Range-squint motion compensation method for synthetic aperture radar based on linear scaling

Abstract

The application provides a synthetic aperture radar range-aperture space-variant motion compensation method based on linear scaling, which adopts the first step of consistent compensation in two-step motion compensation to compensate for main distance non-space-variant motion error components of panoramic echo, obtains distance pulse pressure target migration curve image data, calculates sub-aperture bandwidth parameters by using image minimum defocus principle, and first-order Taylor expansion of residual range-aperture space-variant error, further introduces linear scaling in two-dimensional time domain to compensate for constant components and linear components, synchronously completes residual azimuth phase error compensation, finally splices sub-aperture data time domain to form ideal echo data without motion error, and outputs final panoramic image through traditional imaging processing. The application realizes high-precision residual range-aperture space-variant motion error compensation, has simple principle, is suitable for airborne and missile-borne platforms with complex trajectories, has high accuracy and strong robustness, and has high practicability.

Description

Technical Field

[0001] This invention relates to the field of motion error compensation for missile-borne synthetic aperture radar, and particularly to a range-aperture space-varying motion compensation method for synthetic aperture radar based on linear scaling. Background Technology

[0002] Synthetic Aperture Radar (SAR) is a two-dimensional high-resolution imaging radar. As an active microwave remote sensing device, SAR relies on its own microwave radiation to operate, making it less susceptible to adverse weather and electromagnetic conditions on the battlefield. It boasts the advantage of all-weather, all-day operation and is widely used in airborne, spaceborne, and missile-borne platforms, providing new solutions for applications such as terrain matching, mountain disaster monitoring, and target detection and identification. While digital scene matching navigation modes are susceptible to adverse weather conditions, darkness, smoke, rain, and dust, SAR can obtain two-dimensional high-resolution and high-contrast radar images, making it an effective way to improve the accuracy of precision-guided weapons. However, SAR also faces some challenges in practical applications, especially for airborne / missile-borne SAR. During target illumination, airflow, instability in its own trajectory, and the non-linearity of the ballistic trajectory can cause motion errors, resulting in target displacement and energy leakage in the range direction and defocusing in the azimuth direction, thus degrading image quality.

[0003] Motion errors cause instantaneous slant range variations between radar and targets, exhibiting range spatial variability, azimuth spatial variability, and aperture spatial variability. Based on this, many researchers have addressed these three issues to varying degrees from different perspectives, including echo and image analysis. For example, Sandia Labs abroad has employed a strategy of first reducing range resolution, limiting target range-position offset across range gates, and then introducing azimuth autofocus to solve the problem of inaccurate motion error estimation. However, the compensation performance deteriorates significantly in high-resolution and ultra-high-resolution systems. Professor P. Prats, starting from the temporal sub-aperture, has adopted a strategy of consistently compensating the entire sub-aperture based on motion errors at the time center, which has addressed the aperture spatial variability problem to some extent. However, the compensation performance deteriorates under complex and rapidly changing trajectories. KACamara de The Macedo research team started with image autofocus and solved the problems of azimuth and aperture spatial variation by estimating motion error in reverse by estimating phase error. However, under complex trajectories, the image is severely defocused, the autofocus accuracy decreases, and the estimation error increases sharply. In addition, in China, the research team of the Institute of Electronics, Chinese Academy of Sciences, solved the problems of aperture and azimuth spatial variation by starting from the echo frequency domain and compensating for motion error corresponding to sub-frequency bands in segments. However, this strategy requires precise sub-frequency band division and is prone to paired echoes (i.e., ghosting). The research team of Zhu Daiyin at Nanjing University of Aeronautics and Astronautics solved the problems of range and azimuth spatial variation by starting from the analytical formula of echo slant range error and correcting the envelope after range pulse compression by pulse-by-pulse and sampling point-by-sampling point. However, this algorithm has a large computational load and is prone to envelope error after calibration at ultra-high resolution. Summary of the Invention

[0004] The purpose of this invention is to provide a synthetic aperture radar range-aperture spatial variation motion compensation method based on linear scaling. The method uses linear scaling to quickly solve the residual range-aperture spatial variation operation error after consistent compensation, thereby improving the phase error compensation accuracy.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0006] A method for range-aperture spatially variable motion compensation in synthetic aperture radar based on linear scaling includes the following steps:

[0007] S1: Perform range non-space variation compensation and range pulse compression processing on the panoramic SAR echo data to generate a coarsely compensated target migration curve image;

[0008] S2: Based on the radar northeast sky GPS position data, perform coarse compensation and image Doppler spectrum sub-band segmentation, fill with zeros, and perform inverse Fourier transform to return a two-dimensional time domain image;

[0009] S3: Based on the radar-target geometry and GPS position information, perform the analytical relationship between aperture and instantaneous slant angle, and calculate the Doppler slant range error at all azimuth times;

[0010] S4: Based on the slant range error of the distance-aperture air variable, the center distance is Taylor expanded to the first term, and linear scaling is used to complete the residual distance-aperture air variable motion error compensation.

[0011] S5: After performing motion compensation as described in S3 and S4 on all sub-apertures, the echo data without motion error is output after being added and synthesized in the two-dimensional time domain. Traditional imaging processing is then performed to output a SAR panoramic image.

[0012] In step S1, the coarse compensation for non-space variation is completed using a two-step motion compensation method, including:

[0013] Assuming panoramic SAR echo data is represented by ss(k,r′), where k represents the accumulated pulse number and r′ represents the range sampling coordinates, its analytical expression is:

[0014]

[0015] Where A is the echo signal amplitude, exp(·) is the natural exponential function; j is the imaginary unit; λ is the wavelength of the transmitted signal; K0 = 4πk r / c 2 k r The frequency modulation slope of the emitted signal is the distance, c is the speed of light, and r is the speed of light. a (k,r,θ k ) represents the slant range between the missile and the target on the actual trajectory, and r is the target's zero Doppler surface distance; r a (k,r,θ k (Including the slant distance r of the projectile and target under the ideal straight trajectory) n (k,r), and the slant range error caused by motion error is Δr(k,r,θ). k ), where θ k The instantaneous oblique angle is Δr(k,r,θ). k It has aperture-dependent properties;

[0016] Non-space variable distance compensation is achieved through a two-step motion compensation algorithm, in which θ is ignored. k and Δr(k,r,θ) k The error is decomposed into the variable slant range error Δr. v (k,r|r0) and non-vacuum variable slant range error Δr c (k,r0), where r0 is the reference distance; based on the above, r a (k,r,θ k Then it can be transformed as follows:

[0017] r a (k,r,θ k ) = r n(k,r)+Δr(k,r,θ k )

[0018] ≈r n (k,r)+Δr(k,r|θ k =0)

[0019] ≈r n (k,r)+Δr c (k,r0)+Δr v (k,r|r0)

[0020] Based on radar-based northeast-sky GPS location information, Δr c (k,r0) is calculated as follows:

[0021]

[0022] Where Δy represents the radar's eastward motion error, Δx represents the northward motion error, Δz represents the celestial motion error, and H is the ideal flight altitude; for simplicity, r a (k,r,θ k ), r n (k,r), Δr c (k,r0), Δr v (k,r|r0) are respectively represented by r a r n , Δr c and Δr v Therefore, the range-frequency domain range-direction non-space-varying compensation function is:

[0023] Where f0 is the carrier frequency, f r For range-direction frequency;

[0024] Range pulse compression is performed on the coarsely compensated echo signal, and the two-dimensional time-domain image is as follows:

[0025]

[0026] in T p It is the pulse width of the transmitted signal;

[0027] In step S2, the sub-aperture bandwidth is calculated based on the minimum defocus criterion of the image. The specific description of the sub-aperture segmentation constraints is as follows:

[0028] Based on coarse compensation SS c (k,r′) is subjected to a slow-time Fourier transform to enter the range-Doppler domain, and the entire Doppler frequency band is divided into sub-apertures. The division is based on the fact that the residual slant range error corresponding to the frequencies on both sides of the sub-aperture is less than one-quarter of the wavelength. Therefore, the sub-aperture bandwidth ΔB is constrained as follows:

[0029]

[0030] Where v is the equivalent ground velocity of the radar platform; θ BW Beamwidth; PRF is the pulse repetition frequency;

[0031] After performing sub-aperture division and inverse Fourier transform, using The Doppler center frequency is f d A two-dimensional time-domain signal with a bandwidth of ΔB;

[0032] Step S3 calculates the analytical relationship between the sub-aperture center frequency and the instantaneous oblique angle of the target, as described in detail below:

[0033] Based on radar-target geometry, the Doppler center f d The analytical relationship between the corresponding sub-aperture and the instantaneous angle of view of the radar and the target is as follows:

[0034]

[0035] in It is the actual oblique angle, θ k ′ is the slant angle when there is no lateral motion error. The condition for the above equation to hold is the actual slant range r between the radar and the target. a >>Δx,Δy,Δz;

[0036] Furthermore, calculate sinθ k ′ and instantaneous migration factor cosθ k ′:

[0037]

[0038] Based on the above formula and the GPS position of the radar platform in the northeast sky, after coarse compensation... The residual distance-aperture spatially variable slant range error Δr at any azimuth and time is:

[0039]

[0040] In step S4, the distance-aperture air-variable slant range error compensation based on linear scaling is described in detail below:

[0041] Δr exhibits a distance-aperture spatially variable property; its distance-Taylor expansion is performed.

[0042] Δr=Δr(k,r′=r0)+Δα(k,r0)·(r′-r0)

[0043] Where Δα is the first-order Taylor expansion coefficient of Δr at r′=r0, and its analytical expression is:

[0044]

[0045] For the expression of Δr, the correction based on linear scaling mainly consists of the following four steps:

[0046] Step 1: First, compensate for the constant term in Δr to construct an azimuth time-domain-range frequency compensation filter.

[0047]

[0048] Step 2: Compensate for the linear terms in Δr and construct a linear scaling filter in the two-dimensional time domain.

[0049]

[0050] Step 3: Eliminate the redundant phase error introduced by the scaling filter by constructing a redundant phase error elimination filter in the two-dimensional time domain.

[0051]

[0052] Step 4: Eliminate residual range-aperture Doppler phase error by constructing a residual Doppler phase error filter in the two-dimensional time domain.

[0053]

[0054] in

[0055] Optionally, in step S5, sub-aperture splicing is performed, including:

[0056] After each sub-aperture data segment is compensated, it has the same size as the panoramic image. Sub-aperture stitching is performed by adding the sub-apertures in the two-dimensional time domain. At this point, the traditional range-Doppler imaging method can be directly called, or the traditional wavenumber imaging method can be called after range decompression to output a panoramic synthetic aperture radar image.

[0057] Compared with the prior art, the present invention has the following advantages:

[0058] (1) This invention can quickly achieve distance spatial variation error compensation without distance segmentation, and targets far from the reference center can still be accurately focused;

[0059] (2) The present invention completes all motion error compensation before traditional imaging processing, which has the advantage of not changing the original processing system and can be applied quickly. Attached Figure Description

[0060] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the drawings described below are one embodiment of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort:

[0061] Figure 1 This is a structural diagram of a semiconductor processing device provided in an embodiment of the present invention;

[0062] Figure 2 A schematic diagram of the radar-target geometric relationship under the presence of motion errors.

[0063] Figure 3 This is a schematic diagram of a simulation test scenario;

[0064] Figure 4 A schematic diagram of the northeast celestial motion error added to the simulation experiment;

[0065] Figure 5 The image shows a comparison of the target distance migration curves after distance-aperture spatial variation error correction between the traditional two-step motion compensation method (first row) and the method proposed in this invention (second row). In the image, (a) and (d) represent the addition of northeast celestial motion error in the simulation test for T1, (b) and (e) represent the addition of northeast celestial motion error in the simulation test for T0, and (c) and (f) represent the addition of northeast celestial motion error in the simulation test for T2.

[0066] Figure 6 In the table, (a) and (b) represent the range and azimuth spread functions of T1 to the point target, respectively; (c) and (d) represent the range and azimuth spread functions of T0 to the point target, respectively; and (e) and (f) represent the range and azimuth spread functions of T2 to the point target, respectively. Detailed Implementation

[0067] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer from the following description. It should be noted that the drawings are in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0068] The technical approach of this invention is as follows: The first step of the "two-step motion compensation" process is to consistently compensate for the main non-space-varying motion error components of the panoramic echo, thereby obtaining target migration curve image data after range pulse compression. Then, the sub-aperture bandwidth parameter is calculated using the minimum defocus criterion of the image, and the residual range-aperture spatially varying error is subjected to a first-order Taylor expansion. Furthermore, linear scaling is introduced in the two-dimensional time domain to compensate for constant and linear components, and residual azimuth phase error compensation is completed simultaneously. Finally, the sub-aperture data is added and stitched together in the time domain to form ideal echo data without motion error, and the final panoramic image is output through traditional imaging processing.

[0069] Please refer to Figure 1 The present invention provides a range-aperture spatially variable motion compensation method for synthetic aperture radar based on linear scaling, comprising the following steps:

[0070] S1: Perform range non-space variation compensation and range pulse compression processing on the panoramic SAR echo data to generate a coarsely compensated target migration curve image;

[0071] S2: Based on the radar northeast sky GPS position data, perform coarse compensation and image Doppler spectrum sub-band segmentation, fill with zeros, and perform inverse Fourier transform to return a two-dimensional time domain image;

[0072] S3: Based on the radar-target geometry and GPS position information, perform the analytical relationship between aperture and instantaneous slant angle, and calculate the Doppler slant range error at all azimuth times;

[0073] S4: Based on the slant range error of the distance-aperture air variable, the center distance is Taylor expanded to the first term, and linear scaling is used to complete the residual distance-aperture air variable motion error compensation.

[0074] S5: After performing motion compensation as described in S3 and S4 on all sub-apertures, the echo data without motion error is output after being added and synthesized in the two-dimensional time domain. Traditional imaging processing is then performed to output a SAR panoramic image.

[0075] Specifically, in step S1, the coarse compensation for non-void variation of distance is completed using the two-step motion compensation method (TSMC), which includes:

[0076] Assuming panoramic SAR echo data is represented by ss(k,r′), where k represents the accumulated pulse number and r′ represents the range sampling coordinates, its analytical expression is:

[0077]

[0078] Where A is the echo signal amplitude, exp(·) is the natural exponential function; j is the imaginary unit; λ is the wavelength of the transmitted signal; K0 = 4πk r / c2 k r The frequency modulation slope of the emitted signal is the distance, c is the speed of light, and r is the speed of light. a (k,r,θ k ) represents the slant range between the missile and the target on the actual trajectory, and r is the target's zero Doppler surface distance; r a (k,r,θ k (Including the slant distance r of the projectile and target under the ideal straight trajectory) n (k,r), and the slant range error caused by motion error is Δr(k,r,θ). k ), where θ k The instantaneous oblique angle is Δr(k,r,θ). k It has aperture-dependent properties;

[0079] Non-space variable distance compensation is achieved through a two-step motion compensation algorithm. θ is ignored in the TSMC algorithm. k and Δr(k,r,θ) k The error is decomposed into the variable slant range error Δr. v (k,r|r0) and non-vacuum variable slant range error Δr c (k,r0), where r0 is the reference distance; based on the above, r a (k,r,θ k Then it can be transformed as follows:

[0080] r a (k,r,θ k ) = r n (k,r)+Δr(k,r,θ k )

[0081] ≈r n (k,r)+Δr(k,r|θ k =0)

[0082] ≈r n (k,r)+Δr c (k,r0)+Δr v (k,r|r0)

[0083] Based on radar-based northeast-sky GPS location information, Δr c (k,r0) is calculated as follows:

[0084]

[0085] Where Δy represents the radar's eastward motion error, Δx represents the northward motion error, Δz represents the celestial motion error, and H is the ideal flight altitude; for simplicity, unless otherwise specified, r a (k,r,θ k ), r n (k,r), Δr c(k,r0), Δr v (k,r|r0) are respectively represented by r a r n , Δr c and Δr v Therefore, the range-frequency domain range-direction non-space-varying compensation function is:

[0086] Where f0 is the carrier frequency, f r For range-direction frequency;

[0087] Range pulse compression is performed on the coarsely compensated echo signal, and the two-dimensional time-domain image is as follows:

[0088]

[0089] in T p It is the pulse width of the transmitted signal.

[0090] In step S2, the sub-aperture bandwidth is calculated based on the minimum defocus criterion of the image. The specific description of the sub-aperture segmentation constraints is as follows:

[0091] Based on coarse compensation SS c (k,r′) is subjected to a slow-time Fourier transform to enter the range-Doppler domain, and the entire Doppler frequency band is divided into sub-apertures. The division is based on the fact that the residual slant range error corresponding to the frequencies on both sides of the sub-aperture is less than one-quarter of the wavelength. Therefore, the sub-aperture bandwidth ΔB is constrained as follows:

[0092]

[0093] Where v is the equivalent ground velocity of the radar platform; θ BW Beamwidth; PRF is the pulse repetition frequency;

[0094] After performing sub-aperture division and inverse Fourier transform, using The Doppler center frequency is f d A two-dimensional time-domain signal with a bandwidth of ΔB.

[0095] In step S3, the analytical relationship between the sub-aperture center frequency and the instantaneous oblique angle of the target is calculated, as described below:

[0096] According to the attached Figure 2 The radar-target geometry shown, with the Doppler center f d The analytical relationship between the corresponding sub-aperture and the instantaneous angle of view of the radar and the target is as follows:

[0097]

[0098] in It is the actual oblique angle, θ k ′ is the slant angle when there is no lateral motion error. The condition for the above equation to hold is the actual slant range r between the radar and the target. a >>Δx,Δy,Δz, since r a The values ​​are in the tens or hundreds of kilometers range, while Δx, Δy, and Δz are in the meters range, so the above formula holds true in most cases.

[0099] Furthermore, calculate sinθ k ′ and instantaneous migration factor cosθ k ′:

[0100]

[0101] Based on the above formula and the GPS position of the radar platform in the northeast sky, after coarse compensation... The residual distance-aperture spatially variable slant range error Δr at any azimuth and time is:

[0102]

[0103] In step S4, the distance-aperture air-variable slant range error compensation based on linear scaling is described in detail below:

[0104] From the above equation, we can see that Δr is not only related to the aperture (θ) k ′), and also related to distance (r) n It is related to the distance-aperture spatial variation characteristics, and its distance-Taylor expansion is performed.

[0105] Δr=Δr(k,r′=r0)+Δα(k,r0)·(r′-r0)

[0106] Where Δα is the first-order Taylor expansion coefficient of Δr at r′=r0, and its analytical expression is:

[0107]

[0108] For the expression of Δr, the correction based on linear scaling mainly consists of the following four steps:

[0109] Step 1: First, compensate for the constant term in Δr to construct an azimuth time-domain-range frequency compensation filter.

[0110]

[0111] Step 2: Compensate for the linear terms in Δr and construct a linear scaling filter in the two-dimensional time domain.

[0112]

[0113] Step 3: Eliminate the redundant phase error introduced by the scaling filter by constructing a redundant phase error elimination filter in the two-dimensional time domain.

[0114]

[0115] Step 4: Eliminate residual range-aperture Doppler phase error by constructing a residual Doppler phase error filter in the two-dimensional time domain.

[0116]

[0117] in

[0118] In step S5, sub-aperture splicing is performed, as described in detail below:

[0119] After each sub-aperture data segment is compensated, it has the same size as the panoramic image. Sub-aperture stitching is performed by adding the sub-apertures in the two-dimensional time domain. At this point, the traditional range-Doppler imaging method can be directly called, or the traditional wavenumber imaging method can be called after range decompression to output a panoramic synthetic aperture radar image.

[0120] A specific embodiment of the present invention is as follows:

[0121] Step 1: Based on the parameters in Table 1 and the location of the Northeast Sky Radar, the slant range error of target T0 at the center of the scene is calculated. Range-direction consistency compensation and range-direction pulse compression are performed in the range-frequency-azimuth time domain to obtain the target migration curve image after coarse compensation.

[0122] Step 2: Perform an azimuth-to-Fourier transform on the output image from Step 1 to enter the range-Doppler domain. Calculate the sub-aperture bandwidth according to the minimum defocus criterion for the image. It can be found that the bandwidth of each sub-aperture needs to be less than 2.32Hz. In this experiment, 2.13Hz is used. There are a total of 313 sub-aperture data segments. After completing the sub-aperture segmentation of the full Doppler spectrum, zero-padding is applied to each sub-aperture segment to the full aperture length. The image is then returned to the two-dimensional time domain through an inverse Fourier transform.

[0123] Step 3: Based on the radar-target geometric relationship and GPS location information, calculate the analytical expression of the instantaneous slant angle for each segment of sub-aperture data, and simultaneously calculate the residual slant range error corresponding to the Doppler center (i.e., aperture dependent).

[0124] Step 4: Based on the slant range error in Step 3, perform Taylor expansion of the center distance to the first term, and use linear scaling to complete the range envelope correction and azimuth phase error compensation;

[0125] Step 5: After completing motion compensation for all sub-apertures, the echo data without motion error is output after being added and synthesized in the two-dimensional time domain. Traditional chirp scaling imaging processing is then performed to output a SAR panoramic image.

[0126] The effects of this invention are further illustrated by the following simulation experiments.

[0127] 1) Simulation conditions

[0128] As attached Figure 3 As shown, the imaging scene is set as a "one"-shaped scene consisting of three targets, with the three targets in the surrounding area. Figure 3 The numbers 0, 1, and 2 represent the distances between adjacent targets, with an interval of 80 meters, a scene distance from the center of the scene set to 1000 meters, and an azimuth center set to 3000 meters. The eastward (y-axis), northward (x-axis), and upward (z-axis) motion errors occurring during echo data acquisition are shown in the attached figure. Figure 3 As shown in Table 1, the simulation parameters of the radar system are shown in Table 2, and the motion error of the radar in the northeast direction during the acquisition process is shown in the appendix. Figure 4 As shown, the maximum positional error in the east direction is 2.5m, the maximum positional error in the sky direction is 3m, and the maximum positional error in the north direction is -2.6m.

[0129] Table 1

[0130]

[0131] 2) Simulation content and result analysis

[0132] After all sub-aperture data were compensated and stitched together, the distance migration curves of the three targets are shown in the attached figure. Figure 5 As shown. The first row, from left to right, represents the migration curves of T1, T0, and T2 after TSMC processing. It can be observed that reference T0 achieves good migration compensation, but T1 and T2 still exhibit positional migration due to the range-aperture slant distance error. The second row, from left to right, represents the target migration curves after processing by this invention. It can be observed that all targets are corrected to their respective range cells, and all motion errors are fully compensated. (Appendix) Figure 6The image presents the range and azimuth point spread functions (PSFs) of targets T1, T0, and T2 after processing by TSMC and the method of this invention. It is evident that due to the incompleteness of TSMC in addressing the range-aperture spatially varying slant range error, targets T1 and T2 exhibit energy diffusion in the range direction and defocusing in the azimuth direction. Quantitative results are shown in Table 2 below. In this simulation experiment, resolution, peak sidelobe ratio (PSLR), and integral sidelobe ratio (ISLR) were used to measure the motion compensation accuracy. Since the image range resolution (non-system resolution) is 0.95m and the azimuth resolution is 0.15m, it can be observed that after processing by this invention, all targets achieve the set resolution, while the TSMC method exhibits resolution degradation; for example, the range resolution of T2 is only 1.3m, and the azimuth resolution is only 0.23m. Regarding PSLR and ISLR, after TSMC processing, the T2 azimuth PSLR was -11.98dB and ISLR was -6.3dB. After processing with this invention, they were improved to -13.49dB and -7.8dB respectively, showing a significant improvement.

[0133] Table 2

[0134]

[0135] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for range-aperture spatially variable motion compensation in synthetic aperture radar based on linear scaling, characterized in that, Includes the following steps: S1: Perform range non-space variation compensation and range pulse compression processing on the panoramic SAR echo data to generate a coarsely compensated target migration curve image; S2: Based on the radar northeast sky GPS position data, perform coarse compensation and image Doppler spectrum sub-band segmentation, fill with zeros, and perform inverse Fourier transform to return a two-dimensional time domain image; S3: Based on the radar-target geometry and GPS position information, perform the analytical relationship between aperture and instantaneous slant angle, and calculate the Doppler slant range error at all azimuth times; S4: Based on the slant range error of the distance-aperture air variable, the center distance is Taylor expanded to the first term, and linear scaling is used to complete the residual distance-aperture air variable motion error compensation. S5: After performing motion compensation as described in S3 and S4 on all sub-apertures, the echo data without motion error is output after being added and synthesized in the two-dimensional time domain. Traditional imaging processing is then performed to output a SAR panoramic image. In step S1, the coarse compensation for non-space variation is completed using a two-step motion compensation method, including: Assuming panoramic SAR echo data is represented by ss(k,r′), where k represents the accumulated pulse number and r′ represents the range sampling coordinates, its analytical expression is: Where A is the echo signal amplitude, exp(·) is the natural exponential function; j is the imaginary unit; λ is the wavelength of the transmitted signal; K0 = 4πk r / c 2 k r The frequency modulation slope of the emitted signal is the distance, c is the speed of light, and r is the speed of light. a (k,r,θ k ) represents the slant range between the missile and the target on the actual trajectory, and r is the target's zero Doppler surface distance; r a (k,r,θ k (Including the slant distance r of the projectile and target under the ideal straight trajectory) n (k,r), and the slant range error caused by motion error is Δr(k,r,θ). k ), where θ k The instantaneous oblique angle is Δr(k,r,θ). k It has aperture-dependent properties; Non-space variable distance compensation is achieved through a two-step motion compensation algorithm, in which θ is ignored. k and Δr(k,r,θ) k The error is decomposed into the variable slant range error Δr. v (k,r|r0) and non-vacuum variable slant range error Δr c (k,r0), where r0 is the reference distance; based on the above, r a (k,r,θ k Then it can be transformed as follows: r a (k,r,θ k )=r n (k,r)+Δr(k,r,θ k ) ≈r n (k,r)+Δr(k,r|θ k (=0) ≈r n (k,r)+Δr c (k,r0)+Δr v (k,r|r0) Based on radar-based northeast-sky GPS location information, Δr c (k,r0) is calculated as follows: Where Δy represents the radar's eastward motion error, Δx represents the northward motion error, Δz represents the celestial motion error, and H is the ideal flight altitude; for simplicity, r a (k,r,θ k ), r n (k,r), Δr c (k,r0), Δr v (k,r|r0) are respectively represented by r a r n Δr c and Δr v Therefore, the range-frequency domain range-direction non-space-variable compensation function is: Where f0 is the carrier frequency, f r For range-direction frequency; Range pulse compression is performed on the coarsely compensated echo signal, and the two-dimensional time-domain image is as follows: in T p It is the pulse width of the transmitted signal; In step S2, the sub-aperture bandwidth is calculated based on the minimum defocus criterion of the image. The specific description of the sub-aperture segmentation constraints is as follows: Based on coarse compensation SS c (k,r′) is subjected to a slow-time Fourier transform to enter the range-Doppler domain, and the entire Doppler frequency band is divided into sub-apertures. The division is based on the fact that the residual slant range error corresponding to the frequencies on both sides of the sub-aperture is less than one-quarter of the wavelength. Therefore, the sub-aperture bandwidth ΔB is constrained as follows: Where v is the equivalent ground velocity of the radar platform; θ BW Beamwidth; PRF is the pulse repetition frequency; After performing sub-aperture division and inverse Fourier transform, using The Doppler center frequency is f d A two-dimensional time-domain signal with a bandwidth of ΔB; Step S3 calculates the analytical relationship between the sub-aperture center frequency and the instantaneous oblique angle of the target, as described in detail below: Based on radar-target geometry, the Doppler center f d The analytical relationship between the corresponding sub-aperture and the instantaneous angle of view of the radar and the target is as follows: in It is the actual oblique angle, θ k ′ is the slant angle when there is no lateral motion error. The condition for the above equation to hold is the actual slant range r between the radar and the target. a >>Δx,Δy,Δz; Furthermore, calculate sinθ k ′ and instantaneous migration factor cosθ k ′: Based on the above formula and the GPS position of the radar platform in the northeast sky, after coarse compensation... The residual distance-aperture spatially variable slant range error Δr at any azimuth and time is: In step S4, the distance-aperture air-variable slant range error compensation based on linear scaling is described in detail below: Δr exhibits a distance-aperture spatially variable property; its distance-Taylor expansion is performed. Δr=Δr(k,r′=r0)+Δα(k,r0)·(r′-r0) Where Δα is the first-order Taylor expansion coefficient of Δr at r′=r0, and its analytical expression is: For the expression of Δr, the correction based on linear scaling mainly consists of the following four steps: Step 1: First, compensate for the constant term in Δr to construct an azimuth time-domain-range frequency compensation filter. Step 2: Compensate for the linear terms in Δr and construct a linear scaling filter in the two-dimensional time domain. Step 3: Eliminate the redundant phase error introduced by the scaling filter by constructing a redundant phase error elimination filter in the two-dimensional time domain. Step 4: Eliminate residual range-aperture Doppler phase error by constructing a residual Doppler phase error filter in the two-dimensional time domain. in 2. The method for range-aperture spatially variable motion compensation of synthetic aperture radar based on linear scaling according to claim 1, characterized in that, In step S5, sub-aperture splicing is performed, as described in detail below: After each sub-aperture data segment is compensated, it has the same size as the panoramic image. Sub-aperture stitching is performed by adding the sub-apertures in the two-dimensional time domain. At this point, the traditional range-Doppler imaging method can be directly called, or the traditional wavenumber imaging method can be called after range decompression to output a panoramic synthetic aperture radar image.

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