A method for detecting small floating targets on the sea surface based on average spectrum radius

Abstract

The present invention relates to a method for detecting small floating targets on the sea surface based on average spectrum radius, comprising the following steps: S1, converting sampled data into a random matrix model; S2, calculating the average spectrum radius of the random matrix obtained in S1; S3, using the average spectrum radius as a detection statistic to detect small floating targets on the sea surface. The present invention is based on random matrix theory, uses the average spectrum radius as a detection statistic, and uses the difference in correlation of radar echo data with or without a target to achieve the distinction between a target range gate and a clutter range gate, effectively improving the robustness and detection probability of small floating targets under a sea clutter background.

Description

Technical Field

[0001] The invention relates to the field of sea detection radars, and in particular to a method for detecting small floating targets on the sea surface based on an average spectrum radius. Background Art

[0002] With the miniaturization and stealth of targets, slow-moving, floating small targets on the sea surface and slow-moving small targets flying at low altitudes over the sea have become the focus of radar alert. The strong backscattered echoes generated by the interaction between the rough and undulating sea surface and the electromagnetic waves emitted by the radar are called sea clutter. The echo intensity is high and the space-time variation is complex, which has a serious impact on the target detection performance of the radar. Radar weak target detection under the background of sea clutter has important practical significance in both military and civilian fields, and is also a research hotspot in the current field of radar signal processing.

[0003] At present, weak target detection methods under sea clutter background can be divided into four categories: methods based on statistical models, methods based on time-frequency analysis, methods based on fractals, and detection methods based on multi-feature fusion:

[0004] (1) Detection method based on statistical model

[0005] The classic radar target detection method is the Constant False Alarm Rate (CFAR) detection algorithm based on the statistical model. The basic idea is to estimate the statistical characteristics of the background clutter of the detection unit in real time through the reference unit, such as the optimal detector in the generalized Pareto distribution clutter proposed in the document "Coherent Radar Target Detection in Heavy-Tailed Compound-Gaussian Clutter" (KJSangston, F.Gini and MSGreco, in IEEE Transactions on Aerospace and Electronic Systems, vol.48, no.1, pp.64-77, Jan.2012.).

[0006] (2) Detection method based on time-frequency analysis

[0007] Time-frequency analysis can describe the changes of frequency components at each moment and is suitable for the analysis and processing of non-stationary signals. In recent years, many research works at home and abroad have focused on using the differences between targets and sea clutter in time-frequency space due to different motion characteristics to achieve sea surface target detection, such as the detection method based on short-time fractional Fourier transform proposed in the document "Detection and Extraction of Target With Micromotion in Spiky Sea Clutter Via Short-Time Fractional Fourier Transform" (X. Chen, J. Guan, Z. Bao and Y. He, in IEEE Transactions on Geoscience and Remote Sensing, vol. 52, no. 2, pp. 1002-1018, Feb. 2014.).

[0008] (3) Fractal-based detection method

[0009] The scattering coefficient of the sea surface is a fractal function, and its scattered echo has a fractal structure. The regular target scattering signal will affect the fractal characteristics of the echo, reducing the fractal dimension, and can achieve the distinction between target units and clutter units. In recent years, related research work has proposed designing detection methods using the fractal characteristics of signals in different domains, such as the fractal properties of the autoregressive spectrum of sea clutter discussed in the literature "Fractal properties of autoregressive spectrum and its application on weaktarget detection in sea clutter background" (Fan, Y., et al., IET Radar, Sonar & Navigation, vol. 9, no. 8, pp. 1070–1077, 2015.).

[0010] (4) Detection method based on multi-feature fusion

[0011] With the refinement of observation methods, the characteristics of sea clutter and target echoes have become complex and difficult to accurately statistically model. Multi-feature-based detectors extract features that can effectively distinguish target units and clutter units from the time domain and frequency domain to form a multidimensional feature space, and then transform the binary hypothesis test problem of target detection into an anomaly detection problem or classification problem to detect small floating targets on the sea surface, including the literature "Anomaly Based Sea-Surface SmallTarget Detection Using K-Nearest Neighbor Classification" (Z.-X.Guo and P.-L.Shui, in IEEE Transactions on Aerospace and Electronic Systems, vol.56, no.6, pp.4947-4964, Dec.2020.) which uses 8 features to form a feature space and implements a feature detection method for small sea surface targets based on the nearest node anomaly detection algorithm.

[0012] In recent years, scholars at home and abroad have attempted to apply different signal processing algorithms to solve this problem and have achieved a series of inspiring research results. However, due to the complex changes of sea clutter and the diversity of targets, there is currently no mature method that can achieve real-time and robust detection of weak targets in sea clutter.

[0013] In summary, the detection of small floating targets on the sea surface mainly faces the following difficulties:

[0014] 1. Sea clutter characteristics are affected by environmental factors such as wind speed and wave height, and radar system parameters such as carrier frequency, range resolution and polarization mode. They have strong non-Gaussian and non-stationary characteristics, complex changes and high echo intensity. It is difficult to achieve robust detection performance using traditional model-driven features and detection methods.

[0015] The RCS of small targets floating on the sea surface is small, and the targets may be partially obscured by the waves for a period of time, with serious RCS fluctuations. At the same time, the movement and posture of the targets are seriously disturbed by the sea breeze and waves, and there is no obvious movement pattern, which is difficult to be effectively accumulated. The target echo overlaps in the clutter in both the time domain and the frequency domain, which seriously affects the target detection performance. Summary of the invention

[0016] In order to solve the existing technical problems, the present invention provides a method for detecting small floating targets on the sea surface based on average spectrum radius.

[0017] The specific content of the present invention is as follows: A method for detecting small floating targets on the sea surface based on average spectrum radius comprises the following steps:

[0018] S1, transform the sampled data into a random matrix model;

[0019] S2, calculate the average spectral radius of the random matrix obtained in S1;

[0020] S3, uses the average spectrum radius as the detection statistic to detect small floating targets on the sea surface.

[0021] Furthermore, in S2, calculating the average spectral radius of the random matrix includes:

[0022] S21, normalize the matrix row by row so that the mean of each row is 0 and the variance is 1;

[0023] S22, performing singular value decomposition on the matrix to obtain a left singular matrix;

[0024] S23, calculating the equivalent form of the singular values ​​of the original matrix;

[0025] S24, normalize the obtained matrix row by row so that the variance of each row is 1 / N;

[0026] S25, performing eigenvalue decomposition on the normalized matrix;

[0027] S26, calculate and obtain the average spectrum radius.

[0028] Furthermore, in S1, the random matrix model X N×M =(x1,x2,…x M ), where the column vector x m =(x 1m ,x 2m ,…,x Nm ) T Represents a sampling time series of length N, that is:

[0029]

[0030] In S2, calculate the random matrix X N×M The average spectral radius τ MSR include:

[0031] The matrix X N×M Normalize by row, and get the matrix element The calculation is:

[0032]

[0033] where x i =(x i,1 ,x i,2 ,…,x i,M ) T , Represents xi The mean of each element in , σ(x i ) represents x i The standard deviation of each element in , 1≤i≤N,1≤j≤M.

[0034] After normalization, the matrix Perform singular value decomposition to obtain the left singular matrix U, that is:

[0035]

[0036] Calculating the Matrix The singular value equivalent form of X u :

[0037]

[0038] The matrix X u Normalize by row so that the variance of each row is 1 / N, and get the matrix Its i-th column is represented as:

[0039]

[0040] Pair Matrix Perform eigenvalue decomposition:

[0041]

[0042] in

[0043] calculate The average of all eigenvalue norms gives the average spectral radius:

[0044]

[0045] Furthermore, in S3, the detection of small floating targets on the sea surface includes:

[0046] S31, using the reference unit training data, calculating the mean and variance of the distribution of the test statistic;

[0047] S32, determining a detection threshold according to a given false alarm rate;

[0048] S33, calculating the detection statistic of the unit to be detected;

[0049] S34, comparing the detection statistic of the unit to be detected with the detection threshold to obtain a decision result on whether the target exists.

[0050] Furthermore, in S3, the detection of small floating targets on the sea surface includes:

[0051] By using the sampling time series in the reference unit, the average spectrum radius is calculated according to the steps described in S2, and its mean μ0 and standard deviation σ are counted;

[0052] According to the given false alarm rate P fa According to the requirements, the detection threshold ξ is determined:

[0053] At a given P fa The expression of the detection threshold is:

[0054] ξ=μ0-σQ -1 (P fa )

[0055] Where Q -1 (·) is the inverse function of the right tail function of the standard Gaussian distribution;

[0056] The monitoring statistic τ is obtained from the sampling time series in the unit to be detected according to the steps described in S2. MSR , and compared with the threshold ξ to determine whether the unit to be detected has a target:

[0057]

[0058] The detection of small floating targets on the sea surface under the background of sea clutter is described as the following binary hypothesis testing problem:

[0059]

[0060] The invention is based on random matrix theory, adopts the average spectrum radius as the detection statistic, and utilizes the difference in correlation of radar echo data with and without targets to realize the distinction between target range gate and clutter range gate, effectively improving the robustness and detection probability of small floating targets under sea clutter background. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The specific implementation of the present invention will be further explained below in conjunction with the accompanying drawings.

[0062] Figure 1 The flowchart of the method for detecting small floating targets on the sea surface based on the average spectrum radius of the present invention is as follows;

[0063] Figure 2 Flow chart for calculating the average spectral radius;

[0064] Figure 3 is the matrix with or without target The distribution of the eigenvalues ​​of in the complex plane;

[0065] Figure 4 is the average spectrum radius τ of different range gates MSR The value of

[0066] Figure 5This is a flow chart for detecting small floating targets on the sea surface;

[0067] Figure 6 It is the detection probability diagram under different signal-to-noise ratios;

[0068] Figure 7 The receiver operating characteristic curves of the detection method based on average spectrum radius in four different polarization modes with different length sampling sequences;

[0069] Figure 8 The receiver operating characteristic curves of the detection method based on average spectrum radius and three comparison methods;

[0070] Fig. 9 Detection probabilities of the four compared methods on data of different HH and HV polarizations of IPIX datasets. DETAILED DESCRIPTION

[0071] Combination Figure 1-Figure 5 This embodiment provides a method for detecting small floating targets on the sea surface based on average spectrum radius, comprising the following steps:

[0072] S1, convert the sampled time series into a random matrix model (Random Matrix Model, RMM) X N×M .

[0073] X N×M =(x1,x2,…x M ), where the column vector x m =(x 1m ,x 2m ,…,x Nm ) T Represents a sampling time series of length N, that is:

[0074]

[0075] S2, calculate the random matrix X N×M The average spectral radius τ MSR .

[0076] S21, the matrix X N×M Normalize by row, and get the matrix element The calculation is:

[0077]

[0078] where x i =(x i,1 ,x i,2 ,…,x i,M ) T , Represents xi The mean of each element in , σ(x i ) represents x i The standard deviation of each element in , 1≤i≤N,1≤j≤M.

[0079] S22, the normalized matrix Perform singular value decomposition to obtain the left singular matrix U, that is:

[0080]

[0081] S23, calculation matrix The singular value equivalent form of X u :

[0082]

[0083] S24, the matrix X u Normalize by row so that the variance of each row is 1 / N, and get the matrix Its i-th column can be expressed as:

[0084]

[0085] S25, for the matrix Perform eigenvalue decomposition:

[0086]

[0087] in

[0088] S26, calculation The average of all eigenvalue norms gives the average spectral radius:

[0089]

[0090] S3, using the average spectral radius τ MSR As a detection statistic, target detection is achieved.

[0091] The detection of small floating targets on the sea surface under the background of sea clutter can be described as the following binary hypothesis testing (BHT) problem:

[0092]

[0093] S31, by using the sampling time series in the reference unit, calculate the average spectrum radius according to the steps described in S2, and count its mean μ0 and standard deviation σ.

[0094] S32, according to the given false alarm rate P fa According to the requirements, the detection threshold ξ is determined:

[0095] It can be proved by the central limit theorem that as a linear eigenvalue statistic (LSS), the average spectral radius follows a Gaussian distribution, and its variance is related to the dimension of the matrix. fa The expression of the detection threshold is:

[0096] ξ=μ0-σQ -1 (P fa )

[0097] Where Q -1 (·) is the inverse function of the right tail function of the standard Gaussian distribution.

[0098] S33, obtain the monitoring statistic τ from the sampling time series in the cell under cut (CUT) according to the steps described in S2 MSR , and compared with the threshold ξ to determine whether the unit to be detected has a target:

[0099]

[0100] Figure 3 The distribution of matrix eigenvalues ​​on the complex plane with and without targets is given in . As shown in the figure, the eigenvalues ​​are distributed in a circle with a smaller radius when there is a target, while the eigenvalues ​​are distributed in a circle with a larger radius when there is pure clutter. The average spectrum radius is calculated based on S26.

[0101] Figure 4 The average spectrum radius of different range gates is given in Figure 1, where the 9th range gate is the range gate with a target. As shown in the figure, the average spectrum radius of the range gate with a target is significantly smaller than that of the pure clutter range gate. The average spectrum radius can effectively distinguish the range gate with or without a target.

[0102] This example uses the public IPIX dataset (Available: http: / / soma.ece.mcmaster.ca / ipix / dartmouth / index.html) to verify the effectiveness of the detection method based on average spectral radius for detecting small floating targets in the sea clutter background. The detection probability of this method under different signal-to-clutter ratios (SCR) and the receiver operating characteristic (ROC) curves with different accumulation times are given.

[0103] The method of the present application is compared with the traditional amplitude-based cell average constant false alarm rate (CA-CFAR) detection method, the detection method based on fractal theory and using Hurst index as the detection statistic proposed in the literature "Floating Small Target Detection in Sea Clutter via Normalized Hurst Exponent" (D. Li and P. Shui, Electronics Letters, vol. 50, no. 17, pp. 1240-1242, Aug 2014.), and the literature "Robust Target Detection Within Sea Clutter Based on Graphs" (K. Yan, Y. Bai, H. Wu and X. Zhang, in IEEE Transactions on Geoscience and Remote Sensing). The graph-based detection method proposed in Sensing, vol.57, no.9, pp.7093-7103, Sept.2019) is compared with the receiver operating characteristic curves of the four methods under different data sets and different polarization modes in the public IPIX sea clutter data, verifying that the detection method based on average spectral radius can achieve better detection performance of small floating targets on the sea surface.

[0104] Figure 6 The variation of detection probability with signal-to-clutter ratio of the detection method based on average spectrum radius is given in the figure. The measured sea clutter data of "19980217_214346_ANTSTEP.cdf" in IPIX dataset is used, and simulation targets with different signal-to-clutter ratios are added. The signal-to-clutter ratio is -15dB to 5dB, and the false alarm rate is set to 10 -4 , taking N = 64, M = 128, and the sampling sequence length is 8.192s. The detection method based on the average spectrum radius can realize the detection of small floating targets under the background of sea clutter, and the detection probability increases with the increase of signal-to-clutter ratio.

[0105] Figure 7 The receiver operating characteristic curves of the detection method based on average spectrum radius are given in the figure using sea clutter data in four different polarization modes: HV, VH, HH, and VV in IPIX dataset #18. The lengths of the sampling sequences are set to 2.048s, 4.096s, and 8.192s, respectively. It can be seen from the figure that the detection method based on average spectrum radius can effectively detect small floating targets on the sea surface, and the detection performance improves with the increase of the sampling sequence length.

[0106] Figure 8 The comparison of the receiver operating characteristic curves of the detection method based on the average spectrum radius and the other three methods for detecting small floating targets on the sea surface is given in the figure, using two polarization modes, co-polarization (VV) and cross-polarization (VH) in the IPIX dataset #310. The sampling sequence length of the four methods is set to 8.192s. It can be seen from the figure that the detection probability based on the average spectrum radius can be higher than that of the comparison method.

[0107] Fig. 9 The detection probabilities of four comparison methods on HV and HH polarization data of five different IPIX datasets are given in Figure 2. The sampling sequence length of the four methods is set to 8.192s. As shown in the figure, the detection method based on the average spectral radius can achieve better detection performance and has good robustness.

[0108] Applying random matrix theory, a method for detecting small floating targets on the sea surface based on average spectrum radius is proposed, which can solve the following problems:

[0109] 1. The data-driven approach is used to effectively improve the robustness of detection.

[0110] As a data-driven method, random matrix theory does not rely on prior assumptions and simplifications of the sea clutter model, and effectively avoids the problem of poor robustness of traditional model-driven detection methods in complex and changing sea clutter.

[0111] 2. Effectively improve the detection probability of small targets floating on the sea surface in sea clutter.

[0112] For small targets floating on the sea surface, the target echo is weak and has no obvious movement pattern, so it is difficult to be effectively accumulated. However, compared with pure clutter, the correlation of the echo signal will be enhanced when there is a target. The average spectrum radius effectively reflects the correlation of the echo data and can better distinguish the target range gate from the pure clutter range gate. The detector based on the average spectrum radius can effectively improve the detection performance of small targets floating on the sea surface in a clutter environment.

[0113] Many specific details are described in the above description to facilitate a full understanding of the present invention. However, the above description is only a preferred embodiment of the present invention. The present invention can be implemented in many other ways different from those described herein, so the present invention is not limited to the specific implementation disclosed above. At the same time, any person familiar with the art can make many possible changes and modifications to the technical solution of the present invention using the methods and technical contents disclosed above without departing from the scope of the technical solution of the present invention, or modify it into an equivalent embodiment of equivalent changes. Any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of protection of the technical solution of the present invention.

Claims

1. A method for detecting small floating targets on the sea surface based on average spectrum radius, characterized in that: The steps include: S1, transform the sampled data into a random matrix model; S2, calculate the average spectral radius of the random matrix obtained in S1; S3, using the average spectrum radius as the detection statistic to detect small floating targets on the sea surface; In S1, the random matrix model X N×M =(x1, x2, ...x M ), where the column vector x m =(x 1m , x 2m , ..., x Nm ) T Represents a sampling time series of length N, that is: In S2, calculate the random matrix X N×M The average spectral radius T MSR include: S21, the matrix X N×M Normalize by row, and get the matrix Make each row have a mean of 0, a variance of 1, and an element The calculation is: where x i =(x i，1 , x i，2 , …, x i,M ) T , Represents x i The mean of each element in , σ(x i ) represents x i The standard deviation of each element in, 1≤i≤N, 1≤j≤M; S22, the normalized matrix Perform singular value decomposition to obtain the left singular matrix U, that is: S23, calculation matrix The singular value equivalent form of X u : S24, the matrix X u Normalize by row so that the variance of each row is 1 / N, and get the matrix Its i-th column is represented as: S25, for the matrix Perform eigenvalue decomposition: in S26, calculation The average of all eigenvalue norms gives the average spectral radius: In S3, the detection of small floating targets on the sea surface includes: S31, calculating the average spectrum radius through the sampling time series in the reference unit according to the steps described in S2, and counting its mean μ0 and standard deviation σ; S32, according to the given false alarm rate P fa According to the requirements, the detection threshold ξ is determined: At a given P fa The expression of the detection threshold is: ξ=μ0-σQ -1 (P fa ), Where Q -1 (·) is the inverse function of the right tail function of the standard Gaussian distribution; S33, obtain the detection statistic T from the sampling time series in the unit to be detected according to the steps described in S2. MSR ; S34, the detection statistic T of the unit to be detected MSR Compare with the detection threshold ξ to determine whether the unit to be detected has a target: The detection of small floating targets on the sea surface under the background of sea clutter can be described as the following binary hypothesis testing problem:

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