Target Subspace Fusion Detection Method under Partially Uniform Clutter

Abstract

This invention belongs to the field of radar signal processing technology, specifically relating to a target subspace fusion detection method under partially uniform clutter. It fully utilizes the prior information of the oblique-symmetric structure of the clutter covariance matrix, and jointly uses master data and auxiliary data to improve the estimation accuracy of the unknown oblique-symmetric covariance matrix structure of the clutter, reducing the requirement for auxiliary data and providing favorable support for the realization of target subspace fusion detection under partially uniform clutter. A partially uniform clutter subspace oblique-symmetric Gradient test detector is constructed, which does not require solving the Fisher information matrix, has low computational complexity, and a simple detection statistic structure, making it easy to implement in engineering. Its detection performance is superior to existing unstructured range-extended target subspace detectors.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a target subspace fusion detection method under partially uniform clutter. Background Technology

[0002] Radar target detection is the process of determining whether a target exists within a specific area, which can generally be described as a binary hypothesis testing problem. With the continuous development of electronic science and radar technology, modern radar systems have increasingly sophisticated target imaging, recognition, and tracking functions. However, target detection remains one of the most important and fundamental functions of radar, and is the basis for subsequent target imaging, recognition, and tracking processes. Therefore, radar target detection remains a crucial research area in radar signal processing. The increasingly complex external environment places higher demands on radar target detection. With the continuous increase in radar bandwidth, target detection in high-range resolution radar has gradually become a popular research area. Unlike the "point target" model of traditional narrowband radar, the echo signal of a target in high-range resolution radar may extend into different radial range cells, forming a "range-extended target." If a traditional "point target" detector based on estimating the unknown clutter statistical characteristics using neighboring reference cells is still used, the strong scattering energy of the target will leak into neighboring range cells, forming a "signal pollution" phenomenon, which will greatly affect detection performance and may even lead to complete detector failure.

[0003] In a homogeneous environment, the clutter covariance matrix of the target cell data and the training samples is the same. However, due to rapidly changing terrain, the clutter in the target cell data and the training samples may not have exactly the same statistical properties. A partially homogeneous environment is a widely used non-homogeneous environment that extends the homogeneous environment by introducing an unknown scaling factor between the target cell data and the training samples. The partially homogeneous environment effectively describes the environment of airborne radar with a small number of training samples and is also suitable for wireless communication over multiple interference sources. Furthermore, in commonly used rank-one signal target detection models, the target's steering vector is usually assumed to be a known, fixed vector. However, in practical applications, due to beam pointing errors and multipath propagation, the target's steering vector may be mismatched. To address this issue, a multi-rank subspace model can be considered for modeling the target signal. In the multi-rank subspace model, the signal is represented as the product of a known multi-rank subspace matrix and an unknown coordinate matrix. Under the range-extended target subspace model, using the generalized likelihood ratio test (GLRT), Gradient test, and Rao test, subspace range-extended target detectors based on GLRT, Rao, and two-step methods can be obtained (abbreviated as S-GLRT, S-Gradient, S-Rao, and S-2SD, respectively). In real-world clutter environments, there may be situations with limited auxiliary data and small sample sizes. In such environments, the detection performance of existing detectors will be significantly reduced, making it difficult to achieve ideal detection results. In real-world environments, it is difficult to obtain sufficient pure clutter auxiliary data, and for radar receivers using centrosymmetric linear arrays or centrosymmetric spaced pulse trains, their clutter covariance matrix exhibits a special oblique-symmetric structure. Compared to S-GLRT, S-Gradient, S-Rao, and S-2SD detectors, detectors incorporating oblique-symmetric clutter structured information show a certain performance improvement.

[0004] Currently, most range-extended target detector designs do not consider utilizing clutter structured information, leading to performance degradation in small sample sizes with limited auxiliary data. To address this performance degradation issue under small sample conditions, the key to improving target subspace fusion detection methods under partially uniform clutter is to fully utilize prior clutter information, improve the estimation accuracy of unknown clutter covariance matrices, and construct a subspace range-extended target intelligent detector using superior verification criteria. This approach aims to reduce the need for auxiliary data while ensuring the detector's constant false alarm rate (CFAR) characteristics. It is also one of the urgent challenges that needs to be addressed. Summary of the Invention

[0005] To overcome the problems in the prior art, this invention proposes a target subspace fusion detection method under partially uniform clutter.

[0006] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0007] A method for target subspace fusion detection under partially uniform clutter includes the following steps:

[0008] Step 1. Obtain main data Z from K distance cells to be detected, and obtain auxiliary data Z from R distance cells adjacent to the distance cells to be detected. R Under the assumption of no objective, using the master data Z and auxiliary data Z R The maximum likelihood estimate of the unknown clutter oblique-symmetric covariance matrix structure under the no-target assumption is obtained by taking the derivative of the logarithm of the joint probability density function with respect to the clutter covariance matrix M and setting it to zero; under the target assumption, the main data Z and auxiliary data Z are used. R The logarithm of the joint probability density function is given by the components Θ of the target's coordinate matrix in the subspace. r Find the partial derivative;

[0009] Step 2. Under the assumption of a target, utilize the master data Z and the auxiliary data Z R The maximum likelihood estimate of the unknown clutter oblique-symmetric covariance matrix structure under the objective assumption is obtained by taking the derivative of the logarithm of the joint probability density function with respect to the clutter covariance matrix M and setting it to zero. Under the objective assumption, the main data Z and auxiliary data Z are used. R Taking the partial derivative of the logarithm of the joint probability density function with respect to the coordinate matrix components of the target in the subspace and setting the derivative to zero, we obtain the maximum likelihood estimate of the coordinate matrix components with a target; solving for the maximum likelihood estimate of γ0 under the assumption of no target. Construct the detection statistic t PS-Gradient-PHE ;

[0010] Step 3. Set the detection threshold T according to the preset false alarm probability. PS-Gradient-PHE ; Detection statistic t PS-Gradient-PHE With detection threshold T PS-Gradient-PHE Compare, if t PS-Gradient-PHE ≥T PS-Gradient-PHE If t is true, it is determined that a target exists in the current detection range unit, and the master data is not used as auxiliary data for subsequent detection range units; otherwise, if t is false... PS-Gradient-PHE <T PS-Gradient-PHE If no target is found in the current detection range cell, the master data is used as auxiliary data for other detection range cells.

[0011] Furthermore, in step 1, without the objective hypothesis H0, the main data Z and auxiliary data Z are used. R Taking the derivative of the joint probability density function with respect to the clutter skew-symmetric covariance matrix structure and setting it to zero, we obtain the maximum likelihood estimate of the clutter covariance matrix M under the objective assumption H0. for:

[0012]

[0013] in,

[0014]

[0015] Among them, auxiliary data Z R Represented as an N×R dimensional complex matrix Z R =C R =[c K+1 ,c K+2 ,…,c K+R ], c K+k This represents the auxiliary data component corresponding to the (K+k)th reference distance cell; where c is an N×1 dimensional complex vector. t (t=K+1,K+2,…,K+R) follows a complex circular Gaussian distribution with zero mean and covariance matrix of N×N dimensional complex matrix γM, and the auxiliary data components between different distance cells are independent and identically distributed, where γ is a scaling factor; z k b represents the N×1 dimensional main data component corresponding to the k-th distance cell to be detected. k Let represent the complex coordinate vector of the r×1 dimensional target subspace in the k-th range cell to be detected; j is the imaginary unit, · represents the determinant of the square matrix, tr(·) represents the trace of the matrix, and Re(·) and Im(·) represent taking the real and imaginary parts, respectively. and Let represent the set of m×n dimensional real matrices and the set of complex matrices, respectively. H This indicates the conjugate transpose, (·) * Let J denote conjugation, and let J denote an N×N dimensional permutation matrix in which the diagonal elements are 1 and all other elements are 0.

[0016] Furthermore, in step 2, under the assumption of a target, the main data Z and auxiliary data Z are used. R Taking the partial derivative of the logarithm of the joint probability density function with respect to the coordinate matrix components of the target in the subspace and setting the derivative to zero, we obtain the maximum likelihood estimate of the coordinate matrix components with respect to the target:

[0017]

[0018] Among them, the signal multi-rank subspace matrix U has a skew-symmetric structure, that is, it satisfies U = JU * .

[0019] Furthermore, in step 2, the maximum likelihood estimation of γ0 It is the unique positive solution to the following equation:

[0020]

[0021] Where q = min(N, 2K); λ k (k = 1, 2, ..., q) is The k-th non-zero eigenvalue.

[0022] Furthermore, the detection statistic t constructed in step 2 PS-Gradient-PHE :

[0023]

[0024] in,

[0025] Compared with the prior art, the present invention has the following technical effects:

[0026] 1) By fully utilizing the prior information of the oblique symmetric structure of the clutter covariance matrix, and by jointly using master data and auxiliary data, the estimation accuracy of the unknown clutter oblique symmetric covariance matrix structure is improved, the requirement for auxiliary data is reduced, and a favorable support is provided for the realization of target subspace fusion detection under partially uniform clutter.

[0027] 2) A partially uniform clutter-based subspace oblique-symmetric Gradient test detector was constructed. The detector does not require solving the Fisher information matrix, has low computational complexity, and has a simple detection statistic structure, making it easy to implement in engineering. Its detection performance is superior to existing unstructured range-extended target subspace detectors.

[0028] 3) A corresponding detector was designed for a partially uniform clutter environment, which improved the robustness of the high-range resolution radar to non-uniform background clutter.

[0029] 4) The method of the present invention is applicable to some non-wideband radar detection situations, such as using low / medium resolution radar to detect large targets or to detect groups of spatially adjacent point targets moving at the same speed (such as ship formations, aircraft formations, vehicle formations, etc.), and has good application prospects. Attached Figure Description

[0030] Figure 1 This is a functional block diagram of the target subspace fusion detection method under partially uniform clutter according to the present invention;

[0031] Figure 2 This is a comparison chart of the detection performance of the method of the present invention and existing unstructured distance extended target subspace detectors;

[0032] Figure 3 This is a comparison chart of the detection performance of the method of the present invention and existing oblique symmetric distance extended target subspace detectors;

[0033] Figure 2 Given N=12, K=15, R=12, 24, r=3, the false alarm probability P0fa =10 -3 ;

[0034] Figure 3 Given N=12, K=15, R=8, 24, r=3, the false alarm probability P fa =10 -3 . Detailed Implementation

[0035] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0036] In partially uniform clutter scenarios, to address the performance degradation of range-extended target detection in small sample backgrounds, how can we fully utilize prior clutter information to improve the estimation accuracy of unknown clutter covariance matrix? By constructing a subspace range-extended target intelligent detector using superior testing criteria, we can ensure the detector's constant false alarm rate (CFAR) characteristics while reducing the demand for auxiliary data, thereby further enhancing the target subspace fusion detection capability under partially uniform clutter.

[0037] The present invention provides a method for target subspace fusion detection under partially uniform clutter, comprising the following steps:

[0038] Step 1. Obtain main data Z from K distance cells to be detected, and obtain auxiliary data Z from R distance cells adjacent to the distance cells to be detected. R Under the assumption of no objective, using the master data Z and auxiliary data Z R The maximum likelihood estimate of the unknown clutter oblique-symmetric covariance matrix structure under the no-target assumption is obtained by taking the derivative of the logarithm of the joint probability density function with respect to the clutter covariance matrix M and setting it to zero; under the target assumption, the main data Z and auxiliary data Z are used. R The logarithm of the joint probability density function is given by the components Θ of the target's coordinate matrix in the subspace. r Find the partial derivative;

[0039] The specific steps include:

[0040] For a coherent radar system with N joint space-time channels, assuming the target may occupy K consecutive range cells to be detected, the main data corresponding to its echo signal can be represented as an N×K dimensional complex matrix Z = [z1, z2, ..., zk]. K ], z k This represents the N×1 dimensional main data component corresponding to the k-th distance unit to be detected.

[0041] Under the assumption H0 that no target exists, the master data Z contains only an N×K dimensional clutter component complex matrix C = [c1, c2, ..., c K ], where the N×1 dimensional complex vector c k(k = 1, 2, ..., K) represents the clutter component in the k-th range cell to be detected, which follows a complex circular Gaussian distribution with zero mean and covariance matrix of N×N dimension, and the clutter vectors between different range cells are independent and identically distributed.

[0042] Under the assumption H1 that a target exists, the master data Z consists of an N×K dimensional signal component matrix S and a clutter component matrix C; where the signal component matrix S can be represented as the product of a known N×r dimensional multi-rank subspace complex matrix U and an r×K dimensional unknown complex coordinate matrix B, and B = [b1, b2, ..., b K ], b k Let U represent the complex coordinate vector of the r×1 dimensional target subspace in the k-th distance cell to be detected, where r represents the rank of matrix U.

[0043] To estimate the unknown clutter covariance matrix M, R observation data are obtained from R pure clutter reference range cells adjacent to the range cell to be detected, along with auxiliary data Z corresponding to their echo signals. R It can be represented as an N×R dimensional complex matrix Z R =C R =[c K+1 ,c K+2 ,…,c K+R ], c K+k This represents the auxiliary data component corresponding to the (K+k)th reference distance cell. Here, the N×1 dimensional complex vector c... t (t=K+1,K+2,…,K+R) follows a complex circular Gaussian distribution with zero mean and an N×N complex matrix γM, and the auxiliary data components between different range cells are independent and identically distributed (where γ is a scaling factor). When the radar receiver uses a centrally symmetric linear array or a centrally symmetric interval pulse train, the clutter covariance matrix M and the signal multi-rank subspace matrix U have a skew-symmetric structure, i.e., satisfying M=JM * J, U = JU * Where (@)* denotes conjugation, and J represents an N×N dimensional permutation matrix with diagonal elements of 1 and all other elements of 0.

[0044] The introduction of the oblique symmetric structure can further improve the estimation accuracy of the oblique symmetric covariance matrix structure of unknown clutter, thereby reducing the need for training sample size and providing favorable conditions for achieving adaptive detection of range-extended targets under small sample conditions.

[0045] Modeling distance-extended target detection as a binary hypothesis testing problem:

[0046]

[0047] The skew-symmetric Gradient test criterion can be expressed as:

[0048]

[0049] in, Is it assuming Θ under H1? r Maximum likelihood estimation; It is the maximum likelihood estimate of Θ under the assumption H0; Θ r0 Is it under the assumption H0 Θ r The value of .

[0050] Utilizing the oblique symmetry information in the clutter oblique symmetric covariance matrix structure M, the joint probability density function f1(Z,ZR) of the main data Z and auxiliary data ZR under the objective hypothesis H1 is obtained. R M,B p ,γ) can be represented as:

[0051]

[0052] in,

[0053]

[0054] Where j is the imaginary unit, · represents the determinant of the square matrix, tr(·) represents the trace of the matrix, and Re(·) and Im(·) represent taking the real and imaginary parts, respectively. and Let represent the set of m×n dimensional real matrices and the set of complex matrices, respectively. H This indicates the conjugate transpose.

[0055] Utilizing the oblique symmetry information in the clutter oblique symmetry covariance matrix M, the joint probability density function f0(Z,ZR) of the main data Z and auxiliary data ZR under the objective-free hypothesis H0 is obtained. R M,γ) can be represented as:

[0056]

[0057] in,

[0058] Without the objective hypothesis H0, using the main data Z and auxiliary data Z R Taking the derivative of the joint probability density function with respect to the clutter oblique-symmetric covariance matrix structure and setting it to zero, we obtain the maximum likelihood estimate of the clutter covariance matrix M under the H0 assumption. for

[0059]

[0060] The above formula combines master data and auxiliary data to improve the estimation accuracy of the unknown clutter oblique symmetric covariance matrix structure and reduce the need for auxiliary data.

[0061] Using master data Z and auxiliary data Z R The joint probability density function f1(Z,Z) R M,B p ,γ) for Θ r Find the partial derivative

[0062]

[0063] in, It is the maximum likelihood estimate of M under the H0 assumption.

[0064] Step 2. Under the assumption of a target, utilize the master data Z and the auxiliary data Z R The maximum likelihood estimate of the unknown clutter oblique-symmetric covariance matrix structure under the objective assumption is obtained by taking the derivative of the logarithm of the joint probability density function with respect to the clutter covariance matrix M and setting it to zero. Under the objective assumption, the main data Z and auxiliary data Z are used. R Taking the partial derivative of the logarithm of the joint probability density function with respect to the coordinate matrix components of the target in the subspace and setting the derivative to zero, we obtain the maximum likelihood estimate of the coordinate matrix components with a target; solving for the maximum likelihood estimate of γ0 under the assumption of no target.

[0065] The specific steps include:

[0066] Under the objective hypothesis H1, using the main data Z and auxiliary data Z R Taking the derivative of the joint probability density function with respect to the clutter oblique-symmetric covariance matrix structure and setting it to zero, we obtain the maximum likelihood estimate of the clutter covariance matrix M under the H1 assumption. for

[0067]

[0068] Will Substituting into equation (3), the obtained For B p Taking the derivative and setting it to zero, we get B. p The maximum likelihood estimate under assumption H1 is:

[0069]

[0070] According to formula (2) The definition can be obtained from equation (9).

[0071]

[0072] Note that under the assumption H0, Θ r =0 2rK×1 Substituting equations (7) and (10) into equation (2), we obtain the detection statistic:

[0073]

[0074] Where γ0 is the value of γ under assumption H0.

[0075] Maximum likelihood estimation of γ0 It is the unique positive solution to the following equations.

[0076]

[0077] Where q = min(N, 2K); λ k (k = 1, 2, ..., q) is The k-th non-zero eigenvalue.

[0078] The solution obtained from equation (12) Substituting into equation (11), we can obtain the detection statistic:

[0079]

[0080] in,

[0081] The detector proposed in this paper is also known as the partially uniform clutter subspace oblique symmetric Gradient test detector (PS-Gradient-PHE). The detector does not require solving the Fisher information matrix, has low computational complexity, has a simple detection statistic structure, is easy to implement in engineering, and has CFAR properties for M.

[0082] Step 3. To maintain the CFAR characteristics of the detection method, set the detection threshold T according to the preset false alarm probability. PS-Gradient-PHE ; Detection statistic t PS-Gradient-PHE With detection threshold T PS-Gradient-PHE Compare, if t PS-Gradient-PHE ≥T PS-Gradient-PHE If t is true, it is determined that a target exists in the current detection range unit, and the master data is not used as auxiliary data for subsequent detection range units; otherwise, if t is false... PS-Gradient-PHE <T PS-Gradient-PHE If no target is found in the current detection range cell, the master data is used as auxiliary data for other detection range cells.

[0083] To verify the effectiveness of the method described in this invention, two embodiments are given in this specific implementation. The first embodiment is for a marine exploration environment, and the second embodiment is for a land exploration environment.

[0084] Example 1:

[0085] Refer to the instruction manual appendix Figure 1 The specific implementation of Example 1 consists of the following steps:

[0086] Step A1 uses a maritime surveillance radar to illuminate the sea area to be detected, obtaining main data Z for K range cells to be detected; and illuminates the targetless area surrounding the sea area to be detected, obtaining auxiliary data Z for R reference range cells containing only pure sea clutter. R Combine the primary data Z and the auxiliary data Z. R The data is sent to the decorrelation processing module, where the transformed master data Z is obtained according to equation (3). p And clutter skew-symmetric covariance matrix structure estimation based on auxiliary data On the one hand, the auxiliary data Z p and The data is sent to the joint probability density function module for the main data and auxiliary data under the H0 hypothesis, based on the auxiliary data Z. p and Obtain the joint probability density function of the main data and auxiliary data under the H0 assumption (5); send the joint probability density function of the main data and auxiliary data under the H0 assumption to the maximum likelihood estimation module of the clutter oblique symmetric covariance matrix structure under the H0 assumption, use the joint probability density function of the main data and auxiliary data under the no-target assumption to differentiate the clutter oblique symmetric covariance matrix structure M and set it to zero, and obtain the maximum likelihood estimate of M under the H0 assumption according to equation (6). On the other hand, Z p and The data is sent to the joint probability density function module for the main and auxiliary data under the H1 hypothesis, based on Z. p and Obtain the joint probability density function of the main data and auxiliary data under the H1 hypothesis (3); send the joint probability density function of the main data and auxiliary data under the H1 hypothesis to the joint probability density partial derivative module under the H1 hypothesis, and use the joint probability density function of the main data and auxiliary data under the target hypothesis to evaluate Θ. r Taking the partial derivative, and based on equation (7), we obtain the joint probability density function of the main data and auxiliary data with respect to Θ under the objective assumption. r Partial derivative results.

[0087] It is worth noting that in step A1, the method of the present invention constructs a subspace range-extended target signal model, which avoids the problem that the rank-one signal model is unable to cope with the target guidance vector mismatch and improves the robustness of high-range resolution radar to the target guidance vector mismatch at sea. In addition, the method of the present invention makes full use of the prior information of the oblique symmetric structure of the sea clutter covariance matrix, and jointly uses master data and auxiliary data to improve the estimation accuracy of the unknown sea clutter oblique symmetric covariance matrix structure, reduce the requirement for training sample size, and provide favorable support for the realization of target subspace fusion detection under partially uniform clutter.

[0088] Step A2 involves differentiating the logarithm of the joint probability density function of the main and auxiliary data with respect to the clutter covariance matrix M under the target assumption and setting it to zero. This yields the maximum likelihood estimate of the unknown clutter oblique-symmetric covariance matrix structure under the target assumption. Maximum likelihood estimation of the unknown clutter oblique-symmetric covariance matrix structure under the objective assumption The data is fed into the maximum likelihood estimation module for the coordinate matrix under the H1 assumption. By taking the partial derivative of the logarithm of the joint probability density function of the main data and auxiliary data with respect to the coordinate matrix components of the target in the subspace and setting the derivative to zero, the maximum likelihood estimate of the coordinate matrix components under the target assumption is obtained. Using the maximum likelihood estimation module for γ under the H0 assumption, the maximum likelihood estimate of γ under the H0 assumption is solved; finally, the joint probability density function of the main data and auxiliary data under the objective assumption is applied to Θ. r Partial derivative results, maximum likelihood estimation of the coordinate matrix components with target. Maximum likelihood estimation of M under assumption H0 The maximum likelihood estimate of γ under the H0 assumption is sent to the target subspace fusion detector construction module under partially uniform clutter, and the target subspace fusion detection statistic t under partially uniform clutter is obtained according to Equation (2). PS-Gradient-PHE and t PS-Gradient-PHE It is sent to the detection and judgment module.

[0089] It is worth noting that the method of the present invention constructs a subspace oblique-symmetric Gradient test detector under partially uniform clutter. The detector does not require solving the Fisher information matrix, has low computational complexity, and has a simple detection statistic structure, making it easy to implement in engineering.

[0090] Step A3: Set the detection threshold T according to the preset false alarm probability. PS-Gradient-PHE Specifically, the false alarm probability is set to P. fa According to the Monte Carlo method, based on the previously accumulated 100 / P fa The detection threshold T is calculated using measured sea clutter data. Considering the difficulty in obtaining sea clutter, if the actual amount of pure sea clutter measured data R is less than 100 / Pfa, the missing 100 / Pfa-R clutter data points can be obtained through simulation using a sea clutter simulation model. The model parameters are reasonably estimated and set based on the obtained pure sea clutter measured data. Furthermore, the detection statistic t... PS-Gradient-PHE With detection threshold T PS-Gradient-PHE Compare, if t PS-Gradient-PHE ≥T PS-Gradient-PHE If t > 0, it is determined that there is a target in the current K range cells to be detected, and the master data is not used as auxiliary data for subsequent range cells to be detected; otherwise, if t > 0, the target is determined to be present in the current K range cells to be detected. PS-Gradient-PHE <T PS-Gradient-PHEIf no target is found in the current K detection range units, the master data is used as auxiliary data for the subsequent detection range units.

[0091] A comparison of the detection performance of the method of this invention with existing unstructured range-extended target detection methods on the matching signal is shown in the appendix. Figure 2 The results show that, compared with existing unstructured range-extended target subspace detectors (S-GLRT, S-Gradient, S-Rao, S-2SD, etc.), the method of this invention has better detection performance for weak targets in high-range resolution radar under some uniform sea clutter.

[0092] Example 2:

[0093] Refer to the instruction manual appendix Figure 1 The specific implementation of Example 2 consists of the following steps:

[0094] Step B1 uses a ground detection radar to illuminate the area to be detected, obtaining main data Z for K range cells to be detected; and illuminates the targetless area surrounding the area to be detected with radar, obtaining auxiliary data Z for R reference range cells containing only pure ground clutter. R Combine the primary data Z and the auxiliary data Z. R The data is sent to the decorrelation processing module, where the transformed master data Z is obtained according to equation (3). p And clutter skew-symmetric covariance matrix structure estimation based on auxiliary data On the one hand, the auxiliary data Z p and The data is sent to the joint probability density function module for the main data and auxiliary data under the H0 hypothesis, based on the auxiliary data Z. p and Obtain the joint probability density function of the main data and auxiliary data under the H0 assumption (5); send the joint probability density function of the main data and auxiliary data under the H0 assumption to the maximum likelihood estimation module of the clutter oblique symmetric covariance matrix structure under the H0 assumption, use the joint probability density function of the main data and auxiliary data under the no-target assumption to differentiate the clutter oblique symmetric covariance matrix structure M and set it to zero, and obtain the maximum likelihood estimate of M under the H0 assumption according to equation (6). On the other hand, auxiliary data Z p and The data is sent to the joint probability density function module for the main data and auxiliary data under the H1 hypothesis, based on the auxiliary data Z. p and Obtain the joint probability density function of the main data and auxiliary data under the H1 hypothesis (3); send the joint probability density function of the main data and auxiliary data under the H1 hypothesis to the joint probability density partial derivative module under the H1 hypothesis, and use the joint probability density function of the main data and auxiliary data under the target hypothesis to evaluate Θ.r Taking the partial derivative, and based on equation (7), we obtain the joint probability density function of the main data and auxiliary data with respect to Θ under the objective assumption. r Partial derivative results.

[0095] It is worth noting that in step B1, the method of the present invention constructs a subspace range-extended target signal model, which avoids the problem that the rank-one signal model is unable to cope with target guidance vector mismatch and improves the robustness of high-range resolution radar to ground target guidance vector mismatch. In addition, the method of the present invention makes full use of the prior information of the oblique symmetric structure of the ground clutter covariance matrix, and improves the estimation accuracy of the unknown ground clutter oblique symmetric covariance matrix structure by jointly using master data and auxiliary data, reducing the requirement for training sample size, and providing favorable support for realizing the target subspace fusion detection capability under partially uniform clutter.

[0096] Step B2 involves differentiating the logarithm of the joint probability density function of the main and auxiliary data with respect to the clutter covariance matrix M under the target assumption and setting it to zero. This yields the maximum likelihood estimate of the unknown clutter oblique-symmetric covariance matrix structure under the target assumption. Maximum likelihood estimation of the unknown clutter oblique-symmetric covariance matrix structure under the objective assumption The data is fed into the maximum likelihood estimation module for the coordinate matrix under the H1 assumption. By taking the partial derivative of the logarithm of the joint probability density function of the main data and auxiliary data with respect to the coordinate matrix components of the target in the subspace and setting the derivative to zero, the maximum likelihood estimate of the coordinate matrix components under the target assumption is obtained. Using the maximum likelihood estimation module for γ under the H0 assumption, the maximum likelihood estimate of γ under the H0 assumption is solved; finally, the joint probability density function of the main data and auxiliary data under the objective assumption is applied to Θ. r Partial derivative results, maximum likelihood estimation of the coordinate matrix components with target. Maximum likelihood estimation of M under assumption H0 The maximum likelihood estimate of γ under the H0 assumption is sent to the target subspace fusion detector construction module under partially uniform clutter, and the target subspace fusion detection statistic t under partially uniform clutter is obtained according to Equation (2). PS-Gradient-PHE and t PS-Gradient-PHE It is sent to the detection and judgment module.

[0097] It is worth noting that the method of the present invention constructs a subspace oblique-symmetric Gradient test detector under partially uniform clutter. The detector does not require solving the Fisher information matrix, has low computational complexity, and has a simple detection statistic structure, making it easy to implement in engineering.

[0098] Step B3 sets the detection threshold T based on the preset false alarm probability. PS-Gradient-PHE Specifically, the false alarm probability is set to P. faAccording to the Monte Carlo method, based on the previously accumulated 100 / P fa The detection threshold T is calculated from the measured ground clutter data. Considering the difficulty in obtaining ground clutter, if the actual amount of pure ground clutter measured data R is less than 100 / Pfa, the missing 100 / Pfa-R clutter data points can be obtained through simulation using a ground clutter simulation model. The model parameters are reasonably estimated and set based on the obtained pure ground clutter measured data. Furthermore, the detection statistic t... PS-Gradient-PHE With detection threshold T PS-Gradient-PHE Compare, if t PS-Gradient-PHE ≥T PS-Gradient-PHE If t > 0, it is determined that there is a target in the current K range cells to be detected, and the master data is not used as auxiliary data for subsequent range cells to be detected; otherwise, if t > 0, the target is determined to be present in the current K range cells to be detected. PS-Gradient-PHE <T PS-Gradient-PHE If no target is found in the current K detection range units, the master data is used as auxiliary data for the subsequent detection range units.

[0099] A comparison of the detection performance of the method of this invention with existing oblique symmetric range-extended target detection methods on the matched signal is shown in the appendix. Figure 3 The results show that, compared with existing unstructured range-extended target subspace detectors (S-GLRT, S-Gradient, S-Rao, S-2SD, etc.), the method of this invention has better detection performance for weak targets in high-range resolution radar under partially uniform clutter.

[0100] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for target subspace fusion detection under partially uniform clutter, characterized in that, Includes the following steps: Step 1. From K Each distance unit to be detected acquires master data. Z From the distance unit that is close to the one to be detected R Auxiliary data is obtained from each distance unit. ; Without the assumption of a target, using master data Z and auxiliary data Z R The logarithm of the joint probability density function and the clutter covariance matrix By differentiating and setting the derivative to zero, the maximum likelihood estimate of the unknown clutter oblique-symmetric covariance matrix structure is obtained without the objective assumption; under the objective assumption, the master data is used... Z and auxiliary data Z R The logarithm of the joint probability density function is used to evaluate the components of the target's coordinate matrix in the subspace. Find the partial derivative; Step 2. Under the assumption of a target, utilize master data. Z and auxiliary data Z R The logarithm of the joint probability density function and the clutter covariance matrix By differentiating and setting the derivative to zero, the maximum likelihood estimate of the unknown clutter oblique-symmetric covariance matrix structure under the objective assumption is obtained; under the objective assumption, the master data is used... Z and auxiliary data Z R Taking the partial derivative of the logarithm of the joint probability density function with respect to the coordinate matrix components of the target in the subspace and setting the derivative to zero, we can obtain the maximum likelihood estimate of the coordinate matrix components with respect to the target; solving... Maximum likelihood estimation under no objective assumption Construct detection statistics ; Step 3. Set the detection threshold according to the preset false alarm probability. ; Detection statistics With detection threshold If a comparison is made, If a target is detected in the current detection range cell, the master data will not be used as auxiliary data for subsequent detection range cells; otherwise... If no target is found in the current detection range unit, the master data is used as auxiliary data for other detection range units. In step 1, without the objective hypothesis H0, the master data is used. Z and auxiliary data Z R Taking the derivative of the joint probability density function with respect to the clutter skew-symmetric covariance matrix structure and setting it to zero, we obtain the result under the objective hypothesis. Lower clutter covariance matrix Maximum likelihood estimation for: in, Among them, auxiliary data Represented as 3D complex matrix , Indicates the first K+k Auxiliary data components corresponding to each reference distance cell; among which... 3D complex vector The zero-mean covariance matrix is 3D complex matrix The data follows a complex circular Gaussian distribution, and the auxiliary data components between different distance cells are independent and identically distributed. It is a scaling factor; Indicates the first k The corresponding distance unit to be detected Dimensional master data components, Indicates the first k In each distance unit to be detected A complex coordinate vector of the target subspace; j is the imaginary unit. The determinant of a square matrix. Represents the trace of a matrix. and These represent taking the real part and the imaginary part, respectively. and They represent m × n The set of real matrices and the set of complex matrices of dimension 1. This indicates the conjugate transpose. Indicates conjugate, J represents a diagonal element that is 1 and all other elements that are 0. 3D permutation matrix; The detection statistics constructed in step 2 : in, , This represents the multi-rank subspace matrix of the signal.

2. The target subspace fusion detection method under partially uniform clutter as described in claim 1, characterized in that, In step 2, under the assumption of a target, master data is used. Z and auxiliary data Z R Taking the partial derivative of the logarithm of the joint probability density function with respect to the coordinate matrix components of the target in the subspace and setting the derivative to zero, we obtain the maximum likelihood estimate of the coordinate matrix components with respect to the target: Among them, the signal multi-rank subspace matrix It has a symmetrical structure, that is, it satisfies .

3. The target subspace fusion detection method under partially uniform clutter as described in claim 2, characterized in that, In step 2, Maximum likelihood estimation It is the unique positive solution to the following equation: in, ; yes The k There are 1 non-zero eigenvalues.

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