete range pulse compression.

[0014] S3. Divide the full circumferential aperture into multiple non-overlapping sub-apertures, and use the back projection algorithm to image the sub-aperture data to obtain sub-aperture images.

[0015] S4. A self-focusing algorithm based on the sharpest image criterion is used to process each sub-aperture image for motion error compensation, estimate phase error, and perform multiple iterative estimations.

[0016] S5. The sub-aperture images after autofocus processing are accumulated to obtain a high-precision full-aperture CSAR image.

[0017] The second aspect of the present invention provides a sub-aperture autofocusing CSAR imaging system with terrain undulation error compensation. The system is used in the aforementioned sub-aperture autofocusing CSAR imaging method with terrain undulation error compensation, and includes: a data processing module, a signal processing module, an error compensation module, and an imaging module.

[0018] The data processing module reads the digital elevation model data of the observation scene, supplements the grid points of the imaging area with height information, and eliminates height errors. The signal processing module transforms the echo signal acquired by CSAR to the frequency domain, multiplies it by the reference signal, and converts it into a time domain signal to complete range pulse compression. The error compensation module receives the data output by the data processing module and the signal processing module, divides the full-circumferential aperture into multiple non-overlapping sub-apertures, uses the back projection algorithm to image the sub-aperture data, obtains sub-aperture images, and uses an autofocus algorithm based on the sharpest image criterion to process each sub-aperture image for motion error compensation, estimates phase error, and performs multiple iterative estimations before inputting it to the imaging module. The imaging module accumulates the autofocused sub-aperture images to obtain a high-precision full-aperture CSAR image.

[0019] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0020] This invention provides a sub-aperture autofocusing CSAR imaging method that combines terrain undulation error compensation. It supplements the grid points in the imaging area with elevation information, and after obtaining the sub-aperture image using a back projection algorithm, it performs motion and phase error compensation. This method can solve the problems of terrain undulation in the observation scene and motion errors in airborne CSAR, thereby improving the quality and effect of CSAR imaging. This ensures high-quality CSAR imaging in complex environments, and the acquired high-precision CSAR images provide richer target feature information, facilitating high-precision identification, classification, localization, and tracking of different targets, obtaining the target's position and trajectory, and thus improving image interpretation. Attached Figure Description

[0021] Figure 1 This is a flowchart of a sub-aperture autofocusing CSAR imaging method that incorporates terrain undulation error compensation according to the present invention.

[0022] Figure 2 This is a schematic diagram of the range displacement caused by terrain undulations in CSAR imaging in one embodiment of the present invention.

[0023] Figure 3 Point target in one embodiment of the present invention A geometrical diagram of the ideal motion trajectory of CSAR.

[0024] Figure 4 This is a schematic diagram of onboard CSAR imaging geometry in one embodiment of the present invention when motion errors exist.

[0025] Figure 5 This is an imaging result diagram of a point target with terrain undulation error in one embodiment of the present invention.

[0026] Figure 6 This is an imaging result diagram of point target compensation for terrain undulation error in one embodiment of the present invention.

[0027] Figure 7 This is a azimuth profile before and after terrain undulation error compensation when the point target height errors are 14m, 18m, 10m, and 6m, respectively, in one embodiment of the present invention.

[0028] Figure 8 This is a comparison image of a vehicle with terrain undulation errors of 1m and -1m, and an image with DEM data compensation.

[0029] Figure 9 This is an image showing the results of the Gotcha scene with terrain undulation errors.

[0030] Figure 10 The image shows the result of compensating for terrain undulation errors in the Gotcha scene.

[0031] Figure 11 This is an airborne CSAR flight trajectory diagram for Gotcha data.

[0032] Figure 12 This is a schematic diagram illustrating the experimental results of sub-aperture original BP algorithm imaging and sub-aperture autofocus imaging in one embodiment of the present invention.

[0033] Figure 13 This is an enlarged view and an azimuth cross-sectional view of the results of sub-aperture original BP algorithm imaging and sub-aperture autofocus imaging in one embodiment of the present invention.

[0034] Figure 14 This is a comparison chart of the imaging results of the present invention and the imaging results of the conventional method in a Gotcha scenario in one embodiment.

[0035] Figure 15 This is a schematic diagram of a sub-aperture autofocusing CSAR imaging system that incorporates terrain undulation error compensation according to the present invention. Detailed Implementation

[0036] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0037] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0038] Example 1

[0039] like Figure 1 As shown, this invention provides a sub-aperture autofocusing CSAR imaging method that combines terrain undulation error compensation. This method includes the following steps:

[0040] S1. Read the digital elevation model data of the observation scene, supplement the grid points of the imaging area with height information, and eliminate height error.

[0041] S2. Transform the echo signal acquired by CSAR to the frequency domain, multiply it by the reference signal, and then convert it to a time domain signal to complete range pulse compression.

[0042] S3. Divide the full circumferential aperture into multiple non-overlapping sub-apertures, and use the back projection imaging algorithm to image the sub-aperture data to obtain sub-aperture images.

[0043] S4. A self-focusing algorithm based on the sharpest image criterion is used to process each sub-aperture image for motion error compensation, estimate phase error, and perform multiple iterative estimations.

[0044] S5. The sub-aperture images after autofocus processing are accumulated to obtain a high-precision full-aperture CSAR image.

[0045] Based on the aforementioned technical features, this invention uses Digital Elevation Model (DEM) data of the observation scene to set the CSAR imaging grid, eliminating height-axis errors. Next, range-axis pulse compression processing is performed on the full-circumferential aperture echo signal, and sub-aperture segmentation is performed. The back projection (BP) algorithm is used to image the sub-aperture data, obtaining a pre-focused sub-aperture image. Then, multiple iterative autofocusing processes are performed on the sub-aperture images to obtain well-focused sub-aperture images. Finally, the focused sub-aperture images are incoherently accumulated to obtain a high-precision full-aperture CSAR image. This invention can simultaneously solve terrain undulation errors and CSAR motion errors, obtaining high-precision CSAR images. The impact of terrain undulation errors on CSAR imaging is analyzed, a signal model for CSAR motion errors is established, an autofocusing algorithm based on back projection is studied, and a method for solving motion error estimates based on the image sharpest criterion is analyzed. Then, a high-precision CSAR imaging method combining sub-aperture autofocusing with terrain undulation error compensation is proposed. This method first uses DEM data of the observed scene to compensate for terrain undulation errors, then employs an autofocusing algorithm combined with backpropagation (BP) to focus and image the sub-aperture echo signals. Finally, the focused sub-aperture images are accumulated to obtain a high-precision full-aperture CSAR image. The effectiveness of this method is verified through experimental data. This invention ensures high-quality CSAR imaging in complex environments. The acquired high-precision CSAR images provide richer target feature information, facilitating high-precision identification, classification, localization, and tracking of different targets, obtaining the target's position and trajectory, thereby improving image interpretation.

[0046] In this embodiment, as Figure 2 The diagram shows the calculation of distance displacement caused by terrain undulations. In step S1, the calculation process of supplementing the grid points in the imaging area with height information and eliminating height error is as follows: based on the location of the point target... The height difference between the imaging area plane and the imaging area plane , and slow time Time point target To the radar antenna phase center slant distance The method calculates the error in the projected position of a point target on the imaging plane caused by terrain undulation. Then, based on the positional relationship between the point target and the imaging area plane, it calculates the distance displacement caused by terrain undulation, thereby compensating for the terrain undulation error. For the height of the CSAR motion platform, The location of the point target.

[0047] The calculation formula for step S1 is as follows:

[0048] (1)

[0049] (2)

[0050] in, Representing a point target Image point, and point target Having the same slant distance, i.e., point targets The location in the CSAR image after imaging. This represents the ground distance of the CSAR target in the imaging plane; if the point target... There is an error between the height of the location and the height of the imaging plane. Then the target point The projected distance within the imaging plane can be calculated using the following geometric relationship:

[0051] (3)

[0052] The error in the projected position of the target on the imaging plane caused by terrain undulation error is expressed as:

[0053] (4)

[0054] From equation (4), we can see that... numerical signs and If the target is above the imaging plane, its reflected signal will be received by CSAR earlier than a point in the imaging plane at the same incident angle, and the target's imaging position in the CSAR image will move towards the direction closer to CSAR. If the target is below the imaging plane, the reflected signal will arrive at CSAR later, causing the target's imaging position to move away from CSAR. If the actual height of the target is the same as the height of the imaging plane, there is no deviation in the target's imaging position.

[0055] Because CSAR systems use a 360-degree imaging mode, the displacement of the target image becomes more complex. For example... Figure 3 As shown, let any point in the imaging scene be... CSAR is located at point , its in The projection of a plane is a point. In this embodiment, motion error is ignored. It is assumed that during the imaging process, the CSAR antenna focuses on the center point... The angle of incidence remains unchanged, and is The calculation of the distance displacement caused by terrain undulations based on the positional relationship between the point target and the imaging area plane specifically involves: first, calculating the distance displacement of the point target... beam incident angle Furthermore, it corrects for the error in the target's projected position on the imaging plane caused by terrain undulation, and simultaneously calculates the range displacement caused by terrain undulation. The formula is as follows:

[0056] (5)

[0057] Because the flight altitude of the airborne CSAR system is much greater than the error magnitude caused by terrain undulations, i.e. Points caused by terrain undulations angle of incidence The change can be ignored, then equation (4) can be rewritten as:

[0058] (6)

[0059] Combining equations (4), (5), and (6), we obtain the distance displacement caused by topographic relief as follows:

[0060] (7)

[0061] in, This indicates that the CSAR antenna focuses on the center point during the imaging process. The incident angle, the range displacement caused by terrain undulation is proportional to the terrain undulation error, and the closer the point target is to the CSAR projection point on the imaging plane, the greater the range displacement caused by terrain undulation.

[0062] Therefore, it can be concluded that the range displacement caused by terrain undulation is directly proportional to the amount of terrain undulation error, and the closer the point target is to the CSAR projection point on the imaging plane, the greater the range displacement caused by terrain undulation. Therefore, in order to ensure that CSAR can still perform high-precision imaging of the target even when terrain undulation errors exist in the target observation scene, it is necessary to take terrain undulation error compensation measures.

[0063] In step S2, the CSAR-acquired echo signal is transformed to the frequency domain, multiplied by the reference signal, and then converted to a time domain signal to complete the range-directed pulse compression. The specific process is as follows: Calculate the CSAR... The position vector of the antenna phase center at each azimuth sampling position Position vector of the target point One-way slant distance journey between Based on the impact of motion error on the quality of CSAR two-dimensional imaging, the echo signal received by the antenna is subjected to orthogonal demodulation and range pulse compression processing.

[0064] Due to airflow interference and the inability to precisely control flight trajectories, CSAR inevitably suffers from motion errors when observing targets, resulting in poor imaging quality. The impact of motion errors on the quality of CSAR two-dimensional imaging is analyzed in detail below.

[0065] In one specific embodiment Figure 4 This is a schematic diagram of the three-dimensional spatial geometry of airborne CSAR when motion errors exist. The airborne CSAR platform revolves around... The axis, at a height of Construct a plane with radius... It flies in a 360° circular trajectory. The azimuth angle of the CSAR platform relative to the axis is: Its value is The CSAR beam always points to the center of the scene. Assume that the CSAR beam observation angle remains constant throughout the entire circular motion under far-field conditions. Figure 4 In the diagram, the red curve represents the actual motion curve observed by CSAR, while the black circular curve represents the planned ideal circular motion curve observed by CSAR. It can be seen that there is a deviation between the actual motion curve and the ideal circular curve, requiring motion error compensation measures.

[0066] Step S2 includes the following expression:

[0067] Let CSAR number The phase center position vector of each azimuth sampling position is Set up points For any point target in the observation scene, its position vector is denoted as . Then the antenna phase center Target The one-way slant distance journey between them is as follows:

[0068] (8)

[0069] The echo signal received by the antenna, after orthogonal demodulation and range pulse compression, can be expressed as:

[0070] (9)

[0071] Step S3 specifically involves dividing the full-circumferential aperture into 120 non-overlapping sub-apertures, with each sub-aperture having an azimuth accumulation angle of 3°, and using a back projection algorithm to image the sub-aperture data after CSAR range pulse compression data.

[0072] It should be noted that, within the imaging plane, the vector at any point can be represented as... The CSAR system transmits and receives signals from multiple azimuth positions, each providing a pulse echo signal. The entire imaging process involves the echo signals received from these azimuth positions. Therefore, located at... The imaging results at that location are represented as follows:

[0073] (10)

[0074] (11)

[0075] Therefore, the image obtained by focused imaging is obtained by summing the projection vectors of the echo signals from all sampling locations onto the projection vectors of all grid points in the imaging scene. The mathematical expression is:

[0076] (12)

[0077] Measurement errors exist between the CSAR motion trajectory measured by the sensor and the actual motion trajectory, directly affecting the accuracy and reliability of the imaging system. To specifically analyze the phase error caused by position error, the following mathematical model can be used. Let the phase error measured by the sensor be... The coordinates of the CSAR phase centers are The phase error caused by the measurement error can be expressed as:

[0078] (13)

[0079] Since the variation in the imaging plane grid is usually much smaller than the distance from the CSAR to the target, for simplicity, the phase error compensation model is typically assumed to be much smaller. Regardless of the position of the imaging grid points The impact of the change is represented as When the aforementioned phase error exists, the projection of the range-directed compressed pulse is shifted in phase due to the influence of the phase error. This is manifested by multiplying by an error phase factor, the expression of which is:

[0080] (14)

[0081] When the phase error value is large, directly... Summation can lead to poor imaging focusing, so it is necessary to process the echo signal in blocks and compensate for phase errors.

[0082] Assuming CSAR was performed In sub-azimuth sampling, each sampling location has a corresponding phase error. Let the estimated phase error value for each sampling location be... Therefore, the phase error value needs to be estimated first. Then use the estimated Phase error is compensated by a phase factor to obtain a high-precision CSAR image, expressed as:

[0083] (15)

[0084] Equation (10) is the imaging expression for the BP algorithm of CSAR, where the position vector of the antenna phase center is... The position vector of the point target , This indicates the echo signal after quadrature demodulation and range pulse compression processing. A vector located at any point in the imaging plane Imaging results at the location, Indicates the first CSAR phase center measurement location With imaging plane grid points The slant distance between them Indicates the first CSAR phase center location With imaging plane grid points The slant distance between them Indicates the first The projection vector of the echo signal at each sampling location onto all grid points in the imaging scene. This represents the total number of CSAR azimuth sampling points, located at a certain point in the plane. The back projection value at is The middle is recorded as , This means that the high-precision image with phase error compensation is obtained by accumulating the projection vectors of all grid points in the imaging scene.

[0085] It should be noted that positioning sensors are typically used to measure the trajectory of the aircraft. However, due to factors such as sensor measurement errors, the complexity of CSAR dynamic motion, the limitations of positioning systems, and the special requirements of high-resolution imaging, existing positioning sensors still cannot meet the measurement requirements of high-resolution CSAR imaging. Continuous improvement of sensor technology, data processing algorithms, and system integration methods is needed.

[0086] Based on the above technical characteristics, when there is motion error in the CSAR platform, the echo signal can be modeled as the original echo data multiplied by the phase error exponential factor. In imaging, this means that the received echo signal cannot be effectively accumulated, resulting in blurred imaging. It is necessary to estimate the phase error and compensate for it in order to obtain high-precision imaging results.

[0087] The specific process of step S4 is as follows: a coordinate descent geometric solution autofocus algorithm based on the sharpest image criterion is used to process each sub-aperture image, estimate the phase error of each sub-aperture image, and in each iteration, the sub-aperture image is compensated according to the current error estimate, and the phase error is re-estimated based on the compensated sub-aperture image. After each iteration, the phase error will be smaller. Finally, the sub-aperture image is multiplied by the phase error compensation factor to achieve autofocus processing of the sub-aperture image.

[0088] It should be noted that both the contrast optimization algorithm and the contrast enhancement phase correction algorithm are based on establishing a phase error compensation model, aiming to improve the contrast and quality of SAR images. However, research shows that these models have certain limitations in practical applications, particularly because they ignore the spatial variability of phase error, meaning that these models assume the phase error is constant across the entire image range. However, in reality, phase error may vary with spatial location, especially in complex terrain scenes. Therefore, when applying model-based autofocus algorithms, it is essential to first evaluate whether the phase error satisfies the model's assumptions. This assumption states that the phase error is independent of the grid point position. If this condition is not met, directly applying these algorithms may lead to a decrease in image quality, or even prevent the acquisition of an effectively focused image.

[0089] The autofocus algorithm based on backpropagation (BP) processing is also based on the above model. It uses the sharpest image criterion to estimate the phase error, that is, to seek the optimal solution of the following formula:

[0090] (16)

[0091] in The function for evaluating image sharpness, namely the energy evaluation function, is when... The larger the value, the sharper the image, meaning the more obvious the target features in the image. Since equation (16) has no analytical solution, the coordinate descent method is used for iterative optimization estimation. At this time, the energy evaluation function... Let be the objective function used to measure image quality. If in the th... After several iterations, a set of estimates was obtained. Then in the next iteration, the th Estimation of each parameter The calculation will be performed using the following formula (17):

[0092] (17)

[0093] Equation (17) shows that each update of the estimate depends on the sequence of the previous estimate, where the update of each parameter takes into account maintaining the best estimate of the other parameters in the current or previous iterations.

[0094] To further optimize the imaging results, the expression for the imaging results was rewritten to more intuitively demonstrate the changes in imaging quality during the iteration process. The imaging result at the next estimation iteration is:

[0095] (18)

[0096] That is, find ,and:

[0097] (19)

[0098] Let the fixed constant part be The parameter to be estimated is Then we have:

[0099] (20)

[0100] right After sorting, we get:

[0101] (twenty one)

[0102] make ,have:

[0103] (twenty two)

[0104] Finally, through The phase error can then be estimated.

[0105] It should be noted that, according to terrain undulation error analysis, CSAR imaging requires calculating the distance from the transmitting antenna to the target point. When the target scene has terrain undulation errors, the calculated distance will be inaccurate, resulting in poor image quality. DEM data, however, contains height information of scene grid points, making it easy to combine with the BP imaging algorithm. Therefore, using DEM data to set the imaging scene grid can ensure that the height of the imaging scene grid matches the height of the target, allowing CSAR to project onto accurate image points during slant range projection. This reduces the impact of terrain undulation errors and facilitates imaging processing and geometric correction.

[0106] Existing methods for motion error compensation on airborne CSAR platforms typically involve autofocusing the full-aperture CSAR echo signal. However, this doesn't significantly improve image quality, primarily because the imaging data at certain sub-aperture angles is of poor quality, resulting in sub-aperture imaging quality and consequently, low-quality full-aperture images obtained through coherent accumulation. Therefore, autofocusing of sub-apertures is necessary to ensure good sub-aperture imaging quality, thereby guaranteeing good full-aperture image quality obtained through coherent accumulation.

[0107] Based on the aforementioned technical features, this invention analyzes the impact of terrain undulation errors on CSAR imaging, establishes a signal model for CSAR motion errors, studies an autofocus algorithm based on back projection, and analyzes a method for solving motion error estimates based on the image sharpest criterion. Then, it proposes a high-precision CSAR imaging method combining sub-aperture autofocus with terrain undulation error compensation. This method first uses DEM data of the observation scene to compensate for terrain undulation errors, then uses an autofocus algorithm combined with backpropagation (BP) to focus and image the sub-aperture echo signals. Finally, the focused sub-aperture images are accumulated to obtain a high-precision full-aperture CSAR image. The effectiveness of this method is verified through experimental data. This invention ensures high-quality CSAR imaging in complex environments. The acquired high-precision CSAR images provide richer target feature information, facilitating high-precision identification, classification, localization, and tracking of different targets, obtaining the target's position and trajectory, thereby improving image interpretation.

[0108] Example 2

[0109] Based on the above embodiment 1, combined with Figures 1-14 This invention first analyzes the impact of terrain undulation errors on CSAR imaging, establishes a signal model for CSAR motion errors, studies an autofocus algorithm based on back projection, and analyzes a method for solving motion error estimates based on the image sharpest criterion. Then, it proposes a sub-aperture autofocus CSAR high-precision imaging method that combines terrain undulation error compensation. The detailed steps of the entire invention are described below with reference to the accompanying drawings and examples.

[0110] This embodiment specifically includes the following steps:

[0111] (1) Compensation for terrain undulation error

[0112] First, read the DEM data of the observed scene and supplement the grid points of the imaging area with height information, that is, to correct the height error. Compensation is performed to eliminate altitude error. In the compensated imaging region grid, the echo signal from any point in the scene can be projected onto the correct imaging region grid. Then, the projection results of different antenna phase centers are coherently superimposed to obtain the final imaging result. In the BP algorithm, the echo signal of each CSAR antenna phase center needs to be projected onto the compensated imaging region grid according to the instantaneous slant range.

[0113] (2) Range pulse compression of echo signal

[0114] The echo signal acquired by CSAR is historical phase data of the target scene. Range pulse compression is completed by multiplying the echo signal by a reference signal in the frequency domain and then converting it into a time domain signal.

[0115] (3) Sub-aperture segmentation

[0116] To facilitate subsequent sub-aperture autofocusing imaging, the full-circumference aperture was divided into 120 non-overlapping sub-apertures, with each sub-aperture having an azimuth accumulation angle of 3°.

[0117] (4) Sub-aperture data imaging processing

[0118] To achieve high resolution and low sidelobes in CSAR imaging, the backpropagation (BP) algorithm is used to image the sub-aperture data after CSAR range pulse compression. Furthermore, a graphics processing unit (GPU) is utilized for parallel processing to improve the imaging efficiency of the BP algorithm.

[0119] (5) Sub-aperture image autofocusing processing

[0120] A coordinate descent geometric autofocusing algorithm based on the image's sharpest criterion is employed to process each sub-aperture image and estimate its phase error. To improve the accuracy of the phase error estimation, multiple iterative estimations are typically performed. In each iteration, the sub-aperture image is compensated based on the current error estimate, and the phase error is re-estimated based on the compensated sub-aperture image. After each iteration, the phase error becomes smaller. Finally, the sub-aperture image is multiplied by the phase error compensation factor to achieve autofocusing of the sub-aperture image.

[0121] (6) Sub-aperture autofocusing image accumulation processing

[0122] The images obtained by sub-aperture autofocusing are accumulated to obtain the final high-precision full-aperture CSAR image.

[0123] To verify the effectiveness of the sub-aperture autofocusing CSAR high-precision imaging method with terrain undulation error compensation proposed in this invention, the effectiveness of the method is verified below using point target simulation data, electromagnetic simulation data, and measured data.

[0124] (1) Terrain undulation error compensation based on point target simulation data

[0125] The following is a simulation experiment of point target imaging. The parameter settings of the simulation system are shown in Table 1. It is easy to calculate that the CSAR beam top-down observation angle is 45°.

[0126] Table 1 Parameters of Point Target Simulation System

[0127]

[0128] The observation scene is set up with 9 point targets with the same scattering coefficient but different heights, and the imaging plane height is 0m. Their two-dimensional positions and heights are shown in Table 2.

[0129] Table 2 Target Coordinates

[0130]

[0131] Firstly, if the target point has terrain undulations that cause errors, the imaging quality will be poor. Then, using the read target DEM data, an imaging plane grid is set to ensure that the height of the imaging plane where the target is located matches the actual height of the target, thus ensuring that the image is projected onto an accurate image point during imaging. Figure 5 For imaging point targets with terrain undulation errors, Figure 6 The image shows the focused imaging result after terrain undulation error compensation using DEM data, where the color bar unit is dB.

[0132] The imaging results show that when there are terrain undulation errors, the target will be offset during projection imaging, resulting in a circular image. However, after compensating for the terrain undulation error, the BP imaging algorithm projects the point target to an accurate position, resulting in good focus, concentrated energy, and significantly improved resolution. This fully demonstrates the necessity and effectiveness of terrain undulation error correction measures.

[0133] To more intuitively compare the imaging results of point targets with and without height errors, the following will be used: Figure 5 and Figure 6 Compare the cross-sectional views of the four targets at points A, C, E, and I, as follows: Figure 7 (a) Figure 7 (b) Figure 7 (c) and Figure 7As shown in (d), these are azimuth profiles for point targets with height errors of 14m, 18m, 10m, and 6m, respectively. Since the imaging of an ideal point target exhibits central symmetry in both the azimuth and range directions, the experimental results are only compared using the azimuth profiles.

[0134] like Figure 7 As shown, the magenta curve represents the azimuth profile curve with height error, while the cyan curve represents the azimuth profile curve after height compensation using DEM data. Comparing the azimuth profiles of the point target with and without height error compensation reveals that the larger the height error, the more severe the defocusing, the lower the main lobe peak value, and the more severe the main lobe broadening. When the height error is too large, the point target image becomes a ring, and the azimuth profile exhibits a bimodal distribution.

[0135] After compensating for the height error of the point target, the point target can be refocused, the main lobe is significantly more concentrated, the side lobes are lower, and the 3dB width resolution is higher. It can be observed that this method achieves good focusing effect after compensating for terrain undulation errors, further confirming the effectiveness of terrain undulation compensation measures combined with DEM data in improving image quality.

[0136] (2) Vehicle target terrain undulation error compensation based on electromagnetic simulation data

[0137] The Civil Vehicle Domes (CVDomes) simulation data consists of electromagnetic simulation data of 10 civilian vehicles imaged using X-band electromagnetic waves in CSAR mode. The main parameters of the CVDomes data are shown in Table 3, which includes four sets of simulation data at different elevation angles from 30° to 60° in CSAR overhead view. The following section presents a terrain undulation error compensation experiment on the Toyota Avalon vehicle data from the CVDomes electromagnetic simulation data at a 30° overhead view, verifying the effectiveness of the terrain undulation error compensation method.

[0138] Table 3 Main parameters of CVDome simulation data

[0139]

[0140] First, a terrain undulation error of ±1m is introduced into the target scene. Figures 11-14 The images show the results of the BP algorithm with and without terrain undulation errors, and the results of the BP algorithm using a method that incorporates terrain undulation error compensation. From the imaging results, it can be observed that, for example... Figure 8 As shown in (a), when the imaging plane is 1m (higher than the actual plane where the target is located), there is a 1m height error. The target's image projection shifts in the distance direction, and the vehicle's outline shrinks towards the center, forming a smaller, closed image outline. Conversely, if... Figure 8As shown in (b), when the imaging plane is -1m (lower than the actual plane where the target is located), there is a -1m height error. As the vehicle's outline shifts outwards on all four sides, the vehicle's image outline expands, forming a larger closed image outline. Accurate imaging results can only be obtained when the imaging plane matches the actual plane where the target is located, consistent with the theoretical analysis of target imaging results when terrain undulations exist.

[0141] When there is a terrain undulation and height error, the imaging position of the scattering points on the vehicle surface will be shifted. The superposition of scattering points at different heights on the imaging plane will cause the vehicle imaging to overlap, resulting in a serious loss of vehicle imaging details. Figure 8 (c) and Figure 8 In (d), the white box area represents the image of the four wheel hubs. When there is terrain undulation error, the image of the wheel hubs is blurred. Only after compensating for the height error can many details of the vehicle image be preserved, which illustrates the necessity and effectiveness of terrain undulation error correction measures.

[0142] (3) Terrain undulation error compensation based on Gotcha measured data

[0143] The correctness and effectiveness of the terrain undulation error compensation method proposed in this invention are verified through experiments using Gotcha measured data. The system parameters of the Gotcha measured data are shown in Table 4. The system operates in the X-band.

[0144] Table 4 Gotcha Test Data System Parameters

[0145]

[0146] Introducing a terrain undulation error of -1m into the target scene, and setting the imaging scene size to 120m×120m, the imaging result is as follows: Figure 9 As shown. By Figure 9 It can be observed that when the imaging plane is lower than the actual height of the vehicle, the target imaging projection shifts due to terrain undulation error, and the vehicle target imaging outline expands. This is consistent with the theoretical analysis of the impact of terrain undulation error on the CSAR two-dimensional imaging quality.

[0147] Figure 10 This is the imaging result after compensating for terrain undulation errors using DEM data. (Comparison) Figure 9 and Figure 10It can be observed that when terrain undulation errors exist, the images of cars in densely populated areas overlap and become difficult to distinguish. For targets with strong omnidirectional scattering characteristics, which can uniformly reflect incident waves in all directions (such as objects like hats), it is impossible to focus in a specific direction during imaging, thus forming a ring-shaped defocused image. On the other hand, for targets that reflect energy strongly at a specific angle (such as corner reflectors), the energy is mainly reflected in specific directions, causing the imaging results to spread mainly along these directions, forming a distinct arc-shaped imaging result.

[0148] After using DEM data for terrain undulation error compensation, the reflected echoes of vehicle targets can be projected onto an accurate imaging plane grid, resulting in better vehicle target focusing, more complete outlines, and improved overlay effect. Vehicles in densely populated areas are also more clearly distinguishable. Streetlights and tetrahedral reflectors also show good focusing, with more complete outlines of their top caps, demonstrating the effectiveness of the proposed method.

[0149] (4) Sub-aperture autofocusing imaging

[0150] like Figure 11 The image shows the flight trajectory of an airborne CSAR platform from the Gotcha dataset. It can be observed that the airborne CSAR's altitude is not consistently on a single plane during its flight, exhibiting significant motion errors. The difference between the highest and lowest flight altitudes is 20 meters, affecting image quality. Therefore, it is necessary to employ an autofocus algorithm for motion error compensation and image processing.

[0151] When performing autofocus imaging on sub-aperture data segmented from a full-circumference trajectory, phase angle data is required for calculation. This method first segments the full-circumference data into 360 sub-apertures, i.e., into sub-aperture data of 1 degree each. Then, autofocus imaging is performed on every three 1-degree sub-aperture data to obtain coherent sub-aperture images of autofocus imaging. Finally, incoherent accumulation processing is performed on the coherent sub-aperture images of autofocus imaging to obtain higher quality full-circumference aperture imaging results.

[0152] Figure 12The images show the results of direct BP algorithm imaging and autofocus imaging using a combination of BP algorithm and sub-aperture data. (a) shows the original BP algorithm imaging for sub-aperture 30-60°, (b) shows the autofocus imaging for sub-aperture 30-60°, (c) shows the original BP algorithm imaging for sub-aperture 150-180°, (d) shows the autofocus imaging for sub-aperture 150-180°, (e) shows the original BP algorithm imaging for sub-aperture 300-330°, and (f) shows the autofocus imaging for sub-aperture 300-330°. It can be observed that due to motion errors in airborne CSAR, sub-aperture imaging defocuses, and vehicle targets are distorted. In densely populated vehicle areas, car images overlap, making it difficult to distinguish adjacent vehicles, and the vehicle outlines are incomplete. However, after autofocus processing the sub-aperture imaging results, the vehicle targets are better focused, the outlines are more complete, and the car images in densely populated vehicle areas are easier to distinguish. The top cap and tetrahedral reflectors are also well focused.

[0153] To more intuitively compare the results of sub-aperture autofocus imaging Figure 13 Enlarged views and azimuth profiles of the top right corner imaging results, including the top cap and tetrahedral reflectors, obtained using two algorithms are presented, including sub-aperture imaging using the original BP algorithm and sub-aperture autofocusing imaging using the combined BP algorithm. From Figure 13 It can be observed that the sub-aperture image without autofocus processing exhibits ghosting and double-peak phenomena, while after autofocus processing, the ghosting and double-peak phenomena of the sub-aperture image are significantly improved, and the sub-aperture image quality is good, indicating the effectiveness of autofocus processing. Figure 13 In the middle, (c), (f), and (i) are respectively Figure 13 Orientational profiles of the targets within the white boxes in (a), (b), (d), (e), (g), and (h). Figure 13 (a) is a magnified image of the original BP algorithm image at sub-aperture 30-60°, (b) is a magnified image of the autofocused image at sub-aperture 30-60°, (c) is a comparison image of the azimuth profile at sub-aperture 30-60°, (d) is a magnified image of the original BP algorithm image at sub-aperture 150-180°, (e) is a magnified image of the autofocused image at sub-aperture 150-180°, (f) is a comparison image of the azimuth profile at sub-aperture 150-180°, (g) is a magnified image of the original BP algorithm image at sub-aperture 300-330°, (h) is a magnified image of the autofocused image at sub-aperture 300-330°, and (i) is a comparison image of the azimuth profile at sub-aperture 150-180°. It can be observed that after autofocusing the sub-apertures, the main lobe peak value remains almost unchanged, the main lobe width narrows, and the side lobe level and peak value also decrease, resulting in improved resolution, demonstrating the effectiveness of the autofocusing method.

[0154] (5) Sub-aperture autofocusing CSAR high-precision imaging combined with terrain undulation error compensation

[0155] The following is a high-precision CSAR imaging experiment combining sub-aperture autofocusing with terrain undulation error compensation. After terrain undulation error compensation, the BP algorithm is directly used to image the Gotcha measured data. The results are as follows. Figure 14 As shown in (a), it can be observed that due to the lack of compensation for CSAR platform motion errors, there is a lot of imaging noise, the vehicle target outlines are not clear enough, and the vehicle images in densely populated areas overlap, making it difficult to distinguish adjacent vehicles. Therefore, further processing is required to obtain high-quality CSAR images.

[0156] This method first uses DEM data from the Gotcha scene to set up an imaging plane grid and performs terrain undulation error compensation processing. Then, it performs range pulse compression on the echo signal and divides the full-circumferential aperture into 360 non-overlapping sub-apertures. Since phase data from sub-aperture imaging is required for autofocus processing, this method uses autofocus processing combined with the BP algorithm for sub-aperture coherent imaging to compensate for CSAR motion errors. Because incoherent images can filter out some coherent speckle noise, making the imaging result smoother, this invention takes the amplitude value of the autofocused sub-aperture coherent images and finally incoherently accumulates them to obtain the full-aperture CSAR image, as shown below. Figure 14 As shown in (b).

[0157] from Figure 14 As shown in (b), autofocusing imaging of the sub-aperture data followed by summing the sub-aperture images to obtain the full-aperture image results in a high-quality full-aperture CSAR image with a high signal-to-noise ratio. Vehicle targets show better focusing, with symmetrical vehicle outlines on both sides, reflecting the omnidirectional observation capabilities of CSAR. Vehicle outlines are more complete, and the imaging results of vehicles in densely populated areas are easier to distinguish. Streetlights and tetrahedral reflectors also show good focusing, with more complete outlines of their top caps, and the top cap image is closer to a standard circle, demonstrating the effectiveness of the proposed method in obtaining high-precision CSAR images.

[0158] Example 3

[0159] like Figure 15 As shown, the present invention also provides a sub-aperture autofocusing CSAR imaging system that combines terrain undulation error compensation. The system is used in the aforementioned sub-aperture autofocusing CSAR imaging method that combines terrain undulation error compensation, and includes: a data processing module, a signal processing module, an error compensation module, and an imaging module.

[0160] The data processing module reads the digital elevation model data of the observation scene, supplements the grid points of the imaging area with height information, and eliminates height errors. The signal processing module transforms the echo signal acquired by CSAR to the frequency domain, multiplies it by the reference signal, and converts it into a time domain signal to complete range pulse compression. The error compensation module receives the data output by the data processing module and the signal processing module, divides the full-circumferential aperture into multiple non-overlapping sub-apertures, uses the back projection algorithm to image the sub-aperture data, obtains sub-aperture images, and uses an autofocus algorithm based on the sharpest image criterion to process each sub-aperture image for motion error compensation, estimates phase error, and after multiple iterative estimations, inputs it to the imaging module. The imaging module accumulates the autofocused sub-aperture images to obtain a high-precision full-aperture CSAR image.

[0161] In the embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0162] Alternatively, if the above embodiments of the present invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device to execute all or part of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0163] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. The icons depicting structural positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A sub-aperture autofocusing CSAR imaging method incorporating terrain undulation error compensation, characterized in that, Includes the following steps: S1. Read the digital elevation model data of the observation scene, supplement the grid points of the imaging area with height information, and eliminate height errors; the calculation process of supplementing the grid points of the imaging area with height information and eliminating height errors in step S1 is as follows: based on the height difference Δh between the position P of the point target and the plane of the imaging area, and the height difference Δh between the position P of the point target and the plane of the imaging area at the slow time η, the height difference Δh between the position P of the point target and the plane of the imaging area, and the height difference Δh between the position P of the point target and the height difference Δh at the slow time η, the height difference Δh between the position P of the point target ... p ,y p ,z p The slant range R from the radar antenna phase center (x(η), y(η), H) is used to calculate the error in the projected position of the point target on the imaging plane caused by terrain undulation. Then, based on the positional relationship between the point target and the imaging area plane, the range displacement caused by terrain undulation is calculated, thereby compensating for the terrain undulation error. The calculation formula is as follows: Where P′ represents the image point of point target P, which has the same slant range as point target P, i.e., the position of point target P in the CSAR image after imaging, and R ground This represents the ground distance in the CSAR imaging plane. If there is an error Δh between the height of point target P and the height of the imaging plane, then the projected ground distance of point target P in the imaging plane can be calculated using the following geometric relationship: The error in the projected position of a point target on the imaging plane due to terrain undulation error is expressed as: If the target is above the imaging plane, its imaging position in the CSAR image will move towards the CSAR; if the target is below the imaging plane, its imaging position will move away from the CSAR; if the actual height of the target is the same as the height of the imaging plane, there is no deviation in the target's imaging position. The calculation of the range displacement caused by terrain undulations based on the positional relationship between the point target and the imaging area plane specifically involves: first, calculating the beam incidence angle φ of the point target P. p The error in the target's projected position on the imaging plane caused by terrain undulation is corrected, and the range displacement ΔR caused by terrain undulation is calculated simultaneously. ground The formula is as follows: Where φ0 represents the incident angle of the CSAR antenna on the center point O during the imaging process. The range displacement caused by terrain undulation is proportional to the amount of terrain undulation error. The closer the point target is to the CSAR projection point on the imaging plane, the greater the range displacement caused by terrain undulation. S2. Transform the echo signal acquired by CSAR to the frequency domain, multiply it by the reference signal, and then convert it to a time domain signal to complete range pulse compression. S3. Divide the full circumferential aperture into multiple non-overlapping sub-apertures, and use the back projection algorithm to image the sub-aperture data to obtain sub-aperture images. S4. A self-focusing algorithm based on the sharpest image criterion is used to process each sub-aperture image for motion error compensation, estimate phase error, and perform multiple iterative estimations. S5. The sub-aperture images after autofocus processing are accumulated to obtain a high-precision full-aperture CSAR image.

2. The sub-aperture autofocusing CSAR imaging method combining terrain undulation error compensation according to claim 1, characterized in that, In step S2, the echo signal acquired by CSAR is transformed to the frequency domain, multiplied by the reference signal, and then converted to a time domain signal to complete the range pulse compression. The specific process is as follows: calculate the position vector of the antenna phase center at the nth azimuth sampling position of CSAR. Position vector of the target point One-way slant distance journey between Based on the impact of motion error on the quality of CSAR two-dimensional imaging, the echo signal received by the antenna is subjected to orthogonal demodulation and range pulse compression processing.

3. The sub-aperture autofocusing CSAR imaging method combining terrain undulation error compensation according to claim 2, characterized in that, Step S2 includes the following expression: Wherein, the position vector of the antenna phase center at the nth azimuth sampling position Position vector of point target This indicates the echo signal after orthogonal demodulation and range pulse compression processing.

4. The sub-aperture autofocusing CSAR imaging method combining terrain undulation error compensation according to claim 3, characterized in that, Step S3 specifically involves: dividing the full-circumferential aperture into 120 non-overlapping sub-apertures, with each sub-aperture having an azimuth accumulation angle of 3°; and using a back projection algorithm to image the sub-aperture data after CSAR range pulse compression. The formula for the back projection algorithm is as follows: in, Represents the position vector of any point in the imaging plane. Imaging results at N az b is the total number of CSAR azimuth sampling points. n This represents the projection vector of the echo signal at the nth sampling position onto all grid points in the imaging scene, located at a certain point in the plane. The back projection value at b n The middle is recorded as The coordinates of the nth CSAR phase center obtained by the sensor measurement are Indicates the measurement location of the nth CSAR phase center. With imaging plane grid points The slant distance between them Indicates the position of the nth CSAR phase center With imaging plane grid points The slant distance between them This represents the phase error caused by the measurement error of the nth CSAR phase center. b n A phase shift occurs. The value represents the estimated phase error, and z represents the high-precision image obtained by summing the projection vectors of all grid points in the imaging scene to achieve phase error compensation.

5. The sub-aperture autofocusing CSAR imaging method combining terrain undulation error compensation according to claim 4, characterized in that, The specific process of step S4 is as follows: a coordinate descent geometric solution autofocus algorithm based on the sharpest image criterion is used to process each sub-aperture image, estimate the phase error of each sub-aperture image, and in each iteration, the sub-aperture image is compensated according to the current error estimate, and the phase error is re-estimated based on the compensated sub-aperture image. After each iteration, the phase error will be smaller. Finally, the sub-aperture image is multiplied by the phase error compensation factor to achieve autofocus processing of the sub-aperture image.

6. The sub-aperture autofocusing CSAR imaging method combining terrain undulation error compensation according to claim 5, characterized in that, The specific calculation process for estimating the phase error of the sub-aperture image and performing multiple iterative estimations is as follows: First, assess whether the phase error satisfies the requirements of the model. This assumption is then used to estimate the phase error using the sharpest image criterion, i.e., to find the optimal solution for the following formula: in The function for evaluating image sharpness, namely the energy evaluation function, is when... The larger the value, the sharper the image, meaning the more prominent the target features in the image. The coordinate descent method is used for iterative optimization estimation, at which point the energy evaluation function... Let be the objective function used to measure image quality. If a set of estimates is obtained after the i-th iteration, Then, the estimation of the k-th parameter in the next iteration It will be calculated by the following formula: The imaging result at the i-th estimation iteration is: That is, find and: Let the fixed constant part be (v0). i =|x i | 2 +|y i | 2 The parameter to be estimated is Then we have: v=v0+v φ For v φ After sorting, we get: make have: in φ =acosφ+bsinφ Finally, through The phase error can then be estimated.

7. A sub-aperture autofocusing CSAR imaging system incorporating terrain undulation error compensation, the system being used in the sub-aperture autofocusing CSAR imaging method incorporating terrain undulation error compensation as described in any one of claims 1-6, characterized in that, It includes: a data processing module, a signal processing module, an error compensation module, and an imaging module; The data processing module reads the digital elevation model data of the observation scene, supplements the grid points of the imaging area with height information, and eliminates height errors. The signal processing module transforms the echo signal acquired by CSAR to the frequency domain, multiplies it by the reference signal, and converts it into a time domain signal to complete range pulse compression. The error compensation module receives the data output by the data processing module and the signal processing module, divides the full-circumferential aperture into multiple non-overlapping sub-apertures, uses the back projection algorithm to image the sub-aperture data, obtains sub-aperture images, and uses an autofocus algorithm based on the sharpest image criterion to process each sub-aperture image for motion error compensation, estimates phase error, and after multiple iterative estimations, inputs it to the imaging module. The imaging module accumulates the autofocused sub-aperture images to obtain a high-precision full-aperture CSAR image.

Images