Spaceborne SAR speed rapid estimation method, system and product based on fractional Fourier transform

Abstract

The invention discloses a spaceborne SAR (Synthetic Aperture Radar) speed rapid estimation method, system and product based on fractional Fourier transform, belongs to the technical field of radar remote sensing, and solves the problems that the SAR imaging quality is low due to inaccurate spaceborne SAR speed estimation, and the SAR imaging quality is poor due to the fact that a method based on amplitude or phase is used for spaceborne SAR speed estimation in the prior art. The calculation complexity is high; the time consumption is long; and the estimation precision is limited. SAR echo data are obtained, and coarse estimation is carried out on the SAR speed; sAR imaging is carried out based on SAR echo data to obtain an SAR image, and coarse focusing is carried out on the SAR image in combination with the coarse estimated SAR speed; estimating the residual azimuth modulation frequency of the coarsely focused SAR image by adopting fractional Fourier transform; and obtaining accurate estimation of the SAR speed based on the roughly estimated SAR speed and the residual azimuth modulation frequency. The method is used for realizing rapid and accurate spaceborne SAR speed estimation.

Description

Technical Field

[0001] This invention relates to the field of radar remote sensing technology, specifically to a method, system, and product for rapid estimation of spaceborne SAR velocity based on fractional Fourier transform. Background Technology

[0002] Synthetic Aperture Radar (SAR) is widely used in marine surveillance and resource exploration due to its ability to penetrate clouds, rain, and fog, enabling all-weather, 24 / 7 Earth observation. Spaceborne SAR velocity is a crucial parameter for azimuth frequency estimation. When there is a deviation between the estimated spaceborne SAR velocity and the actual velocity, the calculated azimuth frequency is inaccurate, affecting SAR imaging quality, causing target distortion and deviation from their true positions, and reducing SAR image resolution. Therefore, accurate estimation of spaceborne SAR velocity is of significant research importance.

[0003] Spaceborne SAR velocity estimation can be achieved by estimating the azimuth frequency modulation (AFM). Currently, methods for estimating AFM mainly fall into two categories: amplitude-based methods and phase-based methods. Amplitude-based methods include the maximum contrast method and the azimuth view misalignment method. However, the maximum contrast method uses maximizing the contrast of the SAR image as the optimization function to estimate the AFM, requiring numerous iterations to meet the required accuracy. The azimuth view misalignment method, on the other hand, requires dividing the image into numerous sub-images to achieve accurate AFM estimation, resulting in high computational complexity. Phase-based methods include the phase difference method and the phase gradient method. These methods estimate the AFM by solving for the coefficients of the phase error polynomial from the defocused SAR image using a phase polynomial error model, but suffer from time consumption and limited estimation accuracy.

[0004] In the prior art, Chinese patent document CN111781591A discloses a "rapid estimation method for radar target velocity based on fractional Fourier transform". This method obtains the radar target azimuth signal s(η) using model formulas based on radar target parameters and synthetic aperture radar (SAR) system parameters; determines the fractional Fourier transform (FRFT) angles α and β based on the target velocity range; performs two FRFT transformations on the radar target azimuth signal s(η) with transformation angles α and β respectively; and obtains the corresponding projection length L based on the results of the two FRFTs. α and L β The radar target's modulation frequency and azimuth velocity can be calculated based on the FRFT angle and projection length. However, this technical solution estimates the radar target's velocity and requires prior knowledge of the target's approximate velocity range, which is quite different from the modeling approach for velocity estimation on spaceborne SAR platforms.

[0005] In summary, existing technologies suffer from low SAR imaging quality due to inaccurate velocity estimation of spaceborne SAR, while using amplitude-based or phase-based methods for spaceborne SAR velocity estimation results in high computational complexity, long processing time, and limited estimation accuracy. Summary of the Invention

[0006] This invention solves the technical problems of low SAR imaging quality due to inaccurate spaceborne SAR velocity estimation in existing technologies, and high computational complexity, long time consumption and limited estimation accuracy when using amplitude-based or phase-based methods for spaceborne SAR velocity estimation.

[0007] The present invention discloses a fast velocity estimation method for spaceborne SAR based on fractional Fourier transform, comprising the following steps: Step 1: Acquire SAR echo data and make a rough estimate of SAR velocity; Step 2: Perform SAR imaging based on SAR echo data, and combine it with the coarsely estimated SAR velocity to obtain a coarsely focused SAR image; Step 3: Use fractional Fourier transform to estimate the residual azimuth modulation frequency of the coarsely focused SAR image. Step 4: Based on the coarse estimate of SAR velocity in Step 1 and the residual azimuth modulation frequency in Step 3, obtain the accurate estimate of SAR velocity.

[0008] Furthermore, in one embodiment of the present invention, the coarse estimation of SAR velocity in step 1 specifically involves: Based on the slant range at each azimuth time in the SAR echo data, a coarse estimate of the SAR velocity is obtained through fitting.

[0009] Furthermore, in one embodiment of the present invention, the estimation of the residual azimuth modulation frequency of the coarsely focused SAR image in step 3 specifically includes: From the coarse-focused SAR image, the range gate corresponding to the strong point target is selected and fractional Fourier transform is performed. Peak search is performed on the fractional Fourier transform result to obtain the optimal rotation order. Based on the optimal rotation order, the residual azimuth modulation frequency is obtained.

[0010] Furthermore, in one embodiment of the present invention, the rotation order step size of the fractional Fourier transform is 0.001, and the search range is [-1, 1].

[0011] Furthermore, in one embodiment of the present invention, the optimal rotation order is specifically: Peak search is performed on the fractional Fourier transform results to obtain the optimal rotation order for coarse search. Based on the optimal rotation order of the coarse search, a fractional Fourier transform is performed, and the rotation order corresponding to the maximum value of the fractional Fourier transform result is taken as the optimal rotation order.

[0012] Furthermore, in one embodiment of the present invention, the fractional Fourier transform based on the optimal rotation order of the coarse search is centered on the optimal rotation order of the coarse search. Fractional Fourier transforms are performed within the range with a step size of 0.00001.

[0013] Furthermore, in one embodiment of the present invention, obtaining the residual azimuth tuning frequency based on the optimal rotation order specifically involves: Based on the optimal rotation order, the modulation frequency of the residual linear frequency modulated signal is obtained. The azimuth modulation frequency obtained from the rough estimate of velocity Based on the relationship, the residual azimuth modulation frequency is estimated.

[0014] Furthermore, in one embodiment of the present invention, the precise estimation of SAR velocity in step 4 specifically includes: ; in, For accurate estimation of SAR velocity, For a rough estimate of SAR velocity, The residual azimuth tuning frequency, For wavelength, This represents the slant distance of the strong point target.

[0015] The present invention discloses a fast velocity estimation system for spaceborne SAR based on fractional Fourier transform, comprising the following modules: Module 1: Acquire SAR echo data and use a hyperbolic model to make a coarse estimate of SAR velocity; Module 2 performs SAR imaging based on SAR echo data to obtain SAR images, and then coarsely focuses the SAR images using a coarsely estimated SAR velocity. Module 3 uses fractional Fourier transform to estimate the residual azimuth frequency of the coarsely focused SAR image. Module 4, based on the coarse estimate of SAR velocity described in Module 1 and the residual azimuth modulation frequency described in Module 3, obtains a precise estimate of SAR velocity.

[0016] The computer program product of the present invention includes a computer program or instructions, which, when executed by a processor, implement any of the above-described methods for fast estimation of spaceborne SAR velocity based on fractional Fourier transform.

[0017] This invention solves the technical problems of inaccurate spaceborne SAR velocity estimation leading to low SAR imaging quality, and the high computational complexity, long time consumption, and limited estimation accuracy resulting from using amplitude-based or phase-based methods for spaceborne SAR velocity estimation. Specific beneficial effects include: This invention proposes a fast velocity estimation method for spaceborne SAR based on fractional Fourier transform. First, a coarse estimate of the spaceborne SAR velocity is achieved using SAR echo data based on a hyperbolic model. Then, a chirp scaling algorithm is used to coarsely focus the SAR image. Typical strong targets are selected from the coarsely focused SAR image, and the fractional Fourier transform of the range gate of these strong targets is calculated. The optimal rotation order of the fractional Fourier transform is calculated using a two-step search method. Finally, the residual azimuth modulation frequency is calculated based on this optimal rotation order. Accurate estimation of the spaceborne SAR data is achieved based on the coarsely estimated velocity using the hyperbolic model and the residual azimuth modulation frequency, significantly reducing computational complexity. This method enables fast and accurate estimation of spaceborne SAR velocity and allows for focusing of spaceborne SAR images based on the estimated velocity. Attached Figure Description

[0018] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of the spaceborne SAR velocity estimation method based on fractional Fourier transform as described in Implementation Method 1. Figure 2 This is a schematic diagram of the velocity estimation results of the different methods described in Implementation Method 7; Figure 3 This is a schematic diagram of the azimuth slice results of the point target obtained by imaging using different methods described in Implementation Method 7. Detailed Implementation

[0019] Various embodiments of the present invention will now be clearly and completely described with reference to the accompanying drawings. The embodiments described with reference to the drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0020] Implementation Method 1: A fast velocity estimation method for spaceborne SAR based on fractional Fourier transform, comprising the following steps: Step 1: Acquire SAR echo data and make a rough estimate of SAR velocity; Step 2: Perform SAR imaging based on SAR echo data, and combine it with the coarsely estimated SAR velocity to obtain a coarsely focused SAR image; Step 3: Use fractional Fourier transform to estimate the residual azimuth modulation frequency of the coarsely focused SAR image. Step 4: Based on the coarse estimate of SAR velocity in Step 1 and the residual azimuth modulation frequency in Step 3, obtain the accurate estimate of SAR velocity.

[0021] In existing technologies, when estimating the velocity of spaceborne SAR, if the estimation results are biased or lack accuracy, it will directly lead to problems such as defocusing and geometric distortion in azimuth focusing during SAR imaging, thereby severely reducing the spatial resolution and target positioning accuracy of the final image. Traditional amplitude-based methods require a large number of iterations to meet the estimation accuracy requirements, significantly increasing computational complexity, while phase-based methods often suffer from long processing times and limited estimation accuracy.

[0022] To address the aforementioned problems, this implementation provides a fast velocity estimation method for spaceborne SAR based on fractional Fourier transform, such as... Figure 1 As shown, firstly, a coarse estimate of velocity is performed using SAR echo data and a hyperbolic model. Secondly, the coarsely estimated velocity is used for imaging, and a fractional Fourier transform is performed on the range cells containing strong point targets in the coarsely focused SAR image. A two-step search method improves the estimation velocity and accuracy of the optimal rotation order of the fractional Fourier transform. Then, the residual azimuth modulation frequency is obtained based on the estimated optimal rotation order, thus obtaining the estimated error velocity. Finally, a precise estimation of the spaceborne SAR velocity is achieved based on the coarsely estimated velocity and the error velocity. This solves the technical problems of low SAR imaging quality due to inaccurate spaceborne SAR velocity estimation in existing technologies, and the high computational complexity, long time consumption, and limited estimation accuracy resulting from using amplitude-based or phase-based methods for spaceborne SAR velocity estimation.

[0023] In this embodiment, the coarse-focused SAR image after imaging using the chirp scaling algorithm is: ,in, This is a coarse-focused SAR image. This is a row and column index variable representing a two-dimensional image.

[0024] Implementation Method Two: This implementation method further defines the fast velocity estimation method for spaceborne SAR based on fractional Fourier transform described in Implementation Method One. Specifically, step 1 involves a coarse estimation of the SAR velocity, which is as follows: Based on the slant range at each azimuth time in the SAR echo data, a coarse estimate of the SAR velocity is obtained through fitting.

[0025] In this embodiment, a coarse estimate of the spaceborne SAR velocity is made based on SAR echo data and a hyperbolic model. The SAR echo data is denoted as... Based on satellite position information from SAR echo data and a hyperbolic model, the spaceborne SAR velocity is roughly estimated. The relationship between the equivalent velocity and slant range in the hyperbolic model is as follows: ; in, For a rough estimate of SAR velocity, For a moment The slope distance, The closest slope distance. This represents the time corresponding to the nearest slant distance.

[0026] Given the slant distance at each azimuth time, the fitting coefficients can be optimized through fitting. The estimation, that is, to achieve a coarse estimate of the SAR velocity. The estimate.

[0027] Implementation Method 3: This implementation method further defines the fast velocity estimation method for spaceborne SAR based on fractional Fourier transform described in Implementation Method 1. Specifically, in step 3, estimating the residual azimuth modulation frequency of the coarsely focused SAR image is as follows: From the coarse-focused SAR image, the range gate corresponding to the strong point target is selected and fractional Fourier transform is performed. Peak search is performed on the fractional Fourier transform result to obtain the optimal rotation order. Based on the optimal rotation order, the residual azimuth modulation frequency is obtained.

[0028] The rotation step size of the fractional Fourier transform is 0.001, and the search range is [-1, 1].

[0029] In the prior art, Chinese patent document CN119205577A discloses "a fine focusing method for SAR images based on fractional Fourier transform". This embodiment inherits some technical points of the SAR fine focusing method. However, in order to solve the problem of rapid velocity estimation of spaceborne SAR, this embodiment does not require range-direction segmentation, but only needs to select a single strong point target in the range direction.

[0030] In this embodiment, the residual azimuth modulation frequency is estimated based on the fractional Fourier transform, from a coarsely focused SAR image. Select the distance gate of the strong point target. Performing a fractional Fourier transform (FrFT) is specifically as follows: ; in, In rotation order Perform a fractional Fourier transform operation below. This is the result of the fractional Fourier transform.

[0031] In this embodiment, a coarse search is set. FrFTThe rotation order step size is 0.001, and the search range is [-1, 1].

[0032] of FrFT Defined as: ; in, For the input time domain signal, for The fractional Fourier transform result, The rotation angle is within the range of , , It is an integer.

[0033] Implementation Method Four: This implementation method further defines the fast velocity estimation method for spaceborne SAR based on fractional Fourier transform described in Implementation Method Three. The optimal rotation order is specifically: Peak search is performed on the fractional Fourier transform results to obtain the optimal rotation order for coarse search. Based on the optimal rotation order of the coarse search, a fractional Fourier transform is performed, and the rotation order corresponding to the maximum value of the fractional Fourier transform result is taken as the optimal rotation order.

[0034] The fractional Fourier transform based on the optimal rotation order of the coarse search is centered on the optimal rotation order of the coarse search. Fractional Fourier transforms are performed within the range with a step size of 0.00001.

[0035] To accurately estimate the velocity of a spaceborne SAR, the search step size of the rotation order of the fractional Fourier transform needs to be small enough. However, if the search step size is too small, it will increase the computational complexity of the search.

[0036] To address the aforementioned technical problems, this embodiment employs a two-step search method: first, a large step is used to locate the range of the optimal rotation order; then, a small step is used to achieve an accurate estimate of the optimal rotation order.

[0037] In this embodiment, Peak search is performed to obtain the optimal rotation order for the coarse search. The optimal rotation order is determined by a rough search. Centered on, in Perform fractional Fourier transforms within the range with a step size of 0.00001, and search for the maximum value of the fractional Fourier transform result to obtain the optimal rotation order for fine-grained searching. Calculating the optimal rotation order using a two-step search strategy—first a coarse search, then a fine search—can improve estimation accuracy and reduce estimation time.

[0038] Implementation Method 5: This implementation method further defines the fast velocity estimation method for spaceborne SAR based on fractional Fourier transform described in Implementation Method 3. Specifically, the residual azimuth modulation frequency is obtained based on the optimal rotation order as follows: Based on the optimal rotation order, the modulation frequency of the residual linear frequency modulated signal is obtained. The azimuth modulation frequency obtained from the rough estimate of velocity Based on the relationship, the residual azimuth modulation frequency is estimated.

[0039] In this embodiment, accurate estimation of spaceborne SAR data is achieved based on coarse velocity estimation and residual azimuth frequency modulation, utilizing the optimal rotation order obtained based on a two-step search method. The modulation frequency of the residual linear frequency modulated signal is obtained. for: ; in, The pulse repetition frequency, This represents the number of azimuth units. This is a modulo dicing operation.

[0040] Residual linear frequency modulation signal for: ; in, For azimuth-time variables, For correctly compressed azimuth linear frequency modulated signals The azimuth modulation frequency is obtained to roughly estimate the velocity. The residual azimuth frequency.

[0041] Frequency modulation of residual linear frequency modulation signal Frequency modulation obtained from coarse speed estimation The relationship is: ; The residual azimuth modulation frequency can be estimated. for: ; Implementation Method Six: This implementation method further defines the fast velocity estimation method for spaceborne SAR based on fractional Fourier transform described in Implementation Method One. Specifically, the accurate estimation of SAR velocity in step 4 is as follows: ; in, For accurate estimation of SAR velocity, For a rough estimate of SAR velocity, The residual azimuth tuning frequency, For wavelength, This represents the slant distance of the strong point target.

[0042] This implementation method accurately estimates the velocity of spaceborne SAR by combining the velocity coarsely estimated by the hyperbolic model and the error velocity estimated by the fractional Fourier transform. It selects typical strong point targets for fractional Fourier transform and improves the estimation accuracy and velocity of spaceborne SAR through a two-step search method. This implementation method has high practicality for high-resolution spaceborne SAR velocity estimation.

[0043] In summary, this implementation method first requires a coarse estimate of the velocity of the spaceborne SAR platform, then establishes the relationship between the velocity estimation error and the imaging result error, and finally obtains the imaging result error through fractional Fourier transform, thereby deducing the velocity estimation error and achieving accurate estimation of the spaceborne SAR platform.

[0044] Implementation Method Seven: This implementation method verifies the effectiveness of any of the methods described in Implementation Methods One to Six by simulating high-resolution spaceborne SAR data. The spaceborne SAR echo simulation parameters are shown in Table 1. The velocity estimation effects of the hyperbolic model method, the maximum contrast method, and the method of this patent are compared.

[0045] Table 1

[0046] Table 2 shows the time required for velocity estimation by different methods. It can be seen that the maximum contrast method takes 300.237s, which is quite long, while this method only takes 175.34s, which is about half the time of the maximum contrast method, greatly reducing the spaceborne SAR velocity estimation time.

[0047] Table 2

[0048] The average velocity estimates obtained by different methods are shown in Table 3. It can be seen that the estimation results of the maximum contrast method and our method are similar, while the results of the rough estimate obtained by the hyperbolic model method differ by about 3.5 m / s.

[0049] Table 3

[0050] The velocity estimation results of different methods are as follows Figure 2 As shown, (a) is the estimation result of the hyperbolic model method; (b) is the estimation result of the maximum contrast method; and (c) is the estimation result of our method. It can be seen that the velocity estimated by all methods changes linearly with azimuth and time. The estimation results of the maximum contrast method and our method are similar, and the difference between them and the result estimated by the hyperbolic model method is about 3.5 m / s.

[0051] Point target azimuth slices obtained by imaging methods are as follows: Figure 3 As shown, (a) is the point target azimuth slice result of the hyperbolic model method; (b) is the point target azimuth slice result of the maximum contrast method; and (c) is the point target azimuth slice result of the proposed method. It can be seen that the velocity estimated based on the hyperbolic model method cannot focus on the point target, while the velocity estimated based on the maximum contrast method and the proposed method can focus on the point target better.

[0052] The focusing performance of point targets is quantitatively evaluated based on the peak sidelobe ratio (PSLR), integral sidelobe ratio (ISLR), and main lobe widening (IRW) indices. As shown in Table 4, the velocity imaging based on the hyperbolic model method has poor focusing effect on point targets and cannot be directly used for SAR imaging. The velocity estimated by this method can be well used for focusing point targets. The PSLR, ISLR, and IRW indices are all better than the maximum contrast method, which verifies the effectiveness of this method.

[0053] Table 4

[0054] Implementation Method 8: A fast velocity estimation system for spaceborne SAR based on fractional Fourier transform, comprising the following modules: Module 1: Acquire SAR echo data and use a hyperbolic model to make a coarse estimate of SAR velocity; Module 2 performs SAR imaging based on SAR echo data to obtain SAR images, and then coarsely focuses the SAR images using a coarsely estimated SAR velocity. Module 3 uses fractional Fourier transform to estimate the residual azimuth frequency of the coarsely focused SAR image. Module 4, based on the coarse estimate of SAR velocity described in Module 1 and the residual azimuth modulation frequency described in Module 3, obtains a precise estimate of SAR velocity.

[0055] Implementation Method Nine: A computer program product, comprising a computer program or instructions, which, when executed by a processor, implements any of the above-described methods for rapid estimation of spaceborne SAR velocity based on fractional Fourier transform.

[0056] The foregoing has provided a detailed description of the fast velocity estimation method, system, and product for spaceborne SAR based on fractional Fourier transform proposed in this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A fast velocity estimation method for spaceborne SAR based on fractional Fourier transform, characterized in that, Includes the following steps: Step 1: Acquire SAR echo data and make a rough estimate of SAR velocity; Step 2: Perform SAR imaging based on SAR echo data, and combine it with the coarsely estimated SAR velocity to obtain a coarsely focused SAR image; Step 3: Use fractional Fourier transform to estimate the residual azimuth modulation frequency of the coarsely focused SAR image. Step 4: Based on the coarse estimate of SAR velocity in Step 1 and the residual azimuth modulation frequency in Step 3, obtain the accurate estimate of SAR velocity.

2. The method for fast velocity estimation of spaceborne SAR based on fractional Fourier transform according to claim 1, characterized in that, The coarse estimation of SAR velocity in step 1 is as follows: Based on the slant range at each azimuth time in the SAR echo data, a coarse estimate of the SAR velocity is obtained through fitting.

3. The method for fast estimation of spaceborne SAR velocity based on fractional Fourier transform according to claim 1, characterized in that, In step 3, estimating the residual azimuth modulation frequency of the coarsely focused SAR image specifically involves: From the coarse-focused SAR image, the range gate corresponding to the strong point target is selected and fractional Fourier transform is performed. Peak search is performed on the fractional Fourier transform result to obtain the optimal rotation order. Based on the optimal rotation order, the residual azimuth modulation frequency is obtained.

4. The method for fast estimation of spaceborne SAR velocity based on fractional Fourier transform according to claim 3, characterized in that, The rotation step size of the fractional Fourier transform is 0.001, and the search range is [-1, 1].

5. The method for fast velocity estimation of spaceborne SAR based on fractional Fourier transform according to claim 3, characterized in that, The optimal rotation order is specifically: Peak search is performed on the fractional Fourier transform results to obtain the optimal rotation order for coarse search. Based on the optimal rotation order of the coarse search, a fractional Fourier transform is performed, and the rotation order corresponding to the maximum value of the fractional Fourier transform result is taken as the optimal rotation order.

6. The method for fast velocity estimation of spaceborne SAR based on fractional Fourier transform according to claim 5, characterized in that, The fractional Fourier transform based on the optimal rotation order of the coarse search is centered on the optimal rotation order of the coarse search. Fractional Fourier transforms are performed within the range with a step size of 0.00001.

7. The method for fast estimation of spaceborne SAR velocity based on fractional Fourier transform according to claim 3, characterized in that, The residual azimuth tuning frequency, obtained based on the optimal rotation order, is specifically as follows: Based on the optimal rotation order, the modulation frequency of the residual linear frequency modulated signal is obtained. The azimuth modulation frequency obtained from the rough estimate of velocity Based on the relationship, the residual azimuth modulation frequency is estimated.

8. The fast velocity estimation method for spaceborne SAR based on fractional Fourier transform according to claim 1, characterized in that, The precise estimation of SAR velocity in step 4 is specifically as follows: ； in, For accurate estimation of SAR velocity, For a rough estimate of the SAR velocity, For residual azimuth tuning frequency, For wavelength, This represents the slant distance of the strong point target.

9. A fast velocity estimation system for spaceborne SAR based on fractional Fourier transform, characterized in that, Includes the following modules: Module 1: Acquire SAR echo data and use a hyperbolic model to make a coarse estimate of SAR velocity; Module 2 performs SAR imaging based on SAR echo data and combines it with a coarsely estimated SAR velocity to obtain a coarsely focused SAR image. Module 3 uses fractional Fourier transform to estimate the residual azimuth frequency of the coarsely focused SAR image. Module 4, based on the coarse estimate of SAR velocity described in Module 1 and the residual azimuth modulation frequency described in Module 3, obtains a precise estimate of SAR velocity.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by the processor, they implement the fast spaceborne SAR velocity estimation method based on fractional Fourier transform as described in any one of claims 1-8.

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