SAR frequency domain imaging method for mid-latitude curve based on space-varying azimuth preprocessing

Abstract

This invention discloses a mid-orbit curve SAR frequency domain imaging method based on spatially varied azimuth preprocessing. This invention relates to an imaging algorithm that, under long synthetic aperture time and slant-look observation geometry conditions, suppresses the two-dimensional spatial variation of range cell migration (RCM) through improved azimuth resampling technology, thereby achieving high-precision focusing. This invention is achieved through the following technical solution: Step 1, constructing a two-dimensional spatially varied model of the higher-order slant range history and its parameters for MEO SAR. Step 2, establishing an improved azimuth resampling model based on range gate dependence. Step 3, solving for the optimal azimuth resampling coefficients. Step 4, performing improved azimuth resampling and imaging focusing processing.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing and remote sensing imaging technology, specifically relating to an imaging processing method suitable for Medium Earth Orbit (MEO) Synthetic Aperture Radar (SAR) systems. More specifically, this invention relates to an imaging algorithm that, under conditions of long synthetic aperture time and oblique observation geometry, suppresses the two-dimensional spatial variation of range cell migration (RCM) through improved azimuth resampling technology, thereby achieving high-precision focusing. Background Technology

[0002] Synthetic Aperture Radar (SAR) is an active microwave remote sensing imaging system that transmits and receives electromagnetic waves. It achieves high resolution in the azimuth direction using the synthetic aperture principle and high resolution in the range direction using pulse compression technology. Compared with optical sensors, SAR has unique advantages such as all-weather, all-day operation and the ability to penetrate surface vegetation. Therefore, it is widely used in military reconnaissance, topographic mapping, disaster monitoring, marine observation, and agricultural and forestry yield estimation.

[0003] Traditional spaceborne SAR systems primarily operate in Low Earth Orbit (LEO), typically at altitudes between 500 and 800 kilometers. While LEO SAR technology is mature, its limited orbital altitude restricts its coverage area and results in long revisit cycles, making it difficult to meet the demands for rapid coverage over large areas and high-frequency monitoring of specific hotspots. To overcome these limitations, Medium Earth Orbit (MEO) SAR has gradually become a research hotspot. MEO SAR satellites typically operate in orbits between 2,000 and 20,000 kilometers high. Compared to traditional LEO SAR, MEO SAR offers significant advantages: wider coverage (due to the significantly increased orbital altitude, the observation range per pass is greatly expanded, greatly improving data acquisition efficiency); and shorter revisit cycles (MEO SAR can achieve rapid revisits globally, and even hourly revisits for specific areas).

[0004] However, MEO SAR presents challenges to imaging signal processing in practical applications. To achieve azimuth resolution similar to LEO SAR at higher orbits, the synthetic aperture time must be significantly extended to obtain sufficient Doppler bandwidth. Wide-area observations often require oblique-view observation modes, resulting in significant nonlinear curvature of the relative motion trajectory between the satellite and the target. Traditional "straight-line trajectory" and "stop-go" assumptions fail, and range migration exhibits strong two-dimensional spatial variability (changing drastically with both range and azimuth directions). Conventional imaging methods struggle to accurately compensate for this complex two-dimensional spatially varied error, leading to image defocusing. Existing research often introduces azimuth resampling techniques, which, while maintaining computational efficiency in the frequency domain, "straighten" the curved range migration trajectory by manipulating the time axis, ensuring consistency across different azimuth times and facilitating subsequent batch data processing. However, existing azimuth resampling-based imaging methods still suffer from poor spatial adaptability of parameters and insufficient accuracy of the slant range model under oblique-view and long synthetic aperture conditions.

[0005] To address the issue of edge defocusing in imaging results caused by neglecting the spatial variability of range parameters and low-order approximations of models when processing MEO SAR oblique-look data in existing technologies, this invention provides a MEO SAR frequency domain imaging method based on improved azimuth resampling, which achieves high-precision correction of two-dimensional spatially variable range migration across the entire scene. Summary of the Invention

[0006] The purpose of this invention is to address the image quality degradation problem caused by severe two-dimensional spatial variability of range migration in existing MEO SAR imaging algorithms under conditions of long synthetic aperture time and complex oblique observation geometry. This invention proposes a mid-orbit curve SAR frequency domain imaging method based on spatially varied azimuth preprocessing, and eliminates the two-dimensional spatial variability of RCM by calculating the azimuth resampling coefficients step-by-step through range gates, achieving high-precision focusing across the entire scene.

[0007] The method of this invention is achieved through the following technical solution: A mid-orbit curve SAR frequency domain imaging method based on spatially varied azimuth preprocessing includes: Step 1: Construct a two-dimensional spatially variable model of the high-order slant range history and its parameters of MEO SAR, and characterize the two-dimensional coupling variation of coefficients of each order with the range and azimuth directions, so as to provide an accurate parameter basis for subsequent spatially variable correction. Step 2: Establish an improved azimuth resampling model based on distance gate dependence. Construct the azimuth-time mapping relationship row by row according to the parameters of different distance gates, and reconstruct the correspondence between the slant range history before and after resampling. Step 3: Solve for the optimal azimuth resampling coefficients. With the goal of eliminating the change of the quadratic term coefficients with azimuth time after resampling, the resampling parameters corresponding to each distance gate are analytically obtained, and the numerical inversion method is combined to ensure the accuracy and feasibility of the resampling mapping. Step 4: Perform improved azimuth resampling and imaging focusing processing. Complete the processing according to the process of spatially variable azimuth preprocessing, range compression, and azimuth compression to obtain a high-precision focused image of the entire scene.

[0008] Beneficial effects A range-gate-dependent azimuth resampling strategy is proposed, which no longer uses the parameters at the reference distance as an approximate assumption. This solves the problem of defocusing at the edges caused by the use of reference distance parameters in traditional methods, and ensures consistent high-resolution imaging. It boasts high computational efficiency and is conducive to engineering implementation. This invention introduces a range-gate-based computational processing logic, while the operations are still based on FFT, phase multiplication, and one-dimensional time-domain interpolation. The imaging focusing processing adopts the range CS algorithm and the azimuth NCS algorithm, which maintains computational efficiency comparable to traditional frequency-domain algorithms while ensuring imaging accuracy. Compared with time-domain algorithms, it is more suitable for the rapid processing of large-scale MEO SAR data. Attached Figure Description

[0009] Figure 1 Schematic diagram of the geometric relationship of MEO SAR imaging; Figure 2 A schematic diagram of the k2 spatial variation and the results after optimized polynomial orientation compensation; Figure 3 A schematic diagram of the spatial variation of k2 and the results after improved azimuth resampling processing; Figure 4 A schematic diagram of the algorithm flow of this invention; Figure 5 Schematic diagram of the simulated imaging geometric scene; Figure 6 A comparative diagram showing the changes in the orientation of residual RCM at the edge using different methods; Figure 7 A schematic diagram of the focusing results of typical target points after simulation imaging processing; Figure 8 Method flowchart. Detailed Implementation

[0010] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0011] This invention provides a mid-orbit curve SAR frequency domain imaging method based on spatially varied azimuth preprocessing. The core of this method lies in constructing a two-dimensional spatially varied model of the high-order slant range history and its parameters for MEO SAR, and eliminating the two-dimensional spatial variation of RCM by calculating the azimuth resampling coefficients through range-by-range gate calculation. The specific process is as follows: Figure 4 As shown, the specific steps include: Step 1: Construct a two-dimensional spatially variable model of the high-order slant range history and its parameters of MEO SAR, and characterize the two-dimensional coupling variation of coefficients of each order with the range and azimuth directions, so as to provide an accurate parameter basis for subsequent spatially variable correction. In MEO SAR imaging, due to the long synthetic aperture time and complex observation geometry under oblique look-out conditions, the traditional LEOSAR straight-track assumption and low-order approximation model are no longer applicable, necessitating the construction of a more accurate geometric model. Firstly, as... Figure 1 As shown, an imaging geometric model of the MEO SAR satellite is established. Let t r Let t be the distance and time. a For azimuth time, t p The time of beam center crossing is given. The expression for the MEO SAR satellite echo signal in the azimuth dimension can be expressed as: (1) Among them, u r and u a Let K represent the envelope functions in the range and azimuth directions, respectively. r R(t) represents the range modulation frequency, λ represents the radar wavelength, and c is the speed of light. a The slant range history (R(t)) represents the instantaneous distance between the satellite and the ground target. Due to the high orbit and long synthetic aperture time of MEO SAR, the slant range history exhibits significant nonlinear characteristics. To accurately describe the nonlinear characteristics of the slant range history, a slant range history R(t) is established. a The fifth-order Taylor series expansion model: (2) Where R0 represents t a =t p The nearest slant distance at time k i Let k1 be the i-th order Taylor expansion coefficients. These coefficients depend not only on the orbital parameters but also on the target's ground position. Before azimuth resampling, linear range cell migration correction (LRCMC) is required. The main purpose of LRCMC is to eliminate the linear range migration caused by the k1 term. After LRCMC processing, the first-order term k1 can be ignored. The two-dimensional spatial variation of the remaining RCM is determined by the coefficients k2-k5, with k2 having the greatest impact on spatial variation. The coefficients k2-k5 are established as a function of the reference distance R0 and the beam center crossing time t. p A changing two-dimensional space-variable model: (3) Where, k aij Indicates ki The j-th order azimuth polynomial coefficients are given, and these coefficients vary with distance R0. This model fully considers the evolution of parameters in the azimuth direction. The reference azimuth t is then used. p = Coefficient k at 0 ai0 (R0) Expand along the distance: (4) Where, k i0 The Taylor coefficient, k, represents the slant distance history at the reference position. ij Indicates k i0 The coefficients of the j-th order distance polynomial.

[0012] Using the stationary phase principle and series inversion method, a sufficiently accurate approximate two-dimensional spectrum can be obtained. Considering only the spectral phase that affects imaging, we can circumferentially revolve it around the range frequency f. r and azimuth frequency f a Performing a Taylor series expansion, we obtain: (5) in This represents the distance-frequency term. For example... Figure 2 As shown in (a), after LRCMC, the two-dimensional spatial variation of RCM is mainly controlled by the k2 coefficient in the slant range model. Figure 2 As shown in (b), the two-dimensional coupling of k2 cannot be completely eliminated using traditional methods, which will result in the image not being ideally focused. Therefore, more refined parameter correction is necessary to eliminate spatial invariance.

[0013] Step 2: Establish an improved azimuth resampling model based on distance gate dependence. Construct the azimuth-time mapping relationship row by row according to the parameters of different distance gates, and reconstruct the correspondence between the slant range history before and after resampling. The limitation of traditional orientation resampling algorithms is that they are based solely on the reference distance R. ref The parameters at the point are used to calculate the resampling coefficients, and the higher-order terms of the parameters are ignored due to approximation during the derivation process, resulting in a significant decrease in imaging accuracy in the scene edge region.

[0014] To address this problem, this invention proposes an improved azimuth resampling model based on distance gate dependence. First, the new azimuth time is calculated. Compared with the original orientation time t a The nonlinear mapping relationship between them is used to establish the time axis relationship before and after interpolation: (6) in, to Let R0 be the azimuth resampling coefficients that vary with distance R0. After azimuth resampling, the new slant range history can be expressed as: (7) Using relation (6), we can Expand on t a - t p The Taylor series. Since the two-dimensional spatial variability of RCM is mainly affected by the k2 coefficient in the slant range model, the change of k2 is mainly considered. The relationship between k2 before resampling and k2 after resampling can be expressed as: (8) Step 3: Solve for the optimal azimuth resampling coefficients. With the goal of eliminating the change of the quadratic term coefficients with azimuth time after resampling, the resampling parameters corresponding to each distance gate are analytically obtained, and the numerical inversion method is combined to ensure the accuracy and feasibility of the resampling mapping. To eliminate azimuth spatial variability, so that the coefficients K2 of the quadratic term after resampling no longer vary with azimuth time t p Changes, assumptions: (9) That is, the resampled K2 is equal to the zero-azimuth time coefficient at that distance gate. This eliminates the variation with azimuth. Solving equations (8) and (9) simultaneously yields the improved azimuth resampling coefficients. to The parsing expression: (10) When performing a resampling operation, it is necessary to know the new timeline. to the old timeline t a The mapping, that is, the need to find the function inverse function Since it is difficult to obtain an accurate analytical inverse function from equation (6), numerical methods such as Newton's iteration method are used in practice to solve the problem in order to ensure computational accuracy and efficiency.

[0015] After resampling, for the new timeline A Taylor series expansion of the slant range history, along with the beam center crossing time R0, is performed to obtain more accurate polynomial coefficients for focusing, resulting in new polynomial coefficients. For example... Figure 3 As shown, by comparing the spatial distributions of k2 and K2 before and after resampling, it can be seen that after processing by the method of the present invention, its variation with orientation is greatly weakened, thus achieving effective correction of the two-dimensional spatial variation of RCM.

[0016] Step 4: Perform improved azimuth resampling and imaging focusing processing. Complete the processing according to the process of spatially variable azimuth preprocessing, range compression, and azimuth compression to obtain a high-precision focused image of the entire scene.

[0017] Based on the above model and coefficients, the complete imaging processing flow is as follows: Data input and information processing: Input SAR echo data and obtain orbital parameters (position, velocity, etc.) and scene parameters (center latitude and longitude, etc.).

[0018] Range-direction FFT and linear phase compensation: The echo signal is subjected to range-direction fast Fourier transform to transform the signal to the range frequency domain-azimuth time domain, and the linear phase caused by the oblique angle is compensated.

[0019] Range compression: To ensure that azimuth interpolation does not affect the phase structure of the linear frequency modulated signal, range compression must be performed before azimuth resampling. This step is achieved through matched filtering.

[0020] Time-domain azimuth resampling: Transform the signal back into the two-dimensional time domain. Use the distance-related resampling coefficients calculated in step three. An improved azimuth resampling operation is performed on the data for each distance gate. By changing the sampling point position in the azimuth direction, the azimuth spatial variation of RCM is offset.

[0021] Distance compression recovery: Since the subsequent CS algorithm needs to be performed in the uncompressed state, a distance compression recovery operation is required after resampling.

[0022] Two-dimensional FFT and higher-order phase compensation: The echo signal is transformed into a two-dimensional frequency domain by two-dimensional FFT, and higher-order phase compensation is performed at the reference distance to correct the residual higher-order range phase error.

[0023] Range-oriented CS and azimuth-oriented NCS focusing: The CS algorithm is used for range processing to correct range migration and achieve range focusing. Subsequently, the azimuth-oriented NCS algorithm is used to correct the azimuth spatial variability of the focusing parameters to achieve azimuth focusing.

[0024] Azimuth IFFT: Finally, the signal is subjected to azimuth inverse fast Fourier transform to obtain a well-focused SAR image.

[0025] Example Table 1 shows some of the simulation parameters required for spaceborne SAR. The simulated imaging geometry is as follows: Figure 5 As shown, the 25 point targets are evenly distributed within a 60km * 60km area.

[0026] Table 1 List of key parameters for SAR satellites

[0027] 1. Comparative Analysis of RCM Correction Effects First, the residual RCM after processing by the literature method, the literature method, and the method of this invention was analyzed through simulation experiments. Figure 6The diagram illustrates the azimuth variation of residual RCM at the edge using different methods. The horizontal axis represents azimuth time, and the vertical axis represents the number of residual RCM elements. After processing with the polynomial compensation method, the curve exhibits significant fluctuations, indicating that this method cannot effectively handle higher-order RCM under oblique views. The curve processed by the method of this invention approximates a straight line with a value close to zero, effectively eliminating spatial variation. This demonstrates the good effectiveness of the proposed method.

[0028] 2. Simulation Analysis of Point Target Imaging Figure 7 The diagrams show contour plots and azimuth profiles of three typical target points (A, B, and C) in the scene. Point B is located at the center of the scene, while points A and C are located at the edges. It can be seen that target B, focused at the scene center, is well-focused; targets A and C, located at the corners of the scene, have rounded and convergent contour plots, and their azimuth profiles show sharp main lobes and low-level side lobes, with no obvious asymmetry. Table 2 lists the quantitative evaluation values ​​of peak sidelobe ratio and integral sidelobe ratio.

[0029] Table 2 Evaluation of Peak Sidelobe Ratio and Integral Sidelobe Ratio

[0030] As can be seen from the data in the table, the method of this invention achieves a peak sidelobe ratio of -13.25 dB and an integral sidelobe ratio of -10.18 dB at point A; and a peak sidelobe ratio of -13.20 dB and an integral sidelobe ratio of -10.21 dB at point C, both close to the theoretical values. This indicates that the algorithm proposed in this invention can maintain consistently high focusing quality across the entire scene range.

[0031] In summary, the simulation results in the embodiments fully demonstrate that the mid-orbit SAR frequency domain imaging algorithm based on improved azimuth resampling proposed in this invention has excellent adaptability to mid-orbit SAR oblique-view imaging, can effectively solve the defocusing problem caused by RCM two-dimensional spatial variation, and achieve high-precision focusing in all scenes.

[0032] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A mid-orbit curve SAR frequency domain imaging method based on spatially varied azimuth preprocessing, characterized in that, include: Step 1: Construct a two-dimensional spatially variable model of the high-order slant range history and its parameters of MEO SAR, and characterize the two-dimensional coupling variation of coefficients of each order with the range and azimuth directions, so as to provide an accurate parameter basis for subsequent spatially variable correction. Step 2: Establish an improved azimuth resampling model based on distance gate dependence. Construct the azimuth-time mapping relationship row by row according to the parameters of different distance gates, and reconstruct the correspondence between the slant range history before and after resampling. Step 3: Solve for the optimal azimuth resampling coefficients. With the goal of eliminating the change of the quadratic term coefficients with azimuth time after resampling, the resampling parameters corresponding to each distance gate are analytically obtained, and the numerical inversion method is combined to ensure the accuracy and feasibility of the resampling mapping. Step 4: Perform improved azimuth resampling and imaging focusing processing. Complete the processing according to the process of spatially variable azimuth preprocessing, range compression, and azimuth compression to obtain a high-precision focused image of the entire scene.

2. The method as described in claim 1, characterized in that, In step one, the MEO SAR slant range history R(t) is established. a The fifth-order Taylor series expansion model of ) is: ； Among them, t a The azimuth time is represented by tp, the beam center crossing time of the point target is represented by R0, and the reference range of the point target is represented by k. i The coefficients are the Taylor expansion coefficients of the i-th order. The two-dimensional space-variable model with Taylor expansion coefficients k2 - k5 is established as follows: ； Where, t p k represents the moment when the beam center of a point target crosses the target. aij Indicates k i The j-th order azimuth polynomial coefficients, all of which vary with the reference distance R0 of the point target; the reference azimuth t p = Coefficient k at 0 ai0 (R0) Expand along the distance: ； Where, k i0 The Taylor coefficient, k, represents the slant distance history at the target point in the scene center. ij Indicates k i0 The coefficients of the j-th order distance polynomial, R0 represents the reference distance of the point target, R ref This indicates the reference distance to the target at the center of the scene.

3. The method as described in claim 1, characterized in that, In step two, calculate the new azimuth time. Compared with the original orientation time t a The nonlinear mapping relationship between them is used to establish the time axis relationship before and after interpolation: ； in, to The azimuth resampling coefficient varies with the reference distance R0 of the point target.

4. The method as described in claim 1, characterized in that, In step two, the relationship between k2 before resampling and k2 after resampling is expressed as: ； Among them, t p Indicates the moment when the beam center of the point target crosses. to The azimuth resampling coefficient varies with the reference distance R0.

5. The method as described in claim 1, characterized in that, In step three, the improved azimuth resampling coefficients to The parsing expression is: ； Where R0 represents the reference distance of the point target, k i Let k be the coefficients of the i-th order Taylor expansion. aij Indicates k i The coefficients of the j-th order orientation polynomial.

6. The method as described in claim 1, characterized in that, In step four, the imaging processing flow includes: Data input and preprocessing: Input SAR echo data and obtain orbital parameters (position, velocity, etc.) and scene parameters (center latitude and longitude, etc.); Range-direction FFT and linear phase compensation: Perform range-direction fast Fourier transform on the echo signal to transform the signal to the range frequency domain-azimuth time domain, and compensate for the linear phase caused by the oblique angle. Range compression: To ensure that azimuth interpolation does not affect the phase structure of the linear frequency modulated signal, range compression must be performed before azimuth resampling; this step is achieved through matched filtering. Time-domain azimuth resampling: Transform the signal back to the two-dimensional time domain; use the distance-related resampling coefficients calculated in step three. An improved azimuth resampling operation is performed on the data for each distance gate; the azimuth spatial variability of RCM is counteracted by changing the sampling point position in the azimuth direction. Distance compression recovery: Since the subsequent CS algorithm needs to be performed in the uncompressed state, a distance compression recovery operation is required after resampling; Two-dimensional FFT and higher-order phase compensation: The echo signal is transformed into a two-dimensional frequency domain by two-dimensional FFT, and higher-order phase compensation is performed at the reference distance to correct residual higher-order distance and phase errors. Range-oriented CS and azimuth-oriented NCS focusing: The CS algorithm is used for range processing to correct range migration and achieve range focusing; subsequently, the azimuth-oriented NCS algorithm is used to correct the azimuth spatial variability of the focusing parameters and achieve azimuth focusing. Azimuth IFFT: Finally, the signal is subjected to azimuth inverse fast Fourier transform to obtain a well-focused SAR image.

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