A sample selection method based on atomic norm minimization to reconstruct clutter similarity

Abstract

The present invention discloses a sample selection method based on atomic norm minimization to reconstruct clutter similarity, which belongs to the field of space-time adaptive processing technology, and includes the following steps: acquiring airborne radar echo data, and using the generalized inner product method to eliminate abnormal data contaminated by strong reflectors; using atomic norm minimization to reconstruct the clutter covariance matrix of training samples; without the need to accurately extract the clutter subspace, using a weighted volume cross-correlation function to evaluate the similarity between the training samples and the samples of the unit to be detected; selecting the training samples in which the clutter distribution is similar to the unit to be detected, and applying them to space-time adaptive processing for clutter suppression. The present invention eliminates the need for the volume cross-correlation method to accurately extract the clutter subspace, and has strong robustness when it is difficult to accurately extract the clutter subspace, thereby improving the clutter suppression performance of the airborne radar in a non-uniform environment.

Description

Technical Field

[0001] The present invention relates to the field of space-time adaptive processing technology, and in particular to a sample selection method based on atomic norm minimization to reconstruct clutter similarity. Background Art

[0002] Airborne phased array radars often face strong ground clutter and interference, which seriously affect the detection of ground targets. Space-time adaptive processing (STAP) is an important technology for airborne MTI radar to suppress clutter and interference. Space-time adaptive processing technology requires accurate estimation of its clutter covariance matrix. In order to accurately estimate the clutter covariance matrix (CCM) of the unit under test (CUT), the number of independent and identically distributed (IID) samples needs to be greater than twice the system degrees of freedom (DOF). However, in practical applications, the detection background of airborne radars is often non-uniform within the range of twice the system degrees of freedom training samples. In particular, non-uniform factors such as terrain changes and target-like interference make it difficult for IID to meet the requirements. Therefore, in non-uniform environments, the detection performance of STAP may be affected.

[0003] In order to improve the performance of STAP, many sample selection methods have been proposed, such as the generalized inner product (GIP) method and the power selection training (PST) method. These methods use secondary data to estimate the CCM of the CUT and have the ability to eliminate abnormal data. However, in non-uniform environments, accurate estimation of CCM is challenging, so these methods show poor performance in non-uniform environments. Sample selection methods using volumetric cross-correlation functions have poor robustness in non-uniform environments because they need to accurately extract the clutter feature space.

[0004] In recent years, sparse recovery has developed rapidly in the field of signal processing. The sparse recovery STAP (SR-STAP) method uses a small number of training samples to obtain a high-resolution clutter power spectrum, such as FOCUSS-STAP and SBL-STAP, which enhances the STAP clutter suppression performance. The CCM reconstructed by sparse recovery can effectively capture the clutter characteristics of the current unit. The sample selection method based on the traditional sparse recovery method can also eliminate the influence of non-uniform clutter and select samples whose clutter positions in the spatiotemporal overcomplete dictionary are similar to the CUT. However, this method does not consider the specific power distribution of the clutter. Summary of the invention

[0005] In view of the above problems, the purpose of the present invention is to provide a sample selection technology based on atomic norm minimization (ANM) to reconstruct clutter similarity. Compared with traditional sample selection methods, this technology shows stronger robustness and more efficient performance in non-uniform environments.

[0006] In order to achieve the above technical objectives, the present invention adopts the following technical solutions to achieve them.

[0007] The present invention discloses a sample selection method based on atomic norm minimization and reconstruction of clutter similarity, comprising the following steps:

[0008] Step 1: Acquire the airborne phased array radar echo data to obtain the original training samples, use the generalized inner product method to preliminarily remove the abnormal data contaminated by strong reflectors, and obtain the preliminarily processed training samples;

[0009] Step 2: Reconstruct the clutter covariance matrix of the training samples by minimizing the atomic norm, perform eigendecomposition on the reconstructed clutter covariance matrix to obtain eigenvalues ​​and eigenvectors, and store the eigenvalues, eigenvectors and clutter covariance matrix reconstructed from each training sample;

[0010] Step 3: Using the weighted volume cross-correlation function, calculate the sample clutter similarity between the training sample and the unit to be detected;

[0011] Step 4: Use the sample clutter similarity to select the training samples whose clutter distribution is similar to the unit to be detected, and obtain the selected training samples.

[0012] Step 5: Use the selected training samples to perform space-time adaptive processing on the detection unit to filter out clutter.

[0013] Preferably, step 1 includes the following sub-steps:

[0014] 1a) Set airborne phased array radar parameters and receive echo data;

[0015] 1b) rearranging each space-time snapshot data in the echo data and storing them as an original training sample set;

[0016] 1c) Use the generalized inner product method to preliminarily remove abnormal data from the original training samples to obtain the preliminarily processed training samples. The generalized inner product test statistic is calculated for the original training samples:

[0017] GIP k =x(k) H R u -1 x(k)

[0018] Among them, GIP k is the generalized inner product statistic output of the k-th distance unit, x(k) is the space-time snapshot of the k-th distance unit, R u is the covariance matrix of the unit to be detected, and the covariance matrix of the unit to be detected is determined by the following formula

[0019]

[0020] Where x(k) is the space-time snapshot of the k-th distance unit, and K is the system degree of freedom;

[0021] 1d) Compare the generalized inner product test statistic of the unit to be detected with the preset threshold η. If the generalized inner product test statistic is greater than the preset threshold, the data of the unit to be detected is removed from the data set, otherwise the data of the unit to be detected is retained.

[0022] Preferably, step 2 includes the following sub-steps:

[0023] 2a) Reconstruct the clutter covariance matrix of the training sample using atomic norm minimization, that is, use the MATLAB convex optimization toolbox to solve the following atomic norm minimization problem

[0024]

[0025] Where Τr(·) is the trace of the matrix, x is the sample to be reconstructed, and Τ(·) is defined as follows: -n1<l1<n1,-n2<l2<n2

[0026]

[0027]

[0028] 2b) Perform eigendecomposition on Τ(U) as follows

[0029] Τ(U)=PΛP H

[0030] Among them, P is the reconstructed clutter eigenvector matrix, and Λ is the diagonal matrix composed of reconstructed clutter eigenvalues. The clutter covariance matrix can be reconstructed according to the following formula

[0031]

[0032] Among them, P is the reconstructed clutter eigenvector matrix, x is the sample to be reconstructed, is the reconstructed clutter covariance matrix.

[0033] 2c) Perform 2b) on all training samples and store the reconstructed clutter covariance matrix, eigenvectors and eigenvalues.

[0034] Preferably, step 3 includes the following sub-steps:

[0035] 3a) For the unit to be detected, calculate the clutter similarity between the training sample and the unit to be detected

[0036] ρ(l0,k)=|Λ H (l0)P H (l0)P(k)Λ(k)|,l0≠k

[0037] Wherein, ρ(l0,k) is the calculated similarity of the reconstructed clutter between the l0th unit to be detected and the kth training sample, P(k) represents the reconstructed clutter feature vector matrix of the kth training sample, P(l0) represents the reconstructed clutter feature vector matrix of the l0th unit to be detected, Λ(k) is the column vector composed of the reconstructed clutter eigenvalues ​​of the kth training sample, and Λ(l0) is the column vector composed of the reconstructed clutter eigenvalues ​​of the l0th unit to be detected.

[0038] 3b) For the unit to be detected, in order to avoid the target signal affecting the sample selection, ρ(l0,l0) is defined as

[0039] ρ(l0,l0)=|x H (l0)QQ H x(l0)|

[0040] Among them, x(l0) is the sample data of the l0th unit to be detected, Q is the orthogonal projection matrix, and x(l0) is projected to the orthogonal space of the target guidance vector.

[0041] Preferably, step 4 includes the following sub-steps:

[0042] 4a) In the sample selection process, the closer ρ(l0,k) is to ρ(l0,l0), the more similar the clutter of the training sample and the unit to be detected is, that is, considering

[0043] η(k)=|ρ(l0,k)-ρ(l0,l0)|

[0044] Compare the similarity with the preset threshold value η0, that is,

[0045]

[0046] 4b) If the similarity is lower than the preset threshold value, it means that the threshold has not been exceeded and the training sample has a high similarity with the clutter of the unit to be detected. At this time, the reconstructed clutter covariance matrix of the training sample is added to the uniform training sample set R Θ middle.

[0047] 4c) If the similarity is higher than the preset threshold value, it means that the threshold is exceeded and the similarity between the training sample and the clutter of the unit to be detected is low. In this case, the training sample is not added to the uniform training sample set R Θ middle.

[0048] Preferably, step 5 includes the following sub-steps:

[0049] 5a) Using the selected uniform training sample set R Θ Calculate the clutter covariance matrix of the unit to be detected

[0050]

[0051] Among them, R c (l) is R Θ The reconstructed training sample of the distance unit numbered l in R Θ The total number of training samples in;

[0052] 5b) Using the covariance matrix of the unit to be detected, the clutter noise covariance matrix is ​​constructed as

[0053] R=R c +δ 2 I K

[0054] Among them, δ 2 is the noise variance, I K is the unit matrix, K is the system degree of freedom;

[0055] 5c) Using the clutter noise covariance matrix to perform space-time adaptive processing, the space-time filter vector is constructed as

[0056]

[0057] Where s is the target space-time steering vector;

[0058] 5d) Using the space-time filter vector, the unit to be detected is filtered to obtain the space-time filter output:

[0059] y=w H x

[0060] Among them, x is the unit data to be detected, and y is the output of the space-time filter;

[0061] 5e) Determine whether the unit to be detected contains a moving target based on the space-time filter output of the unit to be detected.

[0062] The present invention discloses the following technical effects:

[0063] The present invention eliminates the need for accurate extraction of clutter subspaces by the volume cross-correlation method, and has strong robustness in non-uniform environments where it is difficult to accurately extract clutter subspaces. The present invention combines the characteristics of high-precision sparse recovery space-time adaptive processing, and can calculate the similarity between samples under small sample conditions, overcoming the problem of poor robustness of traditional sample selection methods in non-uniform environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0065] Figure 1 It is a curve diagram showing the variation of the test statistics of the GIP method, the VCC method and the method of the present invention with the sequence number of the distance unit under the same experimental conditions;

[0066] Figure 2 It is a curve diagram showing the change of SCNR loss with distance unit number of GIP method, VCC method and the method of the present invention under the same experimental conditions;

[0067] Figure 3 The STAP output power of the GIP method, the VCC method and the method of the present invention varies with the normalized Doppler frequency under the same experimental conditions;

[0068] Figure 4 It is a schematic diagram of the method flow of the present invention. DETAILED DESCRIPTION

[0069] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.

[0070] Traditional sample selection methods such as the generalized inner product (GIP) method perform poorly in non-uniform environments because they directly use secondary data. At the same time, the training method based on the volumetric cross-correlation function (VCC) is difficult to be directly applied to non-ideal environments because it requires an accurate clutter subspace. In order to improve the robustness of the sample training method based on the volumetric cross-correlation function, the present invention proposes a sample selection method based on atomic norm minimization to reconstruct clutter similarity.

[0071] Step 1: Obtain airborne phased array radar echo data to obtain original training samples, and use the generalized inner product method to preliminarily remove abnormal data contaminated by strong reflectors to obtain preliminarily processed training samples.

[0072] The step 1 specifically includes the following sub-steps:

[0073] 1a) Set airborne phased array radar parameters and receive echo data;

[0074] 1b) rearranging each space-time snapshot data in the echo data and storing them as an original training sample set;

[0075] 1c) Using the generalized inner product method to preliminarily remove abnormal data from the original training samples, obtain the preliminarily processed training samples, and calculate the generalized inner product test statistic for the original training samples:

[0076] GIP k =x(k) H R u -1 x(k)

[0077] Among them, GIP k is the generalized inner product test statistic output of the k-th distance unit, x(k) is the space-time snapshot of the k-th distance unit, R u is the covariance matrix of the unit to be detected, and the covariance matrix of the unit to be detected is determined by the following formula

[0078]

[0079] Where x(k) is the space-time snapshot of the k-th distance unit, and K is the system degree of freedom;

[0080] 1d) comparing the generalized inner product test statistic of the unit to be detected with a preset threshold η; if the generalized inner product test statistic is greater than the preset threshold, the data of the unit to be detected is removed from the data set; otherwise, the data of the unit to be detected is retained.

[0081] Step 2: Reconstruct the clutter covariance matrix of the training sample by minimizing the atomic norm, perform eigendecomposition on the reconstructed clutter covariance matrix to obtain eigenvalues ​​and eigenvectors, and store the eigenvalues, eigenvectors and clutter covariance matrix reconstructed from each training sample.

[0082] The step 2 specifically includes the following sub-steps:

[0083] 2a) Reconstructing the clutter covariance matrix of the training sample using atomic norm minimization, that is, using the MATLAB convex optimization toolbox to solve the following atomic norm minimization problem

[0084]

[0085] Where Τr(·) is the trace of the matrix, x is the sample to be reconstructed, and Τ(·) is defined as follows: -n1<l1<n1,-n2<l2<n2

[0086]

[0087]

[0088] 2b) Performing eigendecomposition on the Τ(U) as follows

[0089] Τ(U)=PΛP H

[0090] Among them, P is the reconstructed clutter eigenvector matrix, and Λ is the diagonal matrix composed of reconstructed clutter eigenvalues. The clutter covariance matrix can be reconstructed according to the following formula

[0091]

[0092] Among them, P is the reconstructed clutter eigenvector matrix, x is the sample to be reconstructed, is the reconstructed clutter covariance matrix.

[0093] 2c) performing the operation described in 2b) on all training samples, and storing the reconstructed clutter covariance matrix and the eigenvectors and eigenvalues.

[0094] Step 3: Calculate the sample clutter similarity between the training sample and the unit to be detected using a weighted volume cross-correlation function.

[0095] The step 3 specifically includes the following sub-steps:

[0096] 3a) For the unit to be detected, the clutter similarity between the training sample and the unit to be detected is calculated. First, the principle of using the volume cross-correlation function to calculate the clutter similarity between the training sample and the unit to be detected is considered. The volume cross-correlation function vcc(k,l) is defined as follows:

[0097]

[0098] Among them, [,] is a matrix concatenation operation, P(k) and P(l) are composed of the standard orthogonal clutter eigenvectors of the kth and lth samples respectively. represents the clutter feature space, d1 and d2 represent the dimensions of the clutter subspace, δ1≥δ2≥...≥δ d ≥0 represents a singular value of X.

[0099] In order to illustrate the definition of volume cross-correlation function, the volume cross-correlation function is explained from the relationship between volume cross-correlation function and principal angle. and Its volume cross-correlation function has the following relationship with the main character

[0100]

[0101] Among them, 0≤i≤min(d1,d2), θ i is a protagonist between χ1 and χ2.

[0102] It can be seen that the volume cross-correlation function is actually the sine product of the angle between the two subspaces. When the clutter feature vector cannot be accurately extracted, P(k) may contain the noise feature vector When The angle between P(l) and the will be much smaller than 1, which will cause the volume cross-correlation function vcc(k,l) to be much smaller than the normal value, making it impossible to measure the clutter similarity between samples.

[0103] The present invention considers using eigenvalues ​​to weight the subspace angles, and the reconstructed clutter covariance matrix obtained by minimizing the atomic norm is: The reconstructed clutter eigenvector is obtained by eigendecomposing it:

[0104] P(l)=[p1(l),...,p K (l)]

[0105] Where K is the degree of freedom of the system.

[0106] Arrange the corresponding eigenvalues ​​from large to small into column vectors:

[0107]

[0108] in, is the eigenvalue corresponding to the clutter, is the eigenvalue corresponding to the noise.

[0109] The i-th eigenvector p of the clutter covariance matrix reconstructed by the unit to be detected i The cosine of the angle between (l0) and the eigenvector P(k) of the clutter covariance matrix reconstructed from the kth training sample is i (l0,k) can be obtained by solving the following optimization problem

[0110]

[0111] st|y| 2 =1

[0112] y=P(k)x

[0113] Among them, y represents the column space of P(k) and p iThe vector with the largest angle (l0) can be obtained by linearly weighting the P(k) column vectors. The solution to the above optimization problem is

[0114]

[0115] Among them, y is obtained by linearly weighting the eigenvectors in P(k), and P(k) is related to p i (l0) The smaller the angle, the smaller the eigenvector The larger the proportion of the corresponding component in the equation, the greater the weight of the corresponding component in the equation. However, P(k) and P(l0) contain both clutter eigenvectors and noise eigenvectors, and clutter similarity should only consider clutter eigenvectors. Since the clutter eigenvalue is usually much larger than the noise eigenvalue, we use the eigenvalue to weight the angle. After the eigenvalue is weighted, p i The cosine of the angle between (l0) and P(k) can be expressed as

[0116]

[0117] Among them, λ i (l0) is the i-th reconstructed clutter eigenvalue of the unit to be detected, and Λ(k) is the column vector composed of the reconstructed clutter eigenvalues ​​of the k-th training sample.

[0118] In order to reduce the influence of noise feature vectors, the similarity of reconstructed clutter between P(l0) and P(k) is calculated using the following formula:

[0119]

[0120] Wherein, ρ(l0,k) is the similarity of the reconstructed clutter between the l0th unit to be detected and the kth training sample, P(k) represents the reconstructed clutter feature vector matrix of the kth training sample, P(l0) represents the reconstructed clutter feature vector matrix of the l0th unit to be detected, Λ(k) is the column vector composed of the reconstructed clutter eigenvalues ​​of the kth training sample, Λ(l0) is the column vector composed of the reconstructed clutter eigenvalues ​​of the l0th unit to be detected, ρ(l0,k) is mainly affected by the eigenvectors with larger eigenvalues ​​and smaller angles in P(k) and P(l0);

[0121] 3b) For the unit to be detected, in order to avoid the target signal affecting the sample selection, ρ(l0,l0) is defined as

[0122] ρ(l0,l0)=|x H (l0)QQ H x(l0)|

[0123] Among them, x(l0) is the sample data of the l0th unit to be detected, Q is the orthogonal projection matrix, and x(l0) is projected to the orthogonal space of the target guidance vector.

[0124] Step 4: Using the sample clutter similarity, select training samples whose clutter distribution is similar to that of the unit to be detected, and obtain selected training samples.

[0125] The step 4 specifically includes the following sub-steps:

[0126] 4a) In the sample selection process, the closer ρ(l0,k) is to ρ(l0,l0), the more similar the clutter of the training sample and the unit to be detected is, that is, considering

[0127] η(k)=|ρ(l0,k)-ρ(l0,l0)|

[0128] The similarity is compared with the preset threshold value η0, that is,

[0129]

[0130] If the similarity is lower than the preset threshold value, it means that the threshold is not exceeded and the training sample has a high similarity with the clutter of the unit to be detected. At this time, the reconstructed clutter covariance matrix of the training sample is added to the uniform training sample set R Θ middle.

[0131] 4c) If the similarity is higher than the preset threshold value, it means that the threshold is exceeded and the similarity between the training sample and the clutter of the unit to be detected is low. In this case, the training sample is not added to the uniform training sample set R Θ middle.

[0132] Step 5: Use the selected training samples to perform space-time adaptive processing on the unit to be detected to filter out clutter.

[0133] The step 5 specifically includes the following sub-steps:

[0134] 5a) Using the selected uniform training sample set R Θ Calculate the clutter covariance matrix of the unit to be detected

[0135]

[0136] Among them, R c (l) is R Θ The reconstructed training sample of the distance unit numbered l in R Θ The total number of training samples in;

[0137] 5b) Using the covariance matrix of the unit to be detected to construct the clutter noise covariance matrix is:

[0138] R=R c +δ 2 I K

[0139] Among them, δ 2 is the noise variance, I K is the unit matrix, K is the system degree of freedom;

[0140] 5c) Using the clutter noise covariance matrix to perform space-time adaptive processing, constructing a space-time filter vector

[0141]

[0142] Where s is the target space-time steering vector;

[0143] 5d) Using the space-time filter vector, filtering the detection unit to obtain the space-time filter output is

[0144] y=w H x

[0145] Wherein, x is the unit data to be detected.

[0146] 5e) Determine whether there is any moving target in the unit to be detected based on the space-time filter output of the unit to be detected.

[0147] The present invention eliminates the need for accurate extraction of clutter subspace by the volume cross-correlation method, and has strong robustness in non-uniform environments where it is difficult to accurately extract clutter subspace. The present invention combines the characteristics of high-precision sparse recovery space-time adaptive processing, and can calculate the similarity between samples under small sample conditions, overcoming the problem of poor robustness of traditional sample selection methods in non-uniform environments.

[0148] Embodiment: Simulation analysis: The performance of the method proposed in the present invention is further described below in combination with simulation experiments. This method is compared with the traditional generalized inner product GIP method and volume cross-correlation function VCC method. All three methods use full-dimensional STAP for performance comparison. The main parameters of the simulation experiment are shown in Table 1.

[0149] Table 1 Simulation parameter settings

[0150] Number of array elements 8 Number of pulses per cpi 8 Operating frequency 1.24GHz Aircraft carrier platform speed 100m / s Flight altitude 3073m Pulse repetition frequency 1984Hz bandwidth 800kHz Phased Array Type Front and side view uniform linear array Element spacing Half wavelength

[0151] In the simulation, the echo data of 200 range cells from 230 to 429 are selected for processing. The improved Morchin model is used for clutter simulation. The simulation scene setting has obvious terrain undulation characteristics. Two types of terrain are constructed to form a strong non-uniform clutter area. The range cells [1, 70] and [131, 200] are set as water bodies, obeying the Weibull distribution, with a shape parameter of 2 and a scale parameter of 1. The remaining range cells [71, 130] are set as grasslands, obeying the complex Gaussian distribution. The array amplitude error is uniformly distributed in the range of [0, 0.05], and the array phase error is uniformly distributed in the range of [0, 5]°. A target with a signal-to-noise ratio of 20 is injected into the 100th range cell, the target normalized Doppler frequency is -0.25, and the target normalized spatial frequency is 0.

[0152] In addition, in order to study the performance of the method of the present invention in eliminating outliers, 14 types of interference targets are evenly set in the distance boxes [1, 70] and [131, 200], and their interference-to-noise ratio (JNR) obeys the uniform distribution [10, 20] dB, the normalized Doppler frequency obeys the uniform distribution [-0.3, -0.2], and the normalized spatial frequency obeys the uniform distribution [-0.1, 0.1]. The threshold of the GIP method is set to 0.2, and the color loading factor of the VCC method is set to 0.5. 128 training samples are selected in the GIP and VCC methods, while only 8 training samples are selected in the method of the present invention. To ensure the consistency of the simulation experiments, the results obtained are the average values ​​of 100 Monte Carlo tests.

[0153] The test statistics obtained by the three methods vary with the distance unit as shown in the following curves: Figure 1 As shown in , the test statistic of the distance cells eliminated by the GIP method is set to 1. Figure 1 It can be seen that the method proposed in the present invention can not only select training samples that are most similar to the CUT clutter distribution in a non-uniform environment, but also effectively eliminate significant outliers caused by strong reflectors. Without reducing the target power, clutter and interference can be effectively suppressed.

[0154] Figure 2 The curves of signal-to-noise ratio loss (SCNR Loss) after STAP with normalized Doppler frequency for different training sample selection methods are shown. In the Doppler frequency range where the interference is located, the GIP method and the VCC method have notches of about 11 and 15 dB respectively, while the method of the present invention does not produce obvious notches. This is because the proposed method can effectively eliminate training samples contaminated by outliers.

[0155] At the same time, it can be clearly seen that the method proposed in the present invention has less signal-to-noise ratio loss, which is mainly due to its ability to select training samples that are consistent with the clutter distribution of the unit to be detected, thereby producing more effective clutter suppression performance. In addition, the simulation also shows that the performance of the VCC method is even worse than that of the GIP method, proving the limitations of the VCC method in non-ideal environments and the improvement of the proposed method. Figure 3 The curves of STAP output power changing with distance unit for different training sample selection methods are given. In order to prove that the proposed method also has performance improvement when using the clutter covariance matrix (CCM) obtained by sampling matrix inversion (SMI), Figure 3 The STAP output power in this case is also increased. In comparison, the residual clutter power of the VCC method is only 0.1 dB lower than that of the GIP method, while the residual clutter power of the method of the present invention is 1 dB lower than that of the GIP method when the training samples are used directly, and the residual clutter power of the method of the present invention is 5 dB lower than that of the GIP method when the method of the present invention uses the samples to reconstruct the CCM.

[0156] Figure 3 The results in show that when using the CCM obtained by SMI, the proposed method effectively selects training samples that are more consistent with the clutter distribution of the unit to be detected. It is worth noting that the proposed method combines sample selection with sparse recovery and uses the reconstructed CCM for STAP, which makes it have superior performance in non-uniform environments.

[0157] The present invention provides a method for selecting uniform samples in a non-uniform environment, which can be used to further construct a space-time optimal filter to filter clutter and interference in echo data, thereby providing better quality echo data for subsequent radar target detection.

[0158] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0159] In the description of the present invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0160] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A sample selection method based on atomic norm minimization and reconstruction of clutter similarity, characterized in that: The following steps are involved: Step 1: Acquire the airborne phased array radar echo data to obtain the original training samples, use the generalized inner product method to preliminarily remove the abnormal data contaminated by strong reflectors, and obtain the preliminarily processed training samples; Step 2: Reconstruct the clutter covariance matrix of the training sample by minimizing the atomic norm, perform eigendecomposition on the reconstructed clutter covariance matrix to obtain eigenvalues ​​and eigenvectors, and store the obtained eigenvalues, eigenvectors and reconstructed clutter covariance matrix; Step 3: Calculate the clutter similarity between the training sample and the unit sample to be detected by using a weighted volume cross-correlation function; Step 4: Select training samples using the clutter similarity, and select training samples with clutter distribution similar to that of the unit sample to be detected; Step 5: Use the selected training samples to perform space-time adaptive processing on the unit to be detected to suppress clutter.

2. According to claim 1, a sample selection method based on atomic norm minimization and reconstruction of clutter similarity is characterized in that: The step 1 comprises the following sub-steps: 1a) Set the airborne phased array radar parameters and receive echo data; 1b) rearranging each space-time snapshot data in the echo data and storing them as an original training sample set; 1c) using the generalized inner product method to preliminarily remove abnormal data from the original training samples to obtain preliminarily processed training samples, and calculating the generalized inner product test statistic for the original training samples; 1d) Compare the generalized inner product test statistic of the unit to be detected with a preset threshold η. If the generalized inner product test statistic is greater than the preset threshold, the data of the unit to be detected is removed from the data set, otherwise the data of the unit to be detected is retained.

3. According to claim 2, a sample selection method based on atomic norm minimization and reconstruction of clutter similarity is characterized in that: In the process of obtaining the generalized inner product test statistic, the generalized inner product test statistic is expressed as: GIP k =x(k) H R u -1 x(k) Among them, GIP k is the generalized inner product test statistic output of the k-th distance unit, x(k) is the space-time snapshot of the k-th distance unit, R u is the covariance matrix of the unit to be detected, and the covariance matrix of the unit to be detected is determined by the following formula: Among them, x(k) is the space-time snapshot of the kth distance unit, and K is the system degree of freedom.

4. According to claim 3, a sample selection method based on atomic norm minimization and reconstruction of clutter similarity is characterized in that: The step 2 includes the following sub-steps: 2a) Reconstruct the clutter covariance matrix of the training sample using atomic norm minimization, that is, use the MATLAB convex optimization toolbox to solve the following atomic norm minimization problem: Where Τr(·) is the trace of the matrix, x is the sample to be reconstructed, and Τ(·) is defined as follows: 2b), the Τ(U) is characteristically decomposed as follows: T(U)=PΛP H Where P is the reconstructed clutter eigenvector matrix, Λ is the diagonal matrix composed of reconstructed clutter eigenvalues; The clutter covariance matrix can be reconstructed according to the following formula: Among them, P is the reconstructed clutter eigenvector matrix, x is the sample to be reconstructed, R c ANM is the reconstructed clutter covariance matrix; 2c) Reconstruct clutter for all training samples, and store the reconstructed clutter covariance matrix and the eigenvectors and eigenvalues.

5. According to claim 4, a sample selection method based on atomic norm minimization and reconstruction of clutter similarity is characterized in that: In step 3, for the unit to be detected, the clutter similarity between the training sample and the unit to be detected is calculated: ρ(l0,k)=|Λ H (l0)P H (l0)P(k)Λ(k)|,l0≠k Wherein, ρ(l0,k) is the calculated similarity of the reconstructed clutter between the l0th unit to be detected and the kth training sample, P(k) represents the reconstructed clutter feature vector matrix of the kth training sample, P(l0) represents the reconstructed clutter feature vector matrix of the l0th unit to be detected, Λ(k) is the column vector composed of the reconstructed clutter eigenvalues ​​of the kth training sample, and Λ(l0) is the column vector composed of the reconstructed clutter eigenvalues ​​of the l0th unit to be detected.

6. According to claim 5, a sample selection method based on atomic norm minimization and reconstruction of clutter similarity is characterized in that: In step 3, for the unit to be detected, in order to avoid the target signal affecting the sample selection, ρ(l0,l0) is defined as: ρ(l0,l0)=|x H (l0)QQ H x(l0)| Among them, x(l0) is the sample data of the l0th unit to be detected, Q is the orthogonal projection matrix, and x(l0) is projected to the orthogonal space of the target guidance vector.

7. According to claim 6, a sample selection method based on atomic norm minimization and reconstruction of clutter similarity is characterized in that: The step 4 includes the following sub-steps: 4a) In the sample selection process, the closer ρ(l0,k) is to ρ(l0,l0), the more similar the kth training sample is to the clutter of the unit to be detected, that is, considering: η(k)=|ρ(l0,k)-ρ(l0,l0)| The similarity is compared with the preset threshold value η0, that is: 4b) If the similarity is lower than the preset threshold value, it means that the threshold is not exceeded and the training sample has a high similarity with the clutter of the unit to be detected. At this time, the reconstructed clutter covariance matrix of the training sample is added to the uniform training sample set R Θ middle; 4c) If the similarity is higher than the preset threshold value, it means that the threshold is exceeded and the similarity between the training sample and the clutter of the unit to be detected is low. In this case, the training sample is not added to the uniform training sample set R Θ middle.

8. According to claim 7, a sample selection method based on atomic norm minimization and reconstruction of clutter similarity is characterized in that: The step 5 comprises the following sub-steps: 5a) Using the selected uniform training sample set R Θ Calculate the clutter covariance matrix of the unit to be detected: Among them, R c (l) is R Θ The reconstructed training sample of the distance unit numbered l in R Θ The total number of training samples in; 5b) Using the covariance matrix of the unit to be detected to construct the clutter noise covariance matrix is: R=R c +δ 2 I K Among them, δ 2 is the noise variance, I K is the unit matrix, K is the system degree of freedom; 5c) Using the clutter noise covariance matrix to perform space-time adaptive processing, constructing a space-time filter weight vector as follows: Where s is the target space-time steering vector; 5d) Using the space-time filter vector, filtering the unit to be detected, the space-time filter output is obtained as: y=w H x Among them, x is the unit data to be detected, and y is the output of the space-time filter; 5e) Determine whether the unit to be detected contains a moving target based on the space-time filter output of the unit to be detected.

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