A two-dimensional space-variant correction method for MEO-bistatic SAR imaging

Abstract

The application relates to a two-dimensional space variation correction method for MEO-aircraft bistatic SAR imaging, and relates to the technical field of radar signal processing, in particular to a two-dimensional space variation correction method for MEO-aircraft bistatic SAR imaging. The application aims to solve the two-dimensional space variation problem caused by the complex configuration of an MEO-aircraft bistatic SAR system. The application constructs a complete MEO-aircraft bistatic SAR system configuration, and quantitatively characterizes the root cause of the two-dimensional space variation through a virtual scatterer fitting method. The application adopts a fourth-order Taylor expansion model to ensure the high precision of the MEO-aircraft bistatic SAR geometric modeling. The application develops a high-efficiency compensation algorithm, which can eliminate the two-dimensional space variation, and can be seamlessly combined with the existing LRWC correction technology to realize the joint relief of the two kinds of space variance effects.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and more specifically to a two-dimensional spatial variability correction method for MEO-machine bistatic SAR imaging. Background Technology

[0002] Spaceborne synthetic aperture radar (SAR) is one of the important means of acquiring space remote sensing information. Compared with low Earth orbit (LEO) SAR, medium-high Earth orbit (MEO) SAR has a shorter revisit period and a wider Earth observation coverage; compared with geostationary orbit (GEO) SAR, it has higher spatial resolution and simpler technical implementation. Compared with traditional monostatic MEO SAR systems, the slant range history between the aircraft as the receiver and the target is significantly shortened, effectively reducing electromagnetic wave attenuation. In addition, since the airborne platform itself does not emit electromagnetic waves, its stealth is also significantly improved.

[0003] However, due to the complex system configuration of MEO-based bistatic SAR, spatial variations in the slant range historical data of different scattering points within the observation area occur. If a uniform azimuth matched filter and the same range migration correction function are applied to all targets, phase mismatch and image quality degradation will inevitably result. Current algorithms often focus more on the spatial variations introduced by linear range walk (LRWC) operations, while neglecting the spatial variation characteristics introduced by system configuration. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of two-dimensional spatial variation caused by the complex configuration of MEO-machine bistatic SAR system, and to propose a two-dimensional spatial variation correction method for MEO-machine bistatic SAR imaging.

[0005] The specific process of a two-dimensional spatial variability analysis and correction method for MEO-machine bistatic SAR imaging is as follows:

[0006] Step 1: On the imaging plane, use interpolation to find a set of virtual scattering points with the same shortest slant range, i.e., located in the same range cell, and obtain the Taylor expansion coefficients of the scattering points located in the same range cell; On the imaging plane, use interpolation to find a set of virtual scattering points with the same shortest slant range time, i.e. located in the same azimuth cell, and obtain the Taylor expansion coefficients of the scattering points located in the same azimuth cell.

[0007] Step 2: Perform a two-dimensional FFT transform on the echo signal of a scattering point target to obtain the echo signal of the scattering point target in the frequency domain; the FFT transform is a Fast Fourier Transform; perform a third-order Taylor expansion on the phase of the echo signal of the scattering point target in the frequency domain to obtain the echo signal of the scattering point target in the frequency domain after Taylor expansion; define the phase values ​​of each order based on the echo signal of the scattering point target in the frequency domain after Taylor expansion, and calculate the two-dimensional spatial variation and azimuth spatial variation of each phase value;

[0008] Step 3: Based on the two-dimensional spatial and azimuth spatial changes of the phase values ​​in Step 2, perform uniform range migration correction and range compression on the scene center scattering point to obtain the frequency domain signal after uniform range migration correction and range compression; perform range-dimensional IFFT transform on the frequency domain signal after uniform range migration correction and range compression to obtain the range-Doppler domain signal; the IFFT transform is an inverse fast Fourier transform; perform range-dimensional block processing on the range-Doppler domain signal to obtain each range block; perform range-dimensional FFT on each range block to obtain the two-dimensional frequency domain signal of each range block; compensate the two-dimensional frequency domain signal of each range block to obtain the compensated signal of each range block; until all range blocks have been compensated; perform range-dimensional IFFT transform on the compensated signal of each range block to obtain the range-Doppler domain signal of each range block; until all range blocks have been obtained; stitch together the range-Doppler domain signals of all range blocks to obtain the stitched range-Doppler domain signal.

[0009] Step 4: Perform IFFT transform on the spliced ​​range-Doppler domain signal along the azimuth dimension to obtain a two-dimensional time domain signal; construct a fifth-order perturbation function; based on the Taylor expansion coefficients of the scattering point in Step 1, multiply the fifth-order perturbation function with the two-dimensional time domain signal to obtain the compensated two-dimensional time domain signal.

[0010] Step 5: Perform FFT transformation on the compensated two-dimensional time domain signal along the azimuth direction to convert the data to the RD domain, then perform azimuth pulse compression, and perform IFFT transformation on the azimuth pulse compressed signal to obtain the two-dimensional time domain signal, which is the two-dimensional SAR image.

[0011] The beneficial effects of this invention are as follows: This invention analyzes the two-dimensional spatial variations caused by the complex configuration of MEO-airborne bistatic SAR systems and proposes a targeted solution algorithm. This algorithm can seamlessly integrate with existing algorithms for correcting spatial variability introduced by LRWC, simultaneously correcting both types of spatial variability and demonstrating good versatility. Current research mainly focuses on the spatial variability introduced by delinear range walk (LRWC) technology, which causes targets within the same range cell to actually originate from different range cells with different Doppler parameters. Therefore, uniform azimuth compression leads to imaging defocusing. However, the two-dimensional spatial variations introduced by the MEO-airborne bistatic configuration have received little attention. This invention focuses on the quantitative analysis of the two-dimensional spatial variations caused by the complex configuration of MEO-airborne bistatic synthetic aperture radar systems and proposes a correction algorithm. It compensates for range-varying cell migration (RCM), quadratic phase components, and range-varying cubic phase terms in the range domain through block processing technology; and uses nonlinear chirped scaling (NCS) to correct the spatial variability of the azimuth dimension. Compared with current research, this invention has the following advantages: It constructs a complete MEO-machine bistatic SAR system configuration and quantitatively characterizes the root causes of two-dimensional spatial variations using a virtual scatterer fitting method. It employs a fourth-order Taylor expansion model to ensure high accuracy in MEO-machine bistatic SAR geometric modeling. Furthermore, it develops an efficient compensation algorithm that can eliminate two-dimensional spatial variations and seamlessly integrate with existing LRWC correction techniques to jointly mitigate the two spatial variance effects. Attached Figure Description

[0012] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a system configuration diagram of MEO-machine bistatic SAR. For reference time, for At some point later, OXYZ is the scene coordinate system; the Y-axis direction is in the same direction as the aircraft's velocity. For reference target point and Same point, , These are the other two scattering points in the scene; The velocity vector of the aircraft; for The velocity vector of the satellite at any given moment. for The velocity vector of the satellite at any given moment. for When the plane arrives at its destination The slant range vector, for When the plane arrives at its destination The slant range vector, for When the plane arrives at its destination The slant range vector, for Satellite arrives at target point at all times The slant range vector, for Satellite arrives at target point at all times The slant range vector, for Satellite arrives at target point at all times slant distance vector; Let be the angle between the aircraft's velocity vector and slant range vector. for The satellite's velocity vector and its distance from the target point at any given time The angle between the slant range vectors, Also for The satellite's velocity vector and its distance from the target point at any given time The angle between the slant range vectors; for The satellite's velocity vector and its distance from the target point at any given time The angle between the slant range vectors; Figure 3 The variation of Taylor expansion coefficients of each order along the azimuth dimension for the slant range history of the scattering point: (a) coefficients (b) Coefficients along the azimuth dimension A diagram showing the variation along the azimuth dimension; (c) coefficients A diagram showing the variation along the azimuth dimension; (d) coefficients A diagram showing the variation along the azimuth dimension; Azimuth represents the azimuth dimension. Figure 4 Plot of Taylor expansion coefficients of each order along the range dimension for the slant range history of the scattering point: (a) Coefficients (b) Coefficients A graph showing the variation along the distance dimension; (c) coefficients A graph showing the variation along the distance dimension; (d) coefficients A graph showing the change along the distance dimension; Range represents the distance dimension. Figure 5 The error plot is obtained by performing a third-order Taylor expansion of the phase, where Range Frequency is the range frequency domain and Multiorder PhaseError is the phase error; Figure 6 Two-dimensional spatial variation of each order of phase: (a) two-dimensional spatial variation of the zero-order phase; (b) two-dimensional spatial variation of the first-order phase; (c) two-dimensional spatial variation of the second-order phase; (d) two-dimensional spatial variation of the third-order phase. Figure 7 The azimuth space changes for each order of phase are: (a) azimuth space change for the zeroth order phase; (b) azimuth space change for the first order phase; (c) azimuth space change for the second order phase; and (d) azimuth space change for the third order phase. Figure 8 The image shows a scattering point model for the simulation experiment. The horizontal axis represents the distance dimension, and the vertical axis represents the azimuth dimension. P1-P25 represent 25 evenly distributed scattering points. Figure 9 The image is an image of the result of using the algorithm proposed in this invention. The horizontal axis represents the distance dimension and the vertical axis represents the orientation dimension. Figure 10 Enlarged images of the imaging results of the two algorithms for scattering point 13: (a) Two-dimensional contour map of the proposed algorithm; (b) Two-dimensional contour map of the traditional dual-base RD algorithm; (c) Azimuth profile of the two algorithms; (d) Range profile of the two algorithms, with the horizontal axis representing the range dimension and the vertical axis representing the azimuth dimension. Figure 11 Enlarged images of the imaging results of scattering point 19 using two algorithms: (a) 2D contour map of the proposed algorithm; (b) 2D contour map of the traditional dual-base RD algorithm; (c) azimuth profile of the two algorithms; (d) range profile of the two algorithms, where 2Dcontour is the 2D contour and Range Profile is the azimuth profile. Figure 12 Enlarged images of the imaging results of scattering point 25 using two algorithms: (a) 2D contour map of the proposed algorithm; (b) 2D contour map of the traditional dual-base RD algorithm; (c) azimuth profile of the two algorithms; (d) range profile of the two algorithms; 2Dcontour is the 2D contour line, and Range Profile is the azimuth profile. Figure 13 The image shows the imaging result after performing LRWC operation with a 30° oblique angle, using the algorithm proposed in this invention combined with the NCS algorithm. Figure 14 Enlarged images of the imaging results of scattering point 13 using two algorithms: (a) 2D contour map of the proposed algorithm; (b) 2D contour map using only the NCS algorithm; (c) azimuth profile of the two algorithms; (d) range profile of the two algorithms. Figure 15 Enlarged images of the imaging results of scattering point 19 using two algorithms: (a) 2D contour map of the proposed algorithm; (b) 2D contour map using only the NCS algorithm; (c) azimuth profile of the two algorithms; (d) range profile of the two algorithms. Figure 16 Enlarged images of the imaging results of scattering point 25 using two algorithms: (a) 2D contour map of the proposed algorithm; (b) 2D contour map of the NCS algorithm only; (c) azimuth profile of the two algorithms; (d) range profile of the two algorithms. Figure 17 The following are the imaging results of the hardware-in-the-loop simulation: (a) Imaging result using the traditional bi-basic RD algorithm; (b) Imaging result of region 1 using the traditional bi-basic RD algorithm; (c) Imaging result of region 2 using the traditional bi-basic RD algorithm; (d) Imaging result using this algorithm; (e) Imaging result of region 1 using this algorithm; (f) Imaging result of region 2 using this algorithm. Detailed Implementation

[0013] Specific Implementation Method 1: The specific process of a two-dimensional spatial variability analysis and correction method for MEO-machine dual-base SAR imaging in this implementation method is as follows:

[0014] Step 1: In order to evaluate the two-dimensional spatial variability introduced by the complex configuration of the MEO-airborne dual-base SAR system, it is necessary to determine the azimuth and range directions of the imaging plane under this configuration; use interpolation methods on the imaging plane to find a set of virtual scattering points with the same shortest slant range, that is, located in the same range cell, and obtain the Taylor expansion coefficient of the scattering points located in the same range cell (Formula (7)); use interpolation methods on the imaging plane to find a set of virtual scattering points with the same shortest slant range time, that is, located in the same azimuth cell, and obtain the Taylor expansion coefficient of the scattering points located in the same azimuth cell (Formula (7)).

[0015] Step 2: Perform a two-dimensional FFT transformation on the echo signal of a certain scattering point target (Formula (8)) to obtain the echo signal of the scattering point target in the frequency domain form (Formula (9)); the FFT transformation is a fast Fourier transform; perform a third-order Taylor expansion on the phase of the echo signal of the scattering point target in the frequency domain form (Formula (10)) to obtain the echo signal of the scattering point target in the frequency domain form after Taylor expansion; define the phase values ​​of each order based on the echo signal of the scattering point target in the frequency domain form after Taylor expansion, and calculate the two-dimensional spatial change and azimuth spatial change of each order phase value (Formula (15), Formula (16), Formula (17));

[0016] Step 3: This invention processes spatial variations from two directions. This invention introduces a MEO-based bistatic SAR algorithm, which compensates for spatial variations in the range direction through block processing and employs NCS technology to mitigate variations in the azimuth direction. Since the spatial variations of the second and third-order phase components are relatively small, uniform compensation can be achieved. However, under high range resolution conditions, targets exhibit significant cross-range cell migration, which is detrimental to segmented processing. Therefore, this invention first uses the parameters of a reference point target to perform batch compensation for the first, second, and third-order phase components. Based on the two-dimensional spatial changes and azimuth spatial changes of each phase value in step two, uniform range migration correction and range compression are performed on the scene center scattering point (Equation (18)) to obtain the frequency domain signal after uniform range migration correction and range compression; the frequency domain signal after uniform range migration correction and range compression is subjected to range dimension IFFT transformation to obtain the range Doppler domain signal; the IFFT transformation is an inverse fast Fourier transform; the range Doppler domain signal is processed by range dimension block processing to obtain each range block; the range dimension FFT is performed on each range block to obtain the two-dimensional frequency domain signal of each range block; the two-dimensional frequency domain signal of each range block is compensated to obtain the compensated signal of each range block; until all the compensated signals of all range blocks are obtained; the range dimension IFFT transformation is performed on the compensated signal of each range block to obtain the range-Doppler domain signal of each range block; until all the range-Doppler domain signals of all range blocks are obtained; the range-Doppler domain signals of all range blocks are spliced ​​to obtain the spliced ​​range-Doppler domain signal;

[0017] Step 4: Perform IFFT transform on the spliced ​​range-Doppler domain signal along the azimuth dimension to obtain a two-dimensional time domain signal; construct a fifth-order perturbation function; based on the Taylor expansion coefficients of the scattering point in Step 1, multiply the fifth-order perturbation function with the two-dimensional time domain signal to obtain the compensated two-dimensional time domain signal.

[0018] Step 5: Perform an FFT transform on the compensated two-dimensional time-domain signal along the azimuth direction to convert the data to the RD domain, then perform azimuth pulse compression, and finally perform an IFFT transform on the compressed signal to obtain the two-dimensional time-domain signal (at this point, the target point will be compressed to the corresponding position). The two-dimensional time-domain signal is the two-dimensional SAR image.

[0019] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: in step one, an interpolation method is used on the imaging plane to find a set of virtual scattering points with the same shortest slant range, i.e., located in the same distance cell, and the Taylor expansion coefficients of the scattering points located in the same distance cell are obtained (Formula (7)); an interpolation method is used on the imaging plane to find a set of virtual scattering points with the same shortest slant range time, i.e., located in the same azimuth cell, and the Taylor expansion coefficients of the scattering points located in the same azimuth cell are obtained (Formula (7)); the specific process is as follows:

[0020] Step 11: The slant range history of each scattering point is expressed as a function of slow time. The fourth-order Taylor expansion is expressed as:

[0021] (1)

[0022] in, Represents slow time The nearest slant distance of the scattering point, Represents slow time. The nearest slant distance representing the scattering point. The first-order Taylor expansion coefficients representing the slant distance. The second-order Taylor expansion coefficients representing the slant distance. The third-order Taylor expansion coefficients representing the slant distance. The fourth-order Taylor expansion coefficients represent the slant distance; the specific expression is:

[0023] (2)

[0024] (3)

[0025] (4)

[0026] (5)

[0027] in, This represents the velocity vector between the radar and the target. This represents the slant range vector between the radar and the target. express The model, the upper corner mark Indicates transpose; This represents the acceleration vector between the radar and the target. express The model; This represents the jerk vector between the radar and the target. This represents the acceleration vector between the radar and the target. express The model;

[0028] Steps 1 and 2: Based on Step 1, the slant range history of each scattering point is expressed as a function of slow time. The fourth-order Taylor expansion of the bistatic slant range history in MEO-machine bistatic SAR is expressed as:

[0029] (6)

[0030] in, Indicates the slope distance history of the two bases; This represents the closest slant distance from the MEO satellite to the scattering point. This represents the closest slant distance from the aircraft to the scattering point; Represents the slant range history from the MEO satellite to the scattering point. Taylor expansion coefficients, Represents the slant range history from the aircraft to the scattering point. Taylor expansion coefficients, ; Represents the zero Doppler moment of the scattering body The corresponding distance; Indicates slow time of Power of 1 ; The first-order Taylor expansion coefficients of the bibasic slope distances are represented. The second-order Taylor expansion coefficients representing the slope distances of the two base cases are... The third-order Taylor expansion coefficients representing the slope distances of the two base cases. The fourth-order Taylor expansion coefficients representing the slope distances of the two base cases; according to Figure 3 and Figure 4 The Taylor expansion coefficients of each order at the scattering point exhibit regular variations along both the azimuth and range directions;

[0031] Step 13: This invention applies the following to each group of scattering points (for a fixed...) Value, one for each scattering point A set of scattering points has a set The slant range history coefficients are subjected to a second-order Taylor fit with respect to zero Doppler time and shortest slant range; expressed as:

[0032] (7)

[0033] in, Indicates the slope distance of the two bases Taylor expansion coefficients, ; Represents the central scattering point Taylor expansion coefficients, express The Taylor expansion coefficients along the shortest slant distance Taylor fitting coefficients, express The Taylor expansion coefficients along the zero Doppler time Taylor fitting coefficients; , Represents the fitting coefficient; Represents the zero Doppler moment of the scattering body. Represents the zero Doppler moment of the scattering body The corresponding distance; This represents the zero Doppler moment of the scatterer at the center of the scene. Represents the zero Doppler moment of the scatterer at the center of the scene. The corresponding distance.

[0034] The other steps and parameters are the same as in Specific Implementation Method 1.

[0035] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that: in step 2, a two-dimensional FFT transformation is performed on the echo signal of a certain scattering point target (Formula (8)) to obtain the echo signal of the scattering point target in the frequency domain form (Formula (9)); the FFT transformation is a fast Fourier transform; the phase of the echo signal of the scattering point target in the frequency domain form is expanded by a third-order Taylor expansion (Formula (10)) to obtain the echo signal of the scattering point target in the frequency domain form after Taylor expansion;

[0036] Based on the frequency domain form of the echo signal of the scattering point target after Taylor expansion, define the phase values ​​of each order, and calculate the two-dimensional spatial variation and azimuth spatial variation of each phase value (Equations (15), (16), and (17)); the specific process is as follows:

[0037] Step 2.1: The echo signal of a target at a certain scattering point is represented as:

[0038] (8)

[0039] in, This represents the echo signal from the scattering point target. Indicates a fast time. Indicates slow time; This indicates the historical slant distance between the target and the reference point; Represents the distance window function. This represents the azimuth window function. Represents the speed of light; The radar cross-section (RCS) of the target; Represents the imaginary unit. ;

[0040] Indicates wavelength. Indicates the chirp rate of the transmitted signal;

[0041] Step 2: Ignoring the amplitude window, the two-dimensional spectrum of the signal is derived using the stationary phase principle (POSP) and series inversion method; the echo signal of the scattering point target (Formula (8)) is subjected to two-dimensional FFT transformation to obtain the echo signal of the scattering point target in frequency domain form (Formula (9)).

[0042] Steps two and three: Complex coupling exists between fast and slow time frequencies in the two-dimensional spectrum. To decouple this, the echo signal of the scattering point target in frequency domain form is processed here. phase ( , , , In fast time frequency Performing a Taylor series expansion at the point, we obtain the echo signal of the scattering point target in the frequency domain form after the Taylor expansion; expressed as:

[0043] (10)

[0044] in, Indicates the 0th order phase. Indicates the first-order phase. Indicates second-order phase, Indicates a 3rd order phase; according to Figure 4 a, Figure 4 b、 Figure 4 c. Figure 4 d, the error of the third-order Taylor expansion of the phase is less than Threshold, meeting the accuracy requirements. Step 24: Define the phase values ​​of each order based on the echo signal of the scattering point target in the frequency domain form after Taylor expansion, and calculate the two-dimensional spatial change and azimuth spatial change of each order phase value (Formula (15), Formula (16), Formula (17)).

[0045] Other steps and parameters are the same as in specific implementation method one or two.

[0046] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that: in step two, the amplitude window is ignored, and the two-dimensional spectrum of the signal is derived by using the stationary phase principle (POSP) and series inversion method;

[0047] A two-dimensional FFT transform is performed on the echo signal of the scattering point target (Equation (8)) to obtain the echo signal of the scattering point target in the frequency domain (Equation (9)); as shown in the following equation:

[0048] (9)

[0049] in, This represents the echo signal of a scattering point target in the frequency domain. Indicates fast time frequency. Indicates slow time frequency, Indicates the distance-dimensional tuning frequency. Indicates the carrier frequency.

[0050] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0051] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that: in steps two and three... The specific expression is as follows:

[0052] (11)

[0053] The specific expression is as follows:

[0054] (12)

[0055] The specific expression is as follows:

[0056] (13)

[0057] The specific expression is as follows:

[0058] (14).

[0059] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0060] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that: in step two and four, the phase values ​​of each order are defined based on the echo signal of the scattering point target in the frequency domain form after Taylor expansion, and the two-dimensional spatial changes and azimuth spatial changes of each order phase value are calculated (Formula (15), Formula (16), Formula (17)); the specific process is as follows:

[0061] Based on the analysis in step one, it was found that the slant range history coefficient exhibits a two-dimensional spatial variation characteristic. To evaluate the impact of this variation on each phase order, the phase values ​​of each order at the two-dimensional spectral boundary are defined as follows based on formula (10):

[0062] (15)

[0063] in, Indicates phase order; Represents the two-dimensional spectral boundary; express Phase order; Indicates the bandwidth of the distance dimension; The bandwidth representing the azimuth dimension is the sum of the instantaneous Doppler bandwidth of the antenna illumination and the Doppler bandwidth of the scene; the two-dimensional spatial variations of each phase order originate from the phase difference between each scattering point and the reference scattering point, based on... Phase Calculate the two-dimensional spatial variation and azimuth spatial variation of each phase value; the two-dimensional spatial variation and azimuth spatial variation of each phase value are as follows:

[0064] (16)

[0065] (17)

[0066] in, express Two-dimensional spatial variation of the phase order; express Phase order; express Phase order; express Spatial variation of phase order; express Phase order; . Figure 6 Showing , , and Two-dimensional space-variability, Figure 7 Showing , , and The spatial variation of the two-dimensional phase is shown. It is evident that the spatial variations of the second and third-order phase terms are negligible in both the range and azimuth directions. However, the spatial variations of the first and zeroth-order phase terms are significant and cannot be ignored; therefore, corrections are required in both the range and azimuth dimensions. Other steps and parameters are the same as in any of the specific implementation methods one through five.

[0067] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that: in step three, based on the two-dimensional spatial changes and azimuth spatial changes of each phase value in step two, uniform distance migration correction and distance compression are performed on the scene center scattering point (Formula (18)) to obtain the frequency domain signal after uniform distance migration correction and distance compression; the frequency domain signal after uniform distance migration correction and distance compression is subjected to a distance-dimensional IFFT transform to obtain a distance-Doppler domain signal; the IFFT transform is an inverse fast Fourier transform; the distance-dimensional block processing is performed on the distance-Doppler domain signal. The process involves: obtaining each range block; performing a range-dimensional FFT on each range block to obtain its two-dimensional frequency domain signal; compensating the two-dimensional frequency domain signal of each range block to obtain its compensated signal; repeating this process until all range blocks have their compensated signals obtained; performing a range-dimensional IFFT on the compensated signal of each range block to obtain its range-Doppler domain signal; repeating this process until all range blocks have their range-Doppler domain signals obtained; and finally concatenating the range-Doppler domain signals of all range blocks to obtain a concatenated range-Doppler domain signal. The specific steps are as follows:

[0068] Step 3.1: Perform consistent distance migration correction and distance compression based on the scene's center scattering point; the specific process is as follows:

[0069] (18)

[0070] in, This represents the consistent distance migration correction and distance compression function. This represents the first-order phase of the central scattering point. This represents the second-order phase at the central scattering point. This represents the third-order phase of the central scattering point;

[0071] The frequency domain signal after uniform range migration correction and range compression is expressed as follows:

[0072] (19)

[0073] in, This represents the frequency domain signal after consistent range migration correction and range compression.

[0074] Step 32: Perform a range-dimensional IFFT transform on the frequency domain signal after uniform range migration correction and range compression to obtain the range-Doppler domain signal;

[0075] Step 33: When performing range dimension segmentation within the distance-Doppler (RD) domain, it is necessary to set an appropriate threshold as a standard. For example... Figure 5As shown, spatial variations along the range dimension have negligible effects on second-order and higher-order phase terms, but still significant effects on first-order phase terms. This invention uses the variation in first-order phase error as the segmentation criterion; it performs range-dimensional block processing on the range-Doppler domain signal to obtain each range block; the specific process is as follows:

[0076] Assume the length of each distance block is When dividing the data into blocks, it is necessary to ensure that the first-order phase error within each distance block does not exceed half a resolution cell; the constraint condition is described as follows:

[0077] (20)

[0078] in, Represents the two-dimensional spatial variation of the first-order phase. Represents the two-dimensional spatial variation of the first-order phase. This represents the shortest slant distance from the center scattering point of each distance block. Indicates the bandwidth of the distance dimension;

[0079] Steps 3 and 4: After completing the range block division, perform a range-dimensional FFT on each range block obtained in Step 3 to obtain the two-dimensional frequency domain signal of each range block (the range-dimensional FFT realizes the conversion from the range-Doppler domain to the two-dimensional frequency domain for each range block); compensate the two-dimensional frequency domain signal of each range block (compensate for low-order errors caused by spatial variations in the range dimension), and obtain the compensated signal of each range block; the compensation function is as follows:

[0080] (twenty one)

[0081] in, Represents the compensation function. Indicates the first-order phase. This indicates the first-order phase; repeat steps three and four until the signal after compensation for all range blocks is obtained.

[0082] Step 35: Perform a range-dimensional IFFT transform on the compensated signal of each range block to obtain the range-Doppler domain signal of each range block; repeat step 35 until the range-Doppler domain signals of all range blocks are obtained.

[0083] Step 36: Segment the range-Doppler domain signals of all range blocks to obtain the segmented range-Doppler domain signal; the expression for the segmented range-Doppler domain signal is:

[0084] (twenty two)

[0085] in, This represents the spliced ​​distance-Doppler domain signal. This indicates the 0th order phase. Other steps and parameters are the same as in any of the specific implementation methods one through six.

[0086] Specific Implementation Method Eight: This implementation method differs from one of Specific Implementation Methods One to Seven in that: in step four, the spliced ​​distance-Doppler domain signal is subjected to IFFT transformation along the azimuth dimension to obtain a two-dimensional time domain signal;

[0087] A fifth-order perturbation function is constructed; based on the Taylor expansion coefficients of the scattering points from step one, the fifth-order perturbation function is multiplied by the two-dimensional time-domain signal to obtain the compensated two-dimensional time-domain signal; the specific process is as follows:

[0088] Step 41: Perform IFFT transform on the stitched range-Doppler domain signal along the azimuth dimension to obtain a two-dimensional time-domain signal; the expression for the azimuth time-domain two-dimensional signal is:

[0089] (twenty three)

[0090] in, Represents a two-dimensional time-domain signal;

[0091] Step 42: Based on the azimuth spatial variation characteristics of the echo in the two-dimensional time domain, this invention constructs a fifth-order perturbation function to perform nonlinear scaling (NCS) compensation in the azimuth dimension; the fifth-order perturbation function is expressed as:

[0092] (twenty four)

[0093] in, This represents a fifth-order perturbation function. Indicates the second-order perturbation factor. This represents the third-order perturbation factor. This represents the fourth-order perturbation factor. Indicates the 5th order perturbation factor;

[0094] Step 4.3: Based on the Taylor expansion coefficients of the scattering points from Step 1, the fifth-order perturbation function... With two-dimensional time domain signals Multiplying them together yields the compensated two-dimensional time-domain signal.

[0095] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0096] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the expression for the compensated two-dimensional time-domain signal in step four-three is:

[0097] (25)

[0098] in, This represents the compensated two-dimensional time-domain signal. This represents the first-order Taylor expansion coefficients at the central scattering point. This represents the first-order Taylor fit coefficients of the first-order Taylor expansion along the zero Doppler time. This represents the second-order Taylor expansion coefficients at the central scattering point. This represents the first-order Taylor fitting coefficients of the second-order Taylor expansion along the zero Doppler time. This represents the third-order Taylor expansion coefficients at the central scattering point. This represents the first-order Taylor fitting coefficients of the third-order Taylor expansion along the zero Doppler time. This represents the fourth-order Taylor expansion coefficients at the central scattering point. Table 4 shows the first-order Taylor fitting coefficients of the fourth-order Taylor expansion along the zero Doppler time. , , , satisfy:

[0099] , , , ;when , , , In this case, the first-order spatial variation in the azimuth direction can be effectively compensated. Although this compensation may introduce small second-order and higher-order spatial variations, these higher-order effects are usually negligible in most practical applications. Other steps and parameters are the same as in specific implementation methods one to eight.

[0100] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One through Nine in that: in step five, the compensated two-dimensional time-domain signal is subjected to FFT transformation along the azimuth direction to convert the data to the RD domain, and then azimuth pulse compression is performed. An IFFT transformation is then performed on the azimuth pulse-compressed signal to obtain the two-dimensional time-domain signal (at this time, the target point will be compressed to the corresponding position). The two-dimensional time-domain signal is the two-dimensional SAR image; the specific process is as follows:

[0101] Step 51: For the compensated two-dimensional time-domain signal... Perform FFT along the azimuth dimension to obtain the range-Doppler (RD) domain signal; Step 52: Perform azimuth pulse compression on the range-Doppler (RD) domain signal to obtain the azimuth pulse compressed signal; the azimuth pulse compression function is expressed as:

[0102] (26)

[0103] in, This represents the azimuth pulse compression function. This represents the corrected second-order Taylor expansion coefficients. This represents the corrected third-order Taylor expansion coefficients. This represents the corrected fourth-order Taylor expansion coefficients;

[0104] , , ;

[0105] Step 53: Perform an IFFT transform on the compressed signal of the directional pulse to obtain a two-dimensional time-domain signal (at this time, the target point will be compressed to the corresponding position). The two-dimensional time-domain signal is the two-dimensional SAR image. Other steps and parameters are the same as in specific implementation methods one through nine. It should be noted that when the echo data exhibits a significant tilt angle, existing LRWC operations are typically combined with the method of this invention to improve resolution; the specific process is as follows: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Replace with (in (Represents the first-order coefficients of the Taylor expansion of the slant range model for the target at the scene center point). The new azimuth spatial variability introduced by LRWC can be solved using currently prevalent research algorithms. This algorithm can be combined with algorithms that solve the azimuth spatial variability introduced by LRWC, simultaneously addressing both types of spatial variability problems. Due to the lack of MEO-machine bistatic SAR measured data, this invention mainly utilizes simulation data and semi-physical SAR data for verification; the beneficial effects of this invention are verified through the following embodiments;

[0106] Example demonstration:

[0107] I. Simulation Parameters and Results of Point Targets

[0108]

[0109]

[0110] Within the imaging area, 25 point targets are uniformly distributed along both azimuth and range dimensions, such as... Figure 7 As shown in the figure. The scene covers 1.5 kilometers in the distance dimension and 1 kilometer in the azimuth dimension. Simulation settings are detailed in Tables 1 and 2. To visually demonstrate the performance of the proposed method, a comparative analysis is performed using the traditional bistatic distance-Doppler (RDA) algorithm. The overall imaging results of the proposed algorithm are shown in... Figure 8 In the image, the imaging results for points 13, 19, and 25 are shown respectively. Figure 10 , Figure 11 , Figure 12In addition, to quantitatively evaluate the effectiveness of the proposed algorithm, Table 3 lists the evaluation metrics for all selected target points, including impulse response width (IRW), peak sidelobe ratio (PSLR), and integral sidelobe ratio (ISLR). When the echo data exhibits a significant skew angle, LRWC can be performed as the first step in the workflow. Therefore, it is necessary to address the azimuth-dependent variation introduced by LRWC. In this invention, the reference ENCS algorithm [Y. Zhang, H. Ren, Z. Lu, X. Yang, and G. Li, “Focusing of highly squinted bistatic SAR with MEO transmitter and high maneuvering platform receiver in curved trajectory,” IEEE Trans. Geosci. Remote Sens., Jan. 2024.] is selected and combined with the proposed method to simultaneously address these two spatial variations. The imaging results are then compared with those obtained using only the reference algorithm. This invention employs... Figure 8 The scatterer layout in the image. The overall imaging results of the algorithm proposed in this invention are shown in... Figure 13 In the image, the imaging results for points 13, 19, and 25 are shown respectively. Figure 14 , Figure 15 , Figure 16 In addition, to quantitatively evaluate the effectiveness of the proposed algorithm, Table 4 lists the evaluation metrics for all selected target points, including impulse response width (IRW), peak sidelobe ratio (PSLR), and integral sidelobe ratio (ISLR).

[0111]

[0112]

[0113] The main reason for the image degradation in the comparative algorithms is that the two-dimensional spatial variations introduced by the complex configuration of the MEO-airborne bistatic SAR system are not considered. Different point targets exhibit different phase histories, and using a uniform azimuth matched filter and the same range migration correction function to process all targets inevitably leads to mismatch and image degradation. Traditional algorithms often ignore this spatial variation. The algorithm proposed in this invention deeply analyzes and considers the spatial variability introduced by the complex configuration, thus suppressing this phenomenon. In the comparative algorithms, the azimuth resolution gradually decreases as the target moves further away from the scene center, from 1.2336 meters to 1.586 meters, while PSLR and ISLR increase accordingly. In contrast, the results processed using the proposed algorithm show that even for targets located at the scene edge, the azimuth resolution can still be maintained below 1.2336 meters (i.e., the IRW at the scene center). Compared with the comparative algorithms, both PSLR and ISLR are significantly improved. Secondly, in the range dimension, the three algorithms do not differ much in terms of IRW. However, the algorithm proposed in this invention can further reduce the PSLR and ISLR of point targets. Compared to other studies, this invention focuses on the two-dimensional spatial changes caused by complex configurations in large scenes. The algorithm effectively reduces spatial changes while maintaining low computational complexity and achieves good focusing performance.

[0114] II. Hardware-in-the-loop simulation parameters and results

[0115] Furthermore, to deeply analyze the performance of the proposed algorithm, this invention uses airborne measured SAR echoes to generate semi-realistic MEO-airborne bistatic SAR echoes as input. The system uses the radar and signal parameters provided in Tables 1 and 2. The imaging scene covers an area of ​​1.2 km (azimuth) × 2.1 km (distance), and the proposed algorithm and the traditional bistatic RD algorithm are used for imaging processing respectively. Figure 17 This paper presents two-dimensional focused images obtained by the traditional two-base RD algorithm and the method proposed in this invention. For clear comparison, two regions at the edges of the imaging results are magnified and marked with rectangles. A magnified image of region 1 is shown below. Figure 17 (c) and Figure 17 In the middle (d), a magnified image of region 2 is shown. Figure 17 (e) and Figure 17 (f) Among them, Figure 17 (c) and Figure 17 (e) represents the processing result of the reference algorithm. Figure 17 (d) and Figure 17 (f) shows the processing result of the method proposed in this invention. Figure 17 (d) and Figure 17As can be clearly seen in (f), the energy distribution of the scattering points is more concentrated, and the outlines of roads and houses are clearer. This indicates that the method has good focusing performance, making object features easier to identify. In contrast, the results of the traditional dual-base RD algorithm suffer from severe defocusing.

[0116]

[0117] Furthermore, to quantitatively evaluate the performance of the proposed algorithm, Table 5 shows the evaluation metrics obtained by the two imaging algorithms in Region 1 and Region 2, including image entropy and image contrast. The results show that the proposed method has lower image entropy and higher image contrast in both regions. This indicates that the two-dimensional spatial variations introduced by the complex configuration of the MEO-machine bistatic SAR system cannot be ignored, and the proposed method can effectively correct the spatial variations at the scene edges, fully demonstrating the effectiveness of the proposed algorithm in complex configurations.

[0118] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A two-dimensional spatial variability correction method for MEO-machine bistatic SAR imaging, characterized in that: The specific process of the method is as follows: Step 1: Use interpolation on the imaging plane to find a set of virtual scattering points with the same shortest slant range, i.e., located in the same range cell, and obtain the fourth-order Taylor expansion coefficients of the scattering points located in the same range cell. Using interpolation on the imaging plane, a set of virtual scattering points with the same shortest slant range time are found, i.e. located in the same azimuth cell, and the fourth-order Taylor expansion coefficients of the scattering points located in the same azimuth cell are obtained. Step 2: Perform a two-dimensional FFT transform on the echo signal of a scattering point target to obtain the echo signal of the scattering point target in the frequency domain. FFT is the Fast Fourier Transform. A third-order Taylor expansion is performed on the phase of the echo signal of the scattering point target in the frequency domain to obtain the echo signal of the scattering point target in the frequency domain after Taylor expansion. Based on the frequency domain form of the scattering point target echo signal after Taylor expansion, define the phase values ​​of each order, and calculate the two-dimensional spatial variation and azimuth spatial variation of each order phase value. Step 3: Based on the two-dimensional spatial changes and azimuth spatial changes of each phase value in Step 2, perform consistent range migration correction and range compression on the scene center scattering point to obtain the frequency domain signal after consistent range migration correction and range compression. A range-dimensional IFFT transform is performed on the frequency domain signal after uniform range migration correction and range compression to obtain the range-Doppler domain signal; The IFFT transform is the inverse fast Fourier transform; The range-Doppler domain signal is divided into range-dimensional blocks to obtain each range block; Perform a distance-dimensional FFT on each distance block to obtain the two-dimensional frequency domain signal of each distance block; The two-dimensional frequency domain signal of each range block is compensated to obtain the compensated signal of each range block; Until the signal after all distance blocks have been compensated is obtained; Perform a range-dimensional IFFT transform on the compensated signal of each range block to obtain the range-Doppler domain signal of each range block; Until the range-Doppler domain signals of all range blocks are obtained; The range-Doppler domain signals of all range blocks are stitched together to obtain the stitched range-Doppler domain signal; Step 4: Perform IFFT transform on the spliced ​​range-Doppler domain signal along the azimuth dimension to obtain a two-dimensional time domain signal; Construct a fifth-order perturbation function; Based on the Taylor expansion coefficients of the scattering point in step one, the fifth-order perturbation function is multiplied with the two-dimensional time-domain signal to obtain the compensated two-dimensional time-domain signal. Step 5: Perform FFT transformation on the compensated two-dimensional time domain signal along the azimuth direction to convert the data to the RD domain, then perform azimuth pulse compression, and perform IFFT transformation on the azimuth pulse compressed signal to obtain the two-dimensional time domain signal, which is the two-dimensional SAR image.

2. The two-dimensional spatial variability correction method for MEO-machine bistatic SAR imaging according to claim 1, characterized in that: In step one, an interpolation method is used on the imaging plane to find a set of virtual scattering points with the same shortest slant range, i.e., located in the same distance cell, and the Taylor expansion coefficients of the fourth-order scattering points located in the same distance cell are obtained. Using interpolation on the imaging plane, a set of virtual scattering points with the same shortest slant range time are found, i.e. located in the same azimuth cell, and the fourth-order Taylor expansion coefficients of the scattering points located in the same azimuth cell are obtained. The specific process is as follows: Step 11: The slant range history of each scattering point is expressed as a function of slow time. The fourth-order Taylor expansion is expressed as: (1) in, Represents slow time The nearest slant distance of the scattering point, Represents slow time. The nearest slant distance representing the scattering point. The first-order Taylor expansion coefficients representing the slant distance. The second-order Taylor expansion coefficients representing the slant distance. The third-order Taylor expansion coefficients representing the slant distance. The fourth-order Taylor expansion coefficients represent the slant distance; the specific expression is: (2) (3) (4) (5) in, This represents the velocity vector between the radar and the target. This represents the slant range vector between the radar and the target. express The model, the upper corner mark Indicates transpose; This represents the acceleration vector between the radar and the target. express The model; This represents the jerk vector between the radar and the target. This represents the acceleration vector between the radar and the target. express The model; Steps 1 and 2: Based on Step 1, the slant range history of each scattering point is expressed as a function of slow time. The fourth-order Taylor expansion of the bistatic slant range history in MEO-based bistatic SAR is expressed as: (6) in, Indicates the slope distance history of the two bases; This represents the closest slant distance from the MEO satellite to the scattering point. This represents the closest slant distance from the aircraft to the scattering point; Represents the slant range history from the MEO satellite to the scattering point. Taylor expansion coefficients, Represents the slant range history from the aircraft to the scattering point. Taylor expansion coefficients, ; Represents the zero Doppler moment of the scattering body The corresponding distance; Indicates slow time of Power of 1 ; The first-order Taylor expansion coefficients of the bibasic slope distances are represented. The second-order Taylor expansion coefficients representing the slope distances of the two base cases are... The third-order Taylor expansion coefficients representing the slope distances of the two base cases. The fourth-order Taylor expansion coefficients represent the bibasic slope distances; Step 13: Perform a second-order Taylor fit on the slant range history coefficients of each group of scattering points with respect to the zero Doppler time and the shortest slant range; expressed as: (7) in, Indicates the slope distance of the two bases Taylor expansion coefficients, ; Represents the central scattering point Taylor expansion coefficients, express The Taylor expansion coefficients along the shortest slant distance Taylor fitting coefficients of order 1, express The Taylor expansion coefficients along the zero Doppler time Taylor fitting coefficients; , Represents the fitting coefficient; Represents the zero Doppler moment of the scattering body. Represents the zero Doppler moment of the scattering body The corresponding distance; This represents the zero Doppler moment of the scatterer at the center of the scene. Represents the zero Doppler moment of the scatterer at the center of the scene. The corresponding distance.

3. The two-dimensional spatial variation correction method for MEO-machine bistatic SAR imaging according to claim 2, characterized in that: In step two, a two-dimensional FFT transform is performed on the echo signal of a certain scattering point target to obtain the echo signal of the scattering point target in the frequency domain; the FFT transform is the Fast Fourier Transform. A third-order Taylor expansion is performed on the phase of the echo signal of the scattering point target in the frequency domain to obtain the echo signal of the scattering point target in the frequency domain after Taylor expansion. Based on the frequency domain form of the scattering point target echo signal after Taylor expansion, define the phase values ​​of each order, and calculate the two-dimensional spatial variation and azimuth spatial variation of each order phase value. The specific process is as follows: Step 2.1: The echo signal of a target at a certain scattering point is represented as: (8) in, This represents the echo signal from the scattering point target. Indicates a fast time. Indicates slow time; This indicates the historical slant distance between the target and the reference point; Represents the distance window function. This represents the azimuth window function. Represents the speed of light; The radar cross-section representing the target; Represents the imaginary unit. ; Indicates wavelength. Indicates the chirp rate of the transmitted signal; Step 22: Perform a two-dimensional FFT transform on the echo signal of the scattering point target to obtain the echo signal of the scattering point target in the frequency domain. Steps two and three: Convert the echo signal of the scattering point target into frequency domain form. The phase at fast time frequency Performing a Taylor series expansion at the point, we obtain the echo signal of the scattering point target in the frequency domain form after the Taylor expansion; expressed as: (10) in, Indicates the 0th order phase. Indicates the first-order phase. Indicates second-order phase, Indicates a 3rd order phase; Step 24: Define the phase values ​​of each order based on the frequency domain form of the scattering point target's echo signal after Taylor expansion, and calculate the two-dimensional spatial variation and azimuth spatial variation of each phase value.

4. The two-dimensional spatial variability correction method for MEO-machine bistatic SAR imaging according to claim 3, characterized in that: In step two, a two-dimensional FFT transform is performed on the echo signal of the scattering point target to obtain the echo signal of the scattering point target in the frequency domain, as shown in the following equation: (9) in, This represents the echo signal of a scattering point target in the frequency domain. Indicates fast time frequency. Indicates slow time frequency, Indicates the distance-dimensional tuning frequency. Indicates the carrier frequency.

5. The two-dimensional spatial variability correction method for MEO-machine bistatic SAR imaging according to claim 4, characterized in that: In steps two and three The specific expression is as follows: (11) The specific expression is as follows: (12) The specific expression is as follows: (13) The specific expression is as follows: (14)。 6. The two-dimensional spatial variability correction method for MEO-machine bistatic SAR imaging according to claim 5, characterized in that: In step two and four, the phase values ​​of each order are defined based on the frequency domain form of the echo signal of the scattering point target after Taylor expansion, and the two-dimensional spatial variation and azimuth spatial variation of each order phase value are calculated; the specific process is as follows: The phase values ​​of each order at the two-dimensional spectral boundary are defined as follows: (15) in, Indicates phase order; Represents the two-dimensional spectral boundary; express Phase order; Represents the bandwidth of the distance dimension; The bandwidth representing the azimuth dimension; based on Phase Calculate the two-dimensional spatial variation and azimuth spatial variation of each phase value; The mathematical definitions of the two-dimensional spatial variation and azimuth spatial variation of each phase value are given by the following equation: (16) (17) in, express Two-dimensional spatial variation of the phase order; express Phase order; express Phase order; express Spatial variation of phase order; express Phase order; .

7. The two-dimensional spatial variation correction method for MEO-machine bistatic SAR imaging according to claim 6, characterized in that: In step three, based on the two-dimensional spatial changes and azimuth spatial changes of each phase value in step two, consistent distance migration correction and distance compression are performed on the scene center scattering point to obtain the frequency domain signal after consistent distance migration correction and distance compression. A range-dimensional IFFT transform is performed on the frequency domain signal after uniform range migration correction and range compression to obtain the range-Doppler domain signal; The IFFT transform is the inverse fast Fourier transform; The range-Doppler domain signal is divided into range-dimensional blocks to obtain each range block; Perform a distance-dimensional FFT on each distance block to obtain the two-dimensional frequency domain signal of each distance block; The two-dimensional frequency domain signal of each range block is compensated to obtain the compensated signal of each range block; Until the signal after all distance blocks have been compensated is obtained; Perform a range-dimensional IFFT transform on the compensated signal of each range block to obtain the range-Doppler domain signal of each range block; Until the range-Doppler domain signals of all range blocks are obtained; The range-Doppler domain signals of all range blocks are stitched together to obtain the stitched range-Doppler domain signal; The specific process is as follows: Step 3.1: Perform consistent distance migration correction and distance compression based on the scene's center scattering point; the specific process is as follows: (18) in, This represents the consistent distance migration correction and distance compression function. This represents the first-order phase of the central scattering point. This represents the second-order phase at the central scattering point. This represents the third-order phase of the central scattering point; The frequency domain signal after uniform range migration correction and range compression is expressed as follows: (19) in, This represents the frequency domain signal after consistent range migration correction and range compression. Step 32: Perform a range-dimensional IFFT transform on the frequency domain signal after uniform range migration correction and range compression to obtain the range-Doppler domain signal; Step 3: Perform range-dimensional block processing on the range-Doppler domain signal to obtain each range block; The specific process is as follows: Assume the length of each distance block is When dividing the data into blocks, it is necessary to ensure that the first-order phase error within each distance block does not exceed half a resolution cell; the constraint condition is described as follows: (20) in, Represents the two-dimensional spatial variation of the first-order phase. Represents the two-dimensional spatial variation of the first-order phase. This represents the shortest slant distance from the center scattering point of each distance block. Represents the bandwidth of the distance dimension; Step 3-4: Perform a distance-dimensional FFT on each distance block obtained in Step 3-3 to obtain the two-dimensional frequency domain signal of each distance block; The two-dimensional frequency domain signal of each range block is compensated to obtain the compensated signal of each range block; The compensation function is as follows: (21) in, Represents the compensation function. Indicates the first-order phase. Indicates the first-order phase; Repeat steps three and four until all distance blocks are compensated for and the signal is obtained. Step 35: Perform a range-dimensional IFFT transform on the compensated signal of each range block to obtain the range-Doppler domain signal of each range block; Repeat steps three and five until the range-Doppler domain signals of all range blocks are obtained; Step 36: Segment the range-Doppler domain signals of all range blocks to obtain the segmented range-Doppler domain signal; The expression for the spliced ​​distance-Doppler domain signal is: (22) in, This represents the spliced ​​distance-Doppler domain signal. This indicates the 0th order phase.

8. The two-dimensional spatial variability correction method for MEO-machine bistatic SAR imaging according to claim 7, characterized in that: In step four, the spliced ​​range-Doppler domain signal is subjected to IFFT transformation along the azimuth dimension to obtain a two-dimensional time domain signal; a fifth-order perturbation function is then constructed. Based on the Taylor expansion coefficients of the scattering point in step one, the fifth-order perturbation function is multiplied with the two-dimensional time-domain signal to obtain the compensated two-dimensional time-domain signal. The specific process is as follows: Step 41: Perform IFFT transformation on the spliced ​​range-Doppler domain signal along the azimuth dimension to obtain a two-dimensional time domain signal; The expression for the azimuth time-domain two-dimensional signal is: (23) in, Represents a two-dimensional time-domain signal; Step 42: Construct the fifth-order perturbation function; the fifth-order perturbation function is expressed as: (24) in, This represents a fifth-order perturbation function. Indicates the second-order perturbation factor. This represents the third-order perturbation factor. This represents the fourth-order perturbation factor. Indicates the 5th order perturbation factor; Step 4.3: Based on the Taylor expansion coefficients of the scattering points from Step 1, the fifth-order perturbation function... With two-dimensional time domain signals Multiplying them together yields the compensated two-dimensional time-domain signal.

9. A two-dimensional spatial variability correction method for MEO-machine bistatic SAR imaging according to claim 8, characterized in that: The expression for the compensated two-dimensional time-domain signal in step four-three is as follows: (25) in, This represents the compensated two-dimensional time-domain signal. This represents the first-order Taylor expansion coefficients at the central scattering point. This represents the first-order Taylor fit coefficients of the first-order Taylor expansion along the zero Doppler time. This represents the second-order Taylor expansion coefficients at the central scattering point. This represents the first-order Taylor fitting coefficients of the second-order Taylor expansion along the zero Doppler time. This represents the third-order Taylor expansion coefficients at the central scattering point. This represents the first-order Taylor fitting coefficients of the third-order Taylor expansion along the zero Doppler time. This represents the fourth-order Taylor expansion coefficients at the central scattering point. denoted as the first-order Taylor fitting coefficients along the zero Doppler time, representing the fourth-order Taylor expansion coefficients; , , , satisfy: ， ， ， 。 10. A two-dimensional spatial variation correction method for MEO-machine bistatic SAR imaging according to claim 9, characterized in that: In step five, the compensated two-dimensional time-domain signal is subjected to FFT transformation along the azimuth direction to convert the data to the RD domain. Then, azimuth pulse compression is performed, and the compressed signal is subjected to IFFT transformation to obtain the two-dimensional time-domain signal, which is the two-dimensional SAR image. The specific process is as follows: Step 51: For the compensated two-dimensional time-domain signal... Perform FFT along the azimuth dimension to obtain the range-Doppler domain signal; Step 52: Perform azimuth pulse compression on the range-Doppler domain signal to obtain the azimuth pulse compressed signal; The azimuth pulse compression function is expressed as: (26) in, This represents the azimuth pulse compression function. This represents the corrected second-order Taylor expansion coefficients. This represents the corrected third-order Taylor expansion coefficients. This represents the corrected fourth-order Taylor expansion coefficients; ， ， ； Step 53: Perform IFFT transform on the compressed directional pulse signal to obtain a two-dimensional time-domain signal, which is the two-dimensional SAR image.

Images