Target adaptive fusion detection method based on interference subspace suppression

Abstract

The invention relates to the technical field of broadband radar signal processing, in particular to a target adaptive fusion detection method based on interference subspace suppression. Aiming at the problem that an existing broadband radar distance extension target adaptive detector is difficult to consider CFAR characteristics, detection performance and calculation complexity under a partial uniform Gaussian background, and the problem that pure clutter training data is difficult to obtain due to actual clutter heterogeneity, how to fully excavate clutter covariance matrix structure information, and how to fully excavate clutter covariance matrix structure information, the invention provides a clutter covariance matrix detection method. The requirement for the training data volume is reduced, the estimation precision of an unknown clutter covariance matrix is improved, the target adaptive fusion detection method based on interference subspace suppression in a closed form is constructed, and the detection precision is improved while the CFAR characteristics are ensured. The multi-aspect requirements of intelligent anti-interference, calculation complexity, detection performance and the like of a distance extension target adaptive detection algorithm are considered, and the adaptive detection performance of a multi-channel broadband radar on a weak and small target in a complex interference environment is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of broadband radar signal processing, and in particular to a target adaptive fusion detection method based on interference subspace suppression. Background Art

[0002] As radar bandwidth increases, its range resolution improves significantly. Wideband radars are widely used in modern military and civilian applications, including anti-interference, counter-reconnaissance, precision detection and imaging, high-precision tracking, and target identification. However, adaptive detection of range-extended targets in wideband radars remains a core challenge. Unlike narrowband radars, where target echo signals typically occupy only a single range resolution bin, the energy of a target scattering point in wideband radars can spread to adjacent range bins, presenting a "one-dimensional range profile" and forming a range-extended target. Using traditional point target detection methods to detect targets within a single range bin and relying on neighboring range bin sampling to estimate background clutter characteristics presents two major technical bottlenecks. First, energy leakage from strong scattering points of range-extended targets can contaminate data from adjacent range bins, creating a signal masking effect and significantly degrading point target detection performance. Second, in complex electromagnetic environments, radars must contend with natural and man-made interference sources, such as electronic countermeasures and civilian electromagnetic signals. Furthermore, the variability of the target environment exacerbates the heterogeneity of background clutter, making pure clutter training data that meets the independent and identically distributed (IID) condition extremely limited. Compared with narrowband radar, this problem is more prominent in broadband radar scenarios, making it difficult for existing detection methods to achieve the expected results.

[0003] Although the global uniformity of the complex clutter background is destroyed, local uniformity characteristics of the clutter can still be observed within the local radial range. Based on this characteristic, a partially uniform model can be used to model the clutter, assuming that the clutter components of the detection unit and the reference range unit have the same covariance matrix structure but different power parameters. While this model fully utilizes the local correlation of the clutter, the number of reference range units that can be used is still limited by the actual degree of clutter non-uniformity. In traditional rank-one signal models, the target steering vector is usually assumed to be a known fixed vector, but in actual systems, beam pointing errors and multipath effects can cause mismatches in the target steering vector. To address this problem, a subspace model is introduced to describe the target signal, representing the signal as the product of a known subspace matrix and an unknown coordinate matrix.

[0004] To address the current shortage of pure clutter training data, research has shown that when a radar receiver employs a centrosymmetric linear array or centrosymmetric spaced pulse train, its clutter covariance matrix exhibits a unique skew-symmetric structure. Utilizing this prior information can effectively improve the detector's detection performance and reduce the amount of training data required. Within this framework, a joint dataset is constructed based on test and training data from multiple range bins to be detected. A subspace GLRT detector (abbreviated as P2S-GLRT-PHE) based on interference suppression can be derived for partially uniform clutter. However, the construction of the GLRT detector requires solving the maximum likelihood estimation of the unknown parameters under both the target assumption and the absence of a target assumption, resulting in a complex detector construction process and high computational complexity. If the Rao test criterion is used to construct the detection statistic, although a subspace Rao detector based on interference suppression in a partially uniform clutter background (abbreviated as P2S-Rao-PHE) can be obtained, in practical applications, the technical difficulty of solving the Fisher information matrix must be faced, and the detector construction process is also relatively complicated.

[0005] In the presence of external interference and insufficient uniform training data, how to construct a multi-channel broadband radar range-extended target detection method with low computational complexity and excellent detection performance has become a key issue that needs to be solved urgently. Summary of the Invention

[0006] The purpose of the present invention is to provide a target adaptive fusion detection method based on interference subspace suppression in order to solve at least one of the above technical problems. The method needs to fully exploit the skew-symmetric structure information to reduce the demand for training data, improve the estimation accuracy of the unknown clutter covariance matrix, and achieve effective suppression of interference signals while maintaining the constant false alarm rate (CFAR) characteristics. Ultimately, an effective balance is achieved between computing resources and detection performance, thereby improving the detection capability of broadband radar in complex interference environments and solving a major problem faced by channel broadband radar range-extended target adaptive detection.

[0007] The present invention achieves the above-mentioned purpose through the following technical solutions:

[0008] A target adaptive fusion detection method based on interference subspace suppression includes the following steps:

[0009] Step 1: Get test data Z from K distance units to be detected, and get training data Y from R reference distance units adjacent to the distance unit to be detected; get skew-symmetric transformation test data Z based on test data Z p ;

[0010] Based on the training data Y and the skew-symmetric transformation test data Z pGet respectively: Maximum likelihood estimation of the clutter covariance matrix under the no-target assumption Maximum Likelihood Estimation of the Disturbance Coordinate Matrix Maximum Likelihood Estimation of Clutter Power Factor Skew symmetric transformation test data Z under target assumption p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result and target parameter vector Θ rp-1s The maximum likelihood estimate of

[0011] Step 2: Based on the data obtained in step 1, construct a detection statistic λ of the target adaptive fusion detection method based on interference subspace suppression;

[0012] In step 2, the detection statistic λ is constructed using the following formula:

[0013]

[0014] Among them, λ P1S-Gradient-PHE represents the P1S-Gradient test statistic in PHE; tr[·] represents the trace of the square matrix; I 2K represents the 2K×2K dimensional identity matrix; (·) H represents the conjugate transpose; (·) * represents conjugate; S represents the sample covariance matrix; D N Represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; I N represents the N×N dimensional identity matrix; The first known multi-rank subspace The second most rank subspace known p+q≤N; N represents the product of the number of antenna elements and the number of pulses; Represents a set of complex matrices of m×n dimensions;

[0015] Step 3: Set a detection threshold T according to a preset false alarm probability; compare the detection statistic λ with the detection threshold T; if λ≥T, determine that there is a range extension target in the current K range units to be detected, and the test data is not used as training data for subsequent other range units to be detected; if λ<T, determine that there is no range extension target in the current K range units to be detected, and the test data is used as training data for subsequent other range units to be detected.

[0016] Furthermore, in step 1, the skew-symmetric transformation test data Z is obtained based on the test data Z.p , including: obtaining the skew symmetric transformation test data Z through the following formula p :

[0017]

[0018] Among them, z k represents the N×1 dimensional test data component corresponding to the kth unit to be detected; D N represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; (·)* represents conjugation; Represents a set of N×2K dimensional complex matrices; Represents a set of N×1 complex matrices.

[0019] Furthermore, the maximum likelihood estimate of the clutter covariance matrix under the target-free assumption is obtained by the following formula:

[0020]

[0021] T i =S+(ZB i D)(ZB i D) H / γ

[0022] B i =[iH,J]

[0023] D=[P T ,Q T ] T

[0024] Where i = 0, 1; D N represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; γ represents the clutter power factor; the sample covariance matrix S = YY H ; P represents the target coordinate matrix, Q represents the interference coordinate matrix; (·)* represents conjugate; (·) H represents conjugate transpose; (·) T represents transpose;

[0025] The maximum likelihood estimate of the interference coordinate matrix is obtained by the following formula

[0026]

[0027] in,

[0028] The maximum likelihood estimate of the clutter power factor is obtained by solving the unique positive solution of the following formula:

[0029] Where, s = min(N, 2K); υ represents the unknown quantity; λ k，0 express The kth eigenvalue of I N Represents the N×N dimensional identity matrix.

[0030] Furthermore, the skew symmetric transformation test data Z under the target assumption is obtained by the following formula: p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result of :

[0031]

[0032] Where M represents the clutter covariance matrix; P represents the target coordinate matrix, and Q represents the interference coordinate matrix; γ represents the clutter power factor; Θ rp-1s represents the target parameter vector; vec(·) represents the vectorization of the function implementation matrix; and Respectively represent the real part and imaginary part;

[0033] The target parameter vector Θ is obtained by the following formula rp-1s The maximum likelihood estimate of

[0034] in, represents the known second multi-rank subspace; I N represents the N×N dimensional identity matrix; represents the first known multi-rank subspace; S represents the sample covariance matrix; (·) H represents the conjugate transpose.

[0035] Furthermore, the detection threshold T is set according to the preset false alarm probability, including: setting the false alarm probability to P fa According to the Monte Carlo method, based on the 100 / P accumulated in the early stage fa The detection threshold T is calculated based on the measured clutter data.

[0036] Furthermore, if the actual amount of pure clutter measured data R is less than 100 / P fa , then the missing (100 / P fa -R) clutter data can be obtained by simulation using a clutter simulation model, wherein the model parameters are reasonably estimated and set based on the obtained pure clutter measured data.

[0037] The beneficial effects of the present invention are:

[0038] 1) Efficient closed-form detector: The detector constructed by the present invention has a closed-form statistical expression, which avoids complex iterative operations, significantly reduces the algorithm calculation complexity, and facilitates engineering implementation.

[0039] 2) Computational efficiency advantage: Compared with methods such as Rao detection that require explicit calculation of complex Fisher information matrices, the present invention significantly reduces implementation complexity and has better real-time performance and deployment convenience in engineering applications.

[0040] 3) Small sample adaptive detection capability: By making full use of the skew-symmetric information of the clutter covariance matrix, the present invention significantly improves the estimation accuracy of the unknown clutter covariance matrix, reduces the dependence on the amount of training data, and improves the detection performance of weak targets, especially in the case of scarce training data, providing effective support for the robust detection of distance-extended targets under small sample conditions.

[0041] 4) Intelligent anti-interference performance: The proposed detector can adaptively suppress interference signals of different intensities in structured interference environments, possessing strong intelligent anti-interference capabilities and improving detection reliability in complex electromagnetic environments.

[0042] 5) Wide Applicability: The present invention is not only applicable to broadband radar detection, but can also be extended to some non-broadband radar application scenarios. For example, low- / medium-resolution radar can be used to detect large targets or groups of spatially adjacent point targets with consistent movement speeds (such as ship formations, aircraft formations, vehicle formations, etc.), which has important military and civilian application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a functional module diagram of a target adaptive fusion detector based on interference subspace suppression according to an embodiment of the present invention;

[0044] Figure 2 This is a flow chart of a target adaptive fusion detection method based on interference subspace suppression according to an embodiment of the present invention;

[0045] Figure 3 This is a comparison chart of detection performance between a target adaptive fusion detection method based on interference subspace suppression according to an embodiment of the present invention and an existing detection method when there is sufficient training data;

[0046] Figure 4 This is a comparison chart of the detection performance of the target adaptive fusion detection method based on interference subspace suppression according to an embodiment of the present invention and the existing detection method when training data is scarce.

[0047] in,

[0048] Figure 3 In the example, N=16, K=15, R=32, p=2, q=2, the false alarm probability P fa =10 -4 ,Interference clutter power ratio ICR=15dB;

[0049] Figure 4 In the example, N=16, K=15, R=16, p=2, q=2, P fa =10 -4 ,ICR=15dB. DETAILED DESCRIPTION

[0050] The present invention will now be discussed with reference to exemplary embodiments. It should be understood that the embodiments discussed are only intended to enable those skilled in the art to better understand and implement the present invention, rather than to imply any limitation on the scope of the present invention.

[0051] As used herein, the term "including" and variations thereof are to be interpreted as open-ended terms meaning "including, but not limited to." The term "based on" is to be interpreted as "based, at least in part, on." The terms "one embodiment" and "an embodiment" are to be interpreted as "at least one embodiment."

[0052] The existing wideband radar range-extended target adaptive detector under partially uniform Gaussian background is difficult to balance the CFAR characteristics, detection performance and computational complexity. Considering the problem that the actual clutter non-uniformity makes it difficult to obtain pure clutter training data, how to fully exploit the structural information of the clutter covariance matrix, further reduce the demand for training data volume, and improve the estimation accuracy of the unknown clutter covariance matrix, and then construct a closed-form target adaptive fusion detection method based on interference subspace suppression. While ensuring the CFAR characteristics, it takes into account the multiple requirements of the range-extended target adaptive detection algorithm, such as intelligent anti-interference, computational complexity and detection performance, to improve the adaptive detection performance of multi-channel wideband radar for weak targets in complex interference environments.

[0053] The present invention proposes a target adaptive fusion detection method based on interference subspace suppression, comprising the following steps:

[0054] Step 1, data collection and processing;

[0055] The core tasks of the initial processing stage are data collection and preprocessing, including:

[0056] 1) Construct a test data set Z by collecting echo signals of K range cells to be detected, and construct a training data set Y by selecting echo signals of R adjacent reference cells (i.e., reference range cells);

[0057] 2) For complex scenarios where key parameters such as the clutter covariance matrix M, target coordinate matrix P, interference coordinate matrix Q, and clutter power factor γ are unknown, the unique skew symmetry of the clutter covariance matrix is utilized to perform unitary space transformation on the original test data Z and its associated matrices M, P, and Q. The specific steps are as follows:

[0058] Assume that the radar system collects test data from K adjacent range units. After appropriate sampling and organization, it forms an N×1 dimensional vector, which is expressed as Where N represents the product of the number of antenna elements and the number of pulses, Represents a set of complex matrices of m×n dimensions. The disturbance in the test data consists of clutter components and interference components, which are represented as and t=1,2,...,K. Assume that the interference component j t ,t=1,2,...,K is modeled as a deterministic subspace signal, belonging to the first multi-rank subspace known Represented as j t =Jq t ,in t=1,2,...,K represents the unknown complex coordinate vector of the interference signal; and the clutter component c t ,t=1,2,...,K are independent and identically distributed among different distance units and obey the zero-mean circularly symmetric complex Gaussian distribution with covariance matrix γM, that is, Wherein, the clutter covariance matrix M is an unknown Hermitian positive definite matrix, and γ>0 represents the scaling factor (i.e., clutter power factor) used to describe the unknown power mismatch between the test data and the training data. In addition, assuming that the target signal s t ,t=1,2,...,K is also modeled as a deterministic subspace signal, belonging to the known multi-rank subspace Indicated as s t =Hp t ,in Represents the unknown complex coordinate vector of the target signal. To facilitate subsequent derivation, define In order to estimate the unknown clutter covariance matrix M, it is assumed that there is a set of training data containing only clutter components, which is usually collected from R adjacent reference cells adjacent to the range cell to be measured, denoted as where y l =c l , l=1,2,...,R is also independent and identically distributed and satisfies

[0059] Based on the Gradient test criterion, a target adaptive fusion detector based on interference subspace suppression is constructed. The one-step Gradient test decision formula of the complex signal can be expressed as

[0060]

[0061] Among them, λ 1S-Gradient represents the test statistic; T 1S-Gradient Represents the detection threshold; test data set Target coordinate matrix Interference coordinate matrix γ represents the clutter power factor; Θ r Indicates relevant parameters, Θ s represents the interference parameter, represents the maximum likelihood estimate of Θ under the assumption H0, Represents Θ r The maximum likelihood estimate under the H1 assumption, Θ r0 Represents Θ r True value under the H0 hypothesis; superscript (·) T represents the transpose, and the vec(·) function realizes the vectorization of the matrix; it should be noted that under the H0 assumption, the target does not exist, so Θ r0 =0 pK×1 .f i (Z,Y|M,iP,Q,γ) represents the assumption that H i , i = 0, 1, the joint conditional probability density function of the test data Z and the training data Y. Based on the statistical independence between the test data and the training data, the joint conditional probability density function can be expressed as:

[0062] f i (Z,Y|M,iP,Q,γ)={π N(K+R) γ NK |M| K+R} -1 ×exp[-tr(M -1 T i )],i=0,1 (2)

[0063] in, S=YY H , B i =[iH,J],D=[P T , Q T ] T ; |·| represents the determinant of a square matrix, the tr(·) function represents the trace of a square matrix, the exp(·) function represents the exponential operation, and the superscript (·) H represents the conjugate transpose; the condition p+q≤N must be satisfied to ensure that B=[H,J] is a column-full rank augmented matrix. In addition, by utilizing the skew symmetry of M, we can deduce:

[0064]

[0065] Among them, the superscript (·) * represents conjugation. Therefore, (2) can be rewritten as:

[0066] f i (Z,Y|M,iP,Q,γ)={π N(K+R) γ NK |M| K+R} -1 ×exp[-tr(M -1 T ip )],i=0,1 (4)

[0067] in, and

[0068]

[0069] In the above formula, and denotes the real and imaginary parts, respectively, and

[0070]

[0071] Step 2: Under the assumption of no target, solve the maximum likelihood estimation of the clutter covariance matrix M and the interference coordinate matrix Q; under the assumption of target, solve the target parameter vector Θ rp-1s The maximum likelihood estimate of Z and Y is used to estimate the target parameter vector Θ using the complex Gaussian joint probability density function of Z and Y. rp-1s Obtain the partial derivative, then substitute the maximum likelihood estimate of the clutter covariance matrix M and the interference coordinate matrix Q obtained under the no-target assumption into the derivative result; then substitute this result and the maximum likelihood estimate of the target parameter vector under the target assumption into the range-extended target gradient detection statistic, and finally, combine the maximum likelihood estimate of the clutter power factor γ under the no-target assumption to construct the detection statistic λ of the target adaptive fusion detection method based on interference subspace suppression. The specific steps include:

[0072] To simplify the representation, first let in,

[0073]

[0074] The skew-symmetric one-step gradient (abbreviated as P1S-Gradient) test decision formula in (1) can be rewritten as:

[0075]

[0076] in, Represents Θ p-1sThe maximum likelihood estimation under the H0 hypothesis is: Represents Θ rp-1s Maximum likelihood estimation under the H1 hypothesis.

[0077] Next, under the H1 assumption, the natural logarithm of (4) with respect to Θ rp-1s Taking partial derivatives, we can get:

[0078]

[0079] Under the H0 hypothesis, let the derivative of (4) with respect to M equal to zero, and we can get p The maximum likelihood estimate of M under the conditions of and γ:

[0080]

[0081] The result obtained by (9) Replacing the unknown true covariance matrix M in (4), we can obtain:

[0082]

[0083] Among them, I m represents the m×m dimensional identity matrix. Let (10) be the value of Q p Find the partial derivative and set the result to zero, and you can get Q under the H0 hypothesis p The maximum likelihood estimate of :

[0084]

[0085] in, Substituting (11) into (9) and using the matrix inversion lemma, we can obtain The inverse matrix of :

[0086]

[0087] in,

[0088] Then, substituting (11) and (12) into (8), we can obtain:

[0089]

[0090] in, Similarly, under the H1 assumption, let (4) find the partial derivative with respect to M and set the result to zero, and we can get p The maximum likelihood estimate of M under the conditions of and γ:

[0091]

[0092] Then, substituting (14) into (4), we can obtain:

[0093]

[0094] Let (15) be D p Find the partial derivative and set the result to zero, and we can get D under the assumption H1 p The maximum likelihood estimate of :

[0095]

[0096] in, According to (5), P p The maximum likelihood estimation under the assumption H1 can be derived as:

[0097]

[0098] Therefore, we can directly get Θ under the H1 assumption rp-1s The maximum likelihood estimate of is:

[0099]

[0100] Substituting (13) and (18) into (7), and performing some algebraic operations and simplifications, we can obtain the P1S-Gradient test statistic under a given γ condition:

[0101]

[0102] In order to determine the final test statistic in PHE, it is also necessary to solve the maximum likelihood estimate of γ under the hypothesis H0 is the only positive solution of equation (20):

[0103]

[0104] Among them, υ represents the unknown quantity, s=min(N,2K), λ k，0 yes Therefore, the P1S-Gradient test statistic in PHE (abbreviated as P1S-Gradient-PHE) can be expressed as:

[0105]

[0106] in,

[0107] The method of the present invention constructs a target adaptive fusion detector based on interference subspace suppression. As can be seen from formula (21), the method has a closed-form detection statistic expression, which avoids the complex iterative calculation process. Compared with the P2S-Rao-PHE detector, the proposed method does not need to calculate the Fisher information matrix during the solution process, which significantly reduces the difficulty of algorithm implementation and improves the feasibility of engineering application. It is particularly worth noting that compared with the P2S-GLRT-PHE detector for range-extended targets, the present method has significant advantages in the following two aspects: first, the algorithm calculation complexity is significantly reduced; second, the detection performance of weak targets is better, especially in the case of scarce training data. In summary, the target adaptive fusion detection method based on interference subspace suppression of the present invention achieves an optimal balance among algorithm efficiency, anti-interference ability and detection performance while maintaining the CFAR characteristics, providing an effective solution for weak target detection in complex electromagnetic environments.

[0108] In step 3, to meet the CFAR characteristics of the detection algorithm, a detection threshold is determined based on a preset false alarm probability. Target discrimination is performed by comparing the detection statistic with the threshold. When the detection statistic exceeds the threshold, it is confirmed that a target with extended range exists in the detection unit. At this point, the test sample will no longer participate in the training data screening of subsequent adjacent detection units. Conversely, if the detection statistic is below the threshold, the unit is determined to have no target. The sample will be retained in the training sample set to provide a reference for subsequent detection units.

[0109] Example 1

[0110] Figure 1 This is a functional module diagram of a target adaptive fusion detector based on interference subspace suppression according to an embodiment of the present invention; Figure 2 This is a flow chart of a target adaptive fusion detection method based on interference subspace suppression according to an embodiment of the present invention. Figure 1-2 As shown, according to one embodiment of the present invention, a target adaptive fusion detection method based on interference subspace suppression includes the following steps:

[0111] Step 1-1, obtain test data Z from K distance units to be detected, obtain training data Y from R reference distance units adjacent to the distance unit to be detected; obtain skew-symmetric transformation test data Z based on test data Z p ;

[0112] Step 1-2, based on the training data Y and the skew-symmetric transformation test data Z p Get respectively: Maximum likelihood estimation of the clutter covariance matrix under the no-target assumption Maximum Likelihood Estimation of the Disturbance Coordinate Matrix Maximum Likelihood Estimation of Clutter Power Factor Skew symmetric transformation test data Z under target assumption p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result and target parameter vector Θ rp-1s The maximum likelihood estimate of

[0113] Step 2, based on the data obtained in step 1 (step 1-1 and step 1-2) For the target parameter vector Θ r The derivation result of ), construct the detection statistic λ of the target adaptive fusion detection method based on interference subspace suppression;

[0114] In step 2, the detection statistic λ is constructed using the following formula:

[0115]

[0116] Among them, λ P1S-Gradient-PHE represents the P1S-Gradient test statistic in PHE; tr[·] represents the trace of the square matrix; I 2K represents the 2K×2K dimensional identity matrix; (·) H represents conjugate transpose; (·) * represents conjugate; S represents the sample covariance matrix; D N Represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; I N represents the N×N dimensional identity matrix; The first known multi-rank subspace The second most rank subspace known p+q≤N; N represents the product of the number of antenna elements and the number of pulses; Represents a set of complex matrices of m×n dimensions;

[0117] Step 3: Set a detection threshold T according to a preset false alarm probability; compare the detection statistic λ with the detection threshold T; if λ≥T, determine that there is a range extension target in the current K range units to be detected, and the test data is not used as training data for subsequent other range units to be detected; if λ<T, determine that there is no range extension target in the current K range units to be detected, and the test data is used as training data for subsequent other range units to be detected.

[0118] In this embodiment, a target adaptive fusion detection method based on interference subspace suppression is proposed, which realizes distance extended target detection in complex environments through multi-step collaboration. First, in step 1 (including step 1-1 and step 1-2), test data Z is obtained from the K range cells to be detected, and training data Y is extracted from the adjacent R reference cells; the test data Z is subjected to a skew-symmetric transformation to enhance the signal characteristics. Based on the training data Y and the skew-symmetric transformation test data Z p , respectively obtain the maximum likelihood estimate of the clutter covariance matrix under the no-target assumption Maximum Likelihood Estimation of the Disturbance Coordinate Matrix Maximum Likelihood Estimation of Clutter Power Factor Skew symmetric transformation test data Z under target assumption p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result and target parameter vector Θ rp-1s The maximum likelihood estimate of In step 2, the parameters obtained in step 1 ( For the target parameter vector Θ r The derivation result of ) Input the target adaptive fusion detector construction module based on interference subspace suppression, build the target adaptive fusion detection method based on interference subspace suppression, and calculate the P1S-Gradient test statistic λ in PHE P1S-Gradient-PHE Finally, step 3 sets a detection threshold T based on the preset false alarm probability. By comparing the detection statistic with T, it adaptively determines whether there is a range-extended target in the current K range cells. If the detection statistic exceeds the detection threshold, it is determined that there is a range-extended target and the current test data is excluded from subsequent training data. If it does not exceed the detection threshold, the current test data is used as training data for other range cells to be detected.

[0119] The present invention significantly improves the detection performance of extended-range targets in complex clutter environments. Its technical effects are as follows: 1) skew-symmetric transformation and multi-rank subspace constraints effectively suppress non-uniform clutter and interference, reducing false alarm rates; 2) the combination of joint probability density function derivatives and maximum likelihood estimation achieves high-precision estimation of target parameters; 3) an adaptive threshold decision mechanism dynamically adjusts the detection strategy to avoid the impact of target signals on subsequent training data, improving the stability of multi-frame detection. The present invention performs well in non-Gaussian clutter, low signal-to-noise ratio, and strong interference scenarios, and is suitable for fields such as radar and sonar that require precise target positioning and background suppression.

[0120] According to an embodiment of the present invention, in step 1, the skew symmetric transformation test data Z is obtained based on the test data Z. p, including: obtaining the skew symmetric transformation test data Z through the following formula p :

[0121]

[0122] Among them, z k represents the N×1 dimensional test data component corresponding to the kth unit to be detected; D N represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; (·)* represents conjugation; Represents a set of N×2K dimensional complex matrices; Represents a set of N×1 complex matrices.

[0123] In this embodiment, the test data Z is transformed according to formula (5) and formula (6) to obtain the skew-symmetrical transformed test data Z p , mapping the original data into a feature space with prior structural information, providing structured data support for subsequent interference suppression and target detection.

[0124] The present invention effectively embeds the prior structure information of the clutter covariance matrix through skew-symmetric transformation, significantly improving the detection performance of range-extended targets in complex clutter backgrounds, while reducing the demand for pure clutter training data and achieving efficient suppression of interference signals while maintaining the constant false alarm rate (CFAR) characteristic.

[0125] According to one embodiment of the present invention, the maximum likelihood estimate of the clutter covariance matrix under the no-target assumption is obtained by the following formula:

[0126]

[0127] T i =S+(ZB i D)(ZB i D) H / γ

[0128] B i =[iH,J]

[0129] D=[P T ,Q T ] T

[0130] Where i = 0, 1; D N represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; γ represents the clutter power factor; the sample covariance matrix S = YY H ; P represents the target coordinate matrix, Q represents the interference coordinate matrix; (·)* represents conjugate; (·) H represents conjugate transpose;

[0131] The maximum likelihood estimate of the interference coordinate matrix is obtained by the following formula

[0132]

[0133] in,

[0134] The maximum likelihood estimate of the clutter power factor is obtained by solving the unique positive solution of the following formula:

[0135] Where, s = min(N, 2K); υ represents the unknown quantity; λ k，0 express The kth eigenvalue of I N Represents the N×N dimensional identity matrix.

[0136] In this embodiment, in the maximum likelihood estimation solution module under the H0 hypothesis, M and Q under the H0 hypothesis are obtained according to formula (9), formula (11) and formula (20). p and the maximum likelihood estimate of γ and Under the given interference subspace constraints, the statistical characteristics of clutter and power parameters are jointly estimated synchronously, providing a parameterized clutter background model for the subsequent construction of detection statistics.

[0137] The present invention can maintain stable interference suppression performance under the condition of limited training data volume. At the same time, the closed-form solution design avoids iterative optimization calculations and effectively balances detection performance and algorithm complexity.

[0138] According to one embodiment of the present invention, the skew symmetric transformation test data Z under the target assumption is obtained by the following formula: p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result of :

[0139]

[0140]

[0141] Where M represents the clutter covariance matrix; P represents the target coordinate matrix, Q represents the interference coordinate matrix, γ represents the clutter power factor; Θ rp-1s represents the target parameter vector; vec(·) represents the vectorization of the function implementation matrix; and Respectively represent the real part and imaginary part,

[0142] The target parameter vector Θ is obtained by the following formula rp-1s The maximum likelihood estimate of

[0143] in, represents the known second multi-rank subspace; I N represents the N×N dimensional identity matrix; represents the first known multi-rank subspace; S represents the sample covariance matrix; (·) H represents the conjugate transpose.

[0144] In this embodiment, in the derivative module of the probability density function under the H1 hypothesis, the test data Z under the H1 hypothesis is obtained according to formula (13): p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result of ; In the maximum likelihood estimation solution module under the H1 assumption, according to formula (18) we obtain Θ under the H1 assumption rp-1s The maximum likelihood estimate of

[0145] The present invention significantly improves the target parameter estimation accuracy and anti-interference capability in complex electromagnetic environments by jointly optimizing skew-symmetric transformation data and subspace model parameters.

[0146] According to an embodiment of the present invention, the detection threshold T is set according to the preset false alarm probability, including: setting the false alarm probability to P fa According to the Monte Carlo method, based on the 100 / P accumulated in the early stage fa The detection threshold T is calculated based on the measured clutter data.

[0147] Preferably, if the amount of pure clutter measured data R actually obtained is less than 100 / P fa , then the missing 100 / P fa -R clutter data can be obtained by simulation using a clutter simulation model, where the model parameters are reasonably estimated and set based on the obtained pure clutter measured data.

[0148] In this embodiment, first, according to the preset false alarm probability P fa Determine the sample size required for theoretical threshold calculation 100 / P fa , and give priority to using the R measured clutter unit data accumulated in the early stage to build the initial sample library. faWhen the system automatically triggers the simulation data generation module: Based on the statistical characteristics of the existing measured data, a parametric modeling method is used to generate 100 / P fa -R simulated clutter samples are generated by mixing measured and simulated data to form a complete sample set. Subsequently, the Monte Carlo method is used to conduct multiple independent sampling tests on the mixed sample set. Statistical tests are performed to ensure the distribution consistency of the simulated and measured data. Finally, the detection threshold T is calculated based on the empirical cumulative distribution function.

[0149] The present invention adopts a data enhancement strategy of collaborative measurement and simulation, which not only breaks through the application bottleneck of large demand for pure measured data, but also ensures the credibility of simulation data through parameter calibration. While ensuring the constant false alarm rate (CFAR) characteristics, it significantly improves the reliability of weak target detection in strong clutter background.

[0150] Example 2

[0151] According to one embodiment of the present invention, a target adaptive fusion detection method based on interference subspace suppression of the present invention is applied to a sea detection environment, and its specific implementation includes the following steps:

[0152] Step A1: Use the sea detection radar to illuminate the sea area to be detected and obtain the test data Z of K distance units to be detected; and illuminate the target-free range around the sea area to be detected and obtain the training data Y of R reference distance units containing only pure sea clutter. The test data Z and training data Y are sent to the data transformation module; in the data transformation module, the skew-symmetric transformation test data Z is obtained according to equations (5) and (6). p ; Transform the skew symmetric test data Z p The training data Y is sent to the maximum likelihood estimation solution module under the H0 hypothesis, the probability density function derivation module under the H1 hypothesis, and the maximum likelihood estimation solution module under the H1 hypothesis; in the maximum likelihood estimation solution module under the H0 hypothesis, M and Q under the H0 hypothesis are obtained according to formula (9), formula (11) and formula (20) respectively. p and the maximum likelihood estimate of γ and In the derivative module of the probability density function under the H1 hypothesis, the test data Z under the H1 hypothesis is obtained according to formula (13): p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result of ; In the maximum likelihood estimation solution module under the H1 assumption, according to formula (18) we obtain Θ under the H1 assumption rp-1s The maximum likelihood estimate of

[0153] It is worth noting that in step A1, considering that external interference in the actual ocean environment may adversely affect the adaptive detection of range-extended targets, the target adaptive fusion detection model based on interference subspace suppression constructed by the method of the present invention takes external interference into account during the detector design process and uses subspace signals to model the interference to reduce the possible mismatch effect of the interference signal. In the presence of subspace-structured interference environments, the intelligent detection method of range-extended targets with gradients can effectively suppress interference signals of varying intensities, demonstrating good intelligent anti-interference capabilities. Furthermore, the detector of the present method is applicable to non-uniform sea clutter environments, such as partially uniform ones. By fully exploiting the local uniformity of sea clutter and utilizing the maximum likelihood estimation of the clutter power factor under the no-target assumption, the detector's intelligent adaptability to non-uniform sea clutter environments is improved.

[0154] Step A2 sends the results obtained by the maximum likelihood estimation solution module under the H0 assumption, the derivative module of the probability density function under the H1 assumption, and the maximum likelihood estimation solution module under the H1 assumption to the target adaptive fusion detector construction module based on interference subspace suppression, constructs the detection statistic λ of the target adaptive fusion detection method based on interference subspace suppression according to formula (21), and sends λ to the detection decision module.

[0155] Notably, in step A2, the proposed method achieves superior detection performance compared to detectors such as P2S-GLRT-PHE and P2S-Rao-PHE for range-extended targets, particularly when training data is scarce. Furthermore, the proposed adaptive fusion detector for targets based on interference subspace suppression has a closed-form expression. Compared to existing adaptive detection methods for range-extended targets, this method maintains the CFAR characteristics while striking a reasonable balance between detection performance and computational complexity, thereby enhancing the adaptive detection capabilities of multi-channel broadband radars for small, weak targets on the sea surface in complex electromagnetic environments.

[0156] Step A3 sets the detection threshold T according to the preset false alarm probability: Specifically, the false alarm probability is set to P fa According to the Monte Carlo method, based on the 100 / P accumulated in the early stage fa The detection threshold T is calculated based on the measured sea clutter data. Considering the difficulty of obtaining sea clutter, if the actual amount of pure sea clutter measured data R is less than 100 / P fa , then the missing 100 / P fa-R clutter data can be simulated using a sea clutter simulation model, where the model parameters are reasonably estimated and set based on the obtained pure sea clutter measured data. Furthermore, the detection statistic λ is compared with the detection threshold T. If λ≥T, it is determined that the current K range cells to be detected have a range-extended target, and the test data is not used as training data for the subsequent range cells to be detected. Conversely, if λ<T, it is determined that the current K range cells to be detected do not have a range-extended target, and the test data is used as training data for the subsequent range cells to be detected.

[0157] The performance comparison results of the detector when there is sufficient training data are shown in the attached Figure 3 The results show that compared with existing detectors for range extended targets such as P2S-GLRT-PHE and P2S-Rao-PHE, the detector proposed in this paper has better detection performance when there is sufficient training data.

[0158] Example 3

[0159] According to one embodiment of the present invention, a target adaptive fusion detection method based on interference subspace suppression of the present invention is applied to a ground detection environment, and its specific implementation includes the following steps:

[0160] Step B1 uses a ground detection radar to illuminate the area to be detected and obtain test data Z of K range units to be detected; radar is used to illuminate the target-free range around the area to be detected and obtain training data Y of R reference range units containing only pure ground clutter. The test data Z and training data Y are sent to the data transformation module; in the data transformation module, the skew-symmetric transformation test data Z is obtained according to equations (5) and (6): p ; Transform the skew symmetric test data Z p The training data Y is sent to the maximum likelihood estimation solution module under the H0 hypothesis, the probability density function derivation module under the H1 hypothesis, and the maximum likelihood estimation solution module under the H1 hypothesis; in the maximum likelihood estimation solution module under the H0 hypothesis, M and Q under the H0 hypothesis are obtained according to formula (9), formula (11) and formula (20) respectively. p and the maximum likelihood estimate of γ and In the derivative module of the probability density function under the H1 hypothesis, the test data Z under the H1 hypothesis is obtained according to formula (13): p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result of ; In the maximum likelihood estimation solution module under the H1 assumption, according to formula (18) we obtain Θ under the H1 assumption rp-1s The maximum likelihood estimate of

[0161] It is worth noting that in step B1, considering that there may be external interference in the actual geographical environment that has an adverse effect on the adaptive detection of distance-extended targets, the target adaptive fusion detection model based on interference subspace suppression constructed by the method of the present invention takes external interference into account in the detector design process and uses subspace signals to model the interference to reduce the possible mismatch effect of the interference signal. For interference environments with subspace structure, the intelligent detection method of gradient targets for distance-extended targets of the present invention can effectively suppress interference signals of different intensities and has good intelligent anti-interference performance. At the same time, the detector of the method of the present invention can be applied to non-uniform ground clutter environments such as partially uniform. By fully exploiting the local uniformity of ground clutter and using the maximum likelihood estimation of the clutter power factor under the assumption of no target, the intelligent adaptability of the detector to non-uniform ground clutter environments is improved.

[0162] Step B2 sends the results obtained by the maximum likelihood estimation solution module under the H0 assumption, the derivative module of the probability density function under the H1 assumption, and the maximum likelihood estimation solution module under the H1 assumption to the target adaptive fusion detector construction module based on interference subspace suppression, constructs the detection statistic λ of the target adaptive fusion detection method based on interference subspace suppression according to formula (21), and sends λ to the detection decision module.

[0163] Notably, in step B2, the proposed method achieves superior detection performance compared to detectors such as P2S-GLRT-PHE and P2S-Rao-PHE for range-extended targets, particularly when training data is scarce. Furthermore, the proposed adaptive fusion target detector based on interference subspace suppression has a closed-form expression. Compared to existing adaptive detection methods for range-extended targets, this method maintains the CFAR characteristics while striking a reasonable balance between detection performance and computational complexity, thereby enhancing the adaptive detection capabilities of multi-channel broadband radars for small, weak ground targets in complex electromagnetic environments.

[0164] Step B3 sets the detection threshold T according to the preset false alarm probability: Specifically, the false alarm probability is set to P fa According to the Monte Carlo method, based on the 100 / P accumulated in the early stage fa The detection threshold T is calculated based on the measured ground clutter data. Considering the difficulty of obtaining ground clutter, if the amount of pure ground clutter measured data R actually obtained is less than 100 / P fa , then the missing 100 / P fa-R clutter data can be simulated using a ground clutter simulation model, where the model parameters are reasonably estimated and set based on the obtained pure ground clutter measured data. Furthermore, the detection statistic λ is compared with the detection threshold T. If λ≥T, it is determined that the current K range cells to be detected have a range-extended target, and the test data is not used as training data for the subsequent range cells to be detected. Conversely, if λ<T, it is determined that the current K range cells to be detected do not have a range-extended target, and the test data is used as training data for the subsequent range cells to be detected.

[0165] The comparison results of detector performance when training data is scarce are shown in the attached Figure 4 The results show that compared with existing detectors for range extended targets such as P2S-GLRT-PHE and P2S-Rao-PHE, the detector proposed in this paper has better detection performance when training data is scarce.

[0166] The above description is merely a preferred embodiment of the present application and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of the invention herein is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, but also encompasses other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the inventive concept. For example, a technical solution formed by replacing the above-mentioned features with (but not limited to) technical features having similar functions disclosed in this application.

[0167] It should be understood that the size of the serial numbers of each step in the content of the invention and the embodiments of the present invention does not absolutely mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

Claims

1. A target adaptive fusion detection method based on interference subspace suppression, characterized in that: The following steps are involved: Step 1: Get test data Z from K distance units to be detected, and get training data Y from R reference distance units adjacent to the distance unit to be detected; get skew-symmetric transformation test data Z based on test data Z p ; Based on the training data Y and the skew-symmetric transformation test data Z p Get respectively: Maximum likelihood estimation of the clutter covariance matrix under the no-target assumption Maximum Likelihood Estimation of the Disturbance Coordinate Matrix Maximum Likelihood Estimation of Clutter Power Factor Skew symmetric transformation test data Z under target assumption p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result and target parameter vector Θ rp-1s The maximum likelihood estimate of Step 2: Based on the data obtained in step 1, construct a detection statistic λ of the target adaptive fusion detection method based on interference subspace suppression; In step 2, the detection statistic λ is constructed using the following formula: Among them, λ P1S-Gradient-PHE represents the P1S-Gradient test statistic in PHE; tr[·] represents the trace of the square matrix; I 2K represents the 2K×2K dimensional identity matrix; (·) H represents the conjugate transpose; (·) * represents conjugate; S represents the sample covariance matrix; D N Represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; I N represents the N×N dimensional identity matrix; The first known multi-rank subspace The second most rank subspace known p+q≤N; N represents the product of the number of antenna elements and the number of pulses; Represents a set of complex matrices of m×n dimensions; Step 3: Set a detection threshold T according to a preset false alarm probability; compare the detection statistic λ with the detection threshold T; if λ≥T, determine that there is a range extension target in the current K range units to be detected, and the test data is not used as training data for subsequent other range units to be detected; if λ<T, determine that there is no range extension target in the current K range units to be detected, and the test data is used as training data for subsequent other range units to be detected.

2. The target adaptive fusion detection method based on interference subspace suppression according to claim 1 is characterized in that: In step 1, the skew-symmetric transformation test data Z is obtained based on the test data Z p , including: obtaining the skew symmetric transformation test data Z through the following formula p : Among them, z k represents the N×1 dimensional test data component corresponding to the kth unit to be detected; D N represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; (·) * indicates conjugation; Represents a set of N×2K dimensional complex matrices; Represents a set of N×1 complex matrices.

3. The target adaptive fusion detection method based on interference subspace suppression according to claim 2 is characterized in that: The maximum likelihood estimate of the clutter covariance matrix under the no-target assumption is obtained by the following formula: : T i =S+(Z-B i D)(Z-B i D) H / γ B i =[iH,J] D=[P T ,Q T ] T Where i = 0, 1; D N represents an N×N permutation matrix with all diagonal elements set to 1 and all other elements set to 0; γ represents the clutter power factor; the sample covariance matrix S = YY H ; P represents the target coordinate matrix, Q represents the interference coordinate matrix; (·)* represents conjugate; (·) H represents the conjugate transpose; (·) T represents transpose; The maximum likelihood estimate of the interference coordinate matrix is obtained by the following formula : in, The maximum likelihood estimate of the clutter power factor is obtained by solving the unique positive solution of the following formula: : Where, s = min(N, 2K); υ represents the unknown quantity; λ k，0 express The kth eigenvalue of I N Represents the N×N dimensional identity matrix.

4. The target adaptive fusion detection method based on interference subspace suppression according to claim 2, characterized in that: Obtain the skew symmetric transformation test data Z under the target assumption through the following formula p The complex Gaussian joint probability density function of the training data Y is the target parameter vector Θ r The derivative result of : Where M represents the clutter covariance matrix; P represents the target coordinate matrix, and Q represents the interference coordinate matrix; γ represents the clutter power factor; Θ rp-1s represents the target parameter vector; vec(·) represents the vectorization of the function implementation matrix; and Respectively represent the real part and imaginary part; The target parameter vector Θ is obtained by the following formula rp-1s The maximum likelihood estimate of : in, represents the known second multi-rank subspace; I N represents the N×N dimensional identity matrix; represents the first known multi-rank subspace; S represents the sample covariance matrix; (·) H represents the conjugate transpose.

5. The target adaptive fusion detection method based on interference subspace suppression according to claim 1 is characterized in that: The detection threshold T is set according to the preset false alarm probability, including: setting the false alarm probability to P fa According to the Monte Carlo method, based on the 100 / P accumulated in the early stage fa The detection threshold T is calculated based on the measured clutter data.

6. The target adaptive fusion detection method based on interference subspace suppression according to claim 5, characterized in that: If the actual amount of pure clutter measured data R is less than 100 / P fa , then the missing (100 / P fa -R) clutter data can be obtained by simulation using a clutter simulation model, wherein the model parameters are reasonably estimated and set based on the obtained pure clutter measured data.

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