Sparse strip SAR two-dimensional self-focusing imaging method based on trajectory error modeling
By modeling trajectory errors and employing a hybrid optimization scheme, the problem of two-dimensional phase error correction in sparse SAR imaging was solved, achieving high-quality sparse SAR image reconstruction and improving imaging performance.
Patent Information
- Application Number
- CN202511856314.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-10
- Publication Date
- 2026-03-17
AI Technical Summary
Existing sparse SAR imaging algorithms suffer from poor imaging quality when dealing with two-dimensional phase errors, especially two-dimensional spatially varying phase errors caused by trajectory errors. Traditional methods cannot effectively correct these errors, leading to focusing failure.
By modeling the two-dimensional phase error introduced by trajectory error, a sparse SAR imaging model is constructed. A hybrid optimization scheme is adopted, combining the BiIST algorithm, the Golden Section Search (GSSM) method, and the Parabolic Interpolation Method (PIM) to estimate and correct the two-dimensional phase error, thereby obtaining a focused sparse SAR image.
It effectively corrects the two-dimensional phase error caused by trajectory error, improves the quality of sparse SAR imaging, overcomes the imaging difficulties of traditional methods under downsampled data, and obtains high-quality sparse SAR images.
Smart Images
Figure CN121679579A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the fields of sparse signal processing and microwave imaging, specifically relating to a sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling. Background Technology
[0002] Synthetic Aperture Radar (SAR) is an important microwave remote sensing device. Compared with optical sensors, SAR does not require external light source illumination and is less affected by day-night cycles and weather conditions such as clouds, fog, rain, and snow, enabling true all-day, all-weather observation. With these unique advantages, SAR technology plays a crucial role in both military and civilian fields, and is widely used in land resource exploration, disaster prevention and mitigation, marine dynamic monitoring, and ground moving target indication, and has become an indispensable core component of modern remote sensing.
[0003] In actual SAR imaging, measurement errors inevitably exist between the radar platform's actual trajectory and its ideal linear trajectory. These errors introduce two-dimensional spatially variable phase errors that vary simultaneously with both range and azimuth, leading to defocusing in the imaging results. For such complex two-dimensional coupled phase errors, traditional one-dimensional algorithms such as Phase Gradient Autofocus (PGA), due to their inherent model limitations, can only correct spatially invariant phase errors in the azimuth direction, failing to effectively compensate for the range-varying spatial error components, resulting in focusing failure. Furthermore, electromagnetic interference in the atmosphere and complex observation environments can cause missing received echo data. Traditional two-dimensional autofocus algorithms rely on complete, high signal-to-noise ratio echo data; under non-ideal conditions of missing data, the estimation accuracy of their two-dimensional phase errors deteriorates drastically, or even fails completely, making it difficult to obtain focused, high-quality SAR images.
[0004] To address the imaging requirements of downsampled data, sparse SAR imaging technology can leverage the sparse characteristics of the observed scene to achieve high-quality reconstruction of the scene using echo data acquired at a rate lower than the Nyquist sampling rate, effectively overcoming the dependence on data integrity in traditional matched filtering imaging methods. However, after introducing autofocus processing into the sparse imaging framework, existing research mainly focuses on solving azimuth-space-invariant phase errors. While this can improve image focusing quality to some extent, its models do not fundamentally consider the two-dimensional spatially variable phase error problem caused by trajectory errors. Currently, there is limited research on sparse autofocus algorithms that model and compensate for two-dimensional phase errors, which limits the performance of sparse SAR imaging algorithms. Summary of the Invention
[0005] Purpose of the invention: This invention provides a two-dimensional autofocusing imaging method for sparse strip SAR based on trajectory error modeling to improve the quality of sparse strip SAR imaging.
[0006] Summary of the Invention: The present invention discloses a sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling, comprising the following steps:
[0007] (1) Model the two-dimensional phase error introduced by the trajectory error and construct a sparse SAR imaging model including the two-dimensional phase error;
[0008] (2) Reconstruct sparse SAR images using echo data corrected by a two-dimensional phase error correction matrix;
[0009] (3) The optimization problem of two-dimensional phase error is transformed into the optimization problem of slant range error, and decomposed into N sub-problems;
[0010] (4) Using a hybrid optimization scheme, estimate the slant range error caused by trajectory error at each azimuth sampling point in the image, and then obtain the two-dimensional phase error correction matrix that still needs to be compensated in the corrected echo data;
[0011] (5) Update the two-dimensional phase error correction matrix;
[0012] (6) Perform phase error correction on the echo data to obtain a focused sparse SAR image.
[0013] Furthermore, the implementation process of step (1) is as follows:
[0014] In the phase history domain, the two-dimensional phase error model introduced by trajectory error is expressed as:
[0015]
[0016] in, The echo signal contains two-dimensional phase error. For range frequency, For direction and time, At the speed of light, For carrier frequency, The instantaneous slant range deviation between the actual trajectory and the ideal linear trajectory of the radar platform, which have trajectory errors.
[0017] The matrix form of the two-dimensional phase error model is as follows:
[0018]
[0019] in, for The two-dimensional phase error matrix, This represents the number of sampling points in the azimuth direction. The number of sampling points in the distance direction. for The slant range error matrix, for The distance-frequency matrix is represented as:
[0020]
[0021]
[0022] Based on the two-dimensional phase error model, the sparse strip SAR observation model constructed by the echo simulation operator is expressed as follows:
[0023]
[0024] in, It is two-dimensional echo data. For distance to Fourier transform, This is the inverse Fourier transform of distance. For echo simulation operators, To observe the two-dimensional backscattering coefficient of the scene, For downsampling matrix, For noise;
[0025] set up Reconstructed value Given that, it can be solved by the following method. Norm regularization problem to reconstruct observation scenarios:
[0026]
[0027] in, For reconstructed sparse strip SAR images, For matched filtering imaging operators, This is the regularization parameter.
[0028] Furthermore, the implementation process of step (2) is as follows:
[0029] The two-dimensional backscattering coefficient G of the observed scene is solved using a BiIST-based sparse SAR imaging algorithm. The norm regularization problem is used to obtain phase-preserving sparse SAR images. The algorithm's first... The iteration process is as follows:
[0030] (21) Observation scenario () Solution of the 1st iteration for:
[0031]
[0032] in, Indicates the first The intermediate variables of the next iteration, their initial values. For SAR complex image data of the observed scene; For the first The sparse solution of the observation scene reconstructed in the next iteration, its initial values It is an all-zero matrix;
[0033] (22) The regularization parameter is () Solution of the 1st iteration for:
[0034]
[0035] in, For the image amplitude of the first The largest element value; The sparsity of the scene; parameters The range of values is ;
[0036] (twenty three) No. ( The value of the second iteration for:
[0037]
[0038] (24) Observation scenario () sparse solution of the second iteration for:
[0039]
[0040] (25) Calculate the ( )th The residual of the second iteration :
[0041]
[0042] like If the value exceeds the set threshold, the algorithm continues to repeat steps (21) to (25) until the iteration reaches the threshold. When the value is less than the set threshold, the algorithm converges and outputs the first value of the invention. The sparse SAR image reconstructed in the next iteration operation .
[0043] Furthermore, the implementation process of step (3) is as follows:
[0044] get Later, due to Represented as The function, then the first In the next iteration, regarding The optimization problem is expressed as:
[0045]
[0046] because Since the value is constant, the above optimization problem can be expressed as:
[0047]
[0048] Therefore, the following cost function is obtained:
[0049]
[0050] make Therefore, the first In the nth iteration The cost function for each azimuth sampling point is expressed as:
[0051]
[0052] Therefore, regarding The optimization problem is decomposed into There are independent subproblems, of which the _i ... The optimization problem is represented as:
[0053] .
[0054] Furthermore, the implementation process of step (4) is as follows: a hybrid optimization method combining the Golden Section Search Algorithm (GSSM) and the Parabolic Interpolation Algorithm (PIM) is used to obtain the solution that minimizes the cost function. The solution process is as follows:
[0055] (41) Solve for interval partitioning:
[0056] make To avoid the algorithm falling into local minima, The solution interval can be divided into: There are equidistant intervals, and the range of each interval can be represented as:
[0057]
[0058] in, For the first The minimum point of the cost function within each interval. , ;
[0059] (42) GSSM processing:
[0060] In the Within each interval, let Then initialize interior points and for:
[0061]
[0062]
[0063] in, The golden ratio; comparison and The size, if Then let , ;like Then let , ;
[0064] (43) PIM processing:
[0065] Based on (42), the conditions for using PIM are: ① in If the conditions are met and Select , and Parabolic fitting was performed using PIM at the three points; ② In At that time, if and Select , and Parabolic fitting was performed on the three points using PIM;
[0066] If any of the above conditions are met, then the minimum point of the fitted parabola can be obtained. The minimum value of the fitted parabola is compared with the function values at known points within the interval. If the minimum value of the fitted parabola is the smallest, then it is considered the smallest. Centered on the known interior points in its vicinity, select and If they satisfy , and If so, PIM processing is continued for these three points to obtain new minimum points until the interval length is less than the threshold set by the algorithm.
[0067] If the above conditions are not met, the interval will be processed using GSSM and then judged again according to the usage conditions of PIM until the interval length is less than the threshold set by the algorithm.
[0068] (44) Obtaining the optimal solution:
[0069] When the interval length is less than the threshold set by the algorithm, the currently obtained minimum point is taken as the first minimum point. The minimum point of each interval is obtained. ;right The above solution process was used for each interval, and all intervals were obtained. After finding the minimum value of each interval, compare their sizes, select the smallest one as the global minimum value, and set the corresponding global minimum point as the i-th interval. In the nth iteration Slant distance error estimate for each azimuth sampling point ;
[0070] The above procedures were used to respectively... Estimate the slant distance error of each azimuth sampling point to obtain Based on the constructed two-dimensional phase error model, the following can be obtained: .
[0071] Furthermore, the implementation process of step (5) is as follows:
[0072] make This involves updating the two-dimensional phase error correction matrix; the change in the two-dimensional phase error correction matrix obtained in two adjacent iterations is calculated using the following formula:
[0073]
[0074] in, For the first The two-dimensional phase error correction matrix at the next iteration; if the change between two adjacent iterations is greater than the set threshold, return to step (2), otherwise it means that there is no need to perform phase error estimation again, and output the result of the final estimated two-dimensional phase error correction matrix.
[0075] Furthermore, the implementation process of step (6) is as follows:
[0076] The estimated two-dimensional phase error correction matrix The data is compensated to the echo data, and then a sparse SAR image focusing on the observed scene is obtained through an iterative soft-threshold-based sparse SAR imaging algorithm, represented as:
[0077] .
[0078] The device according to the present invention includes a memory and a processor, wherein:
[0079] Memory is used to store computer programs that can run on a processor;
[0080] The processor is configured to, while running the computer program, execute the steps of the sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling as described above.
[0081] The present invention discloses a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling as described above.
[0082] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention models the two-dimensional phase error introduced by trajectory error and obtains a sparse strip SAR imaging model containing two-dimensional phase error; it uses a BiIST-based sparse SAR imaging algorithm to obtain phase-preserving sparse SAR images, and obtains an estimate of the two-dimensional phase error through the proposed hybrid optimization scheme, corrects the phase error of downsampled echo data, and obtains a focused sparse SAR image, overcoming the shortcomings of traditional autofocusing algorithms that do not consider range-varying phase errors and cannot achieve focused imaging of downsampled data. Attached Figure Description
[0083] Figure 1 This is a flowchart of the present invention;
[0084] Figure 2 The diagram shows the variation of the radar platform's trajectory error in the azimuth, range, and elevation directions with the azimuth sampling points.
[0085] Figure 3 Matched filtering imaging results for echo data without trajectory errors;
[0086] Figure 4 Matched filtering imaging results for echo data with added trajectory errors;
[0087] Figure 5 Imaging results using the PGA algorithm after adding trajectory errors to the echo data;
[0088] Figure 6 The imaging results of this invention are used after adding trajectory errors to the echo data. Detailed Implementation
[0089] The invention will now be further described with reference to the accompanying drawings.
[0090] like Figure 1 As shown, this invention provides a sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling, comprising the following steps:
[0091] Step 1: Model the two-dimensional phase error introduced by the trajectory error and construct a sparse SAR imaging model that includes the two-dimensional phase error.
[0092] In the phase history domain, the two-dimensional phase error model, including the error introduced by trajectory error, can be expressed as:
[0093]
[0094] in, The echo signal contains two-dimensional phase error. For range frequency, For direction and time, At the speed of light, For carrier frequency, This represents the instantaneous slant range deviation between the actual trajectory and the ideal linear trajectory of the radar platform, which suffers from trajectory errors. Considering that the sampled echo data is discrete, the matrix form of the two-dimensional phase error model can be expressed as:
[0095]
[0096] in, for The two-dimensional phase error matrix, This represents the number of sampling points in the azimuth direction. The number of sampling points in the distance direction. for The slant range error matrix, for The distance-frequency matrices can be represented as:
[0097]
[0098]
[0099] Based on the echo signal model with two-dimensional phase error, the sparse strip SAR observation model constructed by the echo simulation operator can be expressed as:
[0100]
[0101] in, It is two-dimensional echo data. For distance to Fourier transform, This is the inverse Fourier transform of distance. For echo simulation operators, To observe the two-dimensional backscattering coefficient of the scene, For downsampling matrix, It is noise.
[0102] For this model, the reconstruction and This can be achieved by solving the following optimization problem:
[0103]
[0104] in, , This is the regularization parameter.
[0105] set up Reconstructed value Given that, we can solve the following... Norm regularization problem implementation scenario reconstruction:
[0106]
[0107] in, For reconstructed sparse strip SAR images, This is a matched filter imaging operator.
[0108] Step 2: Reconstruct the sparse SAR image using the echo data corrected by the two-dimensional phase error correction matrix.
[0109] The above The norm regularization problem can be solved using a BiIST-based sparse SAR imaging algorithm. This algorithm yields reconstructed images that retain phase information, which can be used for subsequent phase error estimation. (The last sentence appears to be incomplete and requires further context.) Taking the second iteration as an example, the iterative process of BiIST can be represented as:
[0110] (2.1) Observation scenario () Solution of the 1st iteration for:
[0111]
[0112] in, Indicates the first The intermediate variables of the next iteration, their initial values. For SAR complex image data of the observed scene; For the first The sparse solution of the observation scene reconstructed in the next iteration, its initial values It is an all-zero matrix;
[0113] (2.2) The regularization parameter is () Solution of the 1st iteration for:
[0114]
[0115] in, For the image amplitude of the first The largest element value; The sparsity of the scene; parameters The range of values is ;
[0116] (2.3) No. ( The value of the second iteration for:
[0117]
[0118] (2.4) Observation scenario () sparse solution of the second iteration for:
[0119]
[0120] (2.5) Calculate the ( )th The residual of the second iteration :
[0121]
[0122] like If the value exceeds the set threshold, the algorithm continues to repeat steps (2.1) to (2.5) until the iteration reaches the threshold. When the value is less than the set threshold, the algorithm converges and outputs the first value of the invention. The sparse SAR image reconstructed in the next iteration operation .
[0123] Step 3: Using a hybrid optimization scheme, estimate the slant range error caused by trajectory error at each azimuth sampling point in the image, and then obtain the two-dimensional phase error correction matrix that still needs to be compensated in the corrected echo data.
[0124] In step 2, a sparse SAR image with phase information preserved was obtained. Later, due to It can be represented as The function, then the first In the next iteration, regarding The optimization problem can be expressed as:
[0125]
[0126] because Since the value is constant, the above optimization problem can be expressed as:
[0127]
[0128] Therefore, the following cost function can be obtained:
[0129]
[0130] make Therefore, the first In the nth iteration The cost function for each azimuth sampling point can be expressed as:
[0131]
[0132] Therefore, regarding The optimization problem can be decomposed into There are independent subproblems, of which the _i ... The optimization problem can be expressed as:
[0133]
[0134] As can be seen from the above optimization problem, this is an unconstrained optimization problem, which can be solved by using gradient-based methods such as the conjugate gradient method and the quasi-Newton method.
[0135] However, the cost function has multiple local minima within its domain, and gradient-based methods are highly sensitive to the initial values. If the initial values are not set appropriately, the solution can easily get trapped in local minima. This invention employs a hybrid optimization scheme combining the Golden Section Search Method (GSSM) and the Parabolic Interpolation Method (PIM) to find the solution that minimizes the cost function. The solution process is as follows:
[0136] (3.1) Solving for interval partitioning:
[0137] make To avoid the algorithm falling into local minima, The solution interval can be divided into: There are equidistant intervals, and the range of each interval can be represented as:
[0138]
[0139] in, For the first The minimum point of the cost function within each interval. , .
[0140] (3.2) GSSM processing:
[0141] In the Within each interval, let Then initialize the interior points of that interval. and for:
[0142]
[0143]
[0144] in, This is the golden ratio. (Comparison) and The size, if Then let , ;like Then let , .
[0145] (3.3) PIM processing:
[0146] Based on (3.2), the conditions for using PIM are: ① In If the conditions are met and Selectable , and Parabolic fitting was performed using PIM at the three points; ② In At that time, if and Selectable , and Parabolic fitting was performed on the three points using PIM.
[0147] If any of the above conditions are met, the minimum point of the fitted parabola can be obtained. The minimum value of the fitted parabola is compared with the function values at known points within the interval. If the minimum value of the fitted parabola is the smallest, then it is considered the smallest. Centered on the known interior points in its vicinity, select and If they satisfy , and If the three points are then processed using PIM, new minimum points will be obtained until the interval length is less than the threshold set by the algorithm.
[0148] If the above conditions are not met, the interval will be processed using GSSM and then judged again according to the usage conditions of PIM until the interval length is less than the threshold set by the algorithm.
[0149] (3.4) Obtaining the optimal solution:
[0150] When the interval length is less than the threshold set by the algorithm, the currently obtained minimum point is taken as the first minimum point. The minimum point of each interval can be found. .right The above solution process was used for each interval, and all intervals were obtained. After finding the minimum value of each interval, compare their sizes, select the smallest one as the global minimum value, and set the corresponding global minimum point as the i-th interval. In the nth iteration Slant distance error estimate for each azimuth sampling point .
[0151] The above procedures were used to respectively... By estimating the slant distance error of each azimuth sampling point, we can obtain... Based on the constructed two-dimensional phase error model, the following can be obtained: .
[0152] Step 4: Update the two-dimensional phase error correction matrix.
[0153] make This allows for the updating of the two-dimensional phase error correction matrix. The change in the two-dimensional phase error correction matrix obtained between two adjacent iterations can be calculated using the following formula:
[0154]
[0155] in, For the first The two-dimensional phase error correction matrix for the next iteration. If the change between two adjacent iterations exceeds the set threshold, return to step 2; otherwise, it means that phase error estimation is no longer necessary, and output the final estimated two-dimensional phase error correction matrix.
[0156] Step 5: Perform phase error correction on the echo data to obtain a focused sparse SAR image.
[0157] The estimated two-dimensional phase error correction matrix The data is compensated to the echo data, and then a sparse SAR image focusing on the observed scene is obtained through an IST-based sparse SAR imaging algorithm, represented as:
[0158] .
[0159] The present invention also provides an apparatus comprising a memory and a processor, wherein: the memory is used to store a computer program capable of running on the processor; and the processor is used to execute, when running the computer program, the steps of the sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling as described above.
[0160] The present invention also provides a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling as described above.
[0161] The following uses C-band airborne strip SAR simulation data as an example to verify the invention according to the parameters in Table 1:
[0162] Table 1 SAR System Parameters
[0163]
[0164] Figure 2 This is a schematic diagram illustrating how the magnitude of the trajectory error of the radar platform in the azimuth, range, and elevation directions varies with the azimuth sampling points; the experimental results are as follows. Figure 3 As shown, the echo data is downsampled by 50% randomly. Figure 3 Matched filtering imaging results for downsampled echo data without added errors; Figure 4 , Figure 5 , Figure 6 Added respectively Figure 2 The results show the imaging results after trajectory error correction using matched filtering, PGA imaging, and the imaging results using the sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling of this invention. Experimental results show that the classical matched filtering algorithm exhibits significant energy dispersion in the imaging of downsampled data. After incorporating trajectory error, the image obtained by the matched filtering method shows even more severe defocusing. The traditional autofocusing method PGA only considers the azimuth phase error and ignores the spatially varying phase error in the range direction. Furthermore, under downsampling conditions, the phase information is destroyed, severely reducing the error estimation performance of PGA and leading to focusing failure. The sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling of this invention can effectively solve these problems. For downsampled echo data with two-dimensional phase error, it can effectively remove the two-dimensional phase error introduced by trajectory error in the echo, obtaining high-quality sparse SAR images.
[0165] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling, characterized in that, Includes the following steps: (1) Model the two-dimensional phase error introduced by the trajectory error and construct a sparse SAR imaging model including the two-dimensional phase error; (2) Reconstruct sparse SAR images using echo data corrected by a two-dimensional phase error correction matrix; (3) The optimization problem of two-dimensional phase error is transformed into the optimization problem of slant range error, and decomposed into N sub-problems; (4) Using a hybrid optimization scheme, estimate the slant range error caused by trajectory error at each azimuth sampling point in the image, and then obtain the two-dimensional phase error correction matrix that still needs to be compensated in the corrected echo data; (5) Update the two-dimensional phase error correction matrix; (6) Perform phase error correction on the echo data to obtain a focused sparse SAR image.
2. The sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling according to claim 1, characterized in that, The implementation process of step (1) is as follows: In the phase history domain, the two-dimensional phase error model introduced by trajectory error is expressed as: in, The echo signal contains two-dimensional phase error. For range frequency, For direction and time, At the speed of light, For carrier frequency, The instantaneous slant range deviation between the actual trajectory and the ideal linear trajectory of the radar platform, which have trajectory errors. The matrix form of the two-dimensional phase error model is as follows: in, for The two-dimensional phase error matrix, This represents the number of sampling points in the azimuth direction. The number of sampling points in the distance direction. for The slant range error matrix, for The distance-frequency matrix is represented as: Based on the two-dimensional phase error model, the sparse strip SAR observation model constructed by the echo simulation operator is expressed as follows: in, It is two-dimensional echo data. For distance to Fourier transform, This is the inverse Fourier transform of distance. For echo simulation operators, To observe the two-dimensional backscattering coefficient of the scene, For downsampling matrix, For noise; set up Reconstructed value Given that, it can be solved by the following method. Norm regularization problem to reconstruct observation scenarios: in, For reconstructed sparse strip SAR images, For matched filtering imaging operators, This is the regularization parameter.
3. The sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling according to claim 1, characterized in that, The implementation process of step (2) is as follows: The two-dimensional backscattering coefficient G of the observed scene is solved using a BiIST-based sparse SAR imaging algorithm. The norm regularization problem is used to obtain phase-preserving sparse SAR images. The algorithm's first... The iteration process is as follows: (21) Observation scenario () Solution of the 1st iteration for: in, Indicates the first The intermediate variables of the next iteration, their initial values. For SAR complex image data of the observed scene; For the first The sparse solution of the observation scene reconstructed in the next iteration, its initial values It is an all-zero matrix; (22) The regularization parameter is () Solution of the 1st iteration for: in, For the image amplitude of the first The largest element value; The sparsity of the scene; parameters The range of values is ; (twenty three) No. ( The value of the second iteration for: (24) Observation scenario () sparse solution of the second iteration for: (25) Calculate the ( )th The residual of the second iteration : like If the value exceeds the set threshold, the algorithm continues to repeat steps (21) to (25) until the iteration reaches the threshold. When the value is less than the set threshold, the algorithm converges and outputs the first value of the invention. The sparse SAR image reconstructed in the next iteration operation .
4. The sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling according to claim 1, characterized in that, The implementation process of step (3) is as follows: get Later, due to Represented as The function, then the first In the next iteration, regarding The optimization problem is expressed as: because Since the value is constant, the above optimization problem can be expressed as: Therefore, the following cost function is obtained: make Therefore, the first In the nth iteration The cost function for each azimuth sampling point is expressed as: Therefore, regarding The optimization problem is decomposed into There are independent subproblems, of which the _i ... The optimization problem is represented as: 。 5. The sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling according to claim 1, characterized in that, The implementation process of step (4) is as follows: A hybrid optimization method combining the Golden Section Search Algorithm (GSSM) and the Parabolic Interpolation Algorithm (PIM) is used to obtain the solution that minimizes the cost function. The solution process is as follows: (41) Solve for interval partitioning: make To avoid the algorithm falling into local minima, The solution interval can be divided into: There are equidistant intervals, and the range of each interval can be represented as: in, For the first The minimum point of the cost function within each interval. , ; (42) GSSM processing: In the Within each interval, let Then initialize interior points and for: in, The golden ratio; comparison and The size, if Then let , ;like Then let , ; (43) PIM processing: Based on (42), the conditions for using PIM are: ① in If the conditions are met and Select , and Parabolic fitting was performed using PIM at the three points; ② In At that time, if and Select , and Parabolic fitting was performed on the three points using PIM; If any of the above conditions are met, then the minimum point of the fitted parabola can be obtained. The minimum value of the fitted parabola is compared with the function values at known points within the interval. If the minimum value of the fitted parabola is the smallest, then it is considered the smallest. Centered on the known interior points in its vicinity, select and If they satisfy , and If so, PIM processing is continued for these three points to obtain new minimum points until the interval length is less than the threshold set by the algorithm. If the above conditions are not met, the interval will be processed using GSSM and then judged again according to the usage conditions of PIM until the interval length is less than the threshold set by the algorithm. (44) Obtaining the optimal solution: When the interval length is less than the threshold set by the algorithm, the currently obtained minimum point is taken as the first minimum point. The minimum point of each interval is obtained. ;right The above solution process was used for each interval, and all intervals were obtained. After finding the minimum value of each interval, compare their sizes, select the smallest one as the global minimum value, and set the corresponding global minimum point as the i-th interval. In the nth iteration Slant distance error estimate for each azimuth sampling point ; The above procedures were used to respectively... Estimate the slant distance error of each azimuth sampling point to obtain Based on the constructed two-dimensional phase error model, the following can be obtained: .
6. The sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling according to claim 1, characterized in that, The implementation process of step (5) is as follows: make This involves updating the two-dimensional phase error correction matrix; the change in the two-dimensional phase error correction matrix obtained in two adjacent iterations is calculated using the following formula: in, For the first The two-dimensional phase error correction matrix at the next iteration; if the change between two adjacent iterations is greater than the set threshold, return to step (2), otherwise it means that there is no need to perform phase error estimation again, and output the result of the final estimated two-dimensional phase error correction matrix.
7. The sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling according to claim 1, characterized in that, The implementation process of step (6) is as follows: The estimated two-dimensional phase error correction matrix The data is compensated to the echo data, and then a sparse SAR image focusing on the observed scene is obtained through an iterative soft-threshold-based sparse SAR imaging algorithm, represented as: 。 8. A device, characterized in that, Includes memory and processor, wherein: Memory is used to store computer programs that can run on a processor; The processor is configured to, while running the computer program, execute the steps of the sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling as described above.
9. A storage medium, characterized in that, The storage medium stores a computer program that, when executed by at least one processor, implements the steps of the sparse strip SAR two-dimensional autofocusing imaging method based on trajectory error modeling as described above.