A bistatic SAR two-dimensional space-variant high-precision phase error compensation processing method

Abstract

This invention discloses a two-dimensional spatially varied high-precision phase error compensation method for bistatic SAR. This method is based on two-dimensional sparse autofocusing bistatic SAR moving target imaging processing. Its main steps include: constructing a bistatic SAR data acquisition geometric model, acquiring echo data, processing it using PFA, and deriving the two-dimensional frequency phase error; analyzing the spatially varied characteristics of the two-dimensional phase error expression; performing coarse compensation on the image based on the derived two-dimensional phase error expression; after coarse compensation, performing range spatially varied compensation in the range direction, azimuth spatially varied compensation, and image segmentation and stitching. Experimental simulations verify the effectiveness of this invention's two-dimensional compensation method under arbitrary tracks and arbitrary motions.

Description

Technical Field

[0001] This invention relates to a two-dimensional high-precision phase error compensation method for bistatic SAR, belonging to the field of radar image processing technology. Background Technology

[0002] Synthetic Aperture Radar (SAR) is an all-weather, all-day, high-resolution imaging radar that is now widely used in important scenarios such as terrain exploration, resource detection, and disaster monitoring. Bistatic SAR, with its transmitter and receiver located on separate platforms, offers advantages over monostatic SAR, including stronger counter-surveillance, anti-jamming, and survivability, making it highly valuable for civilian applications. Bistatic SAR can monitor both stationary and moving targets.

[0003] The Polar Format Algorithm (PFA) is a classic SAR spotting mode imaging algorithm. In bistatic SAR system imaging, PFA is an effective choice. However, in bistatic SAR imaging systems, the plane wavefront assumption in PFA processing introduces range migration and azimuth phase shifts into the radar echo data, leading to image defocusing and quality degradation. One-dimensional azimuth phase error compensation alone cannot achieve good focusing results; therefore, to obtain high-quality, high-resolution SAR images, two-dimensional spatially varied phase error compensation is required. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings and deficiencies of the existing technology by proposing a two-dimensional spatially variable high-precision phase error compensation method for bistatic SAR. This method can derive a two-dimensional phase error model, first pre-compensate the original PFA data, and then perform coarse compensation in the range and azimuth directions to achieve better focusing effect and obtain high-quality focused images.

[0005] The technical solution adopted by this invention to solve its technical problem is: a two-dimensional spatially variable high-precision phase error compensation processing method for bistatic SAR. This method uses phase compensation based on echo signals to achieve good refocusing of bistatic PFA images under any track, including the following steps: Step S1: Construct a bistatic SAR data acquisition geometric model and obtain the echo data model. By constructing a bistatic SAR signal model, the echo signal model is obtained as follows: in Spatial frequency, azimuth sampling time by Centered on, It is the distance-oriented envelope. It is the directional envelope; Step S2: Perform two-dimensional frequency-phase error derivation on the signal after imaging processing. The phase error expression is as follows: in and The numerical value can be obtained by polar coordinate transformation of the bibase PFA, which covers the interpolation error and avoids the analytical expression estimation error introduced by insufficient order of series inversion. Step S3: Perform spatial variation characteristic analysis on the two-dimensional phase error expression; Step S4: Perform coarse compensation on the image based on the derived two-dimensional phase error expression; Step S5: After coarse compensation, perform spatial variation compensation in the distance direction, perform azimuth spatial variation compensation on the image, and stitch the images together in blocks.

[0006] Beneficial effects: 1. This invention derives the two-dimensional phase error of bistatic PFA images under arbitrary tracks, and performs pre-compensation and two-dimensional spatial variation compensation on the original PFA data by decomposing the phase error, thereby achieving image refocusing processing to obtain high-quality focused images.

[0007] 2. Experimental simulation verifies the effectiveness of the two-dimensional compensation method of this invention under arbitrary trajectory and arbitrary motion. Attached Figure Description

[0008] Figure 1 This is a flowchart of the method of the present invention.

[0009] Figure 2 This is a schematic diagram of the passive bistatic SAR signal sampling geometric model in this invention.

[0010] Figure 3 The diagram shows the phase distribution of data in polar coordinate format: (a) Two-dimensional phase distribution before polar coordinate format conversion; (b) Two-dimensional phase distribution after polar coordinate format conversion.

[0011] Figure 4 For the simulation target's higher-order phase error and RCM: (a) Simulated point target; (b) Bistatic PFA image; (c) RCM and (d) higher-order phase error in formula (2) before polar coordinate format conversion; (e) RCM and (f) higher-order phase error after polar coordinate format conversion; (g) RCM and (h) higher-order phase error after RCMC and range-space variable compensation.

[0012] Figure 5For comparison of residual phase error differences: (a) the phase error difference between two targets at the same azimuth position but different range positions; (b) the phase error between targets at the same range but different azimuth positions.

[0013] Figure 6 For the comparison of the target IRF and azimuth profile under the frontal side view, (a) and (b) are bistatic PFA images; (c) and (d) are the azimuth secondary phase error compensation results corresponding to formula (8); (e) and (f) are the two-dimensional compensation results corresponding to formula (10); (g) and (b) are the two-dimensional compensation results of the model corresponding to formula (12).

[0014] Figure 7 Figures (a) and (b) are bistatic PFA images of the target IRFs and azimuth profiles under curved flight paths; Figures (c) and (d) show the azimuth quadratic phase error compensation results corresponding to formula (8); Figures (e) and (f) show the two-dimensional compensation results corresponding to formula (10); Figures (g) and (h) show the two-dimensional compensation results of the model corresponding to formula (12).

[0015] Figure 8 To simulate four transmitter tracks: (a) track 1; (b) track 2; (c) track 3; (d) track 4.

[0016] Figure 9 The phase error in polar coordinate format corresponding to the target under four different trajectories is shown in (a) bistatic PFA image patch; (b) azimuth quadratic phase error compensation result calculated based on formula (8); and (c) two-dimensional filtering result based on formula (9).

[17] (d) Image compensation results calculated based on formula (10). (Note: The image results from left to right correspond to tracks 1-4 respectively.) Figure 10 The calculation deviations for three different models are shown in the diagram: (a) the estimated deviation corresponding to formula (8); (b) the estimated deviation corresponding to formula (9); and (c) the estimated deviation corresponding to the derivation model (10) of this invention.

[0017] Figure 11 Deviation between the MSR model and the target's true phase under track 1 condition: (a) Spatial frequency estimation deviation; (b) Azimuth time calculation error; (c) Schematic diagram of differential distance calculation error.

[0018] Figure 12 The following are schematic diagrams of the simulated point target arrays: (a) Scenario 1; (b) Scenario 2; (c) Scenario 3.

[0019] Figure 13The diagrams show the trajectory offset curves for scenarios (a) 1, (b) 2, and (c) 3.

[0020] Figure 14 The imaging results for Scene 1 are shown in the following diagrams: (a) Bistatic PFA; (b) Azimuth-directed secondary phase error compensation; (c) Two-dimensional phase error compensation based on formula (10); and (d) Schematic diagram of the method of the present invention.

[0021] Figure 15 The imaging results for Scene 2 are shown in the following diagrams: (a) Bistatic PFA; (b) Azimuth-directed secondary phase error compensation; (c) Two-dimensional phase error compensation based on formula (10); and (d) Schematic diagram of the method of the present invention.

[0022] Figure 16 Comparison of target azimuth profiles: (a) center point; (b) target point at the azimuth edge; (c) target point at the range edge. Figure 17 Scenario 3 Imaging results under nonlinear trajectory: (a) Bistatic PFA; (b) Azimuth-direction secondary phase error compensation; (c) Two-dimensional phase error compensation based on formula (10); (d) Schematic diagram of the method of the present invention.

[0023] Figure 18 Comparison of PFA imaging results and the compensation results of the algorithm of this invention: (a) PFA image; (b) Figure 18 (a) corresponds to the distance towards the scene edge; (c) Figure 18 (a) Scene edge in the Chinese orientation; (d) Image after range-direction spatial compensation; (e) Figure 18 (d) Mid-range towards the scene edge; (f) Figure 18 (d) Scene edge in the Chinese orientation; (g) Result after distance and orientation compensation; (h) Figure 18 (g) Mid-range towards the scene edge; (i) Figure 18 (g) Schematic diagram of the scene edge in the Chinese orientation. Detailed Implementation

[0024] To enhance understanding of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. These embodiments are only used to explain the invention and do not limit the scope of protection of the invention.

[0025] like Figure 1 As shown, this invention provides a two-dimensional spatially variable high-precision phase error compensation method for bistatic SAR, which specifically includes the following steps: Step S1: Construct a bistatic SAR data acquisition geometric model and obtain an echo data model; Step S2: Derive the two-dimensional frequency and phase error of the signal after PFA processing; Step S3: Perform spatial variation characteristic analysis on the two-dimensional phase error expression; Step S4: Perform coarse compensation on the image based on the derived two-dimensional phase error expression; Step S5: After coarse compensation, perform spatial variation compensation in the distance direction, perform spatial variation compensation in the azimuth direction, and stitch the image into blocks. Step S6: Experimental simulation verifies the effectiveness of the two-dimensional compensation method in this invention under arbitrary trajectory and arbitrary motion.

[0026] Figure 2 The spatial geometric model of bistatic SAR data acquisition is described. Without loss of generality, the scene center is defined as the origin of the coordinate system, and the transmitter and receiver are placed on different platforms and fly along different tracks. At any azimuth sampling time... The angle of view of the transmitter and receiver is defined as follows: Pitch angle is defined as Bistatic echo signals can be represented as: (1) in Spatial frequency, azimuth sampling time by Centered on, It is the distance-oriented envelope. It is the azimuth envelope. The phase in formula (1) can be expressed as: (2) in: (3a) (3b) (3c) (3d) (3e) It is defined as the difference distance term. In formula (3), and These represent the instantaneous distances from the transmitter and receiver to the center of the scene, respectively. (Symbols) and This corresponds to the distance from the radar platform to the point target. The instantaneous propagation distance. The two-dimensional coordinates of the transmitter and receiver are represented as follows: and .symbol and These represent the heights of the transmitter and receiver, respectively.

[0027] The specific process of step S2 above includes: Bistatic PFA imaging uses the plane wavefront assumption to approximate the phase in formula (3) as: (4) Among them, the distance spatial frequency and azimuth spatial frequency Defined respectively (5a) and (5b) As can be seen from formula (4), the phase of the echo signal on the plane wavefront can be approximately considered as the Fourier transform of the target radar reflection coefficient. However, in a bistatic SAR system, the separate transmission and reception locations result in a change in spatial frequency. and The sampling area is tilted and rotated along a certain angle. At this point, the spatial frequency sampling points are not uniformly distributed, making it impossible to directly perform a Fourier transform on the echo data. Typically, a resampling operation is needed to perform a polar coordinate format transformation, followed by a two-dimensional inverse Fourier transform to obtain the image. To fully utilize the acquired data, the spatial frequency can be rotated before resampling. The rotated spatial frequency is denoted as... and The bistatic SAR signal in formula (1) can be rewritten as: (6) In formula (6), This represents the target coordinates after coordinate system transformation. Then, performing polar coordinate transformation and two-dimensional inverse Fourier transform yields a bistatic SAR image. Bistatic PFA imaging uses the planar wavefront assumption to approximate the echo phase, assuming the received signal is a Fourier transform of the target radar scattering coefficient. After polar coordinate interpolation, this approximation error can be partially compensated, but residual wavefront curvature error still exists, leading to image geometric distortion and defocusing. Existing literature discusses wavefront curvature error in monostatic PFA, but only compensates for the second-order Taylor expansion azimuth phase error. However, in bistatic SAR systems, residual RCM and higher-order modulation phase are more severe and cannot be ignored. Therefore, it is necessary to discuss a more accurate and robust two-dimensional phase error compensation process for bistatic PFA images. This invention mainly discusses in detail the derivation and analysis of two-dimensional phase error.

[0028] After bistatic PFA imaging processing, residual phase error still exists in the target impulse response functions (IRF). , (7) In formula (7), the phase term is simultaneously affected by the residual difference distance. and spatial frequency term The phase term in formula (7) becomes more severe when the target is far from the center of the scene, causing a rapid decline in focus quality, which must be compensated for.

[0029] Typically, the azimuth sampling time The relationship between the resampling spatial frequency and the frequency cannot be directly obtained, making it difficult to derive the analytical expression of formula (7). Considering that azimuth defocus is more severe in bistatic PFA images in most cases, some literature has proposed using the second-order Taylor expansion phase of formula (7) for wavefront bending error correction. At the same time, the residual RCM and higher-order modulation phase that may exist after polar coordinate format transformation are all ignored. [8],

[10] -

[12] In these studies, the azimuth filter function can be expressed as: (8) in These are the second-order modulation coefficients in the azimuth direction. However, the coefficients under a bistatic configuration... The expression is very complex and heavily dependent on the radar platform's flight path. When the platform's path contains errors or is nonlinear, The expression needs to be re-derived, which is not convenient for widespread application. In addition, since the track of the bistatic SAR platform is relatively more complex, the accuracy of the azimuth secondary modulation phase compensation processing may not meet the image focusing quality requirements.

[0030] To further improve the accuracy of phase compensation, a more accurate phase model for wavefront bending error must be derived. The second-order azimuth phase error model relies on the Taylor expansion of equation (7), but its accuracy is limited by the order of the expansion expression, making it far less accurate than directly using the second-order phase error model of equation (7) for compensation. Based on the MSR method, we derived the analytical expression for the two-dimensional phase error: (9) in, as well as The detailed derivation of formula (9) is listed in reference

[17] .

[0031] Typically, when the expansion order used in the MSR method is sufficiently high, the estimation error of the model in Equation (11) can be ignored. However, when the resolution of the bistatic SAR system is high or the scene is large, the above estimation error still exists. Furthermore, the interpolation operation in PFA alters the phase history distribution of the echoes, specifically as follows: Figure 3 As shown, this leads to a further increase in estimation error.

[0032] The second-order azimuth phase error model of this invention neglects residual RCM and higher-order modulation phase, while the two-dimensional MSR model is affected by the order of series inversion and interpolation errors. Furthermore, the derivation of the analytical expressions for the two phase errors mentioned above is very complex and easily affected by radar platform tracks, requiring re-deriving. Therefore, in bistatic SAR systems, when the resolution is high or the scene is large, it is necessary to derive a more accurate two-dimensional phase error model. Typically, it is easy to think of increasing the order of the Taylor expansion and series inversion to improve the accuracy of the wavefront bending error model. However, previous studies have found that simply increasing the order has limited effect on improving the accuracy of the phase error model. This invention proposes a numerical calculation method for a two-dimensional phase error model.

[0033] Define the azimuth time and space frequencies after resampling as and The phase in formula (7) can be rewritten as: (10) In formula (10), and The numerical value can be obtained through polar coordinate transformation of the bistatic PFA, which includes interpolation error and avoids the analytical expression estimation error introduced by insufficient order of series inversion. Therefore, compared with the existing phase error model, the two-dimensional phase error model in formula (10) has higher accuracy, considering not only the azimuth modulation phase, but also the interpolation error, residual RCM, and two-dimensional coupling phase. Therefore, formula (10) can obviously be used as a universal polar coordinate format phase error under any track configuration. In addition, and It can also be represented by fitting. and The analytical function is obtained, and then the analytical expression of formula (10) is obtained.

[0034] Apply formula (10) along and Taylor expansion yields: (11) in (12a) , (12b) (12c) In formula (11), the symbol Represented as The sampled values ​​at the center of the aperture. Represents phase term right and The derivatives of the parts. Formulas (11)-(12) in this invention can all be calculated using numerical methods, and the specific derivation process is given in Appendix A.

[0035] The Taylor expansion approximation in Equation (11) is one of the commonly used operations in existing research. In Equation (11), the coefficients... and These represent the positions of the target in the image domain. Typically, the target's position deviates from its true coordinates after PFA imaging, and this deviation is defined as geometric distortion. Quadratic term The azimuth modulation phase is the main factor causing defocusing in PFA images. As can be seen from formula (11), all the coefficients... All of these are closely related to radar system parameters and target coordinates, and thus exhibit spatially variable characteristics.

[0036] The specific steps of step S3 of this invention are as follows: As can be seen from formula (10), the two-dimensional phase error model is closely related to the radar system parameters and the instantaneous propagation distance of electromagnetic waves. In formula (10), the first term... It is deterministic and uniform for all objectives. In contrast, the difference distance term... This mainly contributes to the spatially varying characteristics of wavefront bending error. Therefore, the analysis of the spatially varying characteristics of wavefront bending error essentially only requires analysis of the differential distance term. Perform the analysis.

[0037] Considering the geometric distortion in PFA images, images with the same bistatic propagation distance... goal This will focus on different azimuth positions within the same range gate unit. Therefore, the difference distance and the true target coordinates will not be discussed here. Instead of studying the relationship between bistatic propagation distance and image domain location, the study shifted to investigating the relationship between bistatic propagation distance and image domain location. The relationship. As is well known, those with the same propagation distance The target will be located on an ellipse after PFA imaging. Based on the ellipse parametric equation, targets imaged at the same range gate will have the following relationship: (13a) (13b) in: In formula (13), and Let represent the two-dimensional coordinates of the transmitter and receiver at the time of the aperture center, respectively. and It is then defined as the flight altitude of the radar platform at the moment of aperture center. coordinates The propagation distance at the center of the aperture at that moment. This represents the centrifugal angle of the target. In formula (13), the foci of the ellipse are respectively... and The lengths of the major and minor axes of the ellipse are respectively and Based on formula (12), the target coordinates can be obtained. and The relationship is: (14) in: Substituting the expression in formula (14) into the bibase distance term and performing a Taylor expansion, we can obtain the following: (15) in: , (16) In formula (15), It is the distance from the center of the aperture to the center of the scene by the sampling time radar, and the coefficient. Given in Appendix B. It can be seen from formula (15) that the wavefront bending error varies with the target's range and azimuth position. When the radar platform along... In axial flight, wavefront bending error mainly depends on and The relevant terms exhibit a strong azimuth spatial dependence and a weak range-position correlation. The last term in formula (15) The spatiotemporal coupling characteristics of dark spacetime are usually small and can be ignored. Therefore, it can be concluded that the range and azimuth spatial variation characteristics of bistatic distances can be decomposed and compensated without loss of generality, and the above conclusions can be extended to any track configuration.

[0038] The specific steps of step S4 in this invention are as follows: the distance and azimuth spatial variation characteristics of the phase error can be decomposed and processed separately. The center position of the sub-image block is defined as... The position of any pixel in the sub-image is In formula (9), the phase can be decomposed into... (17) in: (18a) (18b) (18c) The following relationships exist: , , , It can be decomposed into three components, of which This can be expressed as the phase error at the center of the sub-image. and These are described as range spatial variation and azimuth spatial variation phases, respectively. As stated in the formula above, the target's position in the image domain... It can be represented as its true location. The function. Generally speaking, and The analytical expression can be derived based on formula (12), but the true coordinates of the target can be inferred from the image domain position. and It is difficult to solve directly. This invention employs an iterative solution method to invert the true coordinates of the target. .

[0039] phase As the target distance moves towards the position The change manifests as the spatially varying distance characteristics of the wavefront bending error. Furthermore, As the target's two-dimensional coordinates transform, it can be used to describe the spatial variation characteristics of azimuth and cross-coupling features.

[0040] Typically, given the radar flight path and target coordinates After that, phase It can be calculated based on formula (18a). Then, the sub-image can be obtained by referring to the following phase error. The compensation yielded: (19) Secondary phase compensation processing with existing azimuth

[11] -

[13] Unlike other methods, the operation in formula (19) is implemented in the two-dimensional frequency domain, which not only corrects the azimuth secondary modulation phase, but also considers RCM and higher-order modulation phase compensation, resulting in higher accuracy. When the sub-image is compensated using formula (19), its central target point is refocused, but the wavefront bending error of the target at the scene edge can only be partially compensated, and residual defocus still exists.

[0041] The specific steps of step S5 in this invention are as follows: As can be seen from formula (19), the residual phase error is still two-dimensional spatially variable. In order to achieve high-precision compensation of the residual phase error as much as possible, this invention constructs range-direction and azimuth-direction spatially variable filters for refocusing processing. This invention first provides a detailed introduction to range spatially variable compensation.

[0042] Formula (19) can be approximated based on Taylor expansion as follows: (20) in: (21a) (21b) (21c) (21d) (21e) The residual phase includes the azimuth modulation term. First-order distance spatial frequency term The phase is modulated by higher-order range frequencies. The first-order range spatial frequency term represents the target's residual RCM. Based on experimental data analysis, this first-order term is not sensitive to azimuth spatial frequencies and does not exhibit significant spatial variation characteristics.

[0043] To further verify the above conclusions, this invention simulates bistatic SAR echo data of 29 targets at a resolution of 0.13m. After PFA processing, this echo data yields an image, as shown below. Figure 3 As shown in (a) and (b), the simulated scene size is 700m x 800m, far exceeding the effective focusing range of 200m under this resolution condition. After performing a range-to-Fourier transform on the simulated data and the data after PFA polar coordinate format transformation, the corresponding residual RCM image can be observed. The echo RCM and its spatially variable characteristics have been partially compensated after PFA imaging. The higher-order range-frequency phase error at the scene edge points... The phase error corresponding to the edge point after PFA processing. The higher-order distance-frequency phase error of the edge point after PFA processing is much smaller than... It can be ignored.

[0044] Performing a distance-to-inverse Fourier transform on equation (19) yields: (twenty two) Among them, symbols Represented as the sinc function, its peak position is... In formula (22), the residual RCM is determined by the relative distance from the target to the center of the sub-image, and can be corrected through interpolation or range-frequency domain linear phase compensation. The RCM value to be corrected can be obtained through numerical calculation. Subsequently, a range-space-variable filter can be constructed. (twenty three) In formula (23), the bistatic residual phase error It can be based on the target image domain location The calculation yielded the following result. The range sampling position changes with the range gate unit. This indicates the azimuth position corresponding to the center of the sub-image block. Formula (23) only considers the realization of spatial variation compensation in the range direction and temporarily does not consider the spatial variation characteristics in the azimuth direction.

[0045] After applying range migration correction and range spatial variation compensation to the echo data in formula (23), we can obtain: (twenty four) in, This is the range gate position of the target focus after range migration correction. From formula (24), it can be seen that the range spatial variation characteristic exhibiting response function defocusing in the figure is basically eliminated after compensation by formula (23). Furthermore, the target's corresponding RCM and higher-order phase errors are also compensated after range spatial variation compensation. The target echo RCM has been basically compensated, and the remaining higher-order phase errors are very small and can be ignored.

[0046] Even after range-space variation compensation, residual phase terms still exist in the target echo. This results in the azimuth of the edge targets in the image still exhibiting defocus linearity. Fortunately... Mainly depending on the orientation and position Changes are rarely affected by distance to position. The impact of these changes, specifically as follows: Figure 4 As shown, the phase errors of targets at different azimuth positions differ significantly, while the phase error differences of targets at different range gate elements are very small. This further verifies the conclusion obtained in Section 2 that the cross-coupling phase is small and negligible. Therefore, it can be considered that... Approximately: (25) The phase space variation term in formula (25) can be compensated by the following filter: (26) Since residual defocus mainly varies with azimuth position, the filter function in formula (26) needs to consider the spatial variation characteristics of the azimuth, which can be compensated in each range gate unit. The filter function is constructed as a matrix. Any one of these elements can be represented as: (27) Formula (27) is essentially a spatial frequency of orientation. and directional position The function. Apply the above filter matrix to the data after range spatial variation compensation. It can achieve azimuth-to-space variation compensation.

[0047] After compensation processing, most targets in the sub-image block will achieve refocusing compensation, improving image quality and effectively expanding the scene's focus range. Furthermore, in practical applications, the algorithm of this invention can merge block processing to achieve refocusing processing for larger scenes, as detailed in the following process... Figure 5 As shown. Compared with existing block filtering algorithms, the phase error model of this invention has higher accuracy and stronger robustness. The compensation process of this invention simultaneously considers the distance and azimuth spatial variation characteristics of the target phase error in the sub-image, which can achieve higher precision refocusing and greatly expand the effective focusing range of the sub-image, which is beneficial for large-scene and high-resolution application scenarios.

[0048] The specific steps of S6 of this invention are as follows: experimental simulation verifies the effectiveness of the two-dimensional sparse self-focusing method for moving targets under arbitrary tracks and arbitrary motions in this invention.

[0049] The bistatic echo data of any target in the scene under simulated frontal, side-view and oblique view conditions are obtained. Then, azimuth quadratic filters (azimuth quadratic filter, azimuth quadratic error compensation) are constructed using formula (8).

[10] Formula (9) MSR phase model, and a two-dimensional filter is constructed using formula (10) derived in this invention for compensation processing, and the results are compared and analyzed. The radar simulation parameters are shown in Table 1. Among them, in the case of frontal side view, the radar transmitter and receiver platform are along The axes fly in parallel tracks at speeds of 200 m / s and 259 m / s respectively. In oblique view, the tracks of the two platforms are not parallel, but intersect at a 30° angle.

[0050] The simulated target echo was processed by bistatic PFA imaging and then subjected to impulse response analysis. Its impulse response function (IRF) is as follows: Figure 6 As shown in (a)-(b), the images show a significant wavefront bending error due to the target's distance from the scene's center, resulting in defocusing. The PFA images are compensated by applying formula (8) for azimuthal secondary phase error compensation, formula (9) for the MSR spectrum, and the filter constructed using the two-dimensional phase error model presented in this invention. The corresponding IRF of the target is shown below. Figure 6 (c)-(f) and Figure 7 As shown in (c)-(f), the measured values ​​obtained after impulse response analysis, such as the impulse response width (IRW) and peak sidelobe ratio (PSLR), are listed in Table 2. Comparing the above impulse response analysis results and indicators, it can be found that azimuth quadratic phase error compensation and MSR spectral filtering can improve image focusing quality to some extent, but residual phase errors still exist. In contrast, the phase error compensation accuracy obtained by constructing the filter using the two-dimensional phase error model of this invention is higher.

[0051] Table 1 Simulation Parameter Table Table 2. IRF Analysis Results To further verify the accuracy of the phase error model corresponding to formula (10), this invention further simulated bistatic SAR echo data of any target under different trajectories. The receiver trajectory was kept consistent with the trajectory parameters in the squint case in Table 1, while the transmitter trajectory was set to fly along different paths, such as... Figure 8 As shown in (a)-(d), the simulated echo data were processed by a bistatic PFA and then compensated by the azimuth secondary phase error compensation corresponding to formula (8), the two-dimensional filter constructed by formula (9) and formula (10) of this invention. The results are shown in Figure 9.

[0052] As can be seen from the above results, the azimuth-direction secondary phase error compensation can partially compensate for wavefront bending errors, but it cannot address the residual RCM problem of the target. The two-dimensional filter constructed from the MSR spectrum in formula (9) can achieve refocusing of PFA images in most cases, but the compensation error increases under high resolution, large scenes, or extremely imperfect tracks. In contrast, our phase error model achieves compensation with higher accuracy, greatly improving the focusing quality of the image.

[0053] Further analysis of the above three types of phase error models is needed in Figure 10 The following is given. It is noted that, considering the constant and first-order linear phase error have no effect on image focusing, Figure 10 These two items were removed from the mid-phase error calculation. From... Figure 10 It can be seen that the wavefront bending error estimation accuracy of the model of this invention is higher and the robustness is stronger.

[0054] Furthermore, regarding the MSR spectral phase error model in formula (10)

[17] Further analysis was conducted on the model of this invention. Generally, when the Taylor expansion order used in MSR processing is sufficiently high, the accuracy of the wavefront bending phase estimation corresponding to the spectrum can meet the requirements, and the error is small enough to be negligible. However, in actual simulation processing, it was found that there is an interpolation error after the polar coordinate format conversion of PFA, which leads to a decrease in the accuracy of the MSR spectrum in formula (10). In PFA processing, both the range spatial frequency and the azimuth sampling time are transformed into polar coordinate format through interpolation. Therefore, there are some errors between the value of the parameter variable after the interpolation and the value calculated by the analytical formula, which will affect the accuracy of the MSR spectrum. The following interpolation error formula is defined: in, It is the range-direction spatial frequency estimation error, in Figure 11 As given in (a), For the azimuth time resampling error, in Figure 11 As given in (b), Then it means Figure 11 (c) shows the differential distance error. As can be seen from these figures, the interpolation errors corresponding to the range frequency and azimuth time are usually small, but the differential distance error introduced by the superposition of the two may be amplified and cannot be ignored.

[0055] Simulated bistatic SAR echo data under three different flight paths were used to process the data using the space-variable filtering compensation method described in this invention. A 30×30 rectangular dot matrix was set in the scene, as shown below. Figure 12 As shown in (a). Where any two neighboring target points are... and The axis spacing was set to 20m and 25m (Scenario 1 and Scenario 2), and 15m and 20m (Scenario 3), respectively. The radar simulation parameters are shown in Table 1. However, the flight path differs from the original linear path, exhibiting some deviations, such as... Figure 13 As shown in the figure. Among them, the trajectory deviation in scenario 3 is more severe than that in scenarios 1 and 2.

[0056] Analysis shows that the effective focusing range of a bistatic PFA is approximately 200m. However, due to offsets in the flight path, the effective focusing range in real-world scenarios will be much smaller than 200m. Figure 14-17 As shown. In the simulation of this invention, the size of the scene far exceeds the effective focusing range mentioned above. PFA imaging processing was performed on the simulated echo, and the results are as follows. Figure 14-17 As shown in the figures, the horizontal axis represents the range sampling unit, and the vertical axis represents the azimuth sampling unit. These figures reveal significant defocusing and geometric distortion in bistatic PFA imaging, particularly when the target is far from the scene center, where the defocusing becomes more severe.

[0057] To verify the extension of the effective focusing range of the algorithm in this invention, the bistatic PFA image of the simulated scene was directly applied without block division to azimuth quadratic phase error compensation, MSR spectrum, and the spatially varied two-dimensional filtering processing of this invention. The azimuth quadratic phase error compensation and MSR filter are both calculated based on the center coordinates of the sub-image blocks and the radar track. In the spatially varied filtering processing of this invention, the reference filter is calculated based on the center coordinates of the image blocks, followed by range spatially varied filtering and azimuth spatially varied filtering. The results after the above filtering processing are as follows: Figure 14-15 The results are given. To further verify the effectiveness of the algorithm of this invention, a comparative analysis was conducted on the azimuth profiles corresponding to the IRF of the target in the reconstructed images after the above three processing steps. The results are as follows: Figure 16 As shown.

[0058] from Figure 14-17 As can be seen, due to the lack of block processing and the limited accuracy of the phase error model, defocusing still exists in the image after azimuth secondary phase error compensation and MSR spectral filtering. In contrast, the focus quality of the image reconstructed by the method of this invention is greatly improved. Although no block processing is applied, the focus quality of distance and azimuth edge targets is effectively improved. Compared with the non-block processing results of the other two models, the focus quality and effective focus range of the scene reconstructed by the algorithm of this invention are improved.

[0059] Furthermore, considering that there are some approximations in the spatially varying filtering process of this invention, the algorithm performance may decrease under ultra-high resolution, ultra-large scenes, or more curved paths, such as... Figure 17 As shown in (d). At this point, block processing can also be combined to further improve the performance of the algorithm of the present invention and expand the effective focusing range of the scene.

[0060] To further verify the effectiveness of the algorithm of this invention, large scene gotcha data from the Air Force Research Laboratory (AFRL) in the United States was processed. The range and azimuth resolutions were 0.25m and 0.6m, respectively. PFA imaging was performed on the data without sub-image block decomposition, and compensation processing was performed based on the method described in this invention. The size of the illuminated scene was 4000m×5000m, and the effective focusing range of PFA was 696m.

[11] The PFA image obtained after processing is as follows: Figure 18 As shown in (a), the horizontal axis represents the distance direction and the vertical axis represents the azimuth direction. Figure 18 (a) The image patches within the white rectangles shown represent the regions closest to and oriented towards the scene edge, respectively. The result after magnification of this region is... Figure 18 As shown in (b) and 18(c), the defocusing is more severe when the target is far from the scene. Based on the distance and azimuth spatial variation compensation processing shown in this invention, the distance edge and azimuth edge sub-image blocks are... Figure 18 (e)-(f) and Figure 18 The results are given in (h)-(i). Compared with the original image patch, the compensated image achieves refocusing processing, and the focus quality is improved. Although sub-image patch decomposition is not performed, the effective focus range of the scene is also greatly expanded, verifying the effectiveness of the algorithm of this invention.

[0061] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for high-precision phase error compensation processing in two-dimensional spatially varying bistatic SAR, characterized in that, Includes the following steps: Step S1: Construct a bistatic SAR data acquisition geometric model and obtain the echo data model. By constructing a bistatic SAR signal model, the echo signal model is obtained as follows: in Spatial frequency, azimuth sampling time by Centered on, It is the distance-oriented envelope. It is the directional envelope; Step S2: Perform two-dimensional frequency-phase error derivation on the signal after imaging processing. The phase error expression is obtained as follows: in and The numerical value can be obtained by polar coordinate transformation of the bibase PFA, which covers the interpolation error and avoids the analytical expression estimation error introduced by insufficient order of series inversion. Step S3: Perform spatial variation characteristic analysis on the two-dimensional phase error expression; Step S4: Perform coarse compensation on the image based on the derived two-dimensional phase error expression; Step S5: After coarse compensation, perform spatial variation compensation in the distance direction, perform azimuth spatial variation compensation on the image, and stitch the images together in blocks.

2. The bistatic SAR two-dimensional spatially variable high-precision phase error compensation method according to claim 1, characterized in that, Step S2 includes: bistatic PFA imaging uses the plane wavefront assumption to approximate the phase in formula (3) as follows: , (4) Among them, the distance spatial frequency and azimuth spatial frequency Defined respectively [1] , (5a) and , (5b)。 3. The method for high-precision phase error compensation processing of two-dimensional spatially varying bistatic SAR according to claim 1, characterized in that, Step S3 includes: formula In (10), the first item The difference distance term is deterministic and uniform for all objectives. The spatially varying characteristics of wavefront bending error contribute to this; essentially, the analysis of these characteristics only requires examining the differential distance term. Perform the analysis.

4. The bistatic SAR two-dimensional spatially variable high-precision phase error compensation method according to claim 1, characterized in that, Step S4 includes: the distance and azimuth spatial variation characteristics of the phase error can be decomposed and processed separately, and the center position of the sub-image block is defined as... The position of any pixel in the sub-image is In formula (9), the phase can be decomposed into... (17) in: , (18a) , (18b) , (18c) The following relationships exist: , , , It can be decomposed into three components, of which This can be expressed as the phase error at the center of the sub-image. and Described as range spatial variation and azimuth spatial variation phases respectively, the target's position in the image domain It can be represented as its true location. The function, in general, and The analytical expression can be derived based on formula (12), but the true coordinates of the target can be inferred from the image domain position. and It is difficult to solve directly, so the method described uses an iterative solution to invert the true coordinates of the target. .

5. The bistatic SAR two-dimensional spatially variable high-precision phase error compensation method according to claim 1, characterized in that, Step S5 includes: providing a detailed introduction to distance spatial variation compensation; Formula (19) can be approximated based on Taylor expansion as follows: (20) in: , (21a) (21b) (21c) (21d) (21e) The residual phase includes the azimuth modulation term. First-order distance spatial frequency term And higher-order range frequency modulation phase, where the first-order range spatial frequency term represents the residual RCM of the target. According to experimental data analysis, this first-order term is not sensitive to the azimuth spatial frequency and does not have obvious spatial variation characteristics.

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