A High-Resolution Spaceborne SAR Curved Orbit Compensation Method Based on Spatial Motion Compensation

Abstract

This invention provides a high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation. Addressing the problem of insufficient accuracy in hyperbolic range models in high-resolution spaceborne SAR systems due to satellite motion along curved orbits, the method first divides the echo signal into sub-apertures in the azimuth time domain. Then, in the azimuth Doppler domain, it performs range-gate motion compensation on each pulse within each sub-aperture, thereby compensating the satellite's motion along the curved orbit into uniform linear motion along an ideal track. This method offers high compensation accuracy and excellent performance, ensuring focusing quality for both range-oriented and azimuth-oriented targets at scene edges.

Description

Technical Field

[0001] This invention relates to a method for compensating for curved orbits in spaceborne SAR, which is applied to high-resolution / ultra-high-resolution spaceborne SAR imaging processing and belongs to the field of space microwave radar signal processing. Background Technology

[0002] Synthetic aperture radar (SAR) is a two-dimensional, high-resolution microwave remote sensing device. By controlling the direction of the antenna beam, SAR can effectively overcome the limitations of radar antenna size on azimuth resolution.

[0003] Currently, most satellite systems in orbit are low-Earth orbit (LEO) systems with altitudes below 1000 kilometers. Given the low azimuth resolution of these systems, i.e., short synthetic aperture accumulation (SAP) times, the satellite's motion along a curved trajectory during the SAP accumulation time can be approximated as uniform linear motion. Therefore, the hyperbolic distance model can be used to approximate the change in instantaneous slant range between the satellite and the target. In other words, traditional imaging algorithms based on the hyperbolic distance model can meet the imaging needs of low-resolution LEO satellites. However, as the resolution of spaceborne SAR systems continues to improve and the SAP accumulation time increases, the satellite's motion along a curved trajectory during the SAP accumulation time can no longer be approximated as uniform linear motion. Therefore, continuing to use the hyperbolic distance model to approximate the change in instantaneous slant range between the satellite and the target will introduce significant errors, affecting the final focusing effect on the target.

[0004] Currently, there are two main types of methods widely used to address the insufficient accuracy of hyperbolic distance models. The first type involves deriving a more accurate distance model to replace the hyperbolic distance model and then improving traditional imaging algorithms based on this model to achieve high-precision processing of spaceborne SAR data. However, this derivation process is complex, the results are cumbersome, and its applicability is poor, thus it has not been widely adopted. The second type compensates for the satellite's motion along a curved trajectory to a uniform linear motion along an ideal track, thus facilitating subsequent high-precision processing of spaceborne SAR data using traditional imaging algorithms. However, existing curved trajectory compensation methods based on one-step motion compensation and two-step motion compensation do not consider the impact of the spatial variation characteristics of the azimuth error, which leads to a deterioration in the focusing quality of targets at the edge of the azimuth scene. Summary of the Invention

[0005] The technical problem solved by this invention is to address the insufficient accuracy of hyperbolic range models in high-resolution spaceborne SAR processing, and to provide a curved trajectory compensation method based on spatially variable motion compensation. Compared with curved trajectory compensation methods based on one-step motion compensation and two-step motion compensation, the high-resolution spaceborne SAR curved trajectory compensation method based on spatially variable motion compensation can not only compensate for spatially variable slant range errors, but also compensate for the spatially variable characteristics of slant range errors by utilizing azimuth molecular apertures and performing motion compensation pulse by pulse within the azimuth Doppler domain. This method can better ensure the focusing effect of edge targets in the azimuth scene.

[0006] The technical solutions provided by the present invention are as follows:

[0007] Firstly, a high-resolution spaceborne SAR curved orbit compensation method based on spatially variable motion compensation includes the following steps:

[0008] S1. The echo signal after range pulse compression is segmented in the azimuth time domain to divide it into sub-apertures.

[0009] S2. Using the position of the radar platform at the center of the sub-aperture and the instantaneous Doppler frequency at any azimuth time pulse by pulse, determine the position of the reference point corresponding to different range cells at any azimuth time within the sub-aperture.

[0010] S3. Using the position of the radar platform at the center of the sub-aperture when the satellite moves at a constant speed along an ideal trajectory, the position of the radar platform at the center of the sub-aperture when the satellite moves along a real curved trajectory, and the position of the reference point corresponding to different distance cells at any azimuth time obtained in step S2, determine the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture.

[0011] S4. The sub-aperture signal obtained after dividing S1 into sub-apertures is forward spectrum shifted in the azimuth time domain to obtain the forward spectrum shifted sub-aperture signal.

[0012] S5. Perform an azimuth-direction Fast Fourier Transform (FFT) on the sub-aperture signal after forward spectral shift in S4 to transform the signal into the range-Doppler domain.

[0013] S6. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture obtained in S3, interpolation is used to perform envelope alignment on the sub-aperture signal in the range-Doppler domain obtained in S5 pulse by pulse and distance cell by distance cell to obtain the envelope-aligned range-Doppler domain sub-aperture signal.

[0014] S7. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture obtained in S3, perform phase compensation on the envelope-aligned range-Doppler domain sub-aperture signal obtained in S6 pulse by pulse and distance cell by distance cell to obtain the phase-compensated range-Doppler domain sub-aperture signal.

[0015] S8. Perform an inverse fast fourier transform (IFFT) on the sub-aperture signal in the range-Doppler domain after phase compensation in S7 to transform the sub-aperture signal to the two-dimensional time domain, and obtain the phase-compensated sub-aperture signal in the two-dimensional time domain.

[0016] S9. Perform reverse spectrum shifting on the two-dimensional time-domain sub-aperture signal obtained from S8 after phase compensation to obtain the sub-aperture signal after reverse spectrum shifting.

[0017] S10. By splicing together the two-dimensional time-domain signals obtained after reverse spectrum shifting of different sub-apertures via S9, the full aperture signal after curved track compensation can be obtained.

[0018] Preferably, in S2, the determination of any orientation time within the sub-aperture corresponds to the reference point position (x) of different distance cells. T (t asub ), y T (t asub ), z T (t asub The formula for )) is:

[0019]

[0020] Among them, t asub The azimuth slow time after sub-aperture division, t asub_mid R is the azimuth slow time at the center of the sub-aperture. e and R p These represent the equatorial and polar semi-axis of the ellipsoidal Earth, respectively. I (t asub_mid ), y I (t asub_mid ), z I (t asub_mid R represents the position of the radar platform at the center of the sub-aperture when the satellite is moving at a constant velocity along an ideal trajectory. b f represents the instantaneous slant range corresponding to different distance cells. a For Doppler frequency, The velocity vector of the radar platform. For vectors The modulus, Let $\mathbf{ ... For vectors The modulus.

[0021] Preferably, in S3, the slant distance error of the hyperbolic distance model corresponding to different distance elements at any azimuth time within the sub-aperture can be expressed as:

[0022]

[0023] Among them, R RT (t asub (x) represents the instantaneous true slant range from the radar platform's position to each reference point at the sub-aperture center moment when the satellite is moving along its true curved orbit. R (t asub_mid ), y R (t asub_mid ), z R (t asub_mid R represents the position of the radar platform at the sub-aperture center when the satellite is moving along its true curved orbit. IT (t asub The instantaneous ideal slant range from the radar platform's position to each reference point at the sub-aperture center when the satellite is moving at a constant speed along an ideal trajectory.

[0024] Preferably, in S4, the step of performing a forward spectral shift on the sub-aperture signal obtained after dividing the sub-apertures in the azimuth-time domain to obtain the forward spectral shifted sub-aperture signal can be expressed by the following formula:

[0025] s sub_rc_fdc (t asub ,τ)=s sub_rc (t asub ,τ)·exp[-j2πf dc (t asub_mid )t asub ]

[0026] Among them, s sub_rc_fdc (t asub ,τ) is the sub-aperture signal after positive spectral shift, s sub_rc (t asub ,τ) is the sub-aperture signal after distance pulse compression. τ is the distance-time interval, f dc (t asub_mid The Doppler center frequency corresponding to the oblique angle at the center of the sub-aperture can be expressed as:

[0027]

[0028] Where θ(t) asub_mid() is the oblique angle at the center of the sub-aperture.

[0029] Preferably, in S5, the step of performing an azimuth-directed Fast Fourier Transform (FFT) on the sub-aperture signal after forward spectral shift to transform the signal into the range-Doppler domain is specifically formulated as follows:

[0030] s sub_rc_fdc (f asub ,τ)=FFT{s sub_rc_fdc (t asub ,τ)}

[0031] Among them, s sub_rc_fdc (f asub ,τ) is the sub-aperture signal of the distance Doppler domain.

[0032] Preferably, in S7, the step of performing phase compensation on the envelope-aligned range-Doppler domain sub-aperture signal pulse-by-pulse and range-by-range gate to obtain the phase-compensated range-Doppler domain sub-aperture signal is specifically formulated as follows:

[0033]

[0034] Among them, s sub_pc_fdc (f asub ,τ) represents the sub-aperture signal in the range-Doppler domain after phase compensation, s sub_ea_fdc (f asub ,τ) represents the sub-aperture signal in the range-Doppler domain after envelope alignment.

[0035] Preferably, in step S8, the step of performing an inverse fast fourier transform (IFFT) on the sub-aperture signal in the range-Doppler domain after phase compensation to transform the sub-aperture signal to the two-dimensional time domain is specifically formulated as follows:

[0036] s sub_pc_fdc (t asub ,τ)=IFFT{s sub_pc_fdc (f asub ,τ)}

[0037] Among them, s sub_pc_fdc (t asub ,τ) represents the sub-aperture signal in the two-dimensional time domain after phase compensation.

[0038] Preferably, in S9, the step of performing reverse spectral shifting on the phase-compensated two-dimensional time-domain sub-aperture signal to obtain the reverse spectral shifted sub-aperture signal is specifically formulated as follows:

[0039] s sub_pc (tasub ,τ)=s sub_pc_fdc (t asub ,τ)·exp[j2πf dc (t asub_mid )t asub ]

[0040] Among them, s sub_pc (t asub ,τ) is the sub-aperture signal after reverse spectrum shifting.

[0041] Secondly, a high-resolution spaceborne SAR curved orbit compensation system based on space-variable motion compensation is provided for implementing the high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation described in the first aspect, comprising:

[0042] S1. The echo signal after range pulse compression is segmented in the azimuth time domain to divide it into sub-apertures;

[0043] S2. Using the position of the radar platform at the center of the sub-aperture and the instantaneous Doppler frequency at any azimuth time pulse by pulse, determine the position of the reference point corresponding to different range cells at any azimuth time within the sub-aperture.

[0044] S3. Using the position of the radar platform at the center of the sub-aperture when the satellite moves at a constant speed along the ideal trajectory, the position of the radar platform at the center of the sub-aperture when the satellite moves along the real curved trajectory, and the position of the reference point corresponding to different distance cells at any azimuth time obtained in step S2, determine the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture.

[0045] S4. The sub-aperture signal obtained after dividing the sub-aperture in step S1 is subjected to forward spectrum shifting in the azimuth-time domain to obtain the forward spectrum shifted sub-aperture signal.

[0046] S5. Perform an azimuth-directed fast Fourier transform on the sub-aperture signal after forward spectrum shifting in step S4 to transform the signal into the range Doppler domain.

[0047] S6. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture obtained in step S3, interpolation is used to perform envelope alignment on pulse-by-pulse and distance cell-by-distance cell of the sub-aperture signal in the range-Doppler domain obtained in step S5 to obtain the envelope-aligned range-Doppler domain sub-aperture signal.

[0048] S7. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture obtained in step S3, perform phase compensation on the envelope-aligned range-Doppler domain sub-aperture signal obtained in step S6 pulse by pulse and distance cell by distance cell to obtain the phase-compensated range-Doppler domain sub-aperture signal.

[0049] S8. Perform an azimuth-directed fast inverse Fourier transform on the sub-aperture signal in the range Doppler domain after phase compensation in step S7, and transform the sub-aperture signal to the two-dimensional time domain to obtain the phase-compensated sub-aperture signal in the two-dimensional time domain.

[0050] S9. Perform reverse spectrum shifting on the phase-compensated two-dimensional time-domain sub-aperture signal obtained in step S8 to obtain the sub-aperture signal after reverse spectrum shifting.

[0051] S10. By splicing the two-dimensional time-domain signals obtained after reverse spectrum shifting of different sub-apertures in step S9, the full aperture signal after curved track compensation can be obtained.

[0052] The high-resolution spaceborne SAR curved orbit compensation method based on spatially variable motion compensation provided by the present invention has the following beneficial effects:

[0053] Compared to existing high-resolution spaceborne SAR curved orbit correction methods based on precise range models, this invention has a simpler derivation process and stronger applicability. Compared to curved orbit compensation methods based on one-step motion compensation and two-step motion compensation, this invention can not only compensate for range spatially varying slant range errors, but also compensate for the azimuth spatially varying characteristics of slant range errors by utilizing azimuth molecular apertures and performing motion compensation pulse by pulse within the azimuth Doppler domain. This method can better ensure the focusing effect of targets at the edge of the azimuth scene. Attached Figure Description

[0054] Figure 1 A flowchart of the high-resolution spaceborne SAR curved orbit compensation method based on spatially variable motion compensation provided in the embodiment;

[0055] Figure 2 A schematic diagram showing the reference point positions corresponding to different distance elements at any azimuth time within the sub-aperture, provided for the embodiment;

[0056] Figure 3 This is a schematic diagram of the slant distance error of the hyperbolic distance model at any azimuth within the sub-aperture provided in the embodiment. Detailed Implementation

[0057] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0058] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0059] This invention provides a high-resolution spaceborne SAR curved orbit compensation method based on spatially variable motion compensation, comprising the following steps:

[0060] S1. The echo signal after range pulse compression is segmented in the azimuth time domain to divide it into sub-apertures.

[0061] S2. Calculate the position of the reference point corresponding to different range cells at any azimuth time within the sub-aperture by pulse-by-pulse using the position of the radar platform at the center time of the sub-aperture and the instantaneous Doppler frequency at any azimuth time.

[0062] S3. Calculate the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture by using the position of the radar platform at the sub-aperture center time when the satellite moves at a uniform straight speed along an ideal trajectory, the position of the radar platform at the sub-aperture center time when the satellite moves along a real curved orbit, and the position of the reference point of different distance cells at any azimuth time calculated in S2.

[0063] S4. The sub-aperture signal obtained after dividing S1 into sub-apertures is forward spectrum shifted in the azimuth time domain to obtain the forward spectrum shifted sub-aperture signal.

[0064] S5. Perform an azimuth-direction Fast Fourier Transform (FFT) on the sub-aperture signal after forward spectral shift in S4 to transform the signal into the range-Doppler domain.

[0065] S6. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture calculated in S3, interpolation is used to perform envelope alignment on pulse-by-pulse and distance-by-distance cell of the sub-aperture signal in the range-Doppler domain obtained in S5.

[0066] S7. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture calculated in S3, phase compensation is performed on the sub-aperture signal in the range-Doppler domain after envelope alignment obtained in S6 pulse by pulse and distance cell by distance cell to obtain the sub-aperture signal in the range-Doppler domain after phase compensation.

[0067] S8. Perform an Inverse Fast Fourier Transform (IFFT) on the sub-aperture signal in the range Doppler domain after phase compensation in S7 to transform the sub-aperture signal to the two-dimensional time domain, thus obtaining the phase-compensated sub-aperture signal in the two-dimensional time domain.

[0068] S9. Perform reverse spectrum shifting on the two-dimensional time-domain sub-aperture signal obtained from S8 after phase compensation to obtain the sub-aperture signal after reverse spectrum shifting.

[0069] S10. By splicing together the two-dimensional time-domain signals obtained after reverse spectrum shifting of different sub-apertures via S9, the full aperture signal after curved track compensation can be obtained.

[0070] Example:

[0071] A high-resolution spaceborne SAR curved orbit compensation method based on spatially variable motion compensation, such as... Figure 1 As shown, the steps are as follows:

[0072] (1) Sub-aperture division

[0073] The echo signal after range pulse compression is segmented in the azimuth time domain to divide it into sub-apertures. The formula for the sub-aperture length during sub-aperture division is:

[0074]

[0075] Where, θ azi Let f be the azimuth beamwidth of the antenna, c be the speed of light, and f be the speed of light. c For carrier frequency, R n This represents the shortest slant distance at the center of the sub-aperture. It's important to note that to improve the compensated azimuth time resolution and ensure the stitching effect of the sub-apertures, some pulses need to be reused between each sub-aperture; for example, a reuse rate of 50% can be selected.

[0076] (2) Calculate the reference point position of different distance elements at any azimuth within the sub-aperture at any time.

[0077] like Figure 2 As shown, the position of the reference point corresponding to different range cells at any azimuth time within the sub-aperture can be determined based on the position of the radar platform at the sub-aperture center time and the instantaneous Doppler frequency at any azimuth time, as shown in the formula:

[0078]

[0079] Among them, t asub The azimuth slow time after sub-aperture division, t asub_mid The azimuth time at the center of the sub-aperture, (x T (t asub ), y T (t asub ), z T (t asub )) represents the triaxial position of the reference point, R e and R p These represent the equatorial and polar semi-axis of the ellipsoidal Earth, respectively. I (t asub_mid ), y I (t asub_mid ), z I (tasub_mid R represents the position of the radar platform at the center of the sub-aperture when the satellite is moving at a constant velocity along an ideal trajectory. b f represents the instantaneous slant range corresponding to different distance cells. a For Doppler frequency, The velocity vector of the radar platform. For vectors The modulus, Let $\mathbf{ ... For vectors The modulus.

[0080] (3) Determine the slant distance error of the hyperbolic distance model

[0081] like Figure 3 As shown, the slant range error of the hyperbolic distance model corresponding to different range cells at any azimuth time within the sub-aperture is calculated using the positions of the radar platform at the sub-aperture center time when the satellite moves at a uniform straight speed along an ideal trajectory, the positions of the radar platform at the sub-aperture center time when the satellite moves along a real curved orbit, and the positions of the reference points corresponding to different range cells at any azimuth time obtained in S2. The formula is:

[0082]

[0083] Among them, R RT (t asub (x) represents the instantaneous true slant range from the radar platform's position to each reference point at the sub-aperture center moment when the satellite is moving along its true curved orbit. R (t asub_mid ), y R (t asub_mid ), z R (t asub_mid R represents the position of the radar platform at the sub-aperture center when the satellite is moving along its true curved orbit. IT (t asub The instantaneous ideal slant range from the radar platform's position to each reference point at the sub-aperture center when the satellite is moving at a constant speed along an ideal trajectory.

[0084] (4) Forward spectrum shift

[0085] The sub-aperture signal, after range pulse compression, is subjected to a forward spectral shift in the azimuth time domain to obtain the forward spectral shifted sub-aperture signal, as shown in the formula:

[0086] s sub_rc_fdc (t asub ,τ)=s sub_rc (t asub ,τ)·exp[-j2πf dc(t asub_mid )t asub ]

[0087] Among them, s sub_rc_fdc (t asub ,τ) is the sub-aperture signal after positive spectral shift, s sub_rc (t asub ,τ) is the sub-aperture signal after distance pulse compression. τ is the distance-time interval, f dc (t asub_mid The Doppler center frequency corresponding to the oblique angle at the center of the sub-aperture can be expressed as:

[0088]

[0089] Where θ(t) asub_mid () is the oblique angle at the center of the sub-aperture.

[0090] (5) Orientation FFT

[0091] Performing an azimuth-directed Fast Fourier Transform (FFT) on the sub-aperture signal after forward spectral shift transforms the signal to the range-Doppler domain. The calculation formula is as follows:

[0092] s sub_rc_fdc (f asub ,τ)=FFT{s sub_rc_fdc (t asub ,τ)}

[0093] Among them, s sub_rc_fdc (f asub ,τ) is the sub-aperture signal of the distance Doppler domain.

[0094] (6) Envelope Alignment

[0095] Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture, interpolation is used to perform envelope alignment of the sub-aperture signal in the range-Doppler domain pulse by pulse and distance cell by distance cell, resulting in the envelope-aligned range-Doppler domain sub-aperture signal.

[0096] (7) Phase compensation

[0097] Based on the slant range error of the hyperbolic distance model corresponding to different range cells at any azimuth time within the sub-aperture, phase compensation is performed pulse-by-pulse and range cell-by-range on the sub-aperture signal in the range-Doppler domain after envelope alignment. This yields the phase-compensated sub-aperture signal in the range-Doppler domain. The formula is:

[0098]

[0099] Among them, s sub_pc_fdc (f asub ,τ) represents the sub-aperture signal in the range-Doppler domain after phase compensation, s sub_ea_fdc (f asub ,τ) represents the sub-aperture signal in the range-Doppler domain after envelope alignment.

[0100] (8) Orientation IFFT

[0101] An Inverse Fast Fourier Transform (IFFT) is performed on the sub-aperture signal in the range-Doppler domain after phase compensation to transform the sub-aperture signal to the two-dimensional time domain. The calculation formula is as follows:

[0102] s sub_pc_fdc (t asub ,τ)=IFFT{s sub_pc_fdc (f asub ,τ)}

[0103] Among them, s sub_pc_fdc (t asub ,τ) represents the sub-aperture signal in the two-dimensional time domain after phase compensation.

[0104] (9) Reverse spectrum shift

[0105] The sub-aperture signal in the two-dimensional time domain after phase compensation is subjected to reverse spectral shifting to obtain the sub-aperture signal after reverse spectral shifting. The specific formula is as follows:

[0106] s sub_pc (t asub ,τ)=s sub_pc_fdc (t asub ,τ)·exp[j2πf dc (t asub_mid )t asub ]

[0107] Among them, s sub_pc (t asub ,τ) is the sub-aperture signal after reverse spectrum shifting.

[0108] (10) Data splicing

[0109] By splicing together the two-dimensional time-domain signals obtained after reverse spectral shifting of different sub-apertures, the full aperture signal after curved track compensation can be obtained.

[0110] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0111] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation, characterized in that, The steps include: S1. The echo signal after range pulse compression is segmented in the azimuth time domain to divide it into sub-apertures; S2. Using the position of the radar platform at the center of the sub-aperture and the instantaneous Doppler frequency at any azimuth time pulse by pulse, determine the position of the reference point corresponding to different range cells at any azimuth time within the sub-aperture. S3. Using the position of the radar platform at the center of the sub-aperture when the satellite moves at a constant speed along the ideal trajectory, the position of the radar platform at the center of the sub-aperture when the satellite moves along the real curved trajectory, and the position of the reference point corresponding to different distance cells at any azimuth time obtained in step S2, determine the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture. S4. The sub-aperture signal obtained after dividing the sub-aperture in step S1 is subjected to forward spectrum shifting in the azimuth-time domain to obtain the forward spectrum shifted sub-aperture signal. S5. Perform an azimuth-directed fast Fourier transform on the sub-aperture signal after forward spectrum shifting in step S4 to transform the signal into the range Doppler domain. S6. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture obtained in step S3, interpolation is used to perform envelope alignment on pulse-by-pulse and distance cell-by-distance cell of the sub-aperture signal in the range-Doppler domain obtained in step S5 to obtain the envelope-aligned range-Doppler domain sub-aperture signal. S7. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture obtained in step S3, perform phase compensation on the envelope-aligned range-Doppler domain sub-aperture signal obtained in step S6 pulse by pulse and distance cell by distance cell to obtain the phase-compensated range-Doppler domain sub-aperture signal. S8. Perform an azimuth-directed fast inverse Fourier transform on the sub-aperture signal in the range Doppler domain after phase compensation in step S7, and transform the sub-aperture signal to the two-dimensional time domain to obtain the phase-compensated sub-aperture signal in the two-dimensional time domain. S9. Perform reverse spectrum shifting on the phase-compensated two-dimensional time-domain sub-aperture signal obtained in step S8 to obtain the sub-aperture signal after reverse spectrum shifting. S10. By splicing the two-dimensional time-domain signals obtained after reverse spectrum shifting of different sub-apertures in step S9, the full aperture signal after curved track compensation can be obtained.

2. The high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation according to claim 1, characterized in that, In the step of segmenting the range pulse compressed echo signal in the azimuth time domain to divide it into sub-apertures, the formula for the sub-aperture length during sub-aperture division is: Where, θ azi Let f be the azimuth beamwidth of the antenna, c be the speed of light, and f be the speed of light. c For carrier frequency, R n It is the shortest slope distance at the center of the sub-aperture.

3. The high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation according to claim 1, characterized in that, In the step of determining the position of the reference point corresponding to different distance elements at any azimuth time within the sub-aperture, the position of the reference point (x) T (t asub ), y T (t asub ), z T (t asub ))satisfy: Among them, t asub The azimuth slow time after sub-aperture division, t asub_mid R is the azimuth slow time at the center of the sub-aperture. e and R p These represent the equatorial and polar semi-axis of the ellipsoidal Earth, respectively. I (t asub_mid ), y I (t asub_mid ), z I (t asub_mid R represents the position of the radar platform at the center of the sub-aperture when the satellite is moving at a constant velocity along an ideal trajectory. b f represents the instantaneous slant range corresponding to different distance cells. a For Doppler frequency, The velocity vector of the radar platform. For vectors The modulus, Let $\mathbf{ ... For vectors The modulus.

4. The high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation according to claim 1, characterized in that, The slant distance error of the hyperbolic distance model corresponding to different distance elements at any azimuth time within the sub-aperture is: Among them, R RT (t asub (x) represents the instantaneous true slant range from the radar platform's position to each reference point at the sub-aperture center moment when the satellite is moving along its true curved orbit. R (t asub_mid ), y R (t asub_mid ), z R (t asub_mid R represents the position of the radar platform at the sub-aperture center when the satellite is moving along its true curved orbit. IT (t asub The instantaneous ideal slant range from the radar platform's position to each reference point at the sub-aperture center when the satellite is moving at a constant speed along an ideal trajectory.

5. The high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation according to claim 1, characterized in that, The step of performing a forward spectral shift on the sub-aperture signal obtained after dividing the sub-aperture into the azimuth-directed time domain to obtain the forward spectral shifted sub-aperture signal is implemented in the following manner: s sub_rc_fdc (t asub ,τ)=s sub_rc (t asub ,τ)·exp[-j2πf dc (t as ub_mid )t asub ] Among them, s sub_rc_fdc (t asub ,τ) is the sub-aperture signal after positive spectral shift, s sub_rc (t asub ,τ) is the sub-aperture signal after distance pulse compression. τ is the distance-time interval, f dc (t asub_mid The Doppler center frequency corresponding to the oblique angle at the center of the sub-aperture can be expressed as: Where θ(t) asub_mid () is the oblique angle at the center of the sub-aperture.

6. The high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation according to claim 1, characterized in that, The step of performing phase compensation on the envelope-aligned range-Doppler domain sub-aperture signal pulse-by-pulse and range-gate-by-range to obtain the phase-compensated range-Doppler domain sub-aperture signal is implemented in the following manner: Among them, s sub_pc_fdc (f asub ,τ) represents the sub-aperture signal in the range-Doppler domain after phase compensation, s sub_ea_fdc (f asub ,τ) represents the sub-aperture signal in the range-Doppler domain after envelope alignment.

7. The high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation according to claim 1, characterized in that, The step of performing reverse spectral shifting on the phase-compensated two-dimensional time-domain sub-aperture signal to obtain the reverse spectral shifted sub-aperture signal is implemented in the following manner: s sub_pc (t asub ,τ)=s sub_pc_fdc (t asub ,τ)·exp[j2πf dc (t asub_mid )t asub ] Among them, s sub_pc (t asub ,τ) is the sub-aperture signal after reverse spectrum shifting.

8. A high-resolution spaceborne SAR curved orbit compensation system based on space-variable motion compensation, characterized in that, The method for implementing the high-resolution spaceborne SAR curved orbit compensation method based on space-variable motion compensation as described in any one of claims 1 to 7 includes: S1. The echo signal after range pulse compression is segmented in the azimuth time domain to divide it into sub-apertures; S2. Using the position of the radar platform at the center of the sub-aperture and the instantaneous Doppler frequency at any azimuth time pulse by pulse, determine the position of the reference point corresponding to different range cells at any azimuth time within the sub-aperture. S3. Using the position of the radar platform at the center of the sub-aperture when the satellite moves at a constant speed along the ideal trajectory, the position of the radar platform at the center of the sub-aperture when the satellite moves along the real curved trajectory, and the position of the reference point corresponding to different distance cells at any azimuth time obtained in step S2, determine the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture. S4. The sub-aperture signal obtained after dividing the sub-aperture in step S1 is subjected to forward spectrum shifting in the azimuth-time domain to obtain the forward spectrum shifted sub-aperture signal. S5. Perform an azimuth-directed fast Fourier transform on the sub-aperture signal after forward spectrum shifting in step S4 to transform the signal into the range Doppler domain. S6. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture obtained in step S3, interpolation is used to perform envelope alignment on pulse-by-pulse and distance cell-by-distance cell of the sub-aperture signal in the range-Doppler domain obtained in step S5 to obtain the envelope-aligned range-Doppler domain sub-aperture signal. S7. Based on the slant range error of the hyperbolic distance model corresponding to different distance cells at any azimuth time within the sub-aperture obtained in step S3, perform phase compensation on the envelope-aligned range-Doppler domain sub-aperture signal obtained in step S6 pulse by pulse and distance cell by distance cell to obtain the phase-compensated range-Doppler domain sub-aperture signal. S8. Perform an azimuth-directed fast inverse Fourier transform on the sub-aperture signal in the range Doppler domain after phase compensation in step S7, and transform the sub-aperture signal to the two-dimensional time domain to obtain the phase-compensated sub-aperture signal in the two-dimensional time domain. S9. Perform reverse spectrum shifting on the phase-compensated two-dimensional time-domain sub-aperture signal obtained in step S8 to obtain the sub-aperture signal after reverse spectrum shifting. S10. By splicing the two-dimensional time-domain signals obtained after reverse spectrum shifting of different sub-apertures in step S9, the full aperture signal after curved track compensation can be obtained.

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