Multichannel sar-gmti method based on improved robust principal component analysis

Abstract

The application discloses a kind of multi-channel SAR-GMTI methods based on improved robust principal component analysis, belong to signal processing technical field, including: obtaining the original echo signal of multi-channel synthetic aperture radar, and the original echo signal is imaged and handled, and image domain data is obtained;After image registration based on image domain data, each channel corresponding registration image domain data in each pixel point is sequentially taken as reference pixel, and the residual of each channel corresponding registration image domain data is compensated in combination with the auxiliary pixel in the preset range of reference pixel;Residual-compensated image domain data is detected using an improved robust principal component analysis model;Radial velocity estimation and target positioning are carried out on moving target using adaptive matched filtering algorithm.The application solves the deficiency encountered when processing local error by traditional channel equalization registration algorithm, and has good target detection capability.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a multi-channel SAR-GMTI method based on improved robust principal component analysis. Background Technology

[0002] Ground-based moving target indication (SAR-GMTI), a key technology in modern radar signal processing, can detect and locate moving targets in SAR images, thus attracting widespread attention in both military and civilian fields. In practical applications, radar echoes from moving targets are often masked by complex ground scene echoes, leading to a deterioration in the target signal-to-noise ratio. This not only poses a significant challenge to moving target detection but also increases the demands on clutter suppression and improved target detection performance. Early antenna radar systems primarily relied on the analysis of Doppler center frequency, Doppler modulation frequency, and other related characteristics to detect fast-moving targets. However, for slow-moving targets, which are often submerged in Doppler-widened main lobe clutter, the performance of single-channel detection algorithms degrades.

[0003] Compared to single-channel systems, azimuth multi-channel radar offers greater spatial freedom in suppressing clutter and estimating motion parameters, successfully overcoming its limitations in detecting slow-moving targets. Traditional multi-channel SAR-GMTI methods are generally divided into two categories: non-adaptive and adaptive processing methods. The former includes algorithms such as Along-Track Interferometry (ATI) and Displaced Phase Center Antenna (DPCA). ATI, which detects targets through inter-channel phase interference, is applicable to high signal-to-noise ratio scenarios. DPCA, a typical clutter suppression algorithm, is simple in principle, easy to implement, and widely used in spaceborne and airborne radars. However, meeting the conditions required for DPCA in practical applications is often challenging. To address this issue, image domain interpolation algorithms can be used to overcome the limitations of DPCA conditions and achieve pixel-level registration between images.

[0004] Robust Principal Component Analysis (RPCA) is helpful in effectively separating moving targets from static background clutter in the image domain. However, in non-ideal environments, RPCA is susceptible to channel errors and strong clutter, leading to a decline in target detection performance. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a multi-channel SAR-GMTI method based on improved robust principal component analysis. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a multi-channel SAR-GMTI method based on improved robust principal component analysis, comprising:

[0007] The raw echo signal of the multi-channel synthetic aperture radar is acquired, and the raw echo signal is processed to obtain image domain data.

[0008] After image registration is performed based on the image domain data, each pixel in the registered image domain data corresponding to each channel is taken as a reference pixel, and the residual of the registered image domain data corresponding to each channel is compensated by combining the auxiliary pixels within a preset range of the reference pixels.

[0009] An improved robust principal component analysis model was used to detect moving targets in image domain data after residual compensation.

[0010] The radial velocity of the moving target is estimated and the target is located using an adaptive matched filtering algorithm.

[0011] In one embodiment of the present invention, in the synthetic aperture radar, using the first channel as the reference channel, the instantaneous slant range of the m-th channel is expressed as:

[0012]

[0013] In the formula, m = 1, 2…M, M represents the number of channels of the multi-channel synthetic aperture radar, R0 represents the closest slant range from the moving target to the aircraft's flight path at the initial moment, and the coordinates of the moving target are (X0, Y0, 0), v r v represents the radial velocity of the moving target along the range direction. r =v y sinφ,v y v represents the velocity of the moving target along the Y-axis. x The value represents the velocity of the moving target along the X-axis, φ represents the downward angle of view of the multi-channel synthetic aperture radar, and t represents the velocity of the moving target along the X-axis. k V represents slow time, V represents the aircraft's flight speed along the X-axis, and d represents the physical interval between two adjacent channels.

[0014] The two-way distance of the raw echo signal received by the m-th channel in the synthetic aperture radar is expressed as:

[0015]

[0016] In the formula, R1(t) k ) represents the instantaneous slant distance of the reference channel;

[0017] The raw echo signal received by the m-th channel in the synthetic aperture radar is represented as:

[0018]

[0019] In the formula, c represents the speed of light, j represents the imaginary unit, σ represents the backscattering coefficient of the moving target, and w r (·), w a (·) represent the range window function and the azimuth window function, respectively, t r K and λ represent fast time, chirp rate, and wavelength, respectively.

[0020] In one embodiment of the present invention, the original echo signal S received from the m-th channel is... m (t r ,t k The image domain data I corresponding to the m-th channel is obtained by performing imaging processing. s.m (t r ,t k ) is represented as:

[0021]

[0022] In the formula, A t B represents the amplitude of the energy of the moving target in the image domain data, and B represents the signal bandwidth. d This indicates the Doppler bandwidth.

[0023] In one embodiment of the present invention, after image registration based on the image domain data, the step of sequentially using each pixel in the registered image domain data corresponding to each channel as a reference pixel, and compensating for the residual of the registered image domain data corresponding to each channel in combination with auxiliary pixels within a preset range of the reference pixels, includes:

[0024] Image registration is performed based on the image domain data corresponding to each channel;

[0025] For the registered image domain data corresponding to the m-th channel, the pixel points (n r ,n a Using the reference pixel as a reference pixel, auxiliary pixels (l) within a preset range of the reference pixel are utilized. r ,l a Constructing the joint data vector Z m,J :

[0026] Z m,J =(I m (n r -l r ,n a -l a ),...I m (n r +l r ,n a +l a )) T ;

[0027] In the formula, I m This represents the registered image domain data corresponding to the m-th channel, where T represents transpose;

[0028] Based on the joint data vector Z m,J Construct an optimization function and solve for the optimal weight vector w. m :

[0029]

[0030] In the formula, I1(n) r ,n a ) represents the reference pixel in the registered image domain data I1 corresponding to the reference channel, E represents the expectation, and H represents the conjugate transpose;

[0031] The optimal weight vector w m With the joint data vector Z m,J After multiplication, it replaces the reference pixel.

[0032] In one embodiment of the present invention, the optimal weight vector w is solved according to the following steps. m :

[0033] Using the generalized inner product (GIP) algorithm, sample X = [I1(n) is selected from the registered image domain data corresponding to the m-th channel. r ,n a )Z m,J (n r ,n a )] T ;

[0034] The covariance matrix is ​​obtained based on the sample estimation. And using the estimated covariance matrix Solve for the optimal weight vector w m :

[0035]

[0036] In the formula, * indicates conjugate.

[0037] In one embodiment of the present invention, the step of using an improved robust principal component analysis model to detect moving targets in image domain data after residual compensation includes:

[0038] Constructing an improved robust principal component analysis model:

[0039]

[0040] In the formula, This represents the clutter data matrix to be solved. This represents the moving target data matrix to be solved, and the inter-channel difference matrix. F is the Fourier matrix, D represents the observation matrix obtained by rearranging the image domain data after residual compensation corresponding to M channels, γ, α, and β are all hyperparameters, and δ represents the noise power constraint parameter. F σ represents the Frobenius norm of a matrix, |·|1 represents the 1-norm of a vector, and ||·||1 represents the 1-norm of a matrix. i (A) represents the i-th singular value of a low-rank matrix A in descending order, where i = 1, 2, ..., M, w i σ i (A) non-negative weights;

[0041] The improved robust principal component analysis model is solved using the multiplier alternating direction algorithm to obtain the moving target detection results.

[0042] In one embodiment of the present invention, before the step of solving the improved robust principal component analysis model using the alternating multiplier direction algorithm to obtain the moving target detection result, the method further includes:

[0043] By introducing auxiliary variables Ω1, Ω2, and Ω3, the improved robust principal component analysis model is transformed into the following optimization problem:

[0044]

[0045] The optimization problem can be rewritten as an augmented Lagrange function:

[0046]

[0047] In the formula, μ represents the penalty term, and Y1, Y2, Y3, and Y4 represent the introduced Lagrange multiplier variables.

[0048] In one embodiment of the present invention, the step of solving the improved robust principal component analysis model using the alternating multiplier direction algorithm to obtain the moving target detection result includes:

[0049] The augmented Lagrangian function is solved using the alternating direction multiplier algorithm.

[0050] In one embodiment of the present invention, the step of solving the augmented Lagrangian function using the alternating direction multiplier algorithm includes:

[0051] For matrix Perform singular value decomposition to obtain the singular value diagonal matrix Ξ;

[0052] The closed-form solution of A is calculated based on the singular valued diagonal matrix Ξ:

[0053]

[0054] In the formula, k represents the number of iterations. [Ξ] i,i Let w represent the singular value in the i-th row and i-th column. i The set of A, where U represents the matrix formed by the left singular vectors of A, and V represents the matrix formed by the right singular eigenvectors of A;

[0055] The optimal solution for E is:

[0056]

[0057] In the formula, I represents the identity matrix;

[0058] Calculate variables Ω1, Ω2, and Ω3 as follows:

[0059]

[0060] In the formula,

[0061] The Lagrange multiplier variables Y1, Y2, Y3, and Y4 are updated via gradients:

[0062]

[0063] When the number of iterations k reaches the preset number of iterations, the detection result of the moving target is determined based on the obtained moving target data matrix E.

[0064] In one embodiment of the present invention, the step of using an adaptive matched filtering algorithm to estimate the radial velocity of the moving target and locate the target includes:

[0065] Calculate the optimal weight vector w using the following formula. v :

[0066]

[0067] In the formula, R cn Let a represent the covariance matrix of clutter and noise. s v represents the guidance vector of the moving target in the image domain. r The radial velocity of the moving target along the range direction is represented by H, where H represents the conjugate transpose.

[0068] Using the optimal weight vector w v Estimate the radial velocity of the moving target:

[0069]

[0070] In the formula, z = [I1(n r ,n a )I2(n r ,n a ...I m (n r ,n a )], · indicates modulo;

[0071] The radial velocity of the moving target obtained by estimation The displacement of the moving target is corrected to achieve the positioning of the moving target.

[0072] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0073] This invention provides a multi-channel SAR-GMTI method based on improved robust principal component analysis. It applies data reconstruction algorithms and the generalized inner product (GIP) algorithm to mitigate local channel residuals, exhibiting good channel correlation and effectively addressing the shortcomings of traditional channel equalization registration algorithms in handling local errors. Furthermore, this invention introduces an improved robust principal component analysis model, which, by incorporating a weighted nuclear norm, alleviates the problem of excessive penalty for large singular values, reducing the false alarm rate and providing better target detection capabilities.

[0074] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0075] Figure 1 This is a flowchart of a multi-channel SAR-GMTI method based on improved robust principal component analysis provided in an embodiment of the present invention;

[0076] Figure 2 This is a schematic diagram of a multi-channel SAR-GMTI method based on improved robust principal component analysis provided in an embodiment of the present invention;

[0077] Figure 3a This is a schematic diagram of an airborne radar observation scenario in a simulation experiment;

[0078] Figure 3b These are SAR imaging results from a simulation experiment;

[0079] Figure 4a It is the interference phase spectrum of the original channel;

[0080] Figures 4b-4d These are the interference phase spectra of the original channel after being processed by different methods;

[0081] Figures 5a-5f This is a comparison chart of the moving target detection results. Detailed Implementation

[0082] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0083] Figure 1 This is a flowchart of a multi-channel SAR-GMTI method based on improved robust principal component analysis provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of a multi-channel SAR-GMTI method based on improved robust principal component analysis provided in an embodiment of the present invention, wherein... Figure 2 The red boxes represent moving targets, and the blue boxes represent the location of the moving targets. For example... Figure 1-2 As shown, this embodiment of the invention provides a multi-channel SAR-GMTI method based on improved robust principal component analysis, including:

[0084] S1. Acquire the raw echo signal of the multi-channel synthetic aperture radar and perform imaging processing on the raw echo signal to obtain image domain data.

[0085] S2. After image registration based on image domain data, each pixel in the registered image domain data corresponding to each channel is taken as a reference pixel, and the residual of the registered image domain data corresponding to each channel is compensated by combining the auxiliary pixels within the preset range of the reference pixels.

[0086] S3. Use an improved robust principal component analysis model to detect moving targets in the image domain data after residual compensation;

[0087] S4. Use the adaptive matched filtering algorithm to estimate the radial velocity of the moving target and locate the target.

[0088] Specifically, in this embodiment, a ground observation geometry of a synthetic aperture radar with M channels is considered. Taking the first channel as the reference channel, the instantaneous slant range of the m-th channel is expressed as:

[0089]

[0090] In the formula, m = 1, 2, ..., M, where M represents the number of channels of the multi-channel synthetic aperture radar, R0 represents the closest slant range from the moving target to the aircraft's flight path at the initial moment, and the coordinates of the moving target are (X0, Y0, 0). h represents the flight altitude of the aircraft, v r v represents the radial velocity of a moving target along the range direction. r =v y sinφ,v y v represents the velocity of the moving target along the Y-axis. x The value represents the velocity of the moving target along the X-axis, φ represents the downward angle of view of the multi-channel synthetic aperture radar, and t... kV represents slow time, V represents the aircraft's flight speed along the X-axis, and d represents the physical interval between two adjacent channels.

[0091] Optionally, if the synthetic aperture radar uses narrowband linear frequency hopping (LFM) signals, then the two-way distance of the original echo signal received by the m-th channel in the synthetic aperture radar can be expressed as:

[0092]

[0093] In the formula, R1(t) k () indicates the instantaneous slant distance of the reference channel;

[0094] Furthermore, the raw echo signal received by the m-th channel in the synthetic aperture radar is represented as:

[0095]

[0096] In the formula, c represents the speed of light, j represents the imaginary unit, σ represents the backscattering coefficient of the moving target, and w r (·), w a (·) represent the range window function and the azimuth window function, respectively, t r K and λ represent fast time, chirp rate, and wavelength, respectively.

[0097] In step S1, the original echo signal S received from the m-th channel is... m (t r ,t k The image domain data I corresponding to the m-th channel is obtained by performing imaging processing. s.m (t r ,t k ) is represented as:

[0098]

[0099] In the formula, A t B represents the amplitude of the energy of the moving target in the image domain data, and B represents the signal bandwidth. d This indicates the Doppler bandwidth.

[0100] After imaging processing, the image domain data I s.m (t r ,t k Analysis shows that the steering vector of a moving target in the image domain can be represented as:

[0101]

[0102] For a stable background clutter, the clutter steering vector can be expressed as a. c =[1,…1,…1] TRobust principal component analysis (RPCA) can be used to generate a phase difference between adjacent channels based on the radial velocity of the moving target, thereby separating clutter from the target. However, due to the influence of factors such as temperature, electronic components, and antenna patterns, registration errors and channel imbalances are inevitable. Channel errors and scene inhomogeneity lead to a decrease in GMTI performance, so it is necessary to compensate for the channel residuals and improve the correlation between channels.

[0103] Optionally, to increase the correlation between channels, this embodiment uses a data reconstruction algorithm to compensate for errors using auxiliary pixels around reference pixels in the registered image domain data. Step S2, after image registration based on the image domain data, sequentially uses each pixel in the registered image domain data corresponding to each channel as a reference pixel, and combines auxiliary pixels within a preset range of the reference pixels to compensate for the residuals in the registered image domain data corresponding to each channel. This includes:

[0104] S201. Perform image registration based on the image domain data corresponding to each channel;

[0105] S202. For the registered image domain data corresponding to the m-th channel, the pixel points (n r ,n a Using the reference pixel as a reference pixel, auxiliary pixels (l) within a preset range of the reference pixel are utilized. r ,l a Constructing the joint data vector Z m,J :

[0106] Z m,J =(I m (n r -l r ,n a -l a ),...I m (n r +l r ,n a +l a )) T ;

[0107] In the formula, I m This represents the registered image domain data corresponding to the m-th channel, where T represents transpose;

[0108] S203, Based on joint data vector Z m,J Construct an optimization function and solve for the optimal weight vector w. m :

[0109]

[0110] In the formula, I1(n) r ,na ) represents the reference pixel in the registered image domain data I1 corresponding to the reference channel, E represents the expectation, and H represents the conjugate transpose;

[0111] S204, the optimal weight vector w m With joint data vector Z m,J After multiplication, it replaces the reference pixel.

[0112] Specifically, the optimal weight vector w can be solved by following these steps. m :

[0113] Using the generalized inner product (GIP) algorithm, sample X = [I1(n) is selected from the registered image domain data corresponding to the m-th channel. r ,n a )Z m,J (n r ,n a )] T ;

[0114] The covariance matrix is ​​obtained based on sample estimation. And using the estimated covariance matrix Solve for the optimal weight vector w m :

[0115]

[0116] In the formula, * indicates conjugate.

[0117] After correcting for the accurate registration error and the channel imbalance error, it can be assumed that the clutter received by each channel is strongly correlated. In practical applications, especially in the presence of strong clutter, the incomplete separation of the matrix may lead to a decrease in the performance of moving target detection. This embodiment further introduces an improved robust principal component analysis model.

[0118] For example, step S3, which involves using an improved robust principal component analysis model to detect moving targets in the residual-compensated image domain data, includes:

[0119] S301. Construct an improved robust principal component analysis model:

[0120]

[0121] In the formula, This represents the clutter data matrix to be solved. This represents the moving target data matrix to be solved, and the inter-channel difference matrix. F is the Fourier matrix, D represents the observation matrix obtained by rearranging the image domain data after residual compensation corresponding to M channels, γ, α, and β are all hyperparameters, and δ represents the noise power constraint parameter. F σ represents the Frobenius norm of a matrix, |·|1 represents the 1-norm of a vector, and ||·||1 represents the 1-norm of a matrix. i (A) represents the i-th singular value of a low-rank matrix A in descending order, where i = 1, 2, ..., M, w i σ i (A) non-negative weights;

[0122] S302. The improved robust principal component analysis model is solved using the multiplier alternating direction algorithm to obtain the detection results of moving targets.

[0123] For example, before the step of solving the improved robust principal component analysis model using the alternating multiplier direction algorithm to obtain the moving target detection result, the method further includes:

[0124] By introducing auxiliary variables Ω1, Ω2, and Ω3, the improved robust principal component analysis model is transformed into the following optimization problem:

[0125]

[0126] The optimization problem described above can be rewritten as an augmented Lagrange function:

[0127]

[0128] In the formula, μ represents the penalty term, and Y1, Y2, Y3, and Y4 represent the introduced Lagrange multiplier variables.

[0129] Furthermore, the steps for solving the improved robust principal component analysis model using the alternating multiplier direction algorithm to obtain the moving target detection results include:

[0130] The augmented Lagrangian function is solved using the alternating direction multiplier algorithm.

[0131] Specifically, the steps for solving the augmented Lagrangian function using the alternating multiplier direction algorithm include:

[0132] For matrix Perform singular value decomposition to obtain the singular value diagonal matrix Ξ;

[0133] The closed-form solution of A is calculated from the singular valued diagonal matrix Ξ as follows:

[0134]

[0135] In the formula, k represents the number of iterations. [Ξ] i,iLet w represent the singular value in the i-th row and i-th column. i Let U be a set of left singular eigenvectors of A, and V be a set of right singular eigenvectors of A, where V is the matrix formed by the left singular eigenvectors of A. ε = 10 -16 , Representation matrix The i-th singular value in descending order;

[0136] The optimal solution for E is:

[0137]

[0138] In the formula, I represents the identity matrix;

[0139] Calculate variables Ω1, Ω2, and Ω3 as follows:

[0140]

[0141] In the formula, [Ξ] i,i This represents the singular value in the i-th row and i-th column.

[0142] The Lagrange multiplier variables Y1, Y2, Y3, and Y4 are updated via gradient as follows:

[0143]

[0144] Where, μ (k+1) =max(ημ) (k) ,μ max ), μ max η represents the maximum value of the penalty term μ in the first k iterations, and η represents the penalty factor. Usually, the precision requirement of the penalty term μ in each iteration is greater than zero, for example, it can be 1.1.

[0145] When the number of iterations k reaches the preset number of iterations, the detection result of the moving target is determined based on the obtained moving target data matrix E.

[0146] Step S4, which involves using an adaptive matched filtering algorithm to estimate the radial velocity of the moving target and locate the target, includes:

[0147] S401. Calculate the optimal weight vector w according to the following formula. v :

[0148]

[0149] In the formula, R cn The clutter and noise covariance matrix is ​​estimated from the auxiliary pixels surrounding the reference pixel in the image domain data, a sv represents the orientation vector of the moving target in the image domain. r This represents the radial velocity of the moving target along the range direction, and H represents the conjugate transpose;

[0150] S402, Using the optimal weight vector w v Estimate the radial velocity of the moving target:

[0151]

[0152] In the formula, z = [I1(n r ,n a )I2(n r ,n a ...I m (n r ,n a )], · indicates modulo;

[0153] S403. Utilize the estimated radial velocity of the moving target Correcting the displacement of the moving target enables the positioning of the moving target.

[0154] The following simulation experiment further illustrates the multi-channel SAR-GMTI method based on improved robust principal component analysis provided by this invention.

[0155] It should be noted that the hardware platform used in the simulation experiment in this embodiment is: Intel(R) Core(TM) i5-8265U CPU@1.60GHz, frequency 1.8GHz, Nvidia GeForce MX250, and the software used is MATLAB 2018b.

[0156] This embodiment uses three-channel airborne SAR data with cooperative targets. The main simulation parameters are shown in Table 1:

[0157] Table 1. Overview of Simulation Parameters

[0158] parameter numerical values bandwidth 40MHz carrier frequency 8.85GHz Pulse repetition frequency 1000Hz Number of channels 3 Array spacing 0.559m Platform speed 115m / s

[0159] Figure 3a This is a schematic diagram of an airborne radar observation scenario in a simulation experiment. Figure 3a Using the urban background as clutter and multiple road-traveling targets to be detected as observation targets, the SAR imaging results are as follows: Figure 3b As shown. Due to the target's radial velocity, its trajectory deviates significantly from the tunnel, and the presence of background clutter hinders direct observation of the target.

[0160] Figure 4a It is the interference phase spectrum of the original channel. Figures 4b-4dThese are the interference phase spectra of the original channel after processing using different methods. Compared to the chaotic phase observed before correction, Figure 4b As shown, the interference phase obtained after data equalization DB algorithm generally converges to 0. However, taking the pixels in the red box as an example, the phase of some pixels deviates from 0, indicating that there are residuals between channels, which leads to a decrease in correlation. Figure 4c Reconstructing the interference map after DR algorithm processing reveals that the phase in most areas tends to be consistent, alleviating the fluctuation problem. However, due to the estimation bias of the covariance matrix caused by non-uniform samples, deviation values ​​appear in some non-uniform regions; for example... Figure 4d As shown, after sample selection using the Generalized Inner Product (GIP) algorithm, the performance is significantly improved. This not only enhances the consistency between channels but also compensates for the shortcomings of the DR algorithm in local non-uniform regions.

[0161] Figures 5a-5f This is a comparison chart of the moving target detection results, in which... Figures 5a-5f Moving target detection was performed using traditional Robust Principal Component Analysis (RPCA), Low-Rank Clustering Image Denoising Algorithm (WNNM), Maximum Entropy Fast Robust Low-Rank Matrix Factorization Algorithm (Godec), Dynamic Principal Component Analysis (DPCA), Joint Pixel Dynamic Principal Component Analysis Algorithm (JPDPCA), and the multi-channel SAR-GMTI method based on improved robust principal component analysis provided in this invention. Red circles indicate moving targets to be detected, and green circles indicate false targets. Please refer to [link / reference]. Figure 5a While the traditional RPCA algorithm can detect moving targets, it may generate false alarms due to strong clutter residue; compared to the traditional RPCA algorithm, Figure 5b In this algorithm, the WNNM algorithm retains more sparse components, but because it cannot suppress strong clutter leaking into the sparse matrix, some false alarms still occur; while for Figure 5c When sparsity is unknown, the Godec algorithm has a high false alarm rate; for example... Figure 5d As shown, the false alarm rate is Pfa = 10e -6 Due to registration and imbalance errors, the DPCA algorithm generates a considerable number of false alarms; compared to the DPCA algorithm, Figure 5e The JPDPCA algorithm shown has better clutter suppression performance, but a small number of residual clutter-induced pseudo-targets still exist; compared with traditional clutter suppression algorithms and matrix recovery algorithms, such as Figure 5f As shown, this invention not only achieves accurate channel registration and equalization, but also avoids false alarms caused by strong clutter by using difference matrices and Fourier matrices, and exhibits excellent detection performance even in non-ideal environments.

[0162] As can be seen from the above embodiments, the beneficial effects of the present invention are as follows:

[0163] This invention provides a multi-channel SAR-GMTI method based on improved robust principal component analysis. It applies data reconstruction algorithms and the generalized inner product (GIP) algorithm to mitigate local channel residuals, exhibiting good channel correlation and effectively addressing the shortcomings of traditional channel equalization registration algorithms in handling local errors. Furthermore, this invention introduces an improved robust principal component analysis model, which, by incorporating a weighted nuclear norm, alleviates the problem of excessive penalty for large singular values, reducing the false alarm rate and providing better target detection capabilities.

[0164] In the description of this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0165] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A multi-channel SAR-GMTI method based on improved robust principal component analysis, characterized in that, The method comprises the following steps: acquiring original echo signals of a multi-channel synthetic aperture radar, and performing imaging processing on the original echo signals to obtain image domain data; after image registration based on the image domain data, taking each pixel point in the registered image domain data corresponding to each channel as a reference pixel, and combining auxiliary pixels within a preset range of the reference pixel to compensate for the residual of the registered image domain data corresponding to each channel; performing motion target detection on the image domain data after residual compensation by using an improved robust principal component analysis model; performing radial velocity estimation and target positioning on the motion target by using an adaptive matched filter algorithm; the improved robust principal component analysis model is expressed as: ； In the formula, denotes the clutter data matrix to be solved, denotes the moving target data matrix to be solved, the inter-channel difference matrix , is a Fourier matrix, denotes the observation matrix obtained by rearranging the residual compensated image domain data corresponding to M channels, , and are hyperparameters, denotes a noise power constraint parameter, denotes the Frobenius norm of a matrix, denotes the 1-norm of a vector, denotes the 1-norm of a matrix, denotes the low-rank matrix arranged in descending order singular value, , denotes non-negative weight.

2. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 1, characterized in that, In the synthetic aperture radar, the first channel is taken as a reference channel, and the instantaneous slant range of the second channel is represented as: ​ wherein, , denotes the number of channels of the multi-channel synthetic aperture radar, denotes the closest slant range of the moving target to the flight path of the carrier at the initial time, the coordinates of the moving target being , denotes the radial velocity of the moving target along the range direction, , denotes the moving velocity of the moving target along the axis, denotes the moving velocity of the moving target along the axis, denotes the downward angle of the multi-channel synthetic aperture radar, denotes the slow time, denotes the flight velocity of the carrier along the X axis, denotes the physical interval of the adjacent two channels; The synthetic aperture radar in the first The two-way distance for each channel to receive the original echo signal is expressed as: In the formula, represents the instantaneous slant range of the reference channel; The synthetic aperture radar in the first The original echo signals received by each channel are represented as follows: ； wherein denotes the speed of light, denotes the imaginary unit, denotes the backscatter coefficient of the moving target, , denote the range and azimuth window functions, respectively, , , denote the fast time, the chirp rate and the wavelength, respectively.

3. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 2, characterized in that, For the first The raw echo signal received by each channel Imaging processing was performed to obtain the first... Image domain data corresponding to each channel Represented as: wherein represents the amplitude of the energy of the moving target in the image domain data, represents the signal bandwidth, represents the Doppler bandwidth.

4. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 1, characterized in that, after image registration based on the image domain data, taking each pixel point in the registered image domain data corresponding to each channel as a reference pixel, and combining auxiliary pixels within a preset range of the reference pixel to compensate for the residual of the registered image domain data corresponding to each channel; performing image registration based on the image domain data corresponding to each channel; For the registered image domain data corresponding to the first channel, a pixel point is taken as a reference pixel, and an auxiliary pixel in a preset range of the reference pixel is used to construct a joint data vector : ； wherein represents the registered image domain data corresponding to the channel, represents the transpose; based on the joint data vector constructing an optimization function and solving to obtain an optimal weight vector : ； wherein represents the registered image domain data corresponding to the reference channel represents a reference pixel in the reference channel, represents the expectation, represents the conjugate transpose; The optimal weight vector is multiplied with the joint data vector and replaces the reference pixel.

5. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 4, characterized in that, Solve for the optimal weight vector as follows : The GIP algorithm is used to select samples from the registered image domain data corresponding to the first channel. ; estimating a covariance matrix based on the samples and using the estimated covariance matrix solving for an optimal weight vector : wherein , , , , represents conjugation.

6. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 1, characterized in that, the step of performing motion target detection on the image domain data after residual compensation by using an improved robust principal component analysis model comprises: solving the improved robust principal component analysis model by using a multiplier alternating direction algorithm to obtain a motion target detection result.

7. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 6, characterized in that, Before the step of solving the improved robust principal component analysis model by using a multiplier alternating direction algorithm to obtain a motion target detection result, the method further comprises the following steps: By introducing auxiliary variables , and the improved robust principal component analysis model is transformed into the following optimization problem: rewriting the optimization problem as an augmented Lagrange function: wherein represents the penalty term, , , , represents the introduced Lagrange multiplier variable.

8. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 7, characterized in that, the step of solving the improved robust principal component analysis model by using a multiplier alternating direction algorithm to obtain a motion target detection result comprises: solving the augmented Lagrange function by using a multiplier alternating direction algorithm.

9. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 8, characterized in that, The step of solving the augmented Lagrange function by using a multiplier alternating direction algorithm comprises: On the matrix singular value decomposition to obtain a singular value diagonal matrix ; According to the singular value diagonal matrix Computing The closed-form solution for is: ； wherein denotes the number of iterations, , denotes the singular value of the element in the i-th row and j-th column, i denotes the singular value of the element in the i-th row and j-th column, i denotes the singular value of the element in the i-th row and j-th column, is the set of , denotes the matrix composed of the left singular vectors of , denotes the matrix composed of the right singular vectors of ; The optimal solution of the calculation is: In the formulae, denotes the identity matrix; Computing the variable , , is: ； ； ； In the formulae, , , ; lagrangian multiplier variable 、 、 、 by gradient update: When the number of iterations reaches the preset number of iterations, the detection result of the moving target is determined according to the obtained moving target data matrix reaches the preset number of iterations, the detection result of the moving target is determined according to the obtained moving target data matrix 10. The improved robust principal component analysis based multichannel SAR-GMTI method according to claim 4, characterized in that, the step of performing radial velocity estimation and target positioning on the motion target by using an adaptive matched filter algorithm comprises: The optimal weight vector is calculated according to the following formula : wherein denotes the clutter and noise covariance matrix, denotes the steering vector of the moving target in image domain, denotes the radial velocity of the moving target along the range direction, denotes the conjugate transpose; using the optimal weight vector estimating a radial velocity of the moving object ； wherein , denotes a modulo operation; using the estimated radial velocity of the moving target correcting the displacement of the moving target to achieve positioning of the moving target.

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