Method and System for Detecting Small Sea Targets Based on Multi-Features of Images

Abstract

The present invention discloses a method and system for detecting small sea targets based on multi-graph features. The method and system are divided into two parts: training and detection. The training part includes preprocessing the radar echo data of the training unit, extracting graph features from the preprocessed data and constructing a graph feature vector, and calculating the decision region using the convex hull learning algorithm. The detection part includes preprocessing the radar echo data of the unit to be detected, extracting graph features from the preprocessed data and constructing the graph feature vector of the unit to be detected, and constructing a detection statistic through the decision region and the graph feature vector of the unit to be detected to determine whether a radar target exists. The present invention extracts three different graph features from the sea clutter sequence, and jointly uses these three graph features to distinguish between pure clutter data and echo data containing targets to complete sea target detection. Compared with the existing detectors based on a single graph feature, the present invention considers the correlation between radar echo data from different angles, constructs a graph, extracts multiple graph features, avoids the calculation of matrix eigenvalue decomposition, has a faster feature extraction speed, and has better target detection performance.

Description

Technical Field

[0001] The present invention relates to the technical field of radar target detection, in particular to a method and system for detecting small sea targets based on multi-graph features. Background Art

[0002] In recent years, with the miniaturization and stealth of sea targets, small sea targets such as small boats, speedboats, and aircraft wrecks have become the key objects of radar warning. Generally, the radar cross-section (RCS) of small floating sea targets is weak, and the moving speed is slow. Coherent or non-coherent constant false alarm rate detection algorithms using echo energy for detection have obvious performance bottlenecks when detecting floating small targets. In order to avoid energy detection, some scholars have proposed feature-based target detection methods. These methods extract features by leveraging the differences between clutter and target echoes. The extracted features include fractal features such as single fractal and fractional Fourier transform domain fractal, time-domain features such as relative average amplitude and information entropy in the time domain, frequency-domain features, time-frequency domain features, and polarization features. Detectors based on these features have achieved good detection effects to a certain extent. However, the correlation between data is not considered during the feature extraction process, thus ignoring some key information existing between data, resulting in limited detection performance.

[0003] Graph theory and graph neural networks, as an effective method for describing the correlation between data, have been widely applied in computer science, economic fields, discrete signal processing, etc. In order to utilize the correlation of amplitudes between echo data, graph theory-based methods have been extensively introduced into target detection in the sea clutter background. In the 57th volume of IEEE Transactions on Geoscience and Remote Sensing published in 2019, YAN Kun et al. proposed a graph-based method for detecting small floating sea targets. This method directly processes radar echo signals in the time domain, constructs a directed graph using the amplitudes of the echoes, calculates the maximum eigenvalue of the Laplacian matrix of this directed graph considering the connectivity of the edges, obtains the detection threshold through Monte Carlo experiments, and completes target detection. Compared with the detector based on single fractal features, this detection method has excellent performance, especially when the signal-to-noise ratio is small. However, since the graph features extracted by this method are single, and eigenvalue decomposition is required when calculating the eigenvalues of the Laplacian matrix, the time required for feature extraction is long, so the detection effect needs to be improved. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method and system for detecting small sea targets based on multi-graph features, which utilizes the correlation between sea clutter radar echo data to obtain better target detection performance.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The small sea target detection method based on multi-features of graphs provided by the present invention includes the following steps:

[0007] Step 1: First, a pulse signal is transmitted by a radar transmitter, and a multi-pulse signal reflected by the sea surface is received by a radar receiver. The multi-pulse signal is subjected to matched filtering to obtain radar echo data, which is divided into pure clutter echo data and echo data containing a target;

[0008] Select P range cells from the pure clutter echo data as training cells, and the time series z of the training cells p is: z p =[z p (1), z p (2), …, z p (N)], where p = 1, 2, …, P, P is the number of training cells, and N is the length of the time series; the time series z of the training cells p is evenly divided into short vectors of length L, that is: z p =[z p,1 , z p,2 , …, z p,l , …, z p,N / L , where p = 1, 2, …, P, and z p,l represents the l-th short vector of the time series of the training cell, and l = 1, 2, …, N / L;

[0009] Select a cell r to be detected from the echo data containing a target;

[0010] Step 2: Preprocess the time series z of the training cells p to obtain the normalized Doppler power spectrum p of the time series z of the training cells , that is , where p = 1, 2, …, P, represents the normalized Doppler power spectrum preprocessed from the l-th short vector of the time series z of the training cell p ;

[0011] Step 3: Model the normalized Doppler power spectrum p of the time series z of the training cells into a graph and a graph signal, where each short sequence z of the time series z of the training cells p can be modeled to obtain two undirected graphs and signals on the graphs, and three graph features are calculated: the graph Laplacian regularization η p,l of the normalized Doppler power spectrum can be obtained, and two undirected graphs and signals on the graphs are calculated, and three graph features are obtained: the graph Laplacian regularization η 1 (zp,l ) The trace η of the graph Laplacian matrix 2 (z p,l ) The variance η of the in-degree of the graph vertices 3 (z p,l ), construct a Figure 3 eigenvector from these three features:

[0012] η(z p,l ) = [η 1 (z p,l ), η 2 (z p,l ), η 3 (z p,l )] T ,

[0013] where [·] T denotes the transpose of the matrix; Combine the P training units and the N / L Figure 3 eigenvectors of each training unit to form a training sample set

[0014] Step 4, Obtain a three-dimensional convex hull in the three-dimensional feature space according to the training sample set and, under the given false alarm probability P f , calculate the decision region Ω of the detector using the greedy convex hull learning algorithm;

[0015] Step 5, Calculate the three graph features of the graph Laplacian regularization η 1 (r), the trace η of the graph Laplacian matrix 2 (r), and the variance η of the in-degree of the graph vertices 3 (r) for the unit r to be detected, and construct the Figure 3 eigenvector η(r) of the unit to be detected, i.e., η(r) = [η 1 (r), η 2 (r), η 3 (r)] T ;

[0016] Step 6, Calculate the detection statistic of the unit to be detected according to the decision region Ω of the detector and the Figure 3 eigenvector η(r) of the unit to be detected Judge whether the target exists according to the magnitude of the detection statistic : If the detection statistic is greater than zero, it indicates that the Figure 3 eigenvector η(r) of the unit to be detected is outside the decision region of the detector, and there is a target in the unit to be detected. If the detection statistic is less than zero, it indicates that the Figure 3The eigenvector η(r) is within the decision region of the detector, and there is no target in the unit to be detected.

[0017] Further, in step 2, the time series z of the training units p =[z p,1 ,z p,2 ,…,z p,l ,…,z p,N / L is preprocessed. The specific sub-steps are as follows:

[0018] 2.1 Calculate the Doppler power spectrum of the short vector z of each training unit p,l where Δf is the Doppler frequency sampling interval, T

[0019]

[0020]

[0021] is the pulse repetition interval, L is the number of FFT sampling points, exp() represents the exponential function with base e, and k represents the Doppler cell; r

[0022] 2.2 Calculate the mean spectrum and the standard deviation spectrum

[0023]

[0024]

[0025] where k = -[L / 2],..., [L / 2] - 1;

[0026] 2.3 Calculate the normalized Doppler power spectrum of the short vector z of each training unit according to the mean spectrum the standard deviation spectrum p,l and the Doppler power spectrum of the short vector z of each training unit p,l

[0027]

[0028] Further, in step 3, the normalized Doppler power spectrum p of the time series z of the training units is modeled into a graph and a graph signal. Among them, the short sequence z p of the time series z of the training units p,l the normalized Doppler power spectrum ​​Modeled as two undirected graphs and signals on the graphs, the specific sub - steps for calculating three graph features are as follows:

[0029] 3.1 Perform min - max normalization on the normalized Doppler power spectrum :

[0030]

[0031] where \(k =-\lfloor L / 2\rfloor,\cdots,\lfloor L / 2\rfloor - 1\), denotes the energy data of the \(k\) - th Doppler cell after min - max normalization,

[0032] 3.2 Model as an undirected graph Define the Doppler cells \(\{-\lfloor L / 2\rfloor,\cdots,\lfloor L / 2\rfloor - 1\}\) as the vertices of the undirected graph to obtain the vertex set of the undirected graph and assume that each vertex is connected to \(d\) adjacent vertices, and the weight between the connected vertices is 1, to obtain the adjacency matrix of the undirected graph and the Laplacian matrix Define the energy data of the \(k\) - th Doppler cell after min - max normalization as the graph signal \(x\) of vertex \(v\) k k and represent the signal on the undirected graph k as

[0033]

[0033] 3.3 Perform uniform quantization on according to the quantization interval \(1 / \gamma\):

[0034]

[0035] where \(k =-\lfloor L / 2\rfloor,\cdots,\lfloor L / 2\rfloor - 1\), denotes the energy data of the \(k\) - th Doppler cell after quantization, \(i\) represents the quantization value of the energy data of the Doppler cell, and \(\gamma\) represents the number of quantization levels;

[0036] 3.4 Model as an undirected graph Define the quantization values \(\{0,\cdots,i,\cdots,\gamma\}\) as the vertices of the undirected graph to obtain the vertex set of the undirected graph and define that the vertex corresponding to the quantization value in each Doppler cell is connected to the vertex corresponding to the quantization value in its adjacent Doppler cell, and define the number of connections between the two vertices as the weight between the two vertices, to obtain the adjacency matrix of the undirected graph ​

[0037]

[0038] For an undirected graph of the adjacency matrix sum the elements of each row to obtain the in-degree matrix of the undirected graph wherein,

[0039]

[0040] wherein, represents the in-degree of vertex v i and calculate the Laplacian matrix of the undirected graph wherein,

[0041]

[0042] 3.5 According to the Laplacian matrix of the undirected graph of the undirected graph the signal on the undirected graph the Laplacian matrix of the undirected graph and the in-degree matrix of the undirected graph calculate three graph features: the graph Laplacian regularity η 1 (z p,l ), the trace of the graph Laplacian matrix η(z 2 ), and the variance of the graph vertex in-degree η(z p,l ):) 3 (z p,l )

[0043]

[0044] where Tr(·) represents the trace of a matrix;

[0045] 3.6 According to the graph Laplacian regularity η 1 (z p,l ), the trace of the graph Laplacian matrix η 2 (z p,l ), and the variance of the graph vertex in-degree η 3 (z p,l ), construct Figure 3 the eigenvector: η(z p,l ) = [η 1 (z p,l ), η 2 (z p,l ), η 3 (z p,l )]T 。

[0046] 4. The method for detecting small sea targets based on multi - graph features according to claim 1, wherein in step 4, according to the training sample set at a given false - alarm probability P f the specific sub - steps of calculating the decision region Ω of the detector using the greedy convex hull learning algorithm are as follows:

[0047] 4.1 Define a convex hull CH(S) that contains all samples of the training sample set S:

[0048]

[0049] wherein, SP{·} represents the enclosed space surrounded by triangles, represents the three vertices of the q - th triangular face that constitutes the surface of the convex hull CH(S), and Q represents the total number of triangular faces on the convex hull CH(S);

[0050] 4.2 According to the given false - alarm probability P f and the greedy convex hull learning algorithm, sequentially delete the false - alarm training samples that cause the largest reduction in the convex hull volume, and obtain the remaining training sample set S', where [·] represents rounding down;

[0051] 4.3 According to the remaining training sample set S', form a convex hull CH(S'), and use it as the decision region Ω of the detector, i.e., Ω = CH(S').

[0052] Furthermore, in step 6, according to the decision region Ω = CH(S') of the detector and the feature vector η(r) of the unit to be detected, calculate the detection statistic Figure 3 of the unit to be detected

[0053]

[0054] wherein, det(·) represents the determinant of a matrix, represents the three vertices of the f - th triangular face that constitutes the surface of the convex hull CH(S'), and F represents the total number of triangular faces on the convex hull CH(S').

[0055] The small sea - target detection system based on multi - graph features provided by the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the above - mentioned method is implemented.

[0056] The beneficial effects of the present invention are as follows:

[0057] The method and system for detecting small floating targets on the sea surface based on multi-graph features provided by the present invention transmit pulsed signals through a radar transmitter, receive multi-pulse signals reflected by the sea surface through a radar receiver to obtain radar echo data containing targets, and select a unit r to be detected; preprocess the time series z of the training unit p to obtain the normalized Doppler power spectrum of the time series z of the training unit p , and model the normalized Doppler power spectrum of the time series z of the training unit as a graph and a graph signal, calculate three graph features and construct p the feature vector: According to the training sample set, obtain a three-dimensional convex hull in the three-dimensional feature space, and at a given false alarm probability P , use the greedy convex hull learning algorithm to calculate the decision region Ω of the detector; calculate three graph features for the unit r to be detected, construct the Figure 3 feature vector η(r) of the unit to be detected, and calculate the detection statistic of the unit to be detected according to the decision region Ω of the detector and the f feature vector η(r) of the unit to be detected Figure 3 . Determine the target according to the magnitude of the detection statistic Figure 3 . According to the detection statistic to determine the target

[0058] Extract three different graph features from the sea clutter sequence, and jointly use these three graph features to distinguish pure clutter data from echo data containing targets to complete sea surface target detection. Compared with the existing detectors based on a single graph feature, it avoids the eigen-decomposition calculation of the matrix, has a faster feature extraction speed, and has better target detection performance

[0059] This method utilizes the correlation between sea clutter radar echo data, takes into account some key information existing between the data, and can obtain better target detection performance compared with the existing multi-feature-based detectors. This method considers the correlation between radar echo data from different perspectives, constructs graphs, extracts multiple graph features, avoids the eigen-decomposition calculation of the matrix, has a faster feature extraction speed, and better radar target detection effect

[0060] This method models the normalized Doppler power spectrum as two undirected graphs and signals on the graphs, and jointly uses three graph features: graph Laplacian regularization, the trace of the graph Laplacian matrix, and the variance of the in-degree of graph vertices, takes into account the correlation between sea clutter data, and distinguishes pure clutter data from echo data containing targets

[0061] Other advantages, objects, and features of the present invention will be set forth in part in the following description, and in part will be obvious to those skilled in the art upon examination of the following, or may be learned by practice of the present invention. The objects and other advantages of the present invention may be realized and obtained by the following description. Description of the Drawings

[0062] To make the objectives, technical solutions, and beneficial effects of the present invention clearer, the present invention provides the following drawings for description:

[0063] Figure 1 Flowchart of the implementation of the present invention for the embodiment.

[0064] Figure 2 Flowchart of normalizing the Doppler power spectrum modeling of the embodiment into two undirected graphs and graph signals and obtaining three graph features.

[0065] Figure 3 Comparison graph of the detection performance of the present invention and three existing detectors under four polarizations when the observation time increases exponentially from 0.064 seconds to 4.096 seconds for the embodiment. Detailed Implementation Manner

[0066] The following further describes the present invention in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the specific embodiments cited are not intended to limit the present invention.

[0067] Referring to Figure 1 , the method for detecting small floating targets on the sea surface based on multi-graph features of the present invention is divided into two parts: training and detection. The training part includes preprocessing the radar echo data of the training unit, extracting graph features from the preprocessed data and constructing a graph feature vector, and calculating the decision region using the convex hull learning algorithm; the detection part includes preprocessing the radar echo data of the unit to be detected, extracting graph features from the preprocessed data and constructing the graph feature vector of the unit to be detected, and constructing a detection statistic through the decision region and the graph feature vector of the unit to be detected to determine whether a radar target exists; the specific steps are as follows:

[0068] Step 1, first, a pulse signal is transmitted by a radar transmitter, and a multi-pulse signal reflected from the sea surface is received by a radar receiver. The multi-pulse signal is subjected to matched filtering to obtain radar echo data, which is divided into pure clutter echo data and echo data containing a target;

[0069] Select P range cells from the pure clutter echo data as the training unit, and the time series z p is: z p =[z p(1), z p (2), …, z p (N)], where p = 1, 2, …, P, P is the number of training units, and N is the length of the time series; the time series of the training unit z p is evenly divided into short vectors of length L, that is: z p = [z p,1 , z p,2 , …, z p,l , …, z p,N / L , where p = 1, 2, …, P, and z p,l represents the l-th short vector of the time series of the training unit, l = 1, 2, …, N / L;

[0070] Select the unit to be detected r from the echo data containing the target;

[0071] Step 2, preprocess each short vector z p = [z p,1 , z p,2 , …, z p,l , …, z p,N / L in the time series of the training unit to obtain its normalized Doppler power spectrum p,l The steps are as follows: The steps are as follows:

[0072] 2.1 Calculate the Doppler power spectrum of each short vector z p,l of the training unit

[0073]

[0074]

[0075] where Δf is the Doppler frequency sampling interval, T r is the pulse repetition interval, L is the number of FFT sampling points, exp() represents the exponential function with base e, and k represents the Doppler cell;

[0076] 2.2 Calculate the mean spectrum and the standard deviation spectrum

[0077]

[0078]

[0079] where k = -[L / 2],..., [L / 2] - 1;

[0080] 2.3 According to the mean spectrum Standard deviation spectrum and the short vector z of each training unit p,l Doppler power spectrum Calculate the short vector z of each training unit p,l Normalized Doppler power spectrum

[0081]

[0082] According to the short vector z of each training unit p,l Normalized Doppler power spectrum Obtain the normalized Doppler power spectrum of the training unit time series z p Normalized Doppler power spectrum where p = 1, 2, …, P, and P is the number of training units;

[0083] Step 3, model the normalized Doppler power spectrum of the training unit time series z p Normalized Doppler power spectrum into a graph and a graph signal, where each short sequence z of the training unit time series z p Normalized Doppler power spectrum of z p,l can be modeled to obtain two undirected graphs and signals on the graphs. Three graph features and one eigenvector are calculated from these two undirected graphs and signals on the graphs. Refer to Figure 3 , and the steps are as follows: Figure 2

[0084] 3.1 Perform min-max normalization on the normalized Doppler power spectrum :

[0085]

[0086] where k = -[L / 2], …, [L / 2] - 1, represents the energy data of the k-th Doppler unit after min-max normalization,

[0087] 3.2 Model into an undirected graph Define the Doppler units {-[L / 2], …, [L / 2] - 1} as the vertices of the undirected graph to obtain the vertex set of the undirected graph and assume that each vertex is connected to d adjacent vertices, and the weight between the connected vertices is 1 to obtain the adjacency matrix and the Laplacian matrix of the undirected graph Define the energy data of the k-th Doppler unit after min-max normalization as the vertex v​​k graph signal x k and represent the signal located on the undirected graph as

[0088] 3.3 Perform uniform quantization on according to the quantization interval 1 / γ:

[0089]

[0090] where k = -[L / 2],..., [L / 2] - 1, represents the energy data of the k-th Doppler cell after quantization, i represents the quantization value of the energy data of the Doppler cell, and γ represents the number of quantization levels;

[0091] 3.4 Model into an undirected graph Define the quantization values {0,…,i,…γ} as the vertices of the undirected graph to obtain the vertex set of the undirected graph and define that the vertex corresponding to the quantization value in each Doppler cell is connected to the vertex corresponding to the quantization value in its adjacent Doppler cell, and define the number of connections between the two vertices as the weight between the two vertices, to obtain the adjacency matrix of the undirected graph

[0092]

[0093] For the adjacency matrix of the undirected graph sum the elements of each row to obtain the in-degree matrix of the undirected graph

[0094]

[0095] where, represents the in-degree of vertex v i to calculate the Laplacian matrix of the undirected graph

[0096]

[0097] 3.5 According to the Laplacian matrix of the undirected graph the signal on the undirected graph the Laplacian matrix of the undirected graph and the in-degree matrix of the undirected graph Three graph features are calculated: graph Laplace regularization η 1 (z p,l ), the trace η of the graph Laplacian matrix 2 (z p,l ), the variance of the vertex in-degree of the graph η 3 (z p,l ):

[0098]

[0099] Where Tr(·) means finding the trace of the matrix;

[0100] 3.6 According to the graph Laplace regularization η 1 (z p,l ), the trace η of the graph Laplacian matrix 2 (z p,l ), the variance of the vertex in-degree of the graph η 3 (z p,l ), construct a Figure 3 Eigenvector: η(z p,l )=[η 1 (z p,l ),η 2 (z p,l ),η 3 (z p,l )] T ,in,[·] T Indicates transposing the matrix.

[0101] P training units and N / L training units in each training unit Figure 3 The feature vectors form a training sample set In this example, the number of training samples is 10,000;

[0102] Step 4: Based on the training sample set Obtain a three-dimensional convex hull in the three-dimensional feature space and, given the false alarm probability P f Under this condition, the greedy convex hull learning algorithm is used to calculate the decision area Ω of the detector. The steps are as follows:

[0103] 4.1 Define a convex hull CH(S) containing all samples of the training sample set S:

[0104]

[0105] Among them, SP{·} represents the closed space surrounded by triangles, represents the three vertices of the qth triangular face that make up the surface of the convex hull CH(S), and Q represents the total number of triangular faces on the convex hull CH(S);

[0106] 4.2 According to the given false alarm probability P f and the greedy convex hull learning algorithm, successively delete the [P*N / L*P f false alarm training samples that reduce the convex hull volume the most, and obtain the remaining training sample set S', where [·] represents rounding down;

[0107] 4.3 According to the remaining training sample set S', form the convex hull CH(S'), which is used as the decision region Ω = CH(S') of the detector.

[0108] Step 5: Use the time series z of the unit r to be detected r and the mean spectrum obtained in Step 2.2 and the standard deviation spectrum to preprocess and obtain the normalized Doppler power spectrum of the time series z of the unit r to be detected r and calculate the three graph features of the graph Laplacian regularization η (r), the trace η 1 (r) of the graph Laplacian matrix, and the variance η 2 (r) of the in-degree of the graph vertices. Then, obtain the 3 eigenvector η(r) of the unit to be detected, that is, η(r) = [η Figure 3 (r), η 1 (r), η 2 (r)] 3 (r)] T ;

[0109] Step 6: According to the decision region Ω of the detector and the Figure 3 eigenvector η(r) of the unit to be detected, calculate the detection statistic

[0110]

[0111] where det(·) represents the determinant of the matrix, represents the three vertices of the f-th triangular face that makes up the surface of the convex hull CH(S'), and F represents the total number of triangular faces on the convex hull CH(S');

[0112] and judge whether the target exists according to the size of the detection statistic : If the detection statistic is greater than zero, it indicates that the Figure 3 eigenvector η(r) of the unit to be detected is outside the decision region of the detector, and there is a target in the unit to be detected. If the detection statistic is less than zero, it indicates that the Figure 3 eigenvector η(r) of the unit to be detected is inside the decision region of the detector, and there is no target in the unit to be detected.

[0113] Based on steps 1 to 6, the detection of small floating targets on the sea surface based on multi-graph features is realized.

[0114] The small target detection system on the sea surface based on multi-graph features provided in this embodiment includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the above method is implemented.

[0115] The 10 groups of measured sea clutter data of IPIX radar used in this example were collected in 1993. This data is a recognized measured data set of small targets internationally. The radar installation height is 30 meters, the pulse repetition frequency is 1000 Hz, and the range resolution is 30 meters; each group of data contains four polarization data, two of which are co-polarization data HH and VV, and two are cross-polarization data HV and VH; each polarization data includes 14 range cells, and the data length is 2 17 The experimental target is a metal ball with a diameter of 1 meter. In the experiment, the method of the present invention, the detector based on graph connectivity density, the detector based on three features, and the detector based on fractal features are respectively used for sea surface target detection. Refer to Figure 3 When the observation time increases exponentially from 0.064 seconds to 4.096 seconds, the average detection probability of the method of the present invention for 10 groups of data in each polarization direction is much greater than that of the three existing detectors. In summary, the method of the present invention has better detection performance compared with the above existing detectors.

[0116] The above-described embodiments are merely preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims

1. Sea surface small target detection method based on multi-features of graphs, Characterized in that: It includes the following steps: Step 1, the radar transmitter emits a pulse signal, and the radar receiver receives the multi-pulse signal reflected by the sea surface. After the multi-pulse signal passes through matched filtering, radar echo data is obtained. This echo data is divided into pure clutter echo data and echo data containing targets; Select P range cells from the pure clutter echo data as training cells, and the time series z of the training cells p is: z p =[z p (1), z p (2), …, z p (N)], where p = 1, 2, …, P, P is the number of training cells, and N is the length of the time series; Divide the time series z of the training cells p into short vectors with a length of L on average, that is: z p =[z p,1 , z p,2 , …, z p,l , …, z p,N / L , where p = 1, 2, …, P, and z p,l represents the l-th short vector of the time series of the training cells, l = 1, 2, …, N / L; Select the unit r to be detected from the echo data containing targets; Step 2, preprocess the training unit time series z p to obtain the normalized Doppler power spectrum of the training unit time series z p That is where p = 1, 2, …, P, represents the normalized Doppler power spectrum preprocessed from the l-th short vector of the training unit time series z ; p is the normalized Doppler power spectrum preprocessed from the l-th short vector of the training unit time series z Step 3: Transform the training unit time series z p The normalized Doppler power spectrum Modeled as graph and graph signal, where the training unit time series z p Each short sequence z p,l The normalized Doppler power spectrum By modeling, we can obtain two undirected graphs and the signals on the graphs, and calculate three graph features: graph Laplace regularization η 1 (z p,l ), the trace η of the graph Laplacian matrix 2 (z p,l ), the variance of the vertex in-degree of the graph η 3 (z p,l ), construct a figure three feature vector from these three features: η(z p,l ) = [η 1 (z p,l ), η 2 (z p,l ), η 3 (z p,l )] T , Among them, [·] T represents transposing the matrix; a training sample set is formed by combining P training units and N / L graph three feature vectors of each training unit Step 4, according to the training sample set obtain a three-dimensional convex hull in the three-dimensional feature space, and at a given false alarm probability P f calculate the decision region Ω of the detector by using the greedy convex hull learning algorithm; Step 5: Calculate the graph Laplacian regularization η 1 (r), the trace of the graph Laplacian matrix η 2 (r), and the variance of the in-degrees of the graph vertices η 3 (r). Construct the graph three-feature vector η(r) of the unit under test, that is, η(r) = [η 1 (r), η 2 (r), η 3 (r)] T ; Step 6: Calculate the detection statistic of the unit to be detected according to the decision region Ω of the detector and the Figure 3 feature vector η(r) of the unit to be detected According to the detection statistic judge whether the target exists based on its magnitude: If the detection statistic is greater than zero, it indicates that the Figure 3 feature vector η(r) of the unit to be detected is outside the decision region of the detector, and there is a target in the unit to be detected. If the detection statistic is less than zero, it indicates that the Figure 3 feature vector η(r) of the unit to be detected is inside the decision region of the detector, and there is no target in the unit to be detected.

2. The sea surface small target detection method based on multi-features of graphs according to claim 1, Characterized in that, In step 2, the training unit time series z p =[z p,1 ,z p,2 ,…,z p,l ,…,z p,N / L is preprocessed, and the specific sub-steps are as follows: 2.1 Calculate the short vector z of each training unit p,l Doppler power spectrum of k = -[L / 2],..., [L / 2] - 1, where Δf is the Doppler frequency sampling interval, T r is the pulse repetition interval, L is the number of FFT sampling points, exp() represents the exponential function with base e, and k represents the Doppler cell; 2.2 Calculate the mean spectrum based on P training units and the N / L Doppler power spectra of each training unit and the standard deviation spectrum where k = -[L / 2],..., [L / 2] - 1; 2.3 According to the mean spectrum Standard deviation spectrum And the short vector z of each training unit p,l Doppler power spectrum Calculate the short vector z of each training unit p,l Normalized Doppler power spectrum 3. The method for detecting small sea targets based on multi-features of graphs according to claim 1, characterized in that, in step 3, the normalized Doppler power spectrum of the training unit time series z p is modeled into a graph and a graph signal, wherein the short sequence z of the training unit time series z p and the normalized Doppler power spectrum p,l of the short sequence z are modeled into two undirected graphs and signals on the graphs. The specific sub-steps for calculating three graph features are as follows: 3.1 Perform maximum-minimum normalization on the normalized Doppler power spectrum as follows: k = -[L / 2],..., [L / 2] - 1, where \(k = -[L / 2],\cdots,[L / 2]-1\), denotes the energy data of the \(k\)-th Doppler cell after max-min normalization, 3.2 Model as an undirected graph Define the Doppler cells {-[L / 2],...,[L / 2]-1} as the vertices of the undirected graph to obtain the vertex set of the undirected graph and assume that each vertex is connected to d adjacent vertices with a weight of 1 between the connected vertices to obtain the adjacency matrix of the undirected graph and the Laplacian matrix Define the energy data of the k-th Doppler cell after max-min normalization as the graph signal x k of vertex v k , and represent the signal located on the undirected graph as 3.3 Uniformly quantize according to the quantization interval 1 / γ as follows: where, k = -[L / 2],..., [L / 2] - 1, represents the energy data of the k-th Doppler cell after quantization, i represents the quantization value of the energy data of the Doppler cell, and γ represents the number of quantization levels; 3.4 Transform into an undirected graph Define the quantization values {0, …, i, … γ} as the vertices of the undirected graph to obtain the vertex set of the undirected graph And define that the vertex corresponding to the quantization value in each Doppler cell is connected to the vertex corresponding to the quantization value in its adjacent Doppler cell, and define the number of connections between the two vertices as the weight value between the two vertices to obtain the adjacency matrix of the undirected graph ​​ For an undirected graph of the adjacency matrix sum the elements of each row to obtain the in-degree matrix of the undirected graph ​ Among them, represents the in-degree of vertex v i , and the Laplacian matrix of the undirected graph is calculated 3.5 According to the undirected graph of the Laplacian matrix for the undirected graph of the signal for the undirected graph of the Laplacian matrix and for the undirected graph of the in-degree matrix Three graph features are calculated: the graph Laplacian regularization η 1 (z p,l ), the trace of the graph Laplacian matrix η 2 (z p,l ), and the variance of the graph vertex in-degree η 3 (z p,l ): where Tr(·) represents the trace of a matrix; 3.6 According to the graph Laplacian regular η 1 (z p,l ), the trace of the graph Laplacian matrix η 2 (z p,l ), the variance of the in-degree of the graph vertices η 3 (z p,l ), construct the three-feature vector of the graph: η(z p,l ) = [η 1 (z p,l ), η 2 (z p,l ), η 3 (z p,l )] T .

4. The method for detecting small sea targets based on multi-features of a graph according to claim 1, wherein in step 4, according to the training sample set at a given false alarm probability P f the specific sub-steps of calculating the decision region Ω of the detector by using the greedy convex hull learning algorithm are as follows: 4.1 Define a convex hull CH(S) containing all samples of the training sample set S: where SP{·} represents a closed space enclosed by triangles, denotes the three vertices of the q-th triangular face that constitutes the surface of the convex hull CH(S), and Q represents the total number of triangular faces on the convex hull CH(S); 4.2 According to the given false alarm probability P f and the greedy convex hull learning algorithm, successively delete the [P*N / L*P f false alarm training samples that cause the largest decrease in the convex hull volume to obtain the remaining training sample set S', where [·] represents rounding down; 4.3 According to the remaining training sample set S', form a convex hull CH(S'), and use it as the decision region Ω = CH(S') of the detector.

5. The sea surface small target detection method based on multi-features of graphs according to claim 1, Characterized in that, In step 6, according to the decision region Ω = CH(S') of the detector and the feature vector η(r) of the unit to be detected in Figure 3, calculate the detection statistic of the unit to be detected where det(·) represents the determinant of a matrix, denote the three vertices of the f-th triangular face that forms the surface of the convex hull CH(S'), and F represents the total number of triangular faces on the convex hull CH(S').

6. A sea surface small target detection system based on multi-features of graphs, including a memory, a processor, and a computer program stored on the memory and executable on the processor, Characterized in that, When the processor executes the program, it implements the method described in any one of claims 1 to 5 above.

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