A method for imaging moving targets using SAR based on high-order phase estimation

Abstract

This invention discloses a moving target imaging method based on high-order phase estimation for maneuvering trajectory SAR, belonging to the field of synthetic aperture radar moving target imaging technology. It solves the problem in existing technologies where the imaging model and algorithm mismatch caused by maneuvering platforms leads to large residual migration and phase errors. The method includes: constructing a moving target echo model for maneuvering trajectory SAR and determining the echo signal of the moving target; coarsely focusing the echo signal to obtain a coarsely focused echo signal; compensating for unknown migration in the coarsely focused echo signal to obtain a migration-compensated echo signal; estimating and compensating for unknown phase in the migration-compensated echo signal to obtain a phase-compensated echo signal; and imaging the phase-compensated echo signal to obtain the final image. This achieves imaging of fast-moving targets by a maneuvering platform under three-dimensional acceleration with small errors.

Description

Technical Field

[0001] This invention relates to the field of synthetic aperture radar moving target imaging technology, and in particular to a method for imaging moving targets using SAR based on high-order phase estimation of maneuvering trajectories. Background Technology

[0002] Moving target surveillance (MTS) is an important application area for radar development. Achieving MTS with radar is of great significance, and its surveillance methods have become a hot topic in radar signal processing research. MTS imaging is one of the main research directions for target surveillance. However, due to the limited survivability of stable flight platforms, maneuvering trajectory SAR MTS imaging methods have attracted attention. Maneuvering platforms have strong survivability and can achieve MTS imaging and surveillance in complex environments. When maneuvering platforms image moving targets, due to the influence of three-dimensional acceleration, the application of traditional level-flying platform MTS imaging methods will result in model-algorithm mismatch, leading to large residual migration and phase errors, affecting imaging quality. This invention proposes a maneuvering trajectory SAR MTS imaging algorithm based on high-order phase estimation. First, it achieves coarse focusing of the static scene and the moving target through a maneuvering platform imaging algorithm. Then, after extracting the moving target from the scene, it compensates for residual migration through high-order KT transform and estimates and compensates for residual phase through an extended generalized higher-order ambiguity function (EGHAF), which can effectively improve the imaging quality of maneuvering trajectory SAR MTS.

[0003] Existing solutions: Applied to the field of synthetic aperture radar (SAR) imaging technology, this invention addresses the limitation of existing airborne SAR systems for imaging ships at sea surface, which are only applicable to aircraft in stable flight and do not consider the influence of the platform's three-dimensional acceleration, making them unsuitable for mobile platforms. This invention utilizes the characteristics of a mobile platform to achieve coarse focusing on ship targets. Then, it extracts echo data belonging to individual ship targets from the SAR image through ship detection based on a hybrid visual attention mechanism. Finally, it performs residual range migration correction on individual ship targets to achieve fine focusing imaging. However, the PGA algorithm used in this method for residual phase estimation and compensation is only suitable for low-speed ship targets. When the target's speed is high, the PGA algorithm's estimation of higher-order residual phase is ineffective, leading to a decrease in image quality.

[0004] Therefore, the urgent problem to be solved is how to address the mismatch between the imaging model and algorithm caused by the mobile platform, which leads to large residual migration and phase errors. Summary of the Invention

[0005] This invention provides a moving target imaging method for maneuvering trajectory SAR based on high-order phase estimation, which solves the problem in the prior art of imaging model and algorithm mismatch caused by maneuvering platform, resulting in large residual migration and phase error. It realizes the imaging of fast-moving targets by maneuvering platform under three-dimensional acceleration with small error.

[0006] This invention provides a method for imaging moving targets using SAR based on high-order phase estimation, the method comprising:

[0007] Construct a SAR echo model of a moving target with a maneuvering trajectory and determine the echo signal of the moving target. ;

[0008] For the echo signal Perform coarse focusing to obtain the coarse-focused echo signal. ;

[0009] The coarse-focused echo signal Unknown migration amount compensation is performed to obtain migration-compensated echo signal. ;

[0010] For the migration compensation echo signal Unknown phase estimation and compensation are performed to obtain phase-compensated echo signals;

[0011] The phase-compensated echo signal is imaged to obtain the final image.

[0012] In one possible implementation, constructing the SAR moving target echo model based on a maneuvering trajectory includes:

[0013] Determine the instantaneous slant range between the maneuvering platform and the moving target, and determine the transmission signal of the maneuvering platform based on the instantaneous slant range. ;

[0014] According to the transmitted signal Determine the echo signal of a moving target and according to the transmitted signal and the echo signal Determine the moving target echo model.

[0015] In one possible implementation, the transmitted signal , represented as:

[0016] ;

[0017] in, Represents a rectangular window; Indicates the pulse width; Indicates the frequency modulation slope of the signal; Indicates the carrier frequency. These represent fast time.

[0018] In one possible implementation, the echo signal is coarsely focused to obtain a coarsely focused echo signal. ,include:

[0019] The echo signal is converted to the range frequency domain using a range Fourier transform to obtain the range frequency domain echo signal. ;

[0020] According to the distance frequency domain echo signal Constructing a coarse focusing function with the motion parameters of the motorized platform ;

[0021] Using the range frequency domain echo signal and the coarse focusing function The coarse focusing echo signal was calculated. .

[0022] In one possible implementation, the coarse focusing function , represented as:

[0023] ;

[0024] in, Represents the speed of light; Indicates the carrier frequency; Indicates distance frequency; Indicates the Taylor expansion order; Represents the phase coefficients of each order constructed based on the platform's motion parameters; This indicates the slow time of each order.

[0025] In one possible implementation, the coarse-focused echo signal Unknown migration amount compensation is performed to obtain migration-compensated echo signal. ,include:

[0026] Construct an azimuth time axis and input the azimuth time axis into the coarse-focused echo signal to obtain the scale-transformed echo signal.

[0027] The scaled echo signal is subjected to second-order KT interpolation to eliminate the range migration corresponding to the higher-order terms of the coarse-focused echo signal, thus obtaining the interpolated echo signal. ;

[0028] The distance migration corresponding to the first-order residual term of the interpolated echo signal is eliminated by slope estimation correction, resulting in a migration-compensated echo signal. .

[0029] In one possible implementation, the migration compensation echo signal Unknown phase estimation and compensation are performed to obtain the phase-compensated echo signal, including:

[0030] The migration compensation echo signal Perform range-directed IFFT to obtain the time-domain echo signal. ;

[0031] Extract the migration compensation echo signal Cell echo signal at the same distance cell ;

[0032] use The method for the unit echo signal Calculations are performed to obtain the residual phase coefficient;

[0033] Constructing a compensation function using the residual phase coefficients For the time-domain echo signal Phase compensation is performed to obtain the phase-compensated echo signal.

[0034] In one possible implementation, the utilization The method for the unit echo signal Calculations are performed to obtain the residual phase coefficients, including:

[0035] For the unit echo signal The first unit echo signal is obtained by performing two order reduction processes.

[0036] The echo signal of the first unit is transformed and decoupled by generalized KT transform to obtain a decoupled echo signal;

[0037] Perform a two-dimensional FFT on the decoupled echo signal to obtain a higher-order ambiguity signal. ;

[0038] Using the higher-order fuzzy signal The impulse function is obtained, and the residual phase coefficient is obtained using the impulse function.

[0039] In one possible implementation, the coarse-focused echo signal , represented as:

[0040] ;

[0041] in, Indicates the carrier frequency; Indicates distance frequency; Indicates the coefficients of the residual terms of each order; Indicates the slow time of each order; Indicates the Taylor expansion order; It represents the speed of light.

[0042] In one possible implementation, the migration-compensated echo signal , represented as:

[0043] ;

[0044] in, Indicates distance frequency; Indicates the wavelength of the transmitted signal; Indicates the residual Doppler central coefficient; Indicates the residual Doppler modulation coefficient; This represents the residual higher-order phase coefficients.

[0045] One or more technical solutions provided in this invention have at least the following technical effects or advantages:

[0046] (1) The SAR moving target echo model of the maneuvering trajectory proposed in this invention has strong adaptability and can realize the imaging of fast-moving targets by the maneuvering platform under three-dimensional acceleration;

[0047] (2) The high-order migration correction technology proposed in this invention can correct the distance curvature of unknown moving targets, and can further improve the imaging quality;

[0048] (3) The extended higher-order fuzzy function (EGHAF) proposed in this invention can simultaneously estimate higher-order phase coefficients. Compared with traditional methods, it avoids propagation errors and improves estimation accuracy. Attached Figure Description

[0049] Figure 1 This is a flowchart of the steps of the SAR moving target imaging method based on high-order phase estimation provided in an embodiment of the present invention;

[0050] Figure 2 A modeling schematic diagram provided for an embodiment of the present invention;

[0051] Figure 3 This is an image obtained after coarse focusing and echo signal imaging, provided in an embodiment of the present invention.

[0052] Figure 4 The parameter estimation results provided in the embodiments of the present invention;

[0053] Figure 5 This is an image after imaging the phase-compensated echo signal provided in an embodiment of the present invention;

[0054] Figure 6 This is a phase-compensated azimuth profile of a moving target provided in an embodiment of the present invention. Detailed Implementation

[0055] 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, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0056] This invention provides a method for imaging moving targets using SAR based on high-order phase estimation, such as... Figure 1 As shown, the method includes the following steps S101 to S104.

[0057] S101, Construct a SAR echo model of a moving target with a maneuvering trajectory and determine the echo signal of the moving target. .

[0058] Specifically, in step S101, a moving target SAR echo model based on a maneuvering trajectory is constructed, including:

[0059] (1) Determine the instantaneous slant range between the maneuvering platform and the moving target, and determine the transmission signal of the maneuvering platform based on the instantaneous slant range. .

[0060] (2) Based on the transmitted signal Determine the echo signal of a moving target And according to the transmitted signal and echo signal Determine the moving target echo model; here, the transmitted signal , represented as:

[0061] ;

[0062] in, Represents a rectangular window; Indicates the pulse width; Indicates the frequency modulation slope of the signal; Indicates the carrier frequency. These represent fast time.

[0063] For example, such as Figure 2 As shown, the initial height of the mobile platform ,speed acceleration , from the curved trajectory Point movement to The moving target is in terms of speed from Point movement to The instantaneous slant distance from the maneuvering platform to the moving target during the integration time. for:

[0064] ;

[0065] in, Let be the instantaneous slant range vector pointing from any target point to the carrier platform at the initial moment. This indicates a modulo operation. This refers to the slow time for the location.

[0066] Mobile platform moving target imaging system radar transmission signal for:

[0067] ;

[0068] in, It is a rectangular window. , , , These represent the pulse width, signal modulation slope, carrier frequency, and fast time, respectively.

[0069] According to the transmitted signal Echo signal of moving target It can be represented as:

[0070] ;

[0071] in, It is a window function related to the azimuth antenna pattern. It is related to the instantaneous slant distance The relevant fast time delay can be expressed as , and These represent the wavelength of the transmitted signal and the speed of light, respectively.

[0072] Slant range model Substitution After range pulse compression, the moving target echo signal of the mobile platform can ultimately be expressed as:

[0073] ;

[0074] in, Indicates location and time; Indicates location and time. Indicates the Taylor expansion order; Represents the coefficients of the expansion; Indicates the slow time of each order; Represents the speed of light; Window functions related to the azimuth antenna pattern; Indicates the wavelength of the transmitted signal.

[0075] S102, for echo signal Perform coarse focusing to obtain the coarse-focused echo signal. .

[0076] Specifically, in step S102, the echo signal... Perform coarse focusing to obtain the coarse-focused echo signal. The steps include S1021 to S1023.

[0077] S1021 will transmit the echo signal The range-frequency echo signal is obtained by converting it to the range-frequency domain using a range Fourier transform. .here, ,in, For distance frequency.

[0078] S1022, based on the distance frequency domain echo signal Constructing a coarse focusing function with the motion parameters of the motorized platform Here, the coarse focusing function , represented as:

[0079] ;

[0080] in, Represents the speed of light; Indicates the carrier frequency; Indicates distance frequency; Represents the phase coefficients of each order constructed based on the platform's motion parameters; This indicates the slow time of each order.

[0081] S1023, utilizing distance frequency domain echo signal and coarse focusing function The coarse focusing echo signal was calculated. Here, the echo signal after coarse focusing , represented as:

[0082] ;

[0083] in, Indicates the carrier frequency; Indicates distance frequency; Indicates the coefficients of the residual terms of each order; Indicates the slow time of each order; Indicates the Taylor expansion order; It represents the speed of light.

[0084] For example, coarse focusing function It is based on The result is obtained through [the following process]. Among them:

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] It is based on the instantaneous slope distance The expansion is determined by a third-order Taylor series. The process of determining the third-order Taylor series is as follows:

[0090] Instantaneous slant distance Expanded into a third-order Taylor series: .

[0091] Specifically, in third-order Taylor series: ;

[0092] ;

[0093] ;

[0094] .

[0095] For the known platform speed With unknown moving target speed Resultant velocity:

[0096] ;

[0097] Will and Multiplying yields the residual term after coarse focusing:

[0098] ;

[0099] in:

[0100] ;

[0101] ;

[0102] .

[0103] Because the above residuals include the velocity of non-cooperative motion targets. Furthermore, since distance and orientation are coupled together, unknown residual migration and phase are introduced, affecting image quality.

[0104] S103, for the echo signal after coarse focusing Unknown migration amount compensation is performed to obtain migration-compensated echo signal. .

[0105] Specifically, in step S103, the echo signal after coarse focusing is... Unknown migration amount compensation is performed to obtain migration-compensated echo signal. The steps include S1031 to S1033.

[0106] S1031, Construct the azimuth-time axis and input it into the coarse-focused echo signal. In this process, the scaled signal is obtained. Here, the azimuth-time axis is specifically represented as: .

[0107] S1032 performs second-order KT interpolation on the scaled signal to eliminate echo signals after coarse focusing. The higher-order terms in the equation correspond to the distance migration, and the interpolated echo signal is obtained. .

[0108] S1033, Correction of interpolated echo signal through slope estimation. The distance migration corresponding to the first-order residual term is eliminated to obtain the migration-compensated echo signal. Here, the migration-compensated echo signal , represented as:

[0109] ;

[0110] in, Indicates distance frequency; Indicates the wavelength of the transmitted signal; Indicates the residual Doppler central coefficient; Indicates the residual Doppler modulation coefficient; This represents the residual higher-order phase coefficients.

[0111] For example, the azimuth time axis is substituted into the coarsely focused echo signal. And by performing second-order KT interpolation, we obtain:

[0112] ;

[0113] because Much larger The above formula can be approximated as:

[0114] ;

[0115] At this point, the second-order and third-order terms have been decoupled, and their corresponding distance migrations have been eliminated, while the distance migrations corresponding to the first-order terms have not yet been eliminated.

[0116] Since the distance travel of the first-order residual term is represented as a sloping line in the two-dimensional time domain, its slope is related to the coefficient of the residual term. Specifically, Radon transform is used to estimate its slope and then migration correction is performed. After migration correction, the moving target echo signal has completed migration correction.

[0117] ;

[0118] S104, for migration compensation echo signal Unknown phase estimation and compensation are performed to obtain the phase-compensated echo signal.

[0119] Specifically, in step S104, the migration compensation echo signal is processed. Unknown phase estimation and compensation are performed to obtain phase-compensated echo signals, including the following steps S1041 to S1044.

[0120] S1041 will compensate for the migration echo signal Perform range-directed IFFT to obtain the time-domain echo signal. Here, the time-domain echo signal Specifically, it is expressed as follows:

[0121] ;

[0122] In step S1041, the time-domain echo signal The residual phase represented by the exponential term will affect azimuth focusing and needs to be estimated and compensated.

[0123] S1042, Extract migration compensation echo signal Cell echo signal at the same distance cell .

[0124] S1043, utilizing The method for cell echo signals The residual phase coefficient is calculated. Specifically, in step S1043, the residual phase coefficient is obtained using... The method for cell echo signals Calculations are performed to obtain the residual phase coefficients, including:

[0125] (1) For unit echo signal The first unit echo signal is obtained by performing two order reduction processes.

[0126] (2) The echo signal of the first unit is decoupled by generalized KT transformation to obtain the decoupled echo signal;

[0127] (3) Perform a two-dimensional FFT on the decoupled echo signal to obtain the higher-order ambiguity signal. ;

[0128] (4) Utilizing high-order fuzzy signals The impulse function is obtained, and the residual phase coefficient is obtained using the impulse function.

[0129] S1044, constructing a compensation function using the residual phase coefficient. For time-domain echo signals Phase compensation is performed to obtain the phase-compensated echo signal.

[0130] For example, first-order phase coefficient Second and third order phase coefficients affect the azimuth and position of a moving target. , Since moving target imaging quality is affected, this invention uses an extended generalized higher-order ambiguity function (EGHAF) to estimate and compensate for second- and third-order phase coefficients. The estimation and compensation of residual phase parameters include steps 4a to 4e.

[0131] (4a) Extracting echo signals from the same distance cell:

[0132] ;

[0133] (4b) Echo signal Perform two order reduction processes:

[0134] ;

[0135] ;

[0136] in, For a fixed time delay, It is a time delay matrix, usually associated with a slow time matrix. Same. From As can be seen, the time delay and the azimuth slow time are coupled, so decoupling operations should be performed.

[0137] (4c) Decoupling of generalized KT transform, let Substitute The second exponential term, after interpolation, yields:

[0138] ;

[0139] At this point, the time delay and the azimuth slow time are decoupled.

[0140] (4d) Two-dimensional frequency domain peak retrieval parameter estimation: The decoupled echo signal is obtained by performing a two-dimensional FFT.

[0141] ;

[0142] At this point, an impulse function is generated in the two-bit frequency domain. The index position of the impulse function is related to the residual phase coefficient. and Therefore, the residual phase coefficients can be obtained through peak retrieval:

[0143] ;

[0144] in, and These represent the values ​​corresponding to the time delay frequency axis and the slow time frequency axis at the maximum value, respectively.

[0145] (4e) Construct the compensation function and perform compensation. Based on the estimated residual phase coefficients, the compensation function is constructed as follows:

[0146] ;

[0147] With time-domain echo signal Multiplication completes residual phase compensation, and finally range IFF and azimuth FFT are performed to achieve fine imaging of moving targets in the azimuth frequency domain.

[0148] S105, image the phase-compensated echo signal to obtain the final image.

[0149] In a specific embodiment provided by this invention, the method is verified using measured data, such as... Figure 3 The image shown is of a moving target after coarse focusing. It is evident that the moving target is severely defocused due to residual migration and phase distortion. For example... Figure 4 The figure shows the phase coefficients obtained through parameter estimation. A compensation function is constructed and applied using the estimated phase coefficients to obtain the desired result. Figure 5 The focused imaging result is shown. Figure 6 The image shows a comparison of the azimuth profiles before and after compensation. Compared to the image before compensation (red), the image after compensation (blue) has a good main lobe and low sidelobes. It can be seen that the moving target imaging method for SAR based on maneuvering trajectories proposed in this invention can obtain high-quality images of moving targets.

[0150] This invention can be applied to moving target imaging in maneuvering trajectory SAR. As a novel platform, the maneuvering platform possesses three-dimensional acceleration, enabling active avoidance and improving survivability. During target detection, high-resolution target echoes are acquired through a large oblique angle and high-speed motion, achieving refined moving target imaging and laying the foundation for subsequent target identification and classification. This represents an important development direction for target detection and identification. It is widely used in missile-borne, airborne, and UAV-borne SAR systems. However, maneuvering trajectory SAR moving target imaging suffers from Doppler center ambiguity, Doppler spectral aliasing, higher-order migration, and phase distortion. Mismatches with traditional SAR moving target imaging models and algorithms can also lead to excessive residual migration and phase distortion, affecting imaging quality. This invention proposes a maneuvering trajectory SAR moving target imaging method based on higher-order phase estimation, primarily addressing the impact of the maneuvering platform's three-dimensional acceleration on moving target imaging. First, a unified moving target vector geometric model of the maneuvering platform is established. A coarse focusing function is then constructed using this geometric model to initially eliminate the influence of the maneuvering platform's motion parameters on the moving target echo. Then, a higher-order KT transform is used to correct the residual unknown migration, achieving decoupling between range and azimuth. Finally, higher-order phase estimation in the azimuth direction is used to estimate and compensate for the residual phase, effectively improving the imaging quality of moving targets. This has supplementary significance and practical value in application scenarios such as target detection, recognition, and classification.

[0151] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A method for imaging moving targets using SAR based on high-order phase estimation, characterized in that, include: Construct a SAR echo model of a moving target with a maneuvering trajectory and determine the echo signal of the moving target. ; For the echo signal Perform coarse focusing to obtain the coarse-focused echo signal. ; The coarse-focused echo signal Unknown migration amount compensation is performed to obtain migration-compensated echo signal. ; For the migration compensation echo signal Unknown phase estimation and compensation are performed to obtain a phase-compensated echo signal; wherein, the migration compensation echo signal is... Unknown phase estimation and compensation are performed to obtain the phase-compensated echo signal, including: The migration compensation echo signal Perform range-directed IFFT to obtain the time-domain echo signal. ; Extract the migration compensation echo signal Cell echo signal at the same distance cell ; use The method for the unit echo signal Calculations are performed to obtain the residual phase coefficient; here, using The method for the unit echo signal Calculations are performed to obtain the residual phase coefficients, including: for the unit echo signal Two order reduction processes are performed to obtain the first unit echo signal; the first unit echo signal is then transformed and decoupled using a generalized KT transform to obtain a decoupled echo signal; a two-dimensional FFT is performed on the decoupled echo signal to obtain a higher-order ambiguity signal. ; Utilizing the higher-order fuzzy signal The impulse function is obtained, and the residual phase coefficient is obtained using the impulse function; a compensation function is constructed using the residual phase coefficient. For the time-domain echo signal Phase compensation is performed to obtain the phase-compensated echo signal; The phase-compensated echo signal is imaged to obtain the final image.

2. The method for imaging moving targets using SAR based on high-order phase estimation according to claim 1, characterized in that, The construction of the SAR moving target echo model with a maneuvering trajectory includes: Determine the instantaneous slant range between the maneuvering platform and the moving target, and determine the transmission signal of the maneuvering platform based on the instantaneous slant range. ; According to the transmitted signal Determine the echo signal of a moving target and according to the transmitted signal and the echo signal Determine the moving target echo model.

3. The method for imaging moving targets using SAR based on high-order phase estimation according to claim 2, characterized in that, The transmitted signal , is represented as: ； in, Represents a rectangular window; Indicates the pulse width; Indicates the frequency modulation slope of the signal; Indicates the carrier frequency. These represent fast time.

4. The method for imaging moving targets using SAR based on high-order phase estimation according to claim 1, characterized in that, The echo signal is coarsely focused to obtain the coarsely focused echo signal. ,include: The echo signal is converted to the range frequency domain using a range Fourier transform to obtain the range frequency domain echo signal. ; According to the distance frequency domain echo signal Constructing a coarse focusing function with the motion parameters of the motorized platform ; Using the range frequency domain echo signal and the coarse focusing function The coarse focusing echo signal was calculated. .

5. The method for imaging moving targets using SAR based on high-order phase estimation according to claim 4, characterized in that, The coarse focusing function , is represented as: ； in, Represents the speed of light; Indicates the carrier frequency; Indicates distance frequency; Indicates the Taylor expansion order; Represents the phase coefficients of each order constructed based on the platform's motion parameters; This indicates the slow time of each order.

6. The method for imaging moving targets using SAR based on high-order phase estimation according to claim 1, characterized in that, The coarse-focused echo signal Unknown migration amount compensation is performed to obtain migration-compensated echo signal. ,include: Construct an azimuth time axis and input the azimuth time axis into the coarse-focused echo signal. In the process, the scaled signal is obtained; The scaled signal is subjected to second-order KT interpolation to eliminate the coarse-focused echo signal. The distance migration corresponding to the higher-order term is used to obtain the interpolated echo signal. ; The interpolated echo signal is corrected by slope estimation. The distance migration corresponding to the first-order residual term is eliminated to obtain the migration-compensated echo signal. .

7. The method for imaging moving targets using SAR based on high-order phase estimation according to claim 1, characterized in that, The coarse-focused echo signal , is represented as: ； in, Indicates the carrier frequency; Indicates distance frequency; Indicates the coefficients of the residual terms of each order; Indicates the slow time of each order; Indicates the Taylor expansion order; It represents the speed of light.

8. The method for imaging moving targets using SAR based on high-order phase estimation according to claim 1, characterized in that, The migration compensation echo signal , is represented as: ； in, Indicates distance frequency; Indicates the wavelength of the transmitted signal; Indicates the residual Doppler central coefficient; Indicates the residual Doppler modulation coefficient; This represents the residual higher-order phase coefficients.

Images