Oblique symmetry adaptive detection method and system suitable for subspace interference environment

Abstract

The invention belongs to the technical field of multi-channel signal detection, and particularly relates to an oblique symmetry self-adaptive detection method and system suitable for a subspace interference environment, and the method comprises the steps: S1, constructing a target signal matrix, an interference signal matrix, a sampling covariance matrix and a to-be-detected data matrix, the target signal matrix, the interference signal matrix, the sampling covariance matrix and the to-be-detected data matrix are represented by A, J, S and X respectively, the dimensions of A, J, S and X are N * p, N * q, N * N and N * K respectively, (p + q) < = N, K represents the extended dimension of a target, N represents the number of system channels, the sampling covariance matrix represents S = YYH, Y represents a training sample matrix, and a symbol (.) H represents conjugate transpose. According to the method, interference suppression, signal accumulation and constant false alarm characteristics can be integrally realized, and compared with an existing method, the detection performance of an airborne radar in an interference environment is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-channel signal detection, and in particular relates to a skew-symmetric adaptive detection method and system suitable for a subspace interference environment. Background Art

[0002] With the improvement of airborne radar technology and the continuous development of multi-channel signal processing technology, airborne radar can perform effective adaptive target detection on the acquired high-dimensional echo data. However, with the improvement of radar technology, the corresponding electromagnetic interference technology is also constantly iterating and developing. One of the subspace interference signals is particularly threatening the airborne radar target detection system. This subspace interference signal refers to the interference signal located in a certain known subspace, but the corresponding subspace coordinates are unknown;

[0003] Subspace interference has an all-round impact on the radar detection system. When it enters the radar system from the main lobe direction, it will raise the threshold of target detection, resulting in missed detection; when it enters the radar detection system from the side lobe, it may appear as a false target, resulting in false alarms. In addition, the emergence of subspace interference will cause a sharp decrease in the number of available training samples in the detection background, that is, it is difficult to obtain sufficient training samples that are independent and identically distributed with the samples to be detected, causing the performance of existing space-time adaptive detectors to drop sharply;

[0004] For the problem of target detection in the subspace interference background, the existing method is to integrate the subspace interference information into the detection model and design the detector based on the generalized likelihood ratio test (GLRT) criterion. However, the GLRT detector can only achieve good detection performance in some scenes, and does not consider the problem of reduced number of training samples caused by subspace interference. Based on this consideration, the skew-symmetric prior information of background clutter in the present invention is integrated into the detection model to reduce the demand for training samples; then, based on the Wald criterion, a skew-symmetric space-time adaptive detector with excellent performance suitable for subspace interference environment is designed. Summary of the invention

[0005] The purpose of the present invention is to provide a skew-symmetric adaptive detection method and system suitable for a subspace interference environment, which can integrate interference suppression, signal accumulation and constant false alarm characteristics, and improve the detection performance of airborne radar in an interference environment compared with existing methods.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A skew-symmetric adaptive detection method suitable for a subspace interference environment comprises the following steps:

[0008] S1: construct a target signal matrix, an interference signal matrix, a sampling covariance matrix and a data matrix to be detected, wherein the target signal matrix, the interference signal matrix, the sampling covariance matrix and the data matrix to be detected are represented by A, J, S and X respectively;

[0009] The dimensions of A, J, S, and X are N×p, N×q, N×N, and N×K, respectively, where (p+q)≤N, K represents the extended dimension of the target, N represents the number of system channels, and the sampling covariance matrix is ​​expressed as S=YY H , Y represents the training sample matrix, symbol (·) H represents conjugate transpose;

[0010] S2: Construct a skew-symmetric transformation matrix M with a dimension of N×N, and then use the matrix M to perform skew-symmetric transformation on A, J, and S to obtain the corresponding matrix with skew-symmetric characteristics;

[0011] S3: Use the sampling covariance matrix S after oblique transformation to perform quasi-whitening on matrices X, A, and J, and obtain quasi-whitening matrices and

[0012] S4: Using the quasi-whitening matrix Constructing the orthogonal projection matrix of the interference signal And the corresponding complementary projection matrix

[0013] S5: Using quasi-whitening to detect the data matrix Quasi-whitened target signal matrix And the orthogonal projection matrix of the interference signal Construct test statistics;

[0014] S6: Determine the detection threshold using the detection statistic and the preset value of false alarm probability;

[0015] S7: Compare the detection statistic with the detection threshold and determine whether the target exists.

[0016] A skew-symmetric adaptive detection system suitable for subspace interference environment, comprising the following modules:

[0017] Target and interference data matrix construction module: used to construct target signal matrix and interference signal matrix;

[0018] Sampling covariance matrix construction module: used to construct the sampling covariance matrix using training samples;

[0019] Skew-symmetric transformation module: used to perform skew-symmetric transformation on the target signal matrix, the interference signal matrix and the sampling covariance matrix using the skew-symmetric transformation matrix;

[0020] Data quasi-whitening module: used to perform quasi-whitening processing on the target signal matrix, the interference signal matrix and the data matrix to be detected, and obtain the quasi-whitened target signal matrix, the quasi-whitened interference signal matrix and the quasi-whitened data matrix to be detected respectively;

[0021] Detection statistics construction module: used to construct detection statistics using the quasi-whitened target signal matrix, the quasi-whitened interference signal orthogonal projection matrix and the quasi-whitened to-be-detected data matrix;

[0022] Detection threshold calculation module: used to determine the detection threshold using detection statistics and false alarm probability preset value;

[0023] Target decision module: used to compare the detection statistic with the detection threshold and determine whether the target exists.

[0024] The technical effects achieved by the present invention are:

[0025] (1) The present invention uses a skew-symmetric transformation matrix M to perform skew-symmetric transformation processing on the target signal matrix, the interference signal matrix and the sampling covariance matrix, thereby reducing the demand for training samples for the detection method of the present invention.

[0026] (2) The present invention uses the sampling covariance matrix S to perform quasi-whitening processing on the data matrix to be detected, the target signal and the interference signal matrix, so that the detector proposed by the present invention has a constant false alarm characteristic.

[0027] (3) The present invention can solve the problem of target detection in a subspace interference environment and improve the radar target detection performance compared with the existing detection method based on the GLRT criterion. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic diagram of the process of the present invention;

[0029] Figure 2 It is a structural framework diagram of the present invention;

[0030] Figure 3 It is a schematic diagram of the detection performance of the method proposed in the present invention under different SNRs;

[0031] Figure 4 It is a schematic diagram of the detection performance when the training samples are insufficient in the present invention. DETAILED DESCRIPTION

[0032] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0033] In this technical solution, it is assumed that the target signal s and the interference signal h are N×1 dimensional vectors, and both are located in the subspace formed by the unitary matrices A and J, and the corresponding subspace coordinates are φ and ψ, that is, the target signal and the interference signal can be expressed as:

[0034] s=Aφ (1)

[0035] as well as:

[0036] h=Jψ (2)

[0037] Among them, A is an N×p-dimensional column full rank matrix, J is an N×q-dimensional column full rank matrix, and φ and ψ are vectors of dimensions p×1 and q×1, respectively.

[0038] Let n be the clutter and noise components in the data matrix x to be detected, and satisfy the mean value of 0 N×1 , a complex Gaussian distribution with covariance matrix R. Assume that there are L independent and identically distributed training samples x l , l = 1, 2, ..., L, which contains clutter and noise components n e,l , and also obeys the mean of 0 N×1 , a complex Gaussian distribution with covariance matrix R. In summary, the binary hypothesis detection problem in the subspace interference environment can be expressed as:

[0039]

[0040] Among them, H0 means that the data to be detected only contains subspace interference signals and clutter, and H1 means that the data to be detected contains target signals, subspace interference signals and clutter components.

[0041] In order to reduce the detector's demand for training samples and make it more adaptable to the subspace interference detection environment, the skew-symmetric transformation matrix M is used to perform skew-symmetric transformation on each signal component in equation (3). The structure of the skew-symmetric transformation matrix M is designed as:

[0042]

[0043] in, I N is the identity matrix with dimension N×N; F N is a permutation matrix with dimension N×N, whose anti-diagonal element value is equal to 1 and the remaining position elements are equal to 0. After skew symmetric transformation, the detection model in formula (3) can be expressed as:

[0044]

[0045] Among them, Φ=[Re(φ),jIm(φ)], Ψ=[Re(ψ),jIm(ψ)], X=[x e ,x o], Re(·) and Im(·) represent the real and imaginary part operations respectively, x e and x o The definitions are:

[0046]

[0047] in,(·) * Represents the conjugate operation.

[0048] Embodiment 1:

[0049] The purpose of the present invention is to improve the performance of adaptive detectors in subspace interference environments. To achieve the above purpose, please refer to Figure 1 As shown, the present invention provides a skew-symmetric adaptive detection method suitable for subspace interference environment;

[0050] The steps include:

[0051] S1: construct a target signal matrix, an interference signal matrix, a sampling covariance matrix and a data matrix to be detected, wherein the target signal matrix, the interference signal matrix, the sampling covariance matrix and the data matrix to be detected are represented by A, J, S and X respectively;

[0052] The dimensions of A, J, S, and X are N×p, N×q, N×N, and N×K, respectively, where (p+q)≤N, K represents the extended dimension of the target, N represents the number of system channels, and the sampling covariance matrix is ​​expressed as S=YY H , Y represents the training sample matrix, symbol (·) H represents conjugate transpose;

[0053] The constructed target signal matrix A and interference signal matrix J are both column-full rank unitary matrices, and the unitary matrices A and J are linearly independent.

[0054] S2: Construct a skew-symmetric transformation matrix M with a dimension of N×N, and then use the matrix M to perform skew-symmetric transformation on A, J, and S to obtain the corresponding matrix with skew-symmetric characteristics;

[0055] The constructed skew-symmetric transformation matrix M is expressed as:

[0056]

[0057] in, I N is the identity matrix of dimension N×N, F N is a permutation matrix of dimension N×N, whose anti-diagonal element value is equal to 1 and the remaining position elements are equal to 0;

[0058] The target signal matrix A, the interference signal matrix J and the sampling covariance matrix S are transformed by skew-symmetric transformation matrix M, which are expressed as follows: and

[0059] S3: Use the sampling covariance matrix S after oblique transformation to perform quasi-whitening on matrices X, A, and J, and obtain quasi-whitening matrices and

[0060] The quasi-whitening process of matrices X, A and J is performed using the sampling covariance matrix S after oblique transformation. The obtained quasi-whitened data matrix to be detected, quasi-whitened target signal matrix and quasi-whitened interference signal matrix are expressed as and

[0061] S4: Using the quasi-whitening matrix Constructing the orthogonal projection matrix of the interference signal And the corresponding complementary projection matrix

[0062] Using the quasi-whitening interference signal matrix The constructed orthogonal projection matrix and complementary projection matrix are expressed as and

[0063] in(·) -1 represents the inverse of the matrix, I N is the identity matrix of dimension N×N.

[0064] S5: Using quasi-whitening to detect the data matrix Quasi-whitened target signal matrix And the orthogonal projection matrix of the interference signal Construct test statistics;

[0065] Using quasi-whitening to detect the data matrix Quasi-whitened target signal matrix And the orthogonal projection matrix of the interference signal The constructed detection statistic is expressed as:

[0066]

[0067] where tr(·) represents the trace of the matrix, and

[0068] S6: Determine the detection threshold using the detection statistic and the preset value of false alarm probability;

[0069] In S6, the false alarm probability preset value is set to 10 -4 , the detection threshold is expressed as:

[0070] η=t(n)

[0071] Wherein, η represents the detection threshold, n = [Qμ], Q is the number of Monte Carlo simulations, μ represents the false alarm probability value set by the system, [·] represents the rounding operation, and t(n) is the sequence;

[0072]

[0073] The nth largest value when arranged from largest to smallest, express The conjugate transpose of X(k) represents the k-th realization k=1, 2,…,Q of the data to be detected containing only interference and thermal noise components.

[0074] S7: Compare the detection statistic with the detection threshold and determine whether the target exists.

[0075] Embodiment 2:

[0076] See attached Figure 2 Based on Example 1, the present invention proposes a skew-symmetric adaptive detection system suitable for a subspace interference environment, comprising the following modules:

[0077] Target and interference data matrix construction module: used to construct target signal matrix and interference signal matrix;

[0078] Sampling covariance matrix construction module: used to construct the sampling covariance matrix using training samples;

[0079] Skew-symmetric transformation module: used to perform skew-symmetric transformation on the target signal matrix, the interference signal matrix and the sampling covariance matrix using the skew-symmetric transformation matrix;

[0080] Data quasi-whitening module: used to perform quasi-whitening processing on the target signal matrix, the interference signal matrix and the data matrix to be detected, and obtain the quasi-whitened target signal matrix, the quasi-whitened interference signal matrix and the quasi-whitened data matrix to be detected respectively;

[0081] Detection statistics construction module: used to construct detection statistics using the quasi-whitened target signal matrix, the quasi-whitened interference signal orthogonal projection matrix and the quasi-whitened to-be-detected data matrix;

[0082] Detection threshold calculation module: used to determine the detection threshold using detection statistics and false alarm probability preset value;

[0083] Target decision module: used to compare the detection statistic with the detection threshold and determine whether the target exists.

[0084] Embodiment 3:

[0085] like Figure 1-Figure 4 As shown, this embodiment discloses a simulation experiment based on the above embodiment to further illustrate the effect of the present invention, and the simulation experiment process is as follows:

[0086] Assume that the number of radar system channels is N = 12 and the false alarm probability is 1 × 10 -4 , the element at the (i, j)th position of the covariance matrix R of the clutter and noise is set to R(i, j) = 0.95 |i-j| , i,j=1,2,…,N, where the symbol |·| indicates taking the absolute value. Figure 3 The detection probability of the target under different signal-to-noise ratios (SNRs) of the proposed method is given, where the subspace dimensions of the target signal and the interference signal are p=4 and q=2, respectively, the number of training samples is L=2N, the interference-to-noise ratio (INR) is 5dB, and the INR and SNR are:

[0087] INR=ψ H J H R -1 Jψ

[0088] as well as:

[0089] SNR=φ H A H R -1 Aφ

[0090] from Figure 3 It can be seen that when the signal-to-noise ratio is higher than 17dB, the detection probability of the proposed method for the target is higher than 90%. Compared with the existing GLRT criterion detector, the proposed detection method has better detection performance. In addition, Figure 4 The detection probability of the target under different SNRs in the scenario with insufficient training samples is given, where p=4, q=3, the number of training samples L=N, and the interference-to-noise ratio INR=5dB.

[0091] It can be seen from the results that in the scenario with insufficient training samples, the performance of the proposed Wald criterion detector is significantly better than the existing GLRT detector.

[0092] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A skew-symmetric adaptive detection method suitable for subspace interference environment, characterized by: The steps include: S1: construct a target signal matrix, an interference signal matrix, a sampling covariance matrix and a data matrix to be detected, wherein the target signal matrix, the interference signal matrix, the sampling covariance matrix and the data matrix to be detected are represented by A, J, S and X respectively; The dimensions of A, J, S, and X are N×p, N×q, N×N, and N×K, respectively, where (p+q)≤N, K represents the extended dimension of the target, N represents the number of system channels, and the sampling covariance matrix is ​​expressed as S=YY H , Y represents the training sample matrix, symbol (·) H represents conjugate transpose; S2: Construct a skew-symmetric transformation matrix M with a dimension of N×N, and then use the matrix M to perform skew-symmetric transformation on A, J, and S to obtain the corresponding matrix with skew-symmetric characteristics; S3: Use the sampling covariance matrix S after oblique transformation to perform quasi-whitening on matrices X, A, and J, and obtain quasi-whitening matrices and S4: Using the quasi-whitening matrix Constructing the orthogonal projection matrix of the interference signal And the corresponding complementary projection matrix S5: Using quasi-whitening to detect the data matrix Quasi-whitened target signal matrix And the orthogonal projection matrix of the interference signal Construct test statistics; S6: Determine the detection threshold using the detection statistic and the preset value of false alarm probability; S7: Compare the detection statistic with the detection threshold and determine whether the target exists.

2. The skew-symmetric adaptive detection method according to claim 1, characterized in that: In S1, the constructed target signal matrix A and interference signal matrix J are both column-full rank unitary matrices, and the unitary matrices A and J are linearly independent.

3. The skew-symmetric adaptive detection method according to claim 1, characterized in that: In S2, the constructed skew-symmetric transformation matrix M is expressed as: in, I N is the identity matrix of dimension N×N, F N is a permutation matrix of dimension N×N, whose anti-diagonal element value is equal to 1 and the remaining position elements are equal to 0; The target signal matrix A, the interference signal matrix J and the sampling covariance matrix S are transformed by skew-symmetric transformation matrix M, which are expressed as follows: and 4. The skew-symmetric adaptive detection method according to claim 1, characterized in that: In S3, the sampling covariance matrix S after the oblique transformation is used to perform quasi-whitening on the matrices X, A and J, and the obtained quasi-whitened data matrix to be detected, quasi-whitened target signal matrix and quasi-whitened interference signal matrix are expressed as and 5. The skew-symmetric adaptive detection method according to claim 1, characterized in that: In S4, the quasi-whitening interference signal matrix is ​​used The constructed orthogonal projection matrix and complementary projection matrix are expressed as and in(·) -1 represents the inverse of the matrix, I N is the identity matrix of dimension N×N.

6. The skew-symmetric adaptive detection method according to claim 1, characterized in that: In S5, the quasi-whitened data matrix to be detected is used Quasi-whitened target signal matrix And the orthogonal projection matrix of the interference signal The constructed detection statistic is expressed as: where tr(·) represents the trace of the matrix, and 7. The skew-symmetric adaptive detection method according to claim 1, characterized in that: In S6, the false alarm probability preset value is set to 10 -4 , the detection threshold is expressed as: η=t(n) Wherein, η represents the detection threshold, n = [Qμ], Q is the number of Monte Carlo simulations, μ represents the false alarm probability value set by the system, [·] represents the rounding operation, and t(n) is the sequence; and: The nth largest value when arranged from largest to smallest, express The conjugate transpose of X(k) represents the k-th realization k=1, 2,…,Q of the data to be detected containing only interference and thermal noise components.

8. A skew-symmetric adaptive detection system suitable for a subspace interference environment, using the skew-symmetric adaptive detection method according to any one of claims 1 to 7, characterized in that: Includes the following modules: Target and interference data matrix construction module: used to construct target signal matrix and interference signal matrix; Sampling covariance matrix construction module: used to construct the sampling covariance matrix using training samples; Skew-symmetric transformation module: used to perform skew-symmetric transformation on the target signal matrix, the interference signal matrix and the sampling covariance matrix using the skew-symmetric transformation matrix; Data quasi-whitening module: used to perform quasi-whitening processing on the target signal matrix, the interference signal matrix and the data matrix to be detected, and obtain the quasi-whitened target signal matrix, the quasi-whitened interference signal matrix and the quasi-whitened data matrix to be detected respectively; Detection statistics construction module: used to construct detection statistics using the quasi-whitened target signal matrix, the quasi-whitened interference signal orthogonal projection matrix and the quasi-whitened to-be-detected data matrix; Detection threshold calculation module: used to determine the detection threshold using detection statistics and false alarm probability preset value; Target decision module: used to compare the detection statistic with the detection threshold and determine whether the target exists.

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