Frequency modulation step frequency SAR sparse reconstruction algorithm based on approximate observation operator
Through the frequency-modulated step frequency SAR sparse reconstruction algorithm based on the approximate observation operator, the imaging quality reduction caused by motion error in the frequency-modulated step frequency SAR echo is solved, and efficient sparse reconstruction and accurate error phase estimation are achieved. Improved imaging accuracy.
Patent Information
- Application Number
- CN202411628693.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-14
- Publication Date
- 2025-02-11
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
There is motion error in the FM step frequency SAR echo, which leads to mismatch between the approximate observation model and the theoretical model of actual radar imaging, and seriously reduces the sparse reconstruction quality.
The frequency-modulation step frequency SAR sparse reconstruction algorithm based on the approximate observation operator is adopted. By obtaining the echo data, sparse sampling and imaging processing are carried out, phase error is estimated, distance error and azimuth error are derived, distance migration correction and azimuth error compensation are performed. Approximate observation operators are obtained, and the error phase is accurately solved through the maximum likelihood estimator, and the cycle is iteratively until the imaging accuracy requirements are met.
It effectively reduces the mismatch between the imaging theoretical model and the measurement matrix due to platform motion error, and improves the computing efficiency and imaging quality of the sparse reconstruction of FM step frequency SAR.
Smart Images
Figure CN119414352A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of high-resolution imaging of observation scenes, and in particular to a frequency-modulated stepped-frequency SAR sparse reconstruction algorithm based on an approximate observation operator. Background Art
[0002] Frequency modulation step frequency (FMSF) can achieve high-resolution imaging of the observation scene without increasing the instantaneous bandwidth of the radar and the sampling rate of the front-end ADC. Adapting the approximate observation model to the frequency modulation step frequency radar aperture (Synthetic Aperture Radar, SAR) can better solve the problems of large computational complexity and large memory usage in frequency modulation step frequency SAR imaging. However, since the carrier aircraft is inevitably affected by various uncertain factors in the air, there are motion errors in the frequency modulation step frequency SAR echo. The approximate observation operator is derived from the inverse process of the imaging algorithm. If the motion error is not compensated, the theoretical model of the approximate observation model and the actual radar imaging will not match, which will seriously reduce the sparse reconstruction quality of the compressed sensing synthetic aperture radar (CS-SAR). Summary of the invention
[0003] The embodiment of the present invention provides a sparse reconstruction algorithm for a frequency modulated stepped-frequency SAR based on an approximate observation operator, so as to at least solve the technical problem that there is motion error in the echo of the frequency modulated stepped-frequency SAR, the approximate observation model is adapted to the frequency modulated stepped-frequency SAR, and the motion error is not compensated, resulting in a mismatch between the approximate observation model and the theoretical model of actual radar imaging, which seriously reduces the sparse reconstruction quality of the frequency modulated stepped-frequency SAR.
[0004] According to one aspect of an embodiment of the present invention, a sparse reconstruction algorithm for frequency-modulated stepped-frequency SAR based on an approximate observation operator is provided. The algorithm may include: acquiring echo data of the frequency-modulated stepped-frequency SAR, sparsely sampling the echo data of the frequency-modulated stepped-frequency SAR to obtain initial data, performing imaging processing on the initial data through the SFCW-SAR imaging algorithm to obtain an initial scene image corresponding to the initial data, estimating the initial data through the phase gradient autofocusing algorithm based on the initial scene image to obtain the phase error of the initial data, and deriving the distance error and azimuth error of the phase error of the initial data; substituting the distance error and azimuth error into the range migration correction formula and the azimuth error compensation formula respectively to obtain the range migration correction factor and the azimuth compression factor, and obtaining an approximate observation operator based on the range migration correction factor and the azimuth compression factor; processing the fully sampled echo data of the frequency-modulated stepped-frequency SAR to obtain the synthetic bandwidth data of the fully sampled echo data; An imaging operator of full-sampled echo data is constructed, and the imaging operator of the full-sampled echo data is processed to obtain the residual error phase of the full-sampled echo data, wherein the residual error phase includes an approximate observation operator; the synthetic bandwidth data and the residual error phase of the full-sampled echo data are processed by a maximum likelihood estimator to obtain the phase error of the full-sampled echo data; the phase error of the full-sampled echo data is corrected by range migration to obtain a reconstructed scene image of the full-sampled echo data of the frequency-modulated stepped-frequency SAR, and the reconstructed scene image of the full-sampled echo data of the frequency-modulated stepped-frequency SAR is replaced with the echo data of the frequency-modulated stepped-frequency SAR, and an iterative cycle is performed until the reconstructed scene image of the full-sampled echo of the frequency-modulated stepped-frequency SAR meets the imaging accuracy requirement, wherein the imaging accuracy requirement is that the edge of the reconstructed scene image after imaging is a straight line.
[0005] Optionally, the range error and the azimuth error are substituted into the range migration correction formula and the azimuth error compensation formula respectively to obtain the expressions of the range migration correction factor and the azimuth compression factor:
[0006]
[0007] in, is the distance error; is the azimuth error; Slow time for orientation; is the three-dimensional velocity of the SAR carrier platform; is the wavelength of the transmitted signal; is the slope distance; is the distance frequency; is the carrier frequency of the transmitted signal, is the distance migration correction factor, is the azimuth compression factor.
[0008] Optionally, the expression of the approximate observation operator obtained based on the range migration correction factor and the azimuth compression factor is:
[0009] in, It means taking the inverse of each element of the approximate observation operator matrix; Indicates the distance FFT operation; Indicates the azimuth inverse FFT operation; represents the conjugate operation, is the approximate observation operator, for The conjugate operation of ; for The conjugate operation.
[0010] Optionally, the imaging operator of the full-sampled echo data is processed to obtain an expression of the residual error phase of the full-sampled echo data:
[0011] in, is the residual error phase of the fully sampled echo data, Indicates the distance IFFT operation.
[0012] Optionally, the synthetic bandwidth data and the residual error phase of the full-sampled echo data are processed by the maximum likelihood estimator to obtain an expression of the phase error of the full-sampled echo data:
[0013] in, For the The phase error of the fully sampled echo data is Indicates The two-dimensional imaging process of sub-frequency stepped frequency SAR, E is the synthetic bandwidth data corresponding to all the echo data, is the reconstructed scene image obtained by the i-th iteration, represents the regularization parameter; and They represent the 1-norm and 2-norm calculations respectively, L is the sparse sampling matrix of the full-sampled echo data, Represents the Jordan canonical form of a matrix.
[0014] Optionally, the range migration correction is performed on the phase error of the fully sampled echo data to obtain an expression for reconstructing the scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR:
[0015] in, For the The reconstructed scene image of the fully sampled echo data of the sub-frequency stepped-frequency SAR, For the The two-dimensional imaging process of sub-frequency stepped-frequency SAR, For the Reconstructed scene image from fully sampled echo data of sub-FM stepped-frequency SAR.
[0016] Beneficial effects of the present invention: The present invention proposes a sparse reconstruction algorithm for frequency-modulated stepped-frequency SAR based on an approximate observation operator. The algorithm first adapts the approximate observation operator to the frequency-modulated stepped-frequency SAR model, improves the computational efficiency of frequency-modulated stepped-frequency SAR sparse imaging, and reduces the data volume and memory usage of the system. Further utilizing the characteristics of the frequency-modulated stepped-frequency SAR signal, a new sparse self-focusing model is proposed. The model uses the sub-pulse group estimation under full sampling conditions to use the PGA algorithm to estimate the phase error, and derives the two-dimensional motion error, and introduces it into the approximate observation operator, reducing the incompatibility between the imaging theoretical model and the measurement matrix caused by the platform motion error, and performs a preliminary 2-dimensional estimation of the error phase. Then, the above-mentioned approximate observation operator is used to reconstruct the scene G, and the error phase that needs to be accurately estimated is further introduced into the phase compression history domain of the reconstructed scene, and the MLE pair is used to solve it, further improving the accuracy of the error phase estimation, and finally the scene G and the error phase are alternately reconstructed. BRIEF DESCRIPTION OF THE DRAWINGS
[0017] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 The present invention is a flowchart of a frequency-modulated stepped-frequency SAR sparse reconstruction algorithm based on an approximate observation operator according to an embodiment of the present invention. DETAILED DESCRIPTION
[0018] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only embodiments of a part of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.
[0019] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, algorithm, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, algorithms, products or devices.
[0020] Example 1 According to an embodiment of the present invention, a frequency-modulated stepped-frequency SAR sparse reconstruction algorithm based on an approximate observation operator is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system comprising at least one set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.
[0021] Figure 1 is a flow chart of a frequency-modulated stepped-frequency SAR sparse reconstruction algorithm based on an approximate observation operator according to an embodiment of the present invention. Figure 1 As shown, the algorithm may include the following steps: Step S101, acquiring echo data of a frequency-modulated stepped-frequency SAR, sparsely sampling the echo data of the frequency-modulated stepped-frequency SAR to obtain initial data, performing imaging processing on the initial data through a SFCW-SAR imaging algorithm to obtain an initial scene image corresponding to the initial data, estimating the initial data through a phase gradient autofocusing algorithm based on the initial scene image to obtain a phase error of the initial data, and deriving a distance error and an azimuth error of the phase error of the initial data.
[0022] In the technical solution provided in step S101 of the present invention, if Figure 1 As shown, the echo data of the frequency-modulated stepped-frequency SAR is S, and the echo data S of the frequency-modulated stepped-frequency SAR is sparsely sampled to obtain initial data, and the initial data is a sampling matrix B. The sampling matrix B is imaged by the SFCW-SAR imaging algorithm, wherein the initial data is a part of the echo data. The initial data is estimated by the Phase Gradient Autofocus algorithm (PGA) according to the initial scene image to obtain the phase error of the initial data. , derive the distance error of the phase error of the initial data and azimuth error , where the echo data S of the frequency-modulated stepped-frequency SAR is fully sampled to obtain the sampling matrix A.
[0023] Step S102, the range error and the azimuth error are substituted into the range migration correction formula and the azimuth error compensation formula respectively to obtain the range migration correction factor and the azimuth compression factor, and an approximate observation operator is obtained based on the range migration correction factor and the azimuth compression factor.
[0024] In the technical solution provided in the above step S102 of the present invention, the range error is substituted into the range migration correction formula to obtain the range migration correction factor; the azimuth error is substituted into the azimuth error compensation formula to obtain the azimuth compression factor.
[0025] Step S103, processing the full-sampled echo data of the frequency-modulated stepped-frequency SAR to obtain synthetic bandwidth data of the full-sampled echo data.
[0026] In the technical solution provided in the above step S103 of the present invention, the sampling matrix A is processed to obtain the synthetic bandwidth data E of the full-sampled echo data.
[0027] Step S104: construct an imaging operator of the full-sampled echo data, process the imaging operator of the full-sampled echo data, and obtain a residual error phase of the full-sampled echo data, wherein the residual error phase includes an approximate observation operator.
[0028] In the technical solution provided in the above step S104 of the present invention, The introduction of phase error increases the adaptability of the approximate observation operator and the inverse process of the imaging algorithm, and performs preliminary compensation of the error phase in two dimensions. The model proposed in the present invention selects to use MLE to further accurately solve the residual error phase. However, the above-mentioned error phase solution is introduced in the original echo time domain. The algorithm proposed in the present invention adapts the approximate observation operator to the SFMSAR sparse reconstruction model and skips the processing of the original echo data. Therefore, the solution method of the phase error of the above initial data cannot be applied to the SFMSAR sparse autofocusing model. In order to solve the above problem, the present invention constructs the imaging operator as follows: .
[0029] Step S105 , processing the synthetic bandwidth data and the residual error phase of the full-sampled echo data by a maximum likelihood estimator to obtain the phase error of the full-sampled echo data.
[0030] In the technical solution provided in the above step S105 of the present invention, the synthetic bandwidth data and the residual error phase of the fully sampled echo data are processed by the maximum likelihood estimator to obtain the phase error of the fully sampled echo data. The process of obtaining the phase error of the fully sampled echo data is to first calculate the error phase of the mth observation position, and then calculate the phase error of the mth observation position. Next time, m The expression of the phase error of an observation position is:
[0031] in, Indicates phase operation; Indicates taking the mth row of the matrix; represents the conjugate transpose, Represents the matrix First, perform an azimuthal inverse FFT operation, then take out the mth row of the result, and finally perform a conjugate transpose operation on these m rows.
[0032] According to m The phase error of each observation position is obtained to obtain the phase error of all observation positions of the radar carrying the echo data of the frequency-modulated stepped-frequency SAR. That is, the expression of the phase error of all observation positions is:
[0033] when When , the expression of the phase error of the total error is:
[0034] Step S106, performing range migration correction on the phase error of the fully sampled echo data to obtain a reconstructed scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR, replacing the reconstructed scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR with the echo data of the frequency-modulated stepped-frequency SAR, and iterating the loop until the reconstructed scene image of the fully sampled echo of the frequency-modulated stepped-frequency SAR meets the imaging accuracy requirement, wherein the imaging accuracy requirement is that the edge of the reconstructed scene image after imaging is a straight line.
[0035] In the technical solution provided in the above step S106 of the present invention, the phase error of the fully sampled echo data is corrected for range migration to obtain a reconstructed scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR, and the reconstructed scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR is returned to step S101, and sampling is continued, and the cycle is repeated until the reconstructed scene image of the fully sampled echo of the frequency-modulated stepped-frequency SAR meets the imaging accuracy requirements.
[0036] Aiming at the frequency-modulated stepped-frequency SAR signal system, a sparse autofocusing model of frequency-modulated stepped-frequency SAR based on approximate observation operator is proposed, as shown in Table 1: Table 1 Sparse autofocusing model of frequency-modulated stepped-frequency SAR based on approximate observation
[0037] In the table, i represents the algorithm iteration step. Represents the phase error estimated from the echo.
[0038] in, Represents the sparse matrix of scene scattering coefficient reconstruction when the observed scene meets the sparsity condition. Indicates the minimum value; G indicates the scene that needs to be reconstructed. , M and N represent the dimensions of the reconstructed scene; It is the matrix representation of the frequency-modulated stepped-frequency SAR bandwidth synthesis method. is the SAR echo data, M and N represent the dimensions of the echo data; L is the sparse sampling matrix of the echo data; represents the two-dimensional imaging process of frequency-modulated stepped-frequency SAR, and They are respectively expressed as the matrix forms of azimuth FFT and inverse FFT in the Range-Doppler Algorithm (RDA); represents the regularization parameter; and They represent 1-norm and 2-norm calculations respectively, i=0, V0=0, t0=1, number of iterations equals 0, initial speed equals 0, and slow time equals 0.
[0039] represents the soft threshold operator in the FIST algorithm, Represents the search step size of each iteration. This model takes ,parameter , For the matrix The magnitude of the K0th element in which all the elements are sorted in descending order. represents the conjugate of a matrix and is the inverse of the corresponding operator.
[0040] The model uses the phase gradient autofocus algorithm (PGA) of the sub-pulse of the frequency-modulated stepped-frequency SAR to obtain the solution of the phase error, and introduces the solution of the phase error into the range migration correction factor and the azimuth compression factor to achieve the two-dimensional preliminary compensation of the phase error. Then, the range compression phase history domain of the error phase reconstructed image that needs to be accurately solved is introduced, and the maximum likelihood estimator (MLE) is used to accurately solve the residual error phase. By alternately reconstructing the scene and the error phase, high-precision sparse reconstruction of the scene is finally achieved.
[0041] The above algorithm of this embodiment is further introduced below.
[0042] As an optional implementation manner, in step S102, the range error and the azimuth error are substituted into the range migration correction formula and the azimuth error compensation formula respectively to obtain the expressions of the range migration correction factor and the azimuth compression factor:
[0043]
[0044] in, is the distance error; is the azimuth error; Slow time for orientation; is the three-dimensional velocity of the SAR carrier platform; is the wavelength of the transmitted signal; is the slope distance; is the distance frequency; is the carrier frequency of the transmitted signal, is the distance migration correction factor, is the azimuth compression factor.
[0045] In this embodiment, the distance error Substituting into the distance migration correction formula, we get the distance migration correction factor ; The azimuth error Substitute it into the azimuth error compensation formula to obtain the azimuth compression factor .
[0046] As an optional implementation manner, in step S102, the expression of the approximate observation operator obtained based on the range migration correction factor and the azimuth compression factor is:
[0047] It means taking the inverse of each element of the approximate observation operator matrix; Indicates the distance FFT operation; Indicates the azimuth inverse FFT operation; represents the conjugate operation, is the approximate observation operator, for The conjugate operation of ; for The conjugate operation.
[0048] As an optional implementation manner, in step S104, the imaging operator of the full-sampled echo data is processed to obtain an expression of the residual error phase of the full-sampled echo data:
[0049] in, is the residual error phase of the fully sampled echo data, Indicates the distance IFFT operation.
[0050] As an optional implementation manner, step S105, the synthetic bandwidth data and the residual error phase of the full-sampled echo data are processed by the maximum likelihood estimator to obtain the expression of the phase error of the full-sampled echo data:
[0051] in, For the The phase error of the fully sampled echo data is Indicates The two-dimensional imaging process of sub-frequency stepped frequency SAR, E is the synthetic bandwidth data corresponding to all the echo data, is the reconstructed scene image obtained by the i-th iteration, represents the regularization parameter; and They represent the 1-norm and 2-norm calculations respectively, L is the sparse sampling matrix of the full-sampled echo data, Represents the Jordan canonical form of a matrix.
[0052] As an optional implementation manner, in step S106, range migration correction is performed on the phase error of the fully sampled echo data, and the expression of the reconstructed scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR is obtained as follows:
[0053] in, For the The reconstructed scene image of the fully sampled echo data of the sub-frequency stepped-frequency SAR, For the The two-dimensional imaging process of sub-frequency stepped-frequency SAR, For the Reconstructed scene image from fully sampled echo data of sub-FM stepped-frequency SAR.
[0054] In this embodiment, by The phase error of the full sampling echo data is corrected for range migration, and the obtained Reconstructed scene image from fully sampled echo data of frequency modulated stepped-frequency SAR.
[0055] In the embodiment of the present invention, by acquiring echo data of a frequency-modulated stepped-frequency SAR, sparse sampling is performed on the echo data of the frequency-modulated stepped-frequency SAR to obtain initial data, imaging processing is performed on the initial data through a SFCW-SAR imaging algorithm to obtain an initial scene image corresponding to the initial data, the initial data is estimated through a phase gradient autofocusing algorithm based on the initial scene image to obtain a phase error of the initial data, and a range error and an azimuth error of the phase error of the initial data are derived; the range error and the azimuth error are respectively substituted into a range migration correction formula and an azimuth error compensation formula to obtain a range migration error. The range migration correction factor and the azimuth compression factor are used to obtain an approximate observation operator based on the range migration correction factor and the azimuth compression factor; the full-sampled echo data of the frequency-modulated stepped-frequency SAR is processed to obtain the synthetic bandwidth data of the full-sampled echo data; an imaging operator of the full-sampled echo data is constructed, and the imaging operator of the full-sampled echo data is processed to obtain the residual error phase of the full-sampled echo data, wherein the residual error phase includes the approximate observation operator; the synthetic bandwidth data and the residual error phase of the full-sampled echo data are processed by the maximum likelihood estimator to obtain the phase error of the full-sampled echo data. difference; perform range migration correction on the phase error of the full-sampled echo data to obtain a reconstructed scene image of the full-sampled echo data of the frequency-modulated stepped-frequency SAR, replace the reconstructed scene image of the full-sampled echo data of the frequency-modulated stepped-frequency SAR with the echo data of the frequency-modulated stepped-frequency SAR, and iterate until the reconstructed scene image of the full-sampled echo of the frequency-modulated stepped-frequency SAR meets the imaging accuracy requirement, wherein the imaging accuracy requirement is that the edge of the reconstructed scene image after imaging is a straight line, which solves the motion error in the frequency-modulated stepped-frequency SAR echo, and adapts the approximate observation model to the frequency-modulated stepped-frequency SAR. AR, the motion error is not compensated, resulting in the mismatch between the approximate observation model and the theoretical model of actual radar imaging, which seriously reduces the technical problem of the sparse reconstruction quality of the frequency-modulated stepped-frequency SAR. The characteristics of the frequency-modulated stepped-frequency SAR signal are utilized to propose a new sparse autofocusing model. The model uses the sub-pulse group estimation under full sampling conditions to estimate the phase error using the PGA algorithm, and derives the two-dimensional motion error, which is introduced into the approximate observation operator, reducing the incompatibility between the imaging theoretical model and the measurement matrix caused by the platform motion error, and making a preliminary 2D estimate of the error phase. Then the above-mentioned approximate observation operator is used to reconstruct the scene G, and the error phase that needs to be accurately estimated is further introduced into the phase compression history domain of the reconstructed scene, and the MLE pair is used to solve it, further improving the accuracy of the error phase estimation.
[0056] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.
[0057] In the above embodiments of the present invention, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.
[0058] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only schematic. For example, the division of units can be a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.
[0059] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed over multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.
[0060] In addition, each functional unit in each embodiment of the present invention may be integrated into a first processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.
[0061] The above are only preferred embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.
Claims
1. A sparse reconstruction algorithm for frequency-modulated stepped-frequency SAR based on an approximate observation operator, characterized in that: include: Acquire echo data of frequency-modulated stepped-frequency SAR, perform sparse sampling on the echo data of frequency-modulated stepped-frequency SAR to obtain initial data, perform imaging processing on the initial data by using the SFCW-SAR imaging algorithm to obtain an initial scene image corresponding to the initial data, estimate the initial data by using the phase gradient autofocusing algorithm based on the initial scene image to obtain a phase error of the initial data, and derive a distance error and an azimuth error of the phase error of the initial data; Substituting the distance error and the azimuth error into the distance migration correction formula and the azimuth error compensation formula respectively, the distance migration correction factor and the azimuth compression factor are obtained, and based on the distance migration correction factor and the azimuth compression factor, an approximate observation operator is obtained; Processing the full-sampled echo data of the frequency-modulated stepped-frequency SAR to obtain synthetic bandwidth data of the full-sampled echo data; constructing an imaging operator of the full-sampled echo data, processing the imaging operator of the full-sampled echo data, and obtaining a residual error phase of the full-sampled echo data, wherein the residual error phase includes an approximate observation operator; The synthetic bandwidth data and the residual error phase of the full-sampled echo data are processed by a maximum likelihood estimator to obtain the phase error of the full-sampled echo data; The phase error of the fully sampled echo data is corrected by range migration to obtain a reconstructed scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR, and the reconstructed scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR is replaced with the echo data of the frequency-modulated stepped-frequency SAR, and an iterative cycle is performed until the reconstructed scene image of the fully sampled echo of the frequency-modulated stepped-frequency SAR meets the imaging accuracy requirement, wherein the imaging accuracy requirement is that the edge of the reconstructed scene image after imaging is a straight line.
2. The algorithm according to claim 1, characterized in that The range error and the azimuth error are substituted into the range migration correction formula and the azimuth error compensation formula respectively, and the expressions of the range migration correction factor and the azimuth compression factor are obtained as follows: in, is the distance error; is the azimuth error; Slow time for orientation; is the three-dimensional velocity of the SAR carrier platform; is the wavelength of the transmitted signal; is the slope distance; is the distance frequency; is the carrier frequency of the transmitted signal, is the distance migration correction factor, is the azimuth compression factor.
3. The algorithm according to claim 2, characterized in that The expression of the approximate observation operator based on the range migration correction factor and the azimuth compression factor is: in, It means taking the inverse of each element of the approximate observation operator matrix; Indicates the distance FFT operation; Indicates the azimuth inverse FFT operation; represents the conjugate operation, is the approximate observation operator, for The conjugate operation of ; for The conjugate operation.
4. The algorithm according to claim 3, characterized in that The imaging operator of the full-sampled echo data is processed to obtain the expression of the residual error phase of the full-sampled echo data: in, is the residual error phase of the fully sampled echo data, Indicates the distance IFFT operation.
5. The algorithm according to claim 4, characterized in that The synthetic bandwidth data and the residual error phase of the full-sampled echo data are processed by the maximum likelihood estimator to obtain the expression of the phase error of the full-sampled echo data: in, For the The phase error of the fully sampled echo data is Indicates The two-dimensional imaging process of sub-frequency stepped frequency SAR, E is the synthetic bandwidth data corresponding to all the echo data, is the reconstructed scene image obtained by the i-th iteration, represents the regularization parameter; and They represent the 1-norm and 2-norm calculations respectively, L is the sparse sampling matrix of the full-sampled echo data, Represents the Jordan canonical form of a matrix.
6. The algorithm according to claim 5, characterized in that The expression for performing range migration correction on the phase error of the fully sampled echo data to obtain the reconstructed scene image of the fully sampled echo data of the frequency-modulated stepped-frequency SAR is: in, For the The reconstructed scene image of the fully sampled echo data of the sub-frequency stepped-frequency SAR, For the The two-dimensional imaging process of sub-frequency stepped-frequency SAR, For the Reconstructed scene image from fully sampled echo data of sub-FM stepped-frequency SAR.
7. A computer system, characterized in that include: One or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the algorithm of claim 1.
8. A computer-readable storage medium, characterized in that Computer executable instructions are stored, and when the instructions are executed, they are used to implement the algorithm of claim 1.
9. A computer program product, characterized in that The method comprises computer executable instructions, which are used to implement the algorithm of claim 1 when being executed.