Space-based passive coherent location method using ground-based synthetic aperture radar

Abstract

The application discloses a space-based external emitter ground-based synthetic aperture radar far-field pseudo-polar imaging method. The method firstly performs Fourier transform on time-domain signals received by monitoring antennas and reference antennas at different positions, performs conjugate multiplication in the frequency domain, and obtains target echo signals; distance dimension and azimuth dimension of the signals are decoupled; Taylor expansion order is determined according to imaging accuracy and efficiency requirements, and redundant phase terms generated after decoupling are Taylor expanded; decoupled echo signals after compensation under different orders are respectively subjected to two-dimensional fast Fourier transform, so that distance compression and azimuth focusing results are obtained; the results of different orders are accumulated and summed, so that a pseudo-polar coordinate system image is obtained; finally, the pseudo-polar coordinate image is converted into a rectangular coordinate, and a two-dimensional imaging result is output. The application can effectively realize balance between imaging accuracy and efficiency of the space-based external emitter ground-based synthetic aperture radar, and quickly obtain a high-resolution SAR image.

Description

Technical Field

[0001] This invention relates to the field of remote sensing imaging technology, and in particular to a far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar. Background Technology

[0002] Ground-based synthetic aperture radar (GB-SAR) is an important remote sensing tool for displacement measurement, offering millimeter- or sub-millimeter-level accuracy. As a key complement to spaceborne and airborne SAR, its core advantages lie in its continuous monitoring capability and short revisit period—compared to the revisit intervals of several days to tens of days for spaceborne SAR, GB-SAR can achieve dynamic observations from seconds to tens of minutes, making it particularly suitable for scenarios requiring high temporal resolution, such as landslide deformation, bridge displacement, and building structural health monitoring. In recent years, with the integration of multiple-input multiple-output (MIMO) array technology, the data acquisition rate of GB-SAR has been further improved, and the system flexibility has been significantly enhanced. For example, by coordinating multiple traditional GB-SAR or MIMO radar systems, two-dimensional or three-dimensional displacement vectors of targets can be obtained. In system design, GB-SAR typically employs frequency modulated continuous wave (FMCW) or stepped frequency continuous wave (SFCW) signal systems. To achieve high range resolution, its bandwidth is usually several hundred megahertz, and the center frequency is often selected from the Ku band (such as 17 GHz). The centimeter-level wavelength (about 1.7 cm) of this band can support sub-millimeter-level displacement estimation accuracy.

[0003] However, traditional GB-SAR systems still have certain limitations. Their reliance on dedicated transmitters leads to high system costs, and their relatively fixed observation geometry results in insufficient system flexibility. These issues have provided direction for the development of improved systems such as Passive Bistatic Ground-Based Synthetic Aperture Radar System (PB-GB-SAR). The goal is to further reduce costs and improve system flexibility while retaining the core capabilities of GB-SAR, such as continuous illumination, high-resolution imaging, and high-precision displacement estimation. Summary of the Invention

[0004] The purpose of this invention is to provide a far-field pseudo-polar imaging method for space-based external radiation source ground-based synthetic aperture radar to achieve the optimal balance between accuracy and efficiency, and to meet the design requirements of low cost and high flexibility of PB-GB-SAR.

[0005] To achieve the above objectives, the present invention provides the following solution: A far-field pseudo-pole imaging method for a space-based external radiation source ground-based synthetic aperture radar includes the following steps: S1. Perform Fourier transform on the time-domain signals received by the monitoring antenna and the reference antenna at different locations, perform conjugate multiplication in the frequency domain, and obtain the target echo signal based on the plane wave approximation and the far-field assumption. S2. Decouple the target echo signal in the range and direction dimensions, and represent the target echo signal as a function of range wavenumber and antenna position; S3. Determine the Taylor expansion order based on the requirements of imaging accuracy and efficiency, and perform Taylor expansion on the redundant phase terms generated after decoupling. S4. Perform two-dimensional fast Fourier transform on the decoupled echo signals after compensation at different orders to obtain the range compression and azimuth focusing results. S5. The results of each order of distance compression and azimuth focusing are summed to obtain a pseudo-polar coordinate system image with the bibase slant range and azimuth sine value as variables. S6. Finally, convert the pseudo-polar coordinate image to rectangular coordinates and output the two-dimensional imaging result.

[0006] Preferably, in S1, conjugate multiplication is performed in the frequency domain to obtain the target echo signal. The formula is as follows:

[0007] Where, k q Let x be the q-th wave number. p Let yp be the x-coordinate of the p-th antenna position, j be the imaginary unit in engineering, and y0 be the y-coordinate of the target in a two-dimensional Cartesian coordinate system. ref Let θ0 be the fixed ordinate of the reference antenna in a Cartesian coordinate system, and let θ0 be the target azimuth angle. denoted as , and r0 as , where r is the target scattering coefficient and r0 is the target slant range.

[0008] Preferably, in S2, the target echo signal is decoupled in terms of range and direction dimensions, as shown in the following formula:

[0009] in, It is the central wavenumber. Let r0 be the wavenumber difference between the q-th wavenumber and the center wavenumber. bis Let c be the bistatic slant distance in pseudopolar coordinates, and c be the speed of light. , This represents the q-th frequency sample value in the frequency domain of the transmitted signal. The center wavelength is .

[0010] Preferably, in S3, the Taylor expansion order is determined based on the requirements of imaging accuracy and efficiency, specifically including: The Taylor expansion order O of the redundant phase term generated after decoupling is determined based on the requirements of imaging accuracy and efficiency. For example, let the processing time of the two-dimensional fast Fourier transform corresponding to single-order Taylor compensation be... If the system requires the total imaging time to not exceed Then the maximum chosen Taylor expansion order must satisfy the following condition. ,in This indicates rounding down, selecting a higher order to optimize imaging accuracy while ensuring that the imaging time meets the requirements; After determining the expansion order O, a Taylor expansion is performed on the redundant phase terms:

[0011] in, The center frequency.

[0012] Preferably, in S4, two-dimensional fast Fourier transforms are performed on the decoupled echo signals after compensation at different orders to obtain the range compression and azimuth focusing results, as shown in the following formula:

[0013] in, The results are for distance compression and azimuth focusing. and These are two variables defined in pseudopolar coordinates: the bibase slant distance and the azimuth sine. For the inverse Fourier transform operator along the pseudopolar coordinate α direction, This is the Fourier transform operator along the pseudopolar coordinate β direction.

[0014] Preferably, in S5, a pseudo-polar coordinate system image is obtained with the bibase slope distance and azimuth sine value as variables, as shown in the following formula: .

[0015] Preferably, in step S6, the pseudo-polar coordinate image is finally converted to rectangular coordinates, and the two-dimensional imaging result is output, as shown in the following formula:

[0016] Where (x0, y0) are the target coordinates in the rectangular coordinate system.

[0017] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements a far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar as described above.

[0018] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention addresses the challenges of complex imaging geometry in passive bistatic synthetic aperture radar (PB-GB-SAR), where traditional back projection (BPA) algorithms offer optimal imaging accuracy but suffer from extremely high computational costs, hindering real-time imaging. To address these issues, a far-field pseudopolar imaging algorithm (FPFA) is proposed. This algorithm constructs a signal model using plane wave approximation and far-field assumptions, decouples the range and azimuth dimensions using far-field conditions, and simplifies computation through a two-dimensional fast Fourier transform. Simulation results demonstrate that the FPFA algorithm achieves imaging accuracy approaching that of time-domain BPA while improving processing efficiency by more than an order of magnitude, achieving an optimal balance between accuracy and efficiency. This FPFA algorithm is well-suited to the low-cost, high-flexibility design requirements of PB-GB-SAR. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the far-field pseudo-polarization imaging method for a ground-based synthetic aperture radar with a space-based external radiation source provided by the present invention. Figure 2 A simplified system structure diagram of the passive bistatic synthetic aperture radar (PB-GB-SAR) provided by the present invention; Figure 3 This is a schematic diagram of a simplified imaging geometric model of PB-GB-SAR under the plane wave approximation of the present invention; Figure 4 This is a schematic diagram illustrating the peak amplitude stability of the autocorrelation function of the reference signal in this invention; Figure 5 Comparison of FPFA imaging results when the order O is equal to 1, 5, 15, and 30 in the embodiments of the present invention; Among them, (a) is the FPFA imaging result when O=1, (b) is the FPFA imaging result when O=5, (c) is the FPFA imaging result when O=15, and (d) is the FPFA imaging result when O=30. Figure 6 This is an image of the temporal BPA imaging result in an embodiment of the present invention; Figure 7 This is a trend graph showing the imaging accuracy of FPFA approaching TDBP with order O in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] like Figure 1 As shown, the present invention provides a far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar, comprising the following steps: S1. Perform Fourier transform on the time-domain signals received by the monitoring antenna and the reference antenna at different locations, perform conjugate multiplication in the frequency domain, and obtain the target echo signal based on the plane wave approximation and the far-field assumption. S2. Decouple the target echo signal in the range and direction dimensions, and represent the target echo signal as a function of range wavenumber and antenna position; S3. Determine the Taylor expansion order based on the requirements of imaging accuracy and efficiency, and perform Taylor expansion on the redundant phase terms generated after decoupling. S4. Perform two-dimensional fast Fourier transform on the decoupled echo signals after compensation at different orders to obtain the range compression and azimuth focusing results. S5. The results of each order of distance compression and azimuth focusing are summed to obtain a pseudo-polar coordinate system image with the bibase slant range and azimuth sine value as variables. S6. Finally, convert the pseudo-polar coordinate image to rectangular coordinates and output the two-dimensional imaging result.

[0024] Specifically, the method of the present invention includes: To address the limitations of traditional GB-SAR systems, the PB-GB-SAR system proposes an innovative approach of "using an external illumination source instead of a dedicated transmitter," which can improve system flexibility while reducing system costs. Figure 2 As shown.

[0025] However, unlike traditional GB-SAR, PB-GB-SAR employs a bistatic configuration, resulting in more complex imaging geometry and necessitating the development of corresponding imaging algorithms. Prior to PB-GB-SAR imaging research, two mature imaging algorithms had emerged in the GB-SAR field—the Back Projection Algorithm (BPA) and the Range Migration Algorithm (RMA)—but their applicability in passive bistatic scenarios requires further analysis. BPA is the most intuitive SAR imaging algorithm. Its core idea is "point-by-point focusing": for each pixel in the imaging area, the slant range from that point to all antenna positions is calculated. Then, based on the phase delay corresponding to the slant range, the received signals at each antenna position are coherently accumulated to finally obtain the complex amplitude (i.e., scattering intensity) of the pixel. The advantage of BPA is that it does not require any geometric approximation and can be adapted to any imaging scene, especially suitable for near-field targets or complex geometric configurations; however, the disadvantage is that the computational complexity is extremely high—if the imaging area is 100m×100m and the resolution is set to 0.1m, the number of pixels reaches 10 6 If the number of antenna positions is 241 (1.2m synthetic aperture, 5mm step size), then 10 [unclear] need to be completed. 6 ×241=2.41×10 8 Subcoherent accumulation operations are difficult to implement in real-time imaging on ordinary computers. Since BPA does not require any geometric approximation and has theoretically the best imaging accuracy, it is the "benchmark algorithm" for SAR imaging. Therefore, this invention uses it as the core comparison object to verify the accuracy performance of the proposed algorithm.

[0026] Besides BPA, RMA is another classic frequency domain imaging algorithm in the SAR field. It simplifies calculations and reduces computational complexity through the principle of stationary phase and frequency domain transformation. However, the core limitations of this algorithm are fundamentally incompatible with the application scenarios of PB-GB-SAR: PB-GB-SAR is designed for large-scale dynamic monitoring needs such as landslide deformation and bridge displacement, while RMA requires a large amount of zero-padding in the azimuth direction to meet processing conditions when the observation scene is large. This significantly increases the data storage and computational burden, and the time-consuming Stolt interpolation operation in the two-dimensional frequency domain will greatly slow down the imaging speed, making it difficult to adapt to the real-time requirements of large-scale dynamic monitoring. Considering that the core objective of this invention is to study an algorithm with "accuracy comparable to BPA and significantly improved imaging processing efficiency", and that the application scenarios of RMA conflict with the core requirements of PB-GB-SAR, it was not included in this simulation experiment comparison.

[0027] To address the core issues of optimal BPA accuracy but extremely high computational complexity and difficulties in real-time imaging, this invention studies a far-field pseudo-polar format (FPFA) imaging algorithm. This algorithm is applicable to far-field targets, exhibits low computational complexity and high accuracy, and can better meet the core requirements of ground-based synthetic aperture radar (SAR) imaging from space-based external radiation sources. The specific steps are as follows: First, a simplified imaging geometric model of the passive system was constructed under the plane wave assumption, such as... Figure 3 As shown. To facilitate determining the position of the monitoring antenna, it is assumed that its direction of movement is parallel to the wavefront direction of the satellite television signal. To achieve this condition, the reference antenna pointing at the satellite is moved synchronously with the monitoring antenna, and calibration is performed by detecting the stability of the peak amplitude of the autocorrelation function of the received signal. When the direction of movement is parallel to the wavefront, the normalized autocorrelation peak amplitude (with the first measurement as the reference) remains stable along the synthetic aperture, with a mean of 0.997 and a standard deviation of 0.008, as shown. Figure 4 As shown; however, when there is even a tiny wavefront tilt angle in the direction of antenna movement, the normalized amplitude will change significantly along the length of the synthetic aperture, and in this case, motion direction correction must be performed.

[0028] Specifically, in S1, the time-domain signals received by the reference antenna and the monitoring antenna are known to be:

[0029]

[0030] in, and These represent the amplitudes of the signals received by the reference antenna and the monitoring antenna, respectively. Indicates satellite transmission signal, This indicates the distance between the satellite and the reference antenna. Indicates the distance between the satellite and the target. This represents the distance between the target and the monitoring antenna, where c represents the speed of light, and r0 is the slant range of the target (the distance between the target and the monitoring antenna).

[0031] Then, the two are transformed to the frequency domain using Fourier transform to obtain the frequency domain reference signal and monitoring signal:

[0032]

[0033] in, This represents the q-th wave number.

[0034] Next, the carrier wave and modulation information of the satellite itself are canceled out by frequency domain conjugate multiplication, retaining only the phase difference brought by the target echo, thus obtaining the target signal in the range-wavenumber-antenna position domain:

[0035] Here, (.)* denotes complex conjugation, and A0 = A surv A * ref .

[0036] Finally, under the plane wave approximation and the far-field assumption, the calculation of the bistatic slope distance is simplified:

[0037]

[0038] in, This represents the target's coordinates in a two-dimensional rectangular coordinate system. The x-coordinate represents the position of the p-th antenna.

[0039] Finally, we get x p Target signal in the range-wavenumber-antenna position domain at the q-th wavenumber :

[0040] in, This represents the target scattering coefficient.

[0041] In S2, by decoupling the distance dimension and the orientation dimension, we can obtain:

[0042] in, It is the central wavenumber. .

[0043] In S3, the Taylor expansion order O of the redundant phase term generated after decoupling is determined according to the requirements of imaging accuracy and efficiency. For example, let the processing time of the two-dimensional fast Fourier transform corresponding to single-order Taylor compensation be... If the system requires the total imaging time to not exceed Then the maximum selectable Taylor expansion order must satisfy the following condition. ,in This indicates rounding down, selecting the highest possible order to optimize imaging accuracy while ensuring the imaging time meets requirements.

[0044] After determining the expansion order O, perform a Taylor expansion on it:

[0045] Where O is the expansion order.

[0046] In S4, two-dimensional Fourier transforms are performed on the compensated decoupled echo signals of different orders to obtain range compression and azimuth focusing results:

[0047] in, and These are two variables defined in the pseudopolar coordinate system: the bibase slant distance and the azimuth sine.

[0048] In S5, the results of each order are summed to obtain a pseudo-polar coordinate system focused image with the bibase slope range and azimuth sine as variables:

[0049] In S6, the pseudo-polar coordinate image is finally converted to rectangular coordinates, and the two-dimensional imaging result is output:

[0050] 3. Simulation Experiment Results Based on the constructed signal model, a simulation experiment was conducted with the following parameter settings: The synthesized aperture length is 1.2 meters, and the step size is 1.5 centimeters, i.e., x p ∈[-0.6m, 0.6m], nx p = 161, the transmitted signal frequency is 4.85 GHz to 5.15 GHz, n freq =801, center frequency f c It is 5 GHz, and y p = 0m, y ref = -0.15m. A total of 6 point targets are set, each with a slant distance r from the origin. tag = [100; 100; 100; 50; 50; 50], unit is meters; azimuth is θ. tag = [0; -30; 30; 0; -30; 30] × π / 180, in rad; the scattering coefficient (amplitude) is set as σ = [2; 1; 1; 2; 1; 1].

[0051] When considering the ξ term in equation (8), the imaging effects of FPFA at different ξ expansion orders are compared using O=1, O=5, O=15, and O=30 respectively. The results are as follows: Figure 5 As shown in (a)~(d): As can be seen, with the increase of order O, the difference in imaging results compared to when O=1 is not significant, and the focusing effect is still good. This indicates that under the far-field approximation condition, the FPFA algorithm that ignores the ξ term still maintains high imaging accuracy and can meet the system's imaging requirements. It should be noted that in the experiment, we found that the influence of the Taylor expansion term on the collected target signal reaches saturation (below 10%) when the order O reaches 26. -6 Therefore, the imaging result with O=30 here can represent the highest-order processing result.

[0052] Next, the performance of the proposed FPFA algorithm is demonstrated by comparing its imaging processing results and processing time with those of temporal BPA. The comparison results are as follows: Figure 6 As shown in Table 1 (Comparison of Processing Time): Table 1

[0053] To further demonstrate the variation of FPFA imaging accuracy with the Taylor expansion order O and its approximation of TDBP characteristics, a plot was drawn. Figure 7 (NMSE trend with O). The horizontal axis represents the Taylor expansion order O, and the vertical axis represents the NMSE of FPFA and TDBP imaging amplitudes (the smaller the value, the closer the accuracy). As shown in the figure, the accuracy follows a "rapid decrease - gradual transition - saturation" pattern as O increases: when O=1, the NMSE is 0.038, which is close to the accuracy of TDBP; when O=2~20, the NMSE decreases from 0.024 to 0.0016, and the higher-order gain gradually weakens; when O≥26, the NMSE stabilizes at 0.0015 (the influence of Taylor expansion accounts for <10-6, reaching saturation). This figure verifies the core advantage of FPFA: high accuracy of NMSE≤0.012 can be achieved with low-order (O≤5), while the improvement in high-order accuracy is limited but the processing time increases significantly (see Table 1). Therefore, by flexibly adjusting O, accuracy and efficiency can be balanced to meet the low-cost and high-flexibility requirements of PB-GB-SAR.

[0054] The core of adjusting the Taylor expansion order O is to balance imaging accuracy and processing efficiency based on the actual application scenario of PB-GB-SAR. For example, low order (O≤5) is suitable for efficiency-priority scenarios such as landslide acceleration early warning and real-time bridge displacement monitoring. At this order, the NMSE is small, meeting the core requirements of sub-millimeter level, and the processing time is short, which can support real-time output. At the same time, it is compatible with embedded hardware and fits the low-cost design. High order (O≥26) is suitable for accuracy-priority scenarios such as long-term dam settlement monitoring. At this time, the NMSE is slightly improved, but the accuracy is still close to the time domain BPA. Although the processing time is increased, there is no redundant calculation, which can compensate for the small phase error under the far-field approximation. It is especially suitable for scenarios with long target slant range or long synthetic aperture. In practical applications, the value of O can be flexibly selected according to the priority of accuracy and real-time requirements.

[0055] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements a far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar as described above.

[0056] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0057] 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. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar, characterized in that, Includes the following steps: S1. Perform Fourier transform on the time-domain signals received by the monitoring antenna and the reference antenna at different locations, perform conjugate multiplication in the frequency domain, and obtain the target echo signal based on the plane wave approximation and the far-field assumption. S2. Decouple the target echo signal in the range and direction dimensions, and represent the target echo signal as a function of range wavenumber and antenna position; S3. Determine the Taylor expansion order based on the requirements of imaging accuracy and efficiency, and perform Taylor expansion on the redundant phase terms generated after decoupling. S4. Perform two-dimensional fast Fourier transform on the decoupled echo signals after compensation at different orders to obtain the range compression and azimuth focusing results. S5. The results of each order of distance compression and azimuth focusing are summed to obtain a pseudo-polar coordinate system image with the bibase slant range and azimuth sine value as variables. S6. Finally, convert the pseudo-polar coordinate image to rectangular coordinates and output the two-dimensional imaging result.

2. The far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar according to claim 1, characterized in that, In step S1, the time-domain signals received by the monitoring antennas and reference antennas at different locations are subjected to Fourier transform, and then conjugate multiplication is performed in the frequency domain to obtain the target echo signal based on the plane wave approximation and far-field assumptions. The formula is as follows: Where, k q Let x be the q-th wave number. p Let yp be the x-coordinate of the p-th antenna position, j be the imaginary unit in engineering, and y0 be the y-coordinate of the target in a two-dimensional Cartesian coordinate system. ref Let θ0 be the fixed ordinate of the reference antenna in a Cartesian coordinate system, and let θ0 be the target azimuth angle. denoted as , and r0 as , where r is the target scattering coefficient and r0 is the target slant range.

3. The far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar according to claim 2, characterized in that, In step S2, the target echo signal is decoupled from the range and direction dimensions, as shown in the following formula: in, It is the central wavenumber. Let r0 be the wavenumber difference between the q-th wavenumber and the center wavenumber. bis Let c be the bistatic slant distance in pseudopolar coordinates, and c be the speed of light. , This represents the q-th frequency sample value in the frequency domain of the transmitted signal. The center wavelength is .

4. The far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar according to claim 3, characterized in that, In step S3, the Taylor expansion order is determined based on the requirements for imaging accuracy and efficiency, specifically including: The Taylor expansion order O of the redundant phase term generated after decoupling is determined based on the requirements of imaging accuracy and efficiency. For example, let the processing time of the two-dimensional fast Fourier transform corresponding to single-order Taylor compensation be... If the system requires the total imaging time to not exceed Then the maximum chosen Taylor expansion order must satisfy the following condition. ,in This indicates rounding down, selecting a higher order to optimize imaging accuracy while ensuring that the imaging time meets the requirements; After determining the expansion order O, a Taylor expansion is performed on the redundant phase terms: in, The center frequency.

5. The far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar according to claim 4, characterized in that, In step S4, two-dimensional fast Fourier transforms are performed on the compensated decoupled echo signals of different orders to obtain the range compression and azimuth focusing results, as shown in the following formula: in, The results are for distance compression and azimuth focusing. and These are two variables defined in pseudopolar coordinates: the bibase slant distance and the azimuth sine. For the inverse Fourier transform operator along the pseudopolar coordinate α direction, This is the Fourier transform operator along the pseudopolar coordinate β direction.

6. The far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar according to claim 5, characterized in that, In step S5, a pseudo-polar coordinate system image is obtained with the bibase slope distance and azimuth sine value as variables, as shown in the following formula: 。 7. The far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar according to claim 6, characterized in that, In step S6, the pseudo-polar coordinate image is finally converted to rectangular coordinates, and the two-dimensional imaging result is output, as shown in the following formula: Where (x0, y0) are the target coordinates in the rectangular coordinate system.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements a far-field pseudo-polarization imaging method for a space-based external radiation source ground-based synthetic aperture radar as described in any one of claims 1-7.

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