Ground moving target detection method combining information geometry and improved robust principal component analysis

Abstract

The invention discloses a ground moving target detection method combining information geometry and improved robust principal component analysis, and the method comprises the steps: reconstructing multi-channel image data, carrying out the vectorization of the reconstructed multi-channel image data, and obtaining an original observation matrix; adopting preset robust principal component analysis to construct an optimization model, wherein the optimization model is represented by a low-rank background matrix and a sparse target matrix; removing non-uniform sample units in rows and columns in the low-rank background matrix by adopting a preset KL divergence-based generalized inner product sample selection method; initializing the row index set, the column index set and the observation matrix through an improved robust principal component analysis method, carrying out iteration until a preset condition is met or a preset number of iterations is reached, obtaining an updated observation matrix, and further obtaining a sparse target matrix; and carrying out rearrangement and threshold detection on the sparse target matrix, and extracting target features. According to the method, efficient and low-false-alarm target detection under the non-uniform strong clutter background can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and in particular relates to a ground moving target detection method combining information geometry with improved robust principal component analysis. Background Art

[0002] Synthetic Aperture Radar (SAR) is an active remote sensing radar system that works around the clock and in all weather conditions, and can obtain high-resolution radar images of long-distance observation scenes. It is widely used.

[0003] Multi-channel moving target detection methods mainly include: phase center offset antenna technology (DPCA), which mainly draws on the clutter cancellation technology of ground radar to suppress clutter and detect moving targets; along-track interferometry (ATI), which mainly uses the interference phase between multiple channels placed along the track to detect moving targets using phase or amplitude-phase combination methods; space-time adaptive processing technology (STAP), which mainly uses the statistical characteristics of clutter in the spatial and Doppler domains to construct space-time filters to adaptively suppress clutter; robust principal component analysis (RPCA), which separates clutter and moving targets by quantizing the echo vectors of each channel into a new matrix and taking advantage of the fact that clutter channels have consistent correlation while moving targets are sparsely distributed throughout the scene, thereby achieving moving target detection. The effectiveness of multi-channel moving target detection is directly related to the correlation between channels. If the correlation between channels decreases, strong clutter cannot be effectively suppressed, and the detection performance is seriously impaired.

[0004] To avoid issues like inter-channel correlation, experts and scholars have proposed using single-channel synthetic aperture radar systems to detect moving targets. Time-frequency analysis methods, among others, image moving targets by accumulating their energy in different time and frequency domains. They estimate target parameters using the Doppler center and modulation rate. Typical methods include the Wigner-Ville distribution, the extended wavelet transform, and the fractional Fourier transform. Robust principal component analysis is a popular technique for extracting and analyzing the low-dimensional structure of data. It can significantly reduce the number of dimensions required to represent the observed data and effectively reveal hidden internal connections within the data. By decomposing the observed data into low-rank and sparse components, robust principal component analysis effectively enhances the robustness of target detection in heterogeneous clutter environments. This method, based on an unsupervised learning mechanism, avoids the problem of training data dependence. However, practical engineering applications face two challenges: first, the complex matrix decomposition and iterative computations lead to insufficient algorithm timeliness; second, the sensitivity of the input parameters can easily lead to anomalies in detection results, resulting in false alarms and missed alarms.

[0005] Therefore, based on the characteristics of multi-channel radar systems, building a fast-converging optimization model and designing a parameter adaptive adjustment mechanism have become key technical paths to improve the efficiency and accuracy of moving target detection. Summary of the Invention

[0006] To address the above-mentioned problems in the prior art, the present invention provides a ground moving target detection method that combines information geometry with improved robust principal component analysis. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0007] In a first aspect, the present invention provides a ground moving target detection method combining information geometry with improved robust principal component analysis, comprising:

[0008] Build a front-side multi-channel radar detection model, obtain raw data, and reconstruct multi-channel image data;

[0009] Vectorize the reconstructed multi-channel image data to obtain the original observation matrix;

[0010] An improved robust principal component analysis is used to construct an optimization model, which is represented by a low-rank background matrix and a sparse target matrix after decomposition of the original observation matrix. The low-rank background matrix includes multiple rows and columns, and each row and column includes multiple sample units.

[0011] The preset generalized inner product sample selection method based on KL divergence is used to remove non-uniform sample units in the rows and columns of the low-rank background matrix, and the sample units in the remaining rows and columns are used as the observation area. The low-rank background matrix after removing the non-uniform sample units is used as the observation matrix to obtain the row index set and column index set in the observation matrix;

[0012] Initialize the row index set, column index set, and observation matrix, and iterate until a preset condition is met or a preset number of iterations is reached, thereby obtaining an updated observation matrix; wherein, during the iteration process, the observation matrix is decomposed into a row matrix, a column matrix, and a cross matrix according to preset requirements to update the observation matrix;

[0013] According to the updated observation matrix, the sparse target matrix is obtained;

[0014] The sparse target matrix is rearranged and threshold detected to extract target features.

[0015] Beneficial effects of the present invention:

[0016] The present invention provides a ground moving target detection method that combines information geometry with improved robust principal component analysis. To address the problems of high false alarm rate and low solution efficiency in the RPCA moving target detection process under clutter background, the generalized inner product selection criterion based on KL divergence is used to select uniform sample units, and an iterative CUR decomposition algorithm is further adopted for efficient solution to achieve robust moving target detection. This method can effectively improve the matrix solution efficiency and improve the existing sample unit selection method to achieve efficient and low false alarm target detection under non-uniform strong clutter background.

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flow chart of a ground moving target detection method combining information geometry and improved robust principal component analysis provided by an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of a multi-channel radar detection model provided by an embodiment of the present invention;

[0020] Figure 3 This is a schematic diagram of target detection results using different algorithms provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0022] In the existing technology, the current single-channel target detection methods mainly include Wigner-Ville distribution, extended wavelet transform, and fractional Fourier transform; the multi-channel target detection methods mainly include space-time adaptive processing (STAP), along-track interferometry (ATI), offset phase center method (DPCA) and robust principal component analysis (RPCA).

[0023] 1. The Wigner-Ville distribution is based on a bilinear transformation of the signal, generating a time-frequency distribution through the instantaneous autocorrelation function, providing a high-resolution representation of time-frequency energy. Although the Wigner-Ville distribution can accurately locate the time and frequency of single-component signals (such as linear frequency modulation), multi-component signals can produce cross-term interference (spurious energy).

[0024] 2. The extended wavelet transform (ELT) introduces adaptive parameters (such as scale optimization and complex wavelet design) based on the traditional wavelet transform to improve its adaptability to non-stationary signals. Although the ELT can perform multi-resolution analysis and is suitable for processing transient signals (such as fault shock waves), improper selection of basis functions can significantly degrade its performance.

[0025] 3. The fractional Fourier transform method combines the Wigner-Ville distribution with the Hough transform to map linear features (such as frequency-modulated signals) in the time-frequency plane into parameter space for detection. Although the fractional Fourier transform method can suppress cross-term interference and enhance the detection of linear frequency-modulated signals (LFM), it is computationally complex and expensive.

[0026] 4. Space-time adaptive processing (STAP) technology mainly uses the statistical characteristics of clutter in the spatial and Doppler domains to construct space-time filters to adaptively suppress clutter, but it consumes a lot of resources for target search.

[0027] 5. Along-track interferometry (ATI) mainly uses the interference phase between multiple channels placed along the track to detect moving targets using phase or amplitude-phase combination methods, but the phase stability is poor at low signal-to-noise ratios.

[0028] 6. Phase center offset antenna technology (DPCA) mainly draws on the ground radar clutter cancellation technology to suppress clutter and detect moving targets, but the clutter suppression freedom is insufficient.

[0029] 7. Pseudo-frame decomposition is typically implemented using CUR decomposition, which is suitable for real-time processing and large-scale data. Redundant frame systems can tolerate noise or data loss, enhancing the ability to capture local signal features. Optimization algorithms (such as compressed sensing) can achieve sparse signal representation within a pseudo-frame, reducing storage or transmission overhead. However, the parameter sensitivity and design complexity of pseudo-frame decomposition techniques depend on the selection of parameters (such as filter length and redundancy). Improper design can significantly affect performance, and when processing high-dimensional signals, memory usage and computational complexity can increase dramatically.

[0030] 8. Robust principal component analysis (RPCA) reduces dimensionality by reducing data dimensionality, preserving key information while reducing dimensional redundancy. However, in synthetic aperture radar ground moving target detection (SAR-GMTI) scenarios, traditional RPCA methods face a conflict between real-time requirements and computational resources. Furthermore, the low-rank / sparse nature of RPCA in real-world environments is compromised, further limiting the stability of detection performance. Engineering applications face two challenges: first, high computational complexity due to iterative calculations and matrix decomposition; second, parameter deviations can easily lead to reduced detection reliability.

[0031] In view of this, the present invention provides a ground moving target detection method that combines information geometry with improved robust principal component analysis. To address the problems of high false alarm rate and low solution efficiency of RPCA in the process of moving target detection under clutter background, it is proposed to use a generalized inner product sample selection method based on KL divergence to select uniform sample units, and then adopt an iterative CUR decomposition algorithm for efficient solution to achieve robust moving target detection.

[0032] See Figure 1 , Figure 1 This is a flow chart of a ground moving target detection method combining information geometry and improved robust principal component analysis provided by an embodiment of the present invention. The ground moving target detection method combining information geometry and improved robust principal component analysis provided by the present invention includes:

[0033] S101. Construct a front-side-view multi-channel radar detection model, obtain raw data, and reconstruct multi-channel image data.

[0034] Specifically, in this embodiment, see Figure 2 , Figure 2 This is a schematic diagram of a multi-channel radar detection model provided by an embodiment of the present invention. A front-view side-view multi-channel radar detection model is constructed. The radar height is H and it flies along the X-axis at a speed v. N radar channels with a spacing of d are evenly set in the flight path. The first channel is used as the reference channel to transmit signals. All channels receive echoes. The azimuth slow time t is defined. m , m is the pulse index. Assume that a target at the zero position (x0, y0, 0) moves from a to b during the data acquisition process. Its azimuth velocity and radial projection velocity are v a With v c .

[0035] According to the equivalent phase center criterion and the geometric relationship between the radar and the target, the instantaneous slant range between the target and the nth channel is obtained. Expressed as:

[0036]

[0037] Where R0 represents the minimum slant distance of the target beam center at that moment, v e Indicates the relative speed between the target and the radar, v r represents the target radial projection velocity, t m represents the azimuth slow time, m represents the pulse index, x0 represents the target initial position, v represents the flight speed of the airborne radar, v a Indicates the target azimuth velocity, n indicates the channel index;

[0038] When the target azimuth velocity v a and the target radial projection velocity v c When they are equal, the instantaneous slant range of the clutter is obtained. , expressed as:

[0039]

[0040] Get the target echo data received by channel n, expressed as:

[0041]

[0042]

[0043] Among them, rect(x) represents the echo range envelope, w a (·) represents the azimuth window function, c represents the speed of light, t represents the fast time of the transmitted pulse, T p represents the duration of the transmitted pulse, μ represents the frequency modulation of the transmitted pulse, and λ represents the wavelength of the transmitted pulse;

[0044] After range compression, range migration correction and azimuth focusing processing, the updated target echo data is expressed as:

[0045]

[0046] Where B represents the radar transmission bandwidth, B D Indicates the modulation bandwidth in the target azimuth direction;

[0047] Similarly, clutter echo data is obtained, which is expressed as:

[0048]

[0049] It can be seen that after imaging processing, the moving target between channels has equivalent azimuth position offset and phase term related to radial velocity. After channel registration, the image azimuth offset can be effectively processed, and the multi-channel target echo data is vectorized to obtain the target echo vector data, which is expressed as:

[0050] s=[s1,s2,…,s N ] T ;

[0051] in,(·) Τ represents the transpose operation, s n Indicates the target echo data of channel n;

[0052] The multi-channel clutter echo data is vectorized to obtain the clutter echo vector data, which is expressed as:

[0053] c=[c1,c2,…,c N ] T ;

[0054] According to the target echo vector data and the clutter echo vector data, the multi-channel single-pixel echo vector data is obtained, which is expressed as:

[0055] z(p,u)=s(p,u)+c(p,u)+n(p,u);

[0056] Among them, (p,u) represents the two-dimensional index of distance and orientation of a single pixel, and n(p,u) represents the Gaussian white noise vector.

[0057] In this embodiment, ideally, after registration, the clutter information between channels is consistent and the moving target spatial guidance vector meets the theoretical analysis. However, due to deviations in registration and channel phase in practice, residual errors still exist between channels after processing. To ensure clutter suppression and target detection performance, precise registration is required to improve inter-channel coherence and perform adaptive data reconstruction by combining pixels to reconstruct multi-channel image data, including:

[0058] Reconstruct the multi-channel single-pixel echo vector data to obtain the reconstructed single-pixel echo vector data, which is expressed as:

[0059] z r (p,u)=[z1(p,u),z r_2 (p,u),…,z r_N (p,u)] Τ ;

[0060] According to the reconstructed single pixel vector data, the reconstructed N channel image data {Z1, Z r_2 ,…,Z r_N}.

[0061] S102: vectorize the reconstructed multi-channel image data to obtain an original measurement matrix.

[0062] Specifically, in this embodiment, the expression of the original measurement matrix D is:

[0063] D=[vec(Z1),vec(Z r_2 ),…,vec(Z r_N )];

[0064] Here, vec(·) represents a vectorized operation.

[0065] S103. An improved robust principal component analysis is used to construct an optimization model, and the optimization model is represented by a low-rank background matrix and a sparse target matrix after decomposition of the original observation matrix; wherein the low-rank background matrix includes multiple rows and multiple columns, and the rows and columns include multiple sample units.

[0066] Specifically, in this embodiment, based on the channel correlation enhancement of data reorganization processing, combined with the sparse characteristics of moving targets in the image domain and the strong low-rank correlation of inter-channel clutter, robust principal component analysis (RPCA) is used to construct an optimization model to achieve target separation. The expression of the optimization model is:

[0067]

[0068] where ||·||* represents the nuclear norm, ||·||1 represents the L1 norm, λ1 represents the regularization parameter, D represents the original observation matrix, L represents the low-rank background matrix, S represents the sparse target matrix, and E represents the noise term.

[0069] S104. Use the preset generalized inner product sample selection method based on KL divergence to eliminate non-uniform sample units in rows and columns in the low-rank background matrix, use the sample units in the remaining rows and columns as the observation area, and use the low-rank background matrix after eliminating the non-uniform sample units as the observation matrix to obtain the row index set and column index set in the observation matrix.

[0070] Specifically, in this embodiment, the elimination of non-uniform sample units in rows and columns of the low-rank background matrix is described as a binary hypothesis testing problem, which is expressed as:

[0071]

[0072] Where H0 represents a sample unit judged as uniform, H1 represents a sample unit judged as non-uniform, Ω0 represents a uniform sample unit set, Ω1 represents a non-uniform sample unit set, i.e., a non-uniform sample unit including discrete interference points, K1 represents the total number of samples in the uniform sample unit set, and K2 represents the total number of samples in the non-uniform sample unit set.

[0073] The type of the sample unit to be detected is determined by solving the value of the generalized inner product sample selection model. In complex scenarios, non-uniform interference leads to a significant decrease in clutter suppression performance and a high false alarm rate. Therefore, the non-uniform sample screening criterion - the generalized inner product criterion (GIP) is applied. That is, based on the estimated value of the clutter covariance matrix of the sample unit to be detected, a generalized inner product sample selection model is constructed, which is expressed as:

[0074]

[0075] Among them, η k Represents the value of the generalized inner product sample selection model for the k-th sample unit, Represents the estimated value of the clutter covariance matrix of the sample unit to be detected, x k represents the echo data of the kth sample unit, (·) H represents conjugate transpose;

[0076] When the value of the generalized inner product sample selection model is less than the system degree of freedom, the sample unit to be detected is judged to be a uniform sample unit. When the value of the generalized inner product sample selection model is greater than the system degree of freedom, the sample unit to be detected is judged to be a non-uniform sample unit, which is expressed as:

[0077]

[0078] Where M represents the system degree of freedom.

[0079] In this embodiment, the premise for the effectiveness of the generalized inner product criterion is that the estimated clutter covariance matrix is consistent with the covariance matrix R of the sample unit to be detected; however, the traditional The estimation method is the arithmetic centroid of the sample unit in Euclidean space. When the number of sample units is insufficient or there are a small number of discrete interference points, traditional methods often lead to false screening and missed screening. Studies have shown that under the same power conditions, clutter samples with different statistical characteristics are separated in the manifold, while clutter samples with the same statistical characteristics are closely adjacent in the manifold. Based on this property, the clutter covariance matrix estimation problem is transformed into a geometric centroid optimization problem on the manifold. The covariance matrix estimation problem can be expressed as the following optimization problem:

[0080]

[0081] Among them, R k represents the covariance matrix of the kth sample unit, KL(·) represents R k and KL divergence, K represents the total number of sample units, Represents the weight coefficient of different sample units in estimating the geometric centroid, and R=Ε[xx H ], E[·] represents the mathematical expectation.

[0082] It should be noted that the calculation formula of the KL divergence of matrix R1 and matrix R2 is expressed as:

[0083] d KL (R1,R2)=tr(R2 -1 R1)-logdet(R2 -1 R1)-n.

[0084] It should be noted that in order to address the problem of non-uniform sample interference in the classic RPCA method under complex environments, the present invention constructs a generalized inner product sample selection method based on information geometry. By introducing the KL metric, the influence of sparse targets and non-uniform clutter on the low-rank matrix is weakened, thereby achieving precise decoupling of the clutter basis and target features, providing a better solution for non-uniform sample selection in complex electromagnetic environments.

[0085] S105. Initialize the row index set, column index set and observation matrix, and iterate until the preset conditions are met or the preset number of iterations is reached to obtain an updated observation matrix; wherein, during the iteration process, the observation matrix is decomposed into a row matrix, a column matrix and a cross matrix according to the preset requirements to update the observation matrix.

[0086] Specifically, in view of the limitations of pseudo-frame decomposition in RPCA applications, that is, random selection of rows and columns easily leads to increased false alarms and difficulty in convergence, this embodiment proposes an improved RPCA solution method, assuming a low-rank matrix with rank r The generalized inner product sample selection method based on the joint KL divergence removes non-uniform sample units in the rows and columns of the low-rank matrix. According to the preset requirements, the remaining row index set and column index set are selected to construct the row matrix R = L(I,:), column matrix C = L(:,J) and cross matrix U = L(I,J) to achieve the decomposition of the observation matrix J represents the column index, and I represents the row index;

[0087] The pre-set requirements include:

[0088] When the number of columns is selected as c=r+p and the number of rows is selected as r'=r+q, the probability of satisfying rank(U)=r exceeds 1-δ, δ≈0.01, to ensure the reliability of decomposition; p and q represent redundant parameters.

[0089] It should be noted that, in order to improve the problems of low computational efficiency and long iteration time in the pseudo-frame decomposition algorithm of RPCA, the present invention proposes an efficient non-convex robust principal component analysis algorithm based on iterative CUR decomposition for motion target detection, so as to improve its detection performance, accelerate the convergence speed of the RPCA algorithm, improve the solution efficiency, and alleviate the contradiction between the computational amount and computing power of small platforms.

[0090] In this embodiment, the row index set, column index set, and observation matrix are initialized, and iteration is performed until a preset condition is satisfied to obtain an updated observation matrix, including:

[0091] 1. Before the iteration begins, use the generalized inner product and amplitude probability distribution characteristics to obtain the non-uniform sample row and column index The remaining uniform sample units are used as the observation area Ω for subsequent row and column initialization R ,Ω C (Not including The region, superscript c represents the complement), initialize the row index set I0, column index set J0 and observation matrix L0;

[0092] 2. In the q+1th iteration, a specific number of rows and columns are randomly selected from the row index set and column index set, and the row index set I is updated. q+1 and column index set J q+1 ; According to the sampling operator and the observation matrix L q+1 , calculate the row matrix and column matrix According to the truncation operator Sampling Operator and the observation matrix L q Calculate the cross matrix U q+1 ;

[0093] 3. According to the cross matrix U q+1 , update the row matrix and column matrix Get the row matrix R q+1 and column matrix C q+1 ;

[0094] According to the cross matrix U q+1 , row matrix R q+1 and column matrix C q+1 , calculate the observation matrix

[0095] 4. Until the preset conditions are met or the preset number of iterations is reached, the updated observation matrix L is obtained q+1 ; Among them, the preconditions include e q+1 <ε, ε represents the error threshold.

[0096] S106. Obtain a sparse target matrix based on the updated observation matrix.

[0097] Specifically, in this embodiment, DL q+1 The selected rows and columns are soft-thresholded to project into a sparse matrix set to obtain a sparse target matrix.

[0098] It should be noted that the above-mentioned method effectively avoids the interference of strong scattering points through the adaptive row and column screening mechanism, and at the same time uses the sub-matrix dimension control (c, r'≈1.2r) to reduce the computational complexity from O(n) to N(n) while ensuring the decomposition accuracy. 3 ) dropped to O(nr 2 ), significantly improving real-time processing capabilities. Experiments show that the improved CUR decomposition improves the signal-to-noise ratio while reducing the false alarm rate and accelerating the convergence speed.

[0099] The following is an analysis of the computational complexity of the main steps of the proposed algorithm. First, the computational complexity of the generalized inner product and the power histogram distribution function row and column selection operation is Iterate to obtain U q+1 The amount of operation is When the iteration converges, the pseudo-inverse calculation of the U matrix needs to be performed, and the corresponding operation amount is The traditional pseudo-frame decomposition algorithm also corresponds to the above-mentioned computational complexity. However, the present invention does not actually need to form the entire N×N matrix, but only uses the L q The rows and columns selected in are expressed as:

[0100]

[0101] From the above formula, it can be seen that the computational complexity of iterative CUR decomposition is The above formula also suggests that only the updated CUR component (i.e., U q ) is passed to the next iteration instead of passing the larger computational q ] I,J It can be seen that the complexity of the proposed algorithm is significantly smaller than that of the traditional pseudo-frame decomposition algorithm, and the difference becomes more significant as N increases.

[0102] S107: Rearrange and threshold the sparse target matrix to extract target features.

[0103] Specifically, in this embodiment, based on the sparse target matrix obtained by the improved CUR decomposition, joint estimation of motion parameters is achieved through the following process:

[0104] 1. Data rearrangement: rearrange the sparse target matrix into a multi-channel data matrix according to the channel dimension.

[0105] 2. Constant false alarm detection: Two-dimensional unit averaging-constant false alarm detection (CA-CFAR) processing is performed on the rearranged multi-channel data matrix to extract target detection information.

[0106] 3. Velocity deambiguation: A space-time adaptive processing model is constructed for the target azimuth offset in the target detection information, and a steering vector is established, which is expressed as:

[0107] s(v r )=[1,e -j2πvrT ,...,e -j2πvr(N-1)T ];

[0108] Among them, s(v r ) represents the steering vector, and T represents the pulse repetition interval.

[0109] 4. Adaptive velocity estimation, constructing the optimal weight vector, expressed as:

[0110]

[0111] Among them, w opt (vr) represents the optimal weight vector, R 1,n represents the covariance matrix;

[0112] Solved by the maximum signal-to-interference-and-noise ratio criterion:

[0113]

[0114] Then, the target relocation can be achieved by using the estimated target radial velocity value.

[0115] In summary, the present invention provides a ground moving target detection method that combines information geometry and improved robust principal component analysis. To address the problems of high false alarm rate and low solution efficiency of RPCA in the process of moving target detection under clutter background, the generalized inner product selection criterion based on KL divergence is used to select uniform sample units, and an iterative CUR decomposition algorithm is further adopted for efficient solution to achieve robust moving target detection. This can effectively improve the matrix solution efficiency and improve the existing sample unit selection method to achieve efficient and low false alarm target detection under non-uniform strong clutter background.

[0116] In an optional embodiment of the present invention, the effect of the ground moving target detection method of combining information geometry and improved robust principal component analysis provided in the above embodiment is verified through simulation experiments, specifically:

[0117] 1. Simulation conditions

[0118] The simulated multi-channel radar detection system operates in a straight side view with three channels evenly distributed along the track direction, with a carrier frequency of 8.85 GHz, a bandwidth of 40 MHz, a sampling rate of 60 MHz, a pulse repetition frequency of 1000 Hz, a channel spacing of 0.559 m, and a platform speed of 115 m / s.

[0119] 2. Simulation content and result analysis

[0120] See Figure 3 , Figure 3 This is a schematic diagram of target detection results using different algorithms provided by an embodiment of the present invention. The effectiveness of the pseudo-frame decomposition algorithm proposed by the present invention for detecting moving targets is verified by combining it with actual data processing. Figure 3 Figure a is the target detection result of the algorithm proposed in this invention, where the red area is the detection target position. At this time, the seven cooperative targets are well detected. Figure 3 b~f are the traditional RPCA method, GoDec algorithm, 1,ε The processing results of the norm algorithm, Ap algorithm, and HQF algorithm are shown. It can be seen that the method proposed in the present invention has a lower false alarm rate. The generalized inner product row and column selection strategy based on information geometry avoids the contamination of low-rank matrix reconstruction by target samples. The generalized inner product based on KL divergence is used to eliminate non-uniform samples, effectively reducing the defects of the power sampling and random sampling methods, and improving the target detection performance.

[0121] Table 1 provides the running time of different algorithms under the CPU 2.5GHz Core i7-11700 system. It can be seen that the algorithm proposed in the present invention has the shortest running time.

[0122] Table 1 Running time of different RPCA methods

[0123]

[0124]

[0125] It can be seen that the method proposed in the present invention can effectively improve the efficiency of calculation and solution, have a lower false alarm rate, and thus greatly improve the target detection capability.

[0126] It should be noted that, in this document, relational terms such as first and second are used solely to distinguish one entity or operation from another, and do not necessarily require or imply any actual relationship or order between these entities or operations. Furthermore, the terms "comprise," "include," or any other variations thereof are intended to encompass non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not explicitly listed. Without further limitation, an element defined by the phrase "comprising a..." does not preclude the presence of additional identical elements in the article or device comprising the element. Terms such as "connected" or "connected" are not limited to physical or mechanical connections but may include electrical connections, whether direct or indirect. References to orientations or positional relationships, such as "upper," "lower," "left," and "right," are based on the orientations or positional relationships shown in the accompanying drawings and are intended solely to facilitate description and simplify the description of the present invention. They do not indicate or imply that the device or element referred to must have, be constructed, or operate in a specific orientation, and are therefore not to be construed as limiting the present invention.

[0127] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0128] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A ground moving target detection method combining information geometry and improved robust principal component analysis, characterized in that: include: Build a front-side multi-channel radar detection model, obtain raw data, and reconstruct multi-channel image data; Vectorize the reconstructed multi-channel image data to obtain the original observation matrix; An optimized model is constructed using an improved robust principal component analysis, wherein the optimized model is represented by a low-rank background matrix and a sparse target matrix after decomposition of the original observation matrix; wherein the low-rank background matrix includes multiple rows and multiple columns, and the rows and the columns include multiple sample units; A preset generalized inner product sample selection method based on KL divergence is used to remove non-uniform sample units in the rows and columns of the low-rank background matrix, and the sample units in the remaining rows and columns are used as the observation area. The low-rank background matrix after removing the non-uniform sample units is used as the observation matrix to obtain a row index set and a column index set in the observation matrix; Initializing a row index set, a column index set, and a measurement matrix, and iterating until a preset condition is satisfied or a preset number of iterations is reached, thereby obtaining an updated measurement matrix; wherein, during the iteration process, the measurement matrix is decomposed into a row matrix, a column matrix, and a cross matrix according to preset requirements to update the measurement matrix; Obtaining the sparse target matrix according to the updated observation matrix; The sparse target matrix is rearranged and threshold detected to extract target features.

2. The ground moving target detection method based on information geometry and improved robust principal component analysis according to claim 1 is characterized in that: The method of constructing a front-side-view multi-channel radar detection model and obtaining raw data includes: N channels are set at equal intervals along the track direction, where the interval is d; Get target echo data nt (t,t m ), expressed as: Where B represents the radar transmission bandwidth, B D represents the modulation bandwidth of the target azimuth, R0 represents the minimum slant distance of the target beam center at that moment, v e Indicates the relative speed between the target and the radar, v r represents the target radial projection velocity, t m represents the azimuth slow time, m represents the pulse index, x0 represents the target initial position, v represents the flight speed of the airborne radar, v a represents the target azimuth velocity, n represents the channel index, c represents the speed of light, t represents the fast time of the transmitted pulse, and λ represents the wavelength of the transmitted pulse; Get clutter echo data, expressed as: The target echo data of the multi-channel is vectorized to obtain target echo vector data, which is expressed as: s=[s1,s2,…,s N ] T ; in,(·) Τ represents the transpose operation, s n Indicates the target echo data of channel n; The multi-channel clutter echo data is vectorized to obtain clutter echo vector data, which is expressed as: c=[c1,c2,…,c N ] T ; According to the target echo vector data and the clutter echo vector data, multi-channel single-pixel echo vector data is obtained, which is expressed as: z(p,u)=s(p,u)+c(p,u)+n(p,u); Among them, (p,u) represents the two-dimensional index of distance and orientation of a single pixel, and n(p,u) represents the Gaussian white noise vector.

3. The ground moving target detection method based on information geometry and improved robust principal component analysis according to claim 2 is characterized in that: The reconstructing multi-channel image data comprises: The multi-channel single-pixel echo vector data is reconstructed to obtain reconstructed single-pixel echo vector data, which is expressed as: z r (p,u)=[z1(p,u),z r_2 (p,u),…,z r_N (p,u)] Τ ; According to the reconstructed single pixel vector data, the reconstructed N channel image data {Z1, Z r_2 ,…,Z r_N }.

4. The ground moving target detection method based on information geometry and improved robust principal component analysis according to claim 3 is characterized in that: The expression of the original observation matrix D is: D=[vec(Z1),vec(Z r_2 ),…,thing(Z r_N )]; Here, vec(·) represents a vectorized operation.

5. The ground moving target detection method based on information geometry and improved robust principal component analysis according to claim 1 is characterized in that: The expression of the optimization model is: where ||·||* represents the nuclear norm, ||·||1 represents the L1 norm, λ1 represents the regularization parameter, D represents the original observation matrix, L represents the low-rank background matrix, S represents the sparse target matrix, and E represents the noise term.

6. The ground moving target detection method based on information geometry and improved robust principal component analysis according to claim 1 is characterized in that: The method of using a preset generalized inner product sample selection method based on KL divergence to eliminate non-uniform sample units in rows and columns of the low-rank background matrix includes: Eliminating non-uniform sample units in rows and columns of the low-rank background matrix is described as a binary hypothesis testing problem, which is expressed as: Among them, H0 represents the sample unit judged as uniform, H1 represents the sample unit judged as non-uniform, Ω0 represents the uniform sample unit set, Ω1 represents the non-uniform sample unit set, K1 represents the total number of samples in the uniform sample unit set, and K2 represents the total number of samples in the non-uniform sample unit set; The type of the sample unit to be detected is determined by solving the value of the generalized inner product sample selection model. According to the estimated value of the clutter covariance matrix of the sample unit to be detected, the generalized inner product sample selection model is constructed, which is expressed as: Among them, η k Represents the value of the generalized inner product sample selection model for the k-th sample unit, Represents the estimated value of the clutter covariance matrix of the sample unit to be detected, x k represents the echo data of the kth sample unit, (·) H represents conjugate transpose; When the value of the generalized inner product sample selection model is less than the system degrees of freedom, the sample unit to be detected is judged as a uniform sample unit. When the value of the generalized inner product sample selection model is greater than the system degrees of freedom, the sample unit to be detected is judged as a non-uniform sample unit.

7. The ground moving target detection method based on information geometry and improved robust principal component analysis according to claim 6 is characterized in that: The estimated value of the clutter covariance matrix of the sample unit to be detected The acquisition process includes: The problem of estimating the clutter covariance matrix of the sample unit to be detected is transformed into a geometric centroid optimization problem on the manifold, which can be expressed as: Among them, R k represents the covariance matrix of the kth sample unit, KL(·) represents R k and The KL divergence of It represents the weight coefficient of different sample units in estimating the geometric centroid, and K represents the total number of sample units.

8. The ground moving target detection method based on information geometry and improved robust principal component analysis according to claim 1 is characterized in that: During the iteration process, the measurement matrix is decomposed into a row matrix, a column matrix, and a cross matrix according to preset requirements to update the measurement matrix, including: According to the preset requirements, select from the row index set and column index set to construct the row matrix R = L(I,:), column matrix C = L(:,J) and cross matrix U = L(I,J) to achieve the decomposition of the observation matrix J represents the column index, and I represents the row index; The preset requirements include: When the number of selected columns is c=r+p and the number of selected rows is r'=r+q, the probability of satisfying rank(U)=r exceeds 1-δ, δ≈0.01; p and q represent redundant parameters.

9. The ground moving target detection method combining information geometry and improved robust principal component analysis according to claim 1 is characterized in that: The initialization of the row index set, the column index set and the observation matrix, and iteration until the preset conditions are met to obtain the updated observation matrix, include: Initialize the row index set I0, column index set J0 and observation matrix L0; During the q+1th iteration, a specific number of rows and columns are randomly selected from the row index set and column index set, and the row index set I is updated. q+1 and column index set J q+1 ; According to the sampling operator and the observation matrix L q+1 , calculate the row matrix and column matrix According to the truncation operator Sampling Operator and the observation matrix L q Calculate the cross matrix U q+1 ; According to the cross matrix U q+1 , update the row matrix and column matrix Get the row matrix R q+1 and column matrix C q+1 ; According to the cross matrix U q+1 , row matrix R q+1 and column matrix C q+1 , calculate the observation matrix Until the preset conditions are met or the preset number of iterations is reached, the updated observation matrix L is obtained q+1 ; Wherein, the preset conditions include e q+1 <ε, ε represents the error threshold.

10. The ground moving target detection method combining information geometry and improved robust principal component analysis according to claim 9 is characterized in that: Obtaining the sparse target matrix according to the updated observation matrix includes: DL q+1 The selected rows and columns are soft-thresholded to project into a sparse matrix set to obtain a sparse target matrix.

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