A forward-looking multi-channel SAR motion error compensation method based on PGA and matrix pencil

Abstract

This invention discloses a forward-looking multi-channel SAR motion error compensation method based on PGA and matrix beaming, applied in the field of radar technology. It addresses the problems of existing technologies where compensation effectiveness is highly dependent on navigation equipment accuracy and fails to fully compensate for two-dimensional spatially varying phase and linear error components. This invention obtains RD-domain imaging results by performing deskewing and Fourier transform on the echo with phase error after range compression and migration correction. Then, rootmusic angle measurement is performed on overlapping targets in the RD-domain imaging results, equating the deblurring problem to solving a linear inverse problem, resulting in an optimization problem. Solving the optimization problem yields unblurred RD-domain echoes. The PGA algorithm is then used to estimate higher-order errors in the deblurred echoes. The matrix beaming algorithm is then used to estimate residual linear errors. Finally, the estimated motion error terms are incorporated into the coherent accumulation process to obtain the motion error-compensated imaging result.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and specifically relates to a two-dimensional spatially variable error self-focusing technology for FLMC-SAR that considers linear error compensation. Background Technology

[0002] Synthetic Aperture Radar (SAR) is widely used due to its all-weather observation capabilities, but traditional side-looking modes suffer from forward blind spots. Forward-looking Multichannel Synthetic Aperture Radar (FLMC-SAR) solves the problems of forward-looking imaging and Doppler blurring by using multi-antenna arrays, and has important applications in precision guidance and autonomous landing. However, FLMC-SAR is extremely sensitive to platform motion errors, and the two-dimensional spatially varied phase errors introduced by these errors can severely degrade image quality. In addition, due to the special geometry of forward-looking imaging, linear errors can cause distortion of the imaging results and affect deblurring. Therefore, developing a two-dimensional spatially varied error autofocusing algorithm for FLMC-SAR that considers linear error compensation is of great significance for improving its imaging quality.

[0003] Among the publicly published literature, representative methods for motion error estimation and compensation in forward-looking multichannel SAR mainly include the parametric azimuth-variable motion error compensation method (Reference 1: J. Lu, L. Zhang, Y. Quan, Z. Meng and Y. Cao, "Parametric Azimuth-Variant Motion Compensation for Forward-Looking Multichannel SAR Imagery," in IEEE Transactions on Geoscience and Remote Sensing, vol. 59, no. 10, pp. 8521-8537, Oct. 2021) and the measurement matrix correction method (Reference 2: R. Chen, W. Li, K. Li, Y. Zhang and J. Yang, "A Super-Resolution Scheme for Multichannel Radar Forward-Looking Imaging Considering Failure Channels and Motion Error," in IEEE Geoscience and Remote Sensing Letters, vol. 20, pp. 1-5, 2023, Art no.). 3501305), a forward-looking SAR imaging polar coordinate format algorithm that integrates spatial variation motion compensation (Reference 3: Z. Meng, L. Zhang, J. Lu and X. Wang, "FL-PFA: A PolarFormat Algorithm for Wide-Beam Forward-Looking SAR Imaging IntegratingSpatial-Variant Motion Compensation," in IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1-13, 2024, Art no. 5220313), and a pixel-level Doppler centroid correction method (Reference 4: J. Lu, L. Zhang, Z. Meng, Z. Wang and Y. Wang).Cao, "A Pixel-Level Doppler Centroid Frequency Correction for FLMC-SAR Imaging and Doppler Ambiguity Resolving," in IEEE Transactions on Geoscience and Remote Sensing, vol. 63, pp. 1-13, 2025, Art no. 5222813. However, the above methods all have some problems, such as the compensation effect being highly dependent on the accuracy of the navigation equipment, and the inability to fully compensate for the phase error and linear error components of two-dimensional spatial variation. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a forward-looking multi-channel SAR motion error compensation method based on PGA and matrix beams, which can effectively compensate for motion errors and improve imaging quality.

[0005] The technical solution adopted in this invention is: a forward-looking multi-channel SAR motion error compensation method based on PGA and matrix beam, comprising:

[0006] Acquire forward-looking multi-channel SAR simulation echo data;

[0007] Range compression and migration correction are performed on the simulated echo data of forward-looking multi-channel SAR to obtain echoes with phase errors;

[0008] The RD domain imaging results are obtained by deskewing and Fourier transforming the echo with phase error.

[0009] By rewriting the RD domain imaging results in matrix form and considering the effect of noise, the deblurring problem is equivalent to solving the following linear inverse problem:

[0010] ;

[0011] in, This is the result at the peak of the noisy multi-channel RD domain. It is an additive complex Gaussian white noise vector. The goal is to find the unambiguous imaging results at the peak of the RD domain for the left and right scenes.

[0012] Solving the optimization problem using the Fista algorithm Obtain unambiguous RD domain echo ;

[0013] Unambiguous RD domain echo The phase gradient self-focusing algorithm is used to perform high-order error estimation.

[0014] For the echo after compensating for higher-order errors, the matrix beam algorithm is used to estimate the linear error of each reference point;

[0015] The sum of the higher-order error and linear error estimates is used as the motion error estimated by the reference point;

[0016] The least-squares fitting of the motion errors estimated at all reference points yields the two-dimensional spatially varying error for the entire scene.

[0017] When performing back projection algorithm imaging, the two-dimensional spatial variation error of the entire scene is incorporated into the coherent accumulation process to obtain the imaging result after motion error compensation.

[0018] The beneficial effects of this invention are as follows: This invention simultaneously considers the two-dimensional spatially varying characteristics of forward-looking SAR motion errors and the influence of unique linear errors on imaging and deblurring, thereby improving the imaging quality of forward-looking multi-channel SAR. Compared with traditional forward-looking multi-channel SAR motion error compensation methods, this invention utilizes PGA technology to estimate higher-order phase errors and matrix beam algorithms to estimate linear phase errors. The sum of these two methods provides the total phase error estimate, which is then obtained through least-squares fitting to obtain the two-dimensional spatially varying error estimate. Finally, compensating for the two-dimensional spatially varying errors in BP imaging yields a blurred and distortion-free image. This invention not only effectively removes the two-dimensional spatially varying errors of forward-looking SAR but also solves the imaging distortion problem caused by linear errors, thus improving imaging quality. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the present invention.

[0020] Figure 2 This is a schematic diagram of the SAR platform trajectory in this invention.

[0021] Figure 3 This refers to the simulation target settings used in this invention.

[0022] Figure 4 These are comparison images of simulated multi-point target BP imaging results before and after compensation processing;

[0023] Among them, (a) is the imaging result without motion error, (b) is the imaging result with motion error, and (c) is the result after processing by the proposed compensation algorithm. Detailed Implementation

[0024] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0025] like Figure 1 As shown, the method of the present invention includes the following steps:

[0026] Step 1: Initialize parameters and generate simulation data

[0027] Initialize the radar parameters required for subsequent steps, including: the Pulse Repetition Frequency (PRF) corresponding to the generated image, denoted as... The radar's azimuth modulation frequency is denoted as... The wavelength of the pulse emitted by the radar system is denoted as . The pulse duration transmitted by the radar system is denoted as . The bandwidth of the signal emitted by the radar system is denoted as . The range sampling rate of a radar system is denoted as... The synthetic aperture time of radar is denoted as... The effective velocity of the radar platform is denoted as... The initial position coordinates of the radar platform are denoted as... The coordinates of the scene reference point are denoted as... The number of range sampling points in the radar system is denoted as... The number of azimuth sampling points of the radar system is denoted as... The speed of light is recorded as The above parameters are used to generate forward-looking multi-channel SAR simulation echo data.

[0028] like Figure 2 As shown. Under ideal conditions, the SAR is at an altitude of... At that location, due to disturbance, the SAR platform deviated from its straight trajectory, as shown by the orange solid curve in the figure. If the platform The trajectory deviations in the three directions at time t are respectively At this time, the rectangular coordinates of the central passage are , express The ideal speed in which the direction is not affected by error.

[0029] Consider two initial times located at and symmetrical position ,in It is the initial slant range between the target and the radar platform. Ground targets in the left and right scenes and The initial included angle of the axis, the reflection coefficient is The radar's downward viewing angle is The target, after range compression and migration correction, has the following echo with phase error in the k-th radar receiving channel:

[0030] (1)

[0031] in For fast time sampling sequences, It is a slow-time sampling sequence. For carrier wavelength, This represents the pulse width of the transmitted signal. It is the envelope function after distance compression. , The difference in the position of the receiving channel is given respectively , The small phase difference introduced by the target will be used for subsequent deblurring. , , It is the x-axis coordinate of the k-th receiving channel of the radar.

[0032] and The instantaneous one-way slant ranges of the central reference channel for targets affected by motion errors are as follows:

[0033]

[0034]

[0035] Deskewing and Fourier transform of the echoes in (1) yielded multi-channel range-Doppler (RD) domain imaging results:

[0036] (2)

[0037] in For Fourier transform operators, For slow time For the frequency domain variables after Fourier transform, only second-order descrambling is considered. It is a second-order approximate deslope function. For the signal in formula (1) Performing a slow-time Fourier transform and removing higher-order terms yields the unambiguous RD-domain imaging result of the symmetric target in the central reference channel:

[0038] (3)

[0039] in Represents convolution. This is the Fourier transform of higher-order phase errors. Doppler frequencies affected by motion errors: . They are The derivatives of the platform deviations in the three directions with respect to time are the velocity errors.

[0040] Step 2: Multi-channel deblurring processing

[0041] Root-MUSIC angle measurement was performed on the overlapping targets in the multi-channel RD domain imaging results (2) to obtain... The estimated value By writing the multi-channel RD domain results in (2) in matrix form and considering the influence of noise, the defuzzification problem can be equivalently solved as the following linear inverse problem:

[0042] (4)

[0043] in This is the result at the peak of the noisy multi-channel RD domain. It is a K-dimensional complex vector. express The value of the k-th dimension, where the k-th dimension should be understood as the k-th channel; the direction of arrival (DOA) of the multi-channel echo data s is estimated using the Root-MUSIC algorithm; then, based on the estimated angle information, the corresponding multi-channel steering vector matrix is ​​constructed. , . To represent a complex number, Let represent a K-dimensional complex vector. The two-dimensional function in formula (2) is taken The value at that location is the value at the peak position in the RD domain two-dimensional imaging result. It is an additive complex white Gaussian noise vector, which follows the... , This represents noise power. This represents the noise at the peak of the echo in the k-th channel. yes The identity matrix. The goal is to find the unblurred RD domain peak imaging results for the left and right scenes. Solving equation (4), this linear inverse problem, is equivalent to solving an optimization problem using the Fista algorithm. Unambiguous RD domain echoes are obtained. .

[0044] Step 3: Higher-order error estimation based on PGA

[0045] The Phase Gradient Autofocus (PGA) algorithm is used for high-order error estimation, mainly including the following steps: 1. Strong point selection: After deblurring, isolated strong scattering points with high signal-to-noise ratio are selected from the RD domain image as reference points for phase error estimation; 2. Cyclic shift: The main lobe of each strong point is shifted to the center of the image to eliminate the influence of the target's own phase on the error estimation; 3. Windowing: Windowing is applied to each strong point after cyclic shifting to filter out noise and sidelobe interference, while retaining the phase information within the main lobe; 4. Phase gradient estimation: The phase error gradient is estimated using the phase difference between adjacent azimuth units, and the estimated phase error gradient is integrated to obtain the phase error function.

[0046] After deblurring, we obtained the unblurred RD domain imaging results of the left and right scenes, using... This represents the total echo of the left and right scenes. Whether it specifically represents the echo of the left or right scene is determined by... The sign of the symbol is used to represent the left scene, and the negative sign represents the right scene. The PGA algorithm is then used to estimate higher-order errors in the deblurred echo. First, strong scattering points are selected from the RD domain imaging results. Assume the position of the i-th strong scattering point is... The imaging results in the RD domain are as follows:

[0047] (5)

[0048] Let represent the initial slant range between the i-th strong scattering point and the radar platform. Indicates the i-th strong scatter point and The initial included angle of the axes;

[0049] The frequency domain signal of the current strong scattering point The peak position (i.e., the main lobe) is moved to the center of the image, and an appropriate window function is selected. Multiply by the frequency domain signal, then perform an inverse Fourier transform back to the time domain signal. :

[0050] (6)

[0051] The appropriate window function here This should be understood as a window function that can completely cover strong points after defocusing. In practical applications, it can be determined by the main lobe dropping to -20dB. Here, strong points after defocusing should be understood as strong scattering points whose imaging results were originally focused but became defocused due to motion errors.

[0052] Due to the spatially variable nature of forward-looking SAR, targets at different range gates have different phase errors. Therefore, averaging the phase gradients of different strong points across multiple range gates is not feasible. This is why this invention chooses Fista for multi-channel deblurring. Fista has excellent noise reduction and clutter suppression capabilities, resulting in more accurate phase gradients for individual strong points. At this point, the target's... The phase error gradient over a slow time period can be obtained by the following formula:

[0053] (7)

[0054] in, For slow time echo value at that location, It is slow time The complex conjugate of the echo value, It takes the phase of a complex number.

[0055] By performing discrete integration on equation (7), the phase error function of the entire aperture can be reconstructed:

[0056] (8)

[0057] Since the PGA itself cannot directly estimate or correct linear phase errors, the PGA actually obtains second-order and higher-order error estimates:

[0058] (9)

[0059] in It's a slow point in time. Phase error function at that point It is the phase error function for all slow time points.

[0060] After compensating for higher-order phase errors, only linear errors remain in the echo. That is, we first perform an inverse Fourier transform on formula (5), and then multiply it by the phase term in formula (9), which is expressed as:

[0061] (10)

[0062] in At this point, only the linear error component remains in the echo, affecting the imaging results. The linear term representing the phase error caused by the velocity error is the true error to be estimated. . They are The derivatives of the platform deviations in the three directions with respect to time are the velocity errors.

[0063] Step 4: Linear error estimation based on matrix bundle algorithm

[0064] The linear error estimation using the matrix beam algorithm mainly includes the following steps: 1. Strong point selection: After compensating for higher-order errors, isolated strong scattering points with high brightness are selected from the RD domain image as reference points for phase error estimation. Generally, the points are sorted from largest to smallest signal-to-noise ratio, and the first N points are selected. In this embodiment, N is greater than 3; 2. Actual Doppler frequency estimation: The signals of each strong point are inversely transformed to the range time domain, and the Doppler frequency affected by motion error is estimated using the matrix beam algorithm; 3. Ideal Doppler frequency estimation: The ideal Doppler frequency of each strong point is obtained using the rootmusic estimation result; 4. Linear error estimation: The linear error is estimated by the difference between the actual Doppler frequency and the ideal Doppler frequency.

[0065] The matrix bundle algorithm is a high-resolution parameter estimation method based on subspace decomposition. Its core idea is to transform the signal parameter estimation problem into a generalized eigenvalue problem by constructing a matrix with a specific structure, thereby directly extracting the frequency, attenuation factor, and amplitude of a complex exponential signal. This algorithm avoids the nonlinear search process in traditional spectral estimation and features high computational efficiency and high estimation accuracy.

[0066] For the two-dimensional signal of (10), take The slow-time signal, after discretization, can be represented as:

[0067] (11)

[0068] in , It is the number of slow-time sampling points. It is a slow sampling interval.

[0069] The residual linearity error is estimated using the matrix bundle algorithm. First, a Hankel data matrix is ​​constructed from the discrete signal sequence. Then, this matrix is ​​used to form a matrix bundle, and the signal frequency information can be directly extracted by solving its generalized eigenvalue problem. Specifically, let the constructed Hankel matrix... Represented as:

[0070] (12)

[0071] Where L is the matrix bundle parameter, and the theoretical value of L is less than Na / 2; in this embodiment, L=5. Matrix bundle Defined as:

[0072] (13)

[0073] in and They are matrices The submatrix obtained after removing its last and first columns. Signal frequency information is contained in the generalized eigenvalues ​​of this matrix bundle. The equivalent frequency is then determined through the principal generalized eigenvalue. Export as:

[0074] (14)

[0075] The estimated linear error coefficients can then be obtained from equation (14), where... The result has already been obtained using the Root-MUSIC algorithm:

[0076] (15)

[0077] express The estimated value;

[0078] Thus, a linear error estimate at the current strong scattering point was obtained. The total phase error estimate at this position is the sum of the higher-order error and the linear error estimates. .

[0079] Step 5: Two-dimensional spatial variation error fitting and compensation

[0080] The motion error estimation of multiple target points (i.e., strong points) is performed by a two-dimensional spatially varied least squares fit with respect to the point target positions, thereby obtaining a two-dimensional spatially varied motion error estimate for all targets in the scene. ,in It represents any ground azimuth and radar downward view. During Back Projection Algorithm (BPA) imaging, the estimated two-dimensional spatially varying motion error term is used. By incorporating this into the coherent accumulation process, the imaging result after motion error compensation can be obtained. The motion error estimate in this step is the sum of the estimates of higher-order errors and linear errors.

[0081] This invention primarily employs simulation experiments to verify the feasibility of the proposed scheme. All steps and conclusions have been verified correctly using MATLAB R2022a. The specific implementation steps are as follows:

[0082] Step 1: Initialize parameters and generate simulation data

[0083] Based on the radar parameters provided in Appendix 1, forward-looking multi-channel SAR simulation echoes are generated. The target point settings are as follows:

[0084] Multiple point targets were placed in the imaging area. The area with an azimuth angle greater than 0° was defined as the left scene area, and the area with an azimuth angle less than 0° was defined as the right scene area. Therefore, four point targets were placed in the left scene area, and five point targets were placed in the right scene area. The signal-to-noise ratio was set to 20dB. Specific settings are shown in the attached figure. Figure 3 As shown.

[0085] Table 1 Simulation Parameter Table

[0086]

[0087] Step 2: Multi-channel deblurring processing

[0088] Angle measurement and deblurring are performed on 9 points in the multi-channel RD domain image to obtain RD domain images with separate left and right scenes.

[0089] Step 3: Higher-order error estimation based on PGA

[0090] Phase gradient estimation was performed on the nine target points to obtain higher-order phase errors at nine different locations.

[0091] Step 4: Linear error estimation based on matrix bundle algorithm

[0092] The Doppler shift was estimated using the matrix beam algorithm for each of the nine target points after the higher-order errors were compensated, resulting in linear phase errors at nine different locations.

[0093] Step 5: Two-dimensional spatial variation error fitting and compensation

[0094] The phase error estimates of the nine target points are fitted with least-squares about the two-dimensional positions of the point targets to obtain the motion error estimates of the targets in the entire scene. By incorporating the estimated motion error terms into the coherent accumulation process, the imaging result after motion error compensation can be obtained.

[0095] After the above steps, the motion error estimation and compensation work of forward-looking multi-channel SAR based on PGA and matrix beam algorithm is completed. Figure 4 The images show a comparison of nine target imaging results: no motion error imaging, imaging with motion error imaging, and imaging results processed using the proposed compensation algorithm. Figure 4 In the middle (a), the imaging result is without motion error. Figure 4 (b) shows the imaging result when motion error exists. Figure 4 (c) is the result after processing with the proposed compensation algorithm. Figure 4 It is known that motion errors can cause azimuth defocusing of real point targets. However, the proposed compensation algorithm can significantly improve the imaging performance of point targets, bringing it close to the state of zero motion error. Therefore, the method proposed in this invention can effectively estimate and compensate for motion errors in forward-looking multi-channel SAR imaging, solving the image defocusing problem caused by motion errors.

[0096] Those skilled in the art will recognize that the embodiments described herein are for the purpose of helping to understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A forward-looking multi-channel SAR motion error compensation method based on PGA and matrix beam, characterized in that, include: Acquire forward-looking multi-channel SAR simulation echo data; Range compression and migration correction are performed on the simulated echo data of forward-looking multi-channel SAR to obtain echoes with phase errors; The RD domain imaging results are obtained by deskewing and Fourier transforming the echo with phase error. By rewriting the RD domain imaging results in matrix form and considering the effect of noise, the deblurring problem is equivalent to solving the following linear inverse problem: ； in, The results are at the peak of the noisy multi-channel RD domain. It is an additive complex white Gaussian noise vector. The goal is to find the unambiguous imaging results at the peak of the RD domain for the left and right scenes. Solving the linear inverse problem is equivalent to solving the optimization problem using the Fist algorithm. Unambiguous RD domain echoes are obtained. ; Unambiguous RD domain echo The phase gradient self-focusing algorithm is used to estimate the higher-order error of each reference point. For the echo after compensating for higher-order errors, the matrix beam algorithm is used to estimate the linear error of each reference point; The sum of the higher-order error and linear error estimates is used as the motion error estimated by the reference point; The least-squares fitting of the motion errors estimated at all reference points yields the two-dimensional spatially varying error for the entire scene. When performing back projection algorithm imaging, the two-dimensional spatial variation error of the entire scene is incorporated into the coherent accumulation process to obtain the imaging result after motion error compensation.

2. The forward-looking multi-channel SAR motion error compensation method based on PGA and matrix beam according to claim 1, characterized in that, The expression for the RD domain imaging result is: ； in, For Fourier transform operators, For fast time sampling sequences, For slow time Frequency domain variables after Fourier transform It is the initial slant range between the target and the radar platform. Ground targets in the left and right scenes and The initial included angle of the axis, It is a second-order approximate desloping function.

3. The forward-looking multi-channel SAR motion error compensation method based on PGA and matrix beam according to claim 2, characterized in that, The value of the k-th dimension in is denoted as , Represented as: ； in, To obtain the imaging results in the RD domain The value of time, At the speed of light, The Doppler frequencies of the left scene affected by motion errors; This represents the noise at the peak of the echo in the k-th channel.

4. The forward-looking multi-channel SAR motion error compensation method based on PGA and matrix beam according to claim 3, characterized in that, The higher-order error estimation process is as follows: In the deblurred RD domain image, multiple isolated strong scattering points with high signal-to-noise ratios are selected as reference points for phase error estimation, arranged from high to low signal-to-noise ratio. Assume the position of the i-th strong scatter point is The imaging results in the RD domain are as follows: ； in, express The reflection coefficient at that location, for The Doppler frequency at the location affected by motion error. yes Fourier transform of higher-order phase errors; Will The peak position is shifted to the center of the image, and an appropriate window function is selected. Multiply by the frequency domain signal, then perform an inverse Fourier transform back to the time domain signal. : ； At this time, the target slows down. The phase error gradient at point is obtained by the following formula: ； The phase error function of the entire aperture is reconstructed through discrete integration. : ； in, express The radar view from that location.

5. The forward-looking multi-channel SAR motion error compensation method based on PGA and matrix beam according to claim 4, characterized in that, The linear error estimation process is as follows: based on By performing higher-order error compensation on the RD domain imaging result corresponding to the i-th strong scattering point, we obtain: ； in, , This represents the linear term of phase error caused by velocity error; In the RD domain image after higher-order error compensation, multiple isolated strong scattering points with high signal-to-noise ratios are selected as reference points for phase error estimation, in descending order of signal-to-noise ratio. for ,Pick The slow-time signal, after discretization, is represented as: ； in, , It is the number of slow-time sampling points. It is a slow sampling interval; based on Constructing the Hankel matrix L is the matrix bundle parameter; Matrix bundle Defined as: ； in and They are matrices The submatrix obtained by removing its last and first columns; Signal frequency information is contained in the generalized eigenvalues ​​of this matrix bundle. In the middle; the equivalent frequency is obtained through the principal generalized eigenvalue. Export as: ； The linear error estimate at this target point is then expressed as: ； ； in, express The estimated value, Angles were obtained through Root-MUSIC measurement.

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