Distance extension target detection method under interference and clutter background based on GLRT

Abstract

The invention belongs to the technical field of radar signal processing, and particularly relates to a distance extension target detection method under the interference and clutter background based on GLRT. Assuming that the interference subspace is linearly independent of the signal subspace and coordinates of the two subspaces are unknown, modeling clutter components as complex Gaussian vectors with a mean value of zero; and solving the maximum likelihood estimation of an unknown clutter covariance matrix, an interference coordinate vector and a signal coordinate vector by using a dimensionality reduction subspace method and an oblique symmetry transformation matrix structure, thereby establishing an RPD-GLRT detector, and performing target detection by using an RPD-2GLRT detector. Simulation analysis shows that under the background of interference and unknown clutters, the detection performance of the provided distance expansion target subspace detector is superior to that of a contrast detector, and the distance expansion target subspace detector has a good inhibition effect on interference.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a range-extended target detection method under interference and clutter background based on GLRT. Background Art

[0002] With the rapid development of radar technology, radar signal processing, as a core component of radar systems, has become increasingly important. Especially in modern traffic monitoring (such as VTSL radar systems), there are three core technologies: the first is radar signal processing and data processing technology, the second is solid-state transceiver technology, which gradually replaces magnetrons and achieves national production, and the third is multifunctional VTS radar technology with phased array antennas. Radar signal processing is not only related to the basic detection capability of radar, but also directly affects the detection accuracy and anti-interference ability of radar in complex environments.

[0003] In the field of radar technology, high-range resolution radar decomposes targets in space into multiple scattering points. Multiple scattering points in the radar radial direction are distributed in different distance units to form range-extended targets, thereby achieving effective detection of range-extended targets. The realization of this technology is due to the widespread application of broadband technologies such as radar pulse compression, which effectively solves the inherent contradiction between detection range and detection accuracy of traditional radars, ensures high range resolution, and makes range-extended target detection a hot topic of research.

[0004] However, the challenges faced by broadband radar in practical applications cannot be ignored. On the one hand, with the continuous advancement of electronic countermeasure technology, radar systems are facing threats from complex external environments such as intentional electronic jamming measures and unintentional electromagnetic interference; on the other hand, the clutter components in radar echoes also greatly increase the difficulty of target detection. The existence of these complex external environments requires radar systems to have stronger anti-interference and clutter suppression capabilities.

[0005] In order to improve the detection performance of broadband radar in complex environment with coexistence of interference and clutter, a range extended target detection method based on GLRT in the interference and clutter background is proposed. Summary of the invention

[0006] In order to overcome the problems in the prior art, the present invention proposes a range-extended target detection method under interference and clutter background based on GLRT.

[0007] The technical solution of the present invention to solve the above technical problems is as follows:

[0008] The present invention provides a method for detecting a range-extended target under an interference and clutter background based on GLRT, comprising the following steps:

[0009] Step 1: From K PThe detected distance unit obtains the data to be detected as the main data, and obtains K from the target-free distance unit adjacent to the detected unit. S observation data without target signal is used as auxiliary data; subspace modeling is performed on target signal and interference signal, clutter is modeled as a complex Gaussian distribution with zero mean and unknown positive definite covariance matrix, and a binary hypothesis testing model is established;

[0010] Step 2: Use the skew symmetry of the clutter covariance matrix to transform the constructed binary hypothesis test model, perform dimensionality reduction on the transformed binary hypothesis test model, obtain a new binary hypothesis test model, and then construct the joint probability density function of the primary data and the auxiliary data;

[0011] Step 3: Perform maximum likelihood estimation on the unknown parameters in the joint probability density function and construct the detection statistic under the GLRT test;

[0012] Step 4: Set the detection threshold T according to the preset false alarm probability G , the detection statistic and the detection threshold T G If the detection statistic is greater than or equal to the detection threshold, the current K P There is a distance extension target in the distance unit to be detected; otherwise, if the detection statistic is less than the detection threshold, it is determined that the current K P There is no range extension target in the range unit to be detected.

[0013] Furthermore, in step 1, subspace modeling is performed on the target signal and the interference signal, and the clutter is modeled as a complex Gaussian distribution with a mean of zero and an unknown positive definite covariance matrix, and a binary hypothesis testing model is established, which specifically includes:

[0014]

[0015] In the above formula, H 0 represents the assumption that there is no target signal, H 1 represents the hypothesis that there is a target signal; r k represents the signal received by the kth range unit, represents clutter, p represents the coordinate vector of the unknown target signal in the subspace, q k represents the coordinate vector of the disturbance in the subspace, represents a multi-rank subspace matrix, represents a multi-rank subspace, α k Represents the value of the kth distance unit coordinate vector, k∈Ω P ≡{1,...,K P} represents the number of master data, k∈Ω S ≡{K P +1,...,K P+K S} indicates the number of auxiliary data.

[0016] Furthermore, in step 2, the constructed binary hypothesis test model is transformed by utilizing the skew symmetry of the clutter covariance matrix, and then the transformed binary hypothesis test model is subjected to dimensionality reduction processing to obtain a new binary hypothesis test model, wherein the new binary hypothesis test model is:

[0017]

[0018] in,

[0019]

[0020] In the above formula, H 0 represents the assumption that there is no target signal, H 1 represents the hypothesis that there is a target signal; x k Indicates The signal received by the kth distance unit after matrix transformation, y k Indicates The signal received by the k-th distance unit after matrix transformation, J represents the interference subspace, represents the coordinate vector of the disturbance in the subspace, n k represents a vector of Gaussian distribution, represents the coordinate vector of the unknown target signal in the subspace, and H represents the signal subspace; Represents the signal subspace with corresponding matrix transformation; represents the interference subspace after the corresponding matrix transformation; Indicates that in the k The signal received by the kth distance unit after matrix transformation; Indicates that in the k The signal received by the kth distance unit after matrix transformation, r k represents the signal received by the kth distance unit; (·) H represents conjugate transpose; represents a set of r×1-dimensional real matrices, represents a set of N×1 dimensional complex matrices, where r∈N, N=N a ×N t , indicating N a The antenna array senses K P distance cells, each antenna collects N t samples.

[0021] Furthermore, step 2 includes constructing a joint probability density function:

[0022] H0 Assume that the joint probability density function f 0 (R; M, Q) is:

[0023] f 0 (R; M, Q) = (π) -NK |M| K [exp{-tr[M -1 T 0 ]}] K

[0024] H 1 Assume that the joint probability density function f 1 (R; p, α, M, Q) is:

[0025] f 1 (R; p, α, M, Q) = (π) -NK M K [exp{-tr[M -1 T 1 ]}] K

[0026] In the above formula, Q represents the interference coordinate covariance matrix; M represents the clutter covariance matrix; R = [R P R S ], where R represents the matrix of the main data and auxiliary data, R p is the main data matrix, R s is the auxiliary data matrix; N = N a ×N t , indicating N a The antenna array senses K P distance cells, each antenna collects N t samples; K = K P +K S , K represents the total number of detection distance units, K P Indicates the number of distance units to be detected, K S represents the number of target-free distance units adjacent to the detected unit; M represents the clutter covariance matrix; Use T 0 To make the expression more concise, Q represents the interference coordinate covariance matrix, J represents the interference subspace, S represents the covariance matrix of the auxiliary data; α represents the coordinate vector; p represents the coordinate vector of the unknown target signal in the subspace; is the full column rank matrix function of p; is the full row rank matrix function of q; tr(·) represents the trace of the matrix, (·) H represents conjugate transpose; represents a set of N×(q+1)-dimensional complex matrices, represents (q+1)×K P A collection of dimensional complex matrices.

[0027] Furthermore, in step 2, a joint probability density function of the primary data and the auxiliary data is constructed, including a two-step joint probability density function:

[0028] H 0 Assume that the joint probability density function f 0 (R P ; Q) is:

[0029]

[0030] H 1 Assume that the joint probability density function f 1 (R P ; p, α, Q) is:

[0031]

[0032] In the above formula, H 0 represents the assumption that there is no target signal, H 1 Indicates the hypothesis that there is a target signal; K P Indicates the number of distance units of the data to be detected; N = N a ×N t , indicating N a The antenna array senses K P distance cells, each antenna collects N t samples; R P is the main data matrix; p represents the coordinate vector of the unknown target signal in the subspace; α represents the coordinate vector; Q represents the interference coordinate covariance matrix; M represents the clutter covariance matrix; is the full column rank matrix function of p, H represents the signal subspace, J represents the interference subspace, q∈N; is the full row rank matrix function of q; tr(·) represents the trace of the matrix, (·) H represents the conjugate transpose, represents a set of N×(q+1)-dimensional complex matrices, represents (q+1)×K P A collection of dimensional complex matrices.

[0033] Furthermore, the step 3 specifically includes:

[0034] Step 3-1: the unknown parameters in the joint probability density function include a clutter covariance matrix, target coordinates, and an interference coordinate covariance matrix, and maximum likelihood estimation is performed on the clutter covariance matrix, target coordinates, and interference coordinate covariance matrix in the joint probability density function;

[0035] Step 3-2: Substitute the maximum likelihood estimator of the unknown components in the target coordinates, the transformed interference coordinate covariance estimator, and the estimator of the clutter covariance matrix back into the joint probability density function to construct the detection statistic.

[0036] Furthermore, in step 3-2, the test statistic η under the GLRT test is constructed RPD-GLRT :

[0037]

[0038] In the formula, λ max Indicates finding the maximum eigenvalue of matrix parameters; H S ′=Z H H S H S ′ indicates H S The matrix obtained by matrix transformation, H S represents the matrix obtained by matrix transformation of H, Z represents the slice unitary matrix, H S ′p’s projection matrix, u belongs to H S ′ is the unit norm vector; R P is the main data matrix; S represents the covariance matrix of auxiliary data;

[0039] in,

[0040] In the above formula, A is used to make the expression more concise. represents the identity matrix, I represents the projection matrix projected onto the full column rank matrix; N Represents the identity matrix.

[0041] Furthermore, in step 3-2, the detection statistic η under the two-step GLRT test is constructed RPD -2GLRT:

[0042]

[0043] In the formula, λ max Indicates finding the maximum eigenvalue of matrix parameters; H S ′=Z H H S , H S ′ indicates H S The matrix obtained by matrix transformation, H S represents the matrix obtained by matrix transformation of H, Z represents the slice unitary matrix, H S ′p’s projection matrix, u belongs to H S′ is the unit norm vector; R P is the main data matrix; Represents the auxiliary data estimated covariance matrix.

[0044] Compared with the prior art, the present invention has the following technical effects:

[0045] (1) The present invention combines the dimensionality reduction method with the skew symmetry of the clutter covariance matrix to improve the performance of the range-extended target direction detector under the background of subspace interference plus Gaussian clutter under the condition of lack of auxiliary data; assuming that the interference subspace is linearly independent of the signal subspace and the coordinates of the two subspaces are unknown, the clutter component is modeled as a complex Gaussian vector with a mean of zero, and the maximum likelihood estimate of the unknown clutter covariance matrix, the coordinate vector of the interference and the coordinate vector of the signal is solved by using the dimensionality reduction subspace method and the skew symmetry transformation matrix structure, thereby establishing an RPD-GLRT detector and an RPD-2GLRT detector for target detection; simulation analysis shows that under the background of interference plus unknown clutter, the detection performance of the proposed range-extended target subspace detector is better than that of the comparison detector, and it has a better suppression effect on interference;

[0046] (2) The present invention aligns possible useful signals to an unknown direction, constraining them to belong to a given observable subspace, and solves the adaptive detection problem when the guidance vector does not match; combines the dimensionality reduction method with the skew symmetry of the clutter covariance matrix to improve the performance of the distance extended target direction detector under the background of subspace interference and Gaussian clutter in the absence of auxiliary data; based on the GLRT detection strategy, while ensuring the constant false alarm rate characteristics, the detection performance of the detector is improved, and it has broad potential for promotion and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0048] Figure 1 It is a flow chart for realizing the present invention;

[0049] FIG. 2( a ), FIG. 2( b ), and FIG. 2( c ) are schematic diagrams of CFAR characteristics of the RPD-GLRT detector, the RPD-2GLRT detector, and the RPD-2Wald detector of the present invention, respectively;

[0050] Figure 3(a), Figure 3(b), and Figure 3(c) are respectively N=12, K P =8,K SSchematic diagram of the detection performance simulation experiment under different interference-to-noise ratios when =12, r=3, q=2;

[0051] Figure 4(a), Figure 4(b), and Figure 4(c) are respectively N=12, K S Schematic diagram of the effect of different numbers of master data on the detection performance of the proposed detector when =12, r=3, q=2;

[0052] Figure 5(a), Figure 5(b), and Figure 5(c) are respectively N=12, K P Schematic diagram of the effect of the change in the amount of auxiliary data on the detection performance of the proposed detector when =8, r=3, q=2;

[0053] Figure 6(a), Figure 6(b), and Figure 6(c) are respectively N=12, K P =8,K S Schematic diagram of detection performance curve of signal subspace under different degrees of mismatch when =12, r=3, q=2;

[0054] Figure 7(a), Figure 7(b), and Figure 7(c) are respectively N=12, K P =8, r=3, q=2, INR=10dB, the detection performance comparison diagram of RPD-GLRT detector and other detectors; (a) is K S =4; (b) K S =8; (c) K S =12. DETAILED DESCRIPTION

[0055] In order to further explain the technical means and effects taken by the present invention to achieve the predetermined invention purpose, the specific implementation methods, structures, features and effects of the technical solutions proposed by the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments. The specific features, structures or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used in the present invention have the same meaning as those commonly understood by technicians in the technical field of the present invention.

[0056] Reference Figure 1 In one embodiment of the present invention, a method for detecting a range-extended target in an interference-plus-clutter background based on GLRT is provided, comprising the following steps:

[0057] Step 1: From K P The detected distance unit obtains the data to be detected as the main data, and obtains K from the target-free distance unit adjacent to the detected unit. Sobservation data without target signal is used as auxiliary data; subspace modeling is performed on target signal and interference signal, clutter is modeled as a complex Gaussian distribution with zero mean and unknown positive definite covariance matrix, and a binary hypothesis testing model is established;

[0058] Step 2: Use the skew symmetry of the clutter covariance matrix to transform the constructed binary hypothesis test model and then perform dimensionality reduction on the transformed binary hypothesis test model to obtain a new binary hypothesis test model, and then construct the joint probability density function of the primary data and the auxiliary data;

[0059] Step 3: Perform maximum likelihood estimation on the unknown parameters in the joint probability density function and construct the detection statistic under the GLRT test;

[0060] Step 4: Set the detection threshold T according to the preset false alarm probability G , the detection statistic and the detection threshold T G If the detection statistic is greater than or equal to the detection threshold, the current K P There is a distance extension target in the distance unit to be detected; otherwise, if the detection statistic is less than the detection threshold, it is determined that the current K P There is no range extension target in the range unit to be detected.

[0061] The following is a detailed explanation of each of the above steps:

[0062] Step 1: From K P The detected distance unit obtains the data to be detected as the main data, and obtains K from the target-free distance unit adjacent to the detected unit. S observation data without target signal are used as auxiliary data; assuming that the interference subspace is linearly independent of the signal subspace and the coordinates of the two subspaces are unknown, subspace modeling is performed on the target signal and the interference signal, the clutter is modeled as a complex Gaussian distribution with zero mean and unknown positive definite covariance matrix, and a binary hypothesis testing model is established.

[0063] As an example, this step 1 may include the following steps:

[0064] Assume N a The antenna array senses K P distance cells, each antenna collects N t samples, then the kth distance unit k∈Ω P ≡{1,...,K P The received signal is represented by r k Indicates that it is an N-dimensional complex vector, that is represents the N×1 dimensional vector received from the kth range unit, where N=N a ×N tAssume that the disturbance is the sum of colored clutter and interference, With interference signal i k Two N×1 dimensional vectors are represented. Set H 0 Assume that r k contains only perturbations, assuming that H 1 For r k Contains disturbances and useful target echoes

[0065] Based on the subspace representation, s k Modeled as s k =α k s, here α k Represents the value of the kth distance unit coordinate vector, s belongs to the multi-rank subspace matrix Similarly, the interference signal i k Belongs to a multi-rank subspace And q+r≤N. Therefore, k∈Ω P ,here Represent the coordinate vectors of the unknown target signal and interference in the subspace respectively. Here we assume and is known and The full rank matrix formed is also known, and α k , p and q k Unknown. Clutter is modeled as having zero mean and an unknown positive definite covariance matrix The Gaussian vector of At the same time, it is assumed that a set of adjacent auxiliary data is used, denoted as Here k∈Ω S ≡{K P +1,...,K P +K S}, where K S ≥N, and the auxiliary data only contains clutter components, which have the same statistical characteristics as the clutter components in the primary data. Finally, it is assumed that the clutter is independent and identically distributed.

[0066] Based on the above assumptions, the range extended target detection problem in the subspace interference plus unknown clutter environment can be expressed as a binary hypothesis test to determine whether the target exists in the data to be detected:

[0067]

[0068] Among them, H 0 represents the assumption that there is no target signal, H 1 Indicates the hypothesis that there is a target signal.

[0069] Step 2: Use the skew symmetry of the clutter covariance matrix to transform the constructed binary hypothesis test model and then perform dimensionality reduction on the transformed binary hypothesis test model to obtain a new binary hypothesis test model, and then construct the joint probability density function of the primary data and the auxiliary data.

[0070] As an example, this step 2 may include the following steps:

[0071] The constructed model is transformed by using the skew symmetry of the clutter covariance matrix and then the transformed model is subjected to dimensionality reduction processing to obtain a new binary hypothesis testing model. Then, the joint probability density function of the primary data and the auxiliary data is constructed. Specifically, the skew symmetry characteristics of the radar detection signal are used. It can be seen that in practice and It has an oblique symmetrical structure, as shown below:

[0072]

[0073] In the above formula, D is a permutation matrix with 1 in the anti-diagonal position and 0 in the other positions, see formula (3); (·) * denotes conjugation;

[0074] In the following studies, the skew symmetry was incorporated into the design procedure of radar target direction detectors.

[0075]

[0076] Define the unitary matrix T:

[0077]

[0078] Among them, I N2 represents the N / 2-dimensional identity matrix, I (N-1) / 2 represents the (N-1) / 2-dimensional identity matrix; D N2 represents the N / 2-dimensional permutation matrix, D (N-1) / 2 represents a (N-1) / 2-dimensional permutation matrix, whose off-diagonal elements are 1 and the other elements are 0; i represents the imaginary unit.

[0079] Using the above formula, multiply formula (1) by T on the left to obtain:

[0080]

[0081] in,

[0082]

[0083] In the above formula, Indicates that in the k The signal received by the kth distance unit after matrix transformation; Indicates that in thek The signal received by the kth distance unit after matrix transformation; Represents the signal subspace with corresponding matrix transformation; represents the interference subspace after the corresponding matrix transformation; is a Gaussian distributed vector.

[0084] We further use dimensionality reduction to multiply equation (5) by get:

[0085]

[0086] in,

[0087]

[0088] In the above formula, x k Indicates The signal received by the kth distance unit after matrix transformation, y k Indicates The signal received by the k-th distance unit after matrix transformation, J represents the interference subspace, represents the coordinate vector of the disturbance in the subspace, n k represents a vector of Gaussian distribution, represents the coordinate vector of the unknown target signal in the subspace, and H represents the signal subspace; Indicates that in the k The signal received by the kth distance unit after matrix transformation; Indicates that in the k The signal received by the kth distance unit after matrix transformation; Represents the signal subspace with corresponding matrix transformation; represents the interference subspace after the corresponding matrix transformation; n k is a Gaussian distributed vector, and the covariance matrix is represents a set of r×1-dimensional real matrices, Represents a set of N×1 complex matrices.

[0089] For the convenience of representation, the distance unit signal sensed by the radar antenna is optimized and R is set to [R P R S ],in is the main data matrix, is the auxiliary data matrix, let Disturbance coordinate covariance matrix Coordinate vector And the total number of detection distance units K = K P +K S.

[0090] Construct the joint probability density function:

[0091] Among them, H 0 Assume that the joint probability density function is:

[0092] f 0 (R; M, Q) = (π) -NK |M| K [exp{-tr[M -1 T 0 ]}] K (9)

[0093] In the above formula, use Simplified expression, where the auxiliary covariance matrix

[0094] H 1 Assume that the joint probability density function is:

[0095] f 1 (R; p, α, M, Q) = (π) -NK M K [exp{-tr[M -1 T 1 ]}] K (10)

[0096] In the above formula,

[0097] Construct the two-step joint probability density function:

[0098] H 0 Assume that the joint probability density function of the two-step method is:

[0099]

[0100] H 1 Assume that the joint probability density function of the two-step method is:

[0101]

[0102] here is the full column rank matrix function of p, is the full row rank matrix function of q.

[0103] Step 3: Perform maximum likelihood estimation on the unknown parameters in the joint probability density function and construct the test statistic η under the GLRT test RPD-GLRT , construct the test statistic η under the two-step GLRT test RPD-2GLRT .

[0104] From step 1, we can see that the unknown parameters in the joint probability density function include the clutter covariance matrix M, the target coordinate α k p, interference coordinate covariance matrix Q, therefore, for the clutter covariance matrix M, target coordinate α in the joint probability density function k p, and the interference coordinate covariance matrix Q are used for maximum likelihood estimation.

[0105] In some embodiments, this step may include the following sub-steps:

[0106] Step 3-1-1: Construct the test statistic η under the GLRT test RPD-GLRT The clutter covariance matrix M and target coordinates α in the joint probability density function are k p, interference coordinate covariance matrix Q for maximum likelihood estimation;

[0107] According to formula (9), the unknown parameters Q and the clutter covariance matrix M are solved in H 0 The maximum likelihood estimate of With the clutter covariance matrix M in H 0 The maximum likelihood estimate of Taking the partial derivative of the unknown parameter and setting it to zero, we can get:

[0108]

[0109] The maximum likelihood estimate With the maximum likelihood estimate Substituting into equation (9) we get 0 The probability density function under the assumption:

[0110]

[0111] With H 0 Assuming similarity, we can obtain H by maximum likelihood estimation 1 Assume the estimated values ​​of M and E, and then get the estimated value of α. Substituting it into formula (10) we can get:

[0112]

[0113] Now we only need to obtain the maximum likelihood estimate of p, that is, to find the maximum value of equation (17) containing p:

[0114]

[0115] Formula (17) can be transformed into formula (18):

[0116]

[0117] here

[0118]

[0119] H S ′=Z H H S , is a slice unitary matrix, H S The projection matrix of ′p can be reconstructed as u belongs to H S ′ is the unit norm vector represents the identity matrix, I represents the projection matrix projected onto the full column rank matrix; N represents the identity matrix; substituting it into equation (18) yields the following equation (20):

[0120] det(A)(1-u H Z H S -1 / 2 R P A -1 R P H S -1 / 2 Zu)(20)

[0121] Now finding the maximum likelihood estimate of p is equivalent to finding the maximum value of the latter term in equation (20), and we get equation (21)

[0122]

[0123] Substituting equation (21) into equation (18) and then into equation (16) yields H 1 The assumed probability density function is shown in formula (22).

[0124]

[0125] Step 3-1-2: Based on the clutter covariance matrix M and target coordinates α in the joint probability density function k p, the maximum likelihood estimate of the interference coordinate covariance matrix Q, and the construction of the detection statistic η of the RPD-GLRT detector based on the GLRT test criterion RPD-GLRT ;

[0126] Under the GLRT test, the test statistic can be expressed as:

[0127]

[0128] Where η RPD-GLRT is the test statistic, γ is the detection threshold under the GLRT test; Substituting equations (22) and (15) into equation (23), we can obtain:

[0129]

[0130] In the above formula, λ max It means to find the maximum eigenvalue of matrix parameters.

[0131] Step 3-2-1: Construct the test statistic η under the two-step GLRT test RPD-2GLRT Perform maximum likelihood estimation on the unknown parameters in the joint probability density function described in ;

[0132] In the first step, assuming that the clutter covariance matrix is ​​known, the unknown parameters Q in H are solved according to equation (11). 0 The maximum likelihood estimate of Taking the partial derivative of the unknown parameter and setting it to zero, we can get:

[0133]

[0134] J M =M -1 / 2 J, the maximum likelihood estimate Substituting into equation (11) we get 0 The probability density function under the assumption is as shown in formula (26), where the projection matrix

[0135]

[0136] With H 0 Assuming similarity, we can obtain H by maximum likelihood estimation 1 Assume that the estimated value of E in , and then get the estimated value of α, substitute it into equation (12) to get equation (27), where the projection matrix

[0137]

[0138] Now we only need to obtain the maximum likelihood estimate of p, which is similar to the maximum likelihood estimate of p in step 3-1-1. The maximum likelihood estimate of p can be obtained as:

[0139]

[0140] Substituting equation (28) into (27) yields H 1 Assuming the probability density function:

[0141]

[0142] Step 3-2-2: According to the target coordinate α in the joint probability density function kp and the interference coordinate covariance matrix Q are used for maximum likelihood estimation to construct the detection statistic η under the two-step GLRT test RPD-2GLRT ;

[0143]

[0144] The second step is to estimate the covariance matrix using auxiliary data. Replacing the clutter covariance matrix M, we can obtain the detection statistic η under the two-step GLRT test. RPD-2GLRT :

[0145]

[0146] γ 1 is the threshold of the detector. max It means to find the maximum eigenvalue of matrix parameters.

[0147] Step 3-3: Construct the test statistic η under the two-step Wald test RPD-2Wlad ;

[0148] Under the Wald test, the test statistic can be expressed as:

[0149]

[0150] Among them, γ 3 represents the detection threshold, Θ 1 Indicates that H 1 Assume that the row vector constructed by the total unknown parameters is expressed as where Θ r1 =p,Θ s1 =[α T ,ν 1 ,vec T (Q)] T ; Denoted as Θ 1 The maximum likelihood estimate of ; Indicated as H 1 Assume that Θ r1 The maximum likelihood estimate of r0 Indicates that H 0 Assume that Θ r The value of Represented as I -1 (Θ), and I(Θ) is the Fisher information matrix about Θ, which can be expressed as:

[0151]

[0152] From this we can get:

[0153]

[0154] First take the logarithm of equation (12) and then and Taking the derivative we get:

[0155]

[0156] Then, substituting equations (35) and (36) into equation (33), we can obtain:

[0157]

[0158] Because Θ r0 =0 r×1 , substituting equation (37) into equation (32) yields the Wald test for fixed p, α and M:

[0159] η wald =α H αp H H H M -1 Hp (38)

[0160] The maximum likelihood estimate of α is the first column number of the maximum likelihood estimate of formula E, which can be obtained according to the block matrix inversion formula:

[0161]

[0162] Substituting equation (39) into equation (38) and then using the auxiliary data to estimate the skew-symmetric covariance matrix Replacing the clutter covariance matrix M, we can obtain the detection statistic η under the two-step Wald test. RPD-2Wlad :

[0163]

[0164] in p K yes The principal vector of the matrix.

[0165] Step 4. Set the detection threshold T according to the preset false alarm probability G , respectively, the detection statistic η RPD-GLRT , η RPD-2GLRT With the detection threshold T G If the detection statistic is greater than or equal to the detection threshold, the current K P There is a distance extension target in the distance unit to be detected; otherwise, if the detection statistic is less than the detection threshold, it is determined that the current K P There is no range extension target in the range unit to be detected.

[0166] It is proved that the proposed RPD-GLRT detector, RPD-2GLRT detector and RPD-2Wald detector have good performance in H 0 Assume that the CFAR characteristics of the clutter covariance matrix M are:

[0167] In H 0 Assume that M has the CFAR property and need to verify η RPD-GLRT , η RPD-2GLRT and η RPD-2Wlad It is independent of the clutter covariance matrix M.

[0168] For the RPD-GLRT detector and the RPD-2GLRT detector, first note that the columns of the matrix Z in (24) are stretched into the matrix J S The orthogonal complement space of 0 Assume that R P =JQ+N P , then there is:

[0169] Z H S- 1 / 2 R P =Z H S -1 / 2 (JQ+N P )=Z H S -1 / 2 N P =F (41)

[0170] here

[0171] R P =JQ+N P Substituting into formula (24), we can obtain:

[0172]

[0173] here Using whitening transformation, QR decomposition and block matrix theory, equation (42) can be rewritten as:

[0174]

[0175] in,

[0176]

[0177] is a matrix whose columns are independent and identically distributed complex normal vectors with mean zero and covariance matrix I r ,and N 2B , are all independent random matrices.

[0178] Now it is obvious that in H 0 Assume that η in formula (24) RPD-GLRT The distribution of is independent of M. It can also be seen that the statistic is composed of two independent random matrices N 2B and The maximum eigenvalue of the matrix determined by M is , and the distribution of these two matrices is independent of M. This proves that the RPD-GLRT detector derived above has the CFAR characteristic.

[0179] Since the RPD-GLRT detector differs from the RPD-2GLRT detector only in the A matrix, the CFAR characteristics of the RPD-2GLRT detector can also be proved by the same logic.

[0180] For the RPD-2Wald detector, its statistics can be written as:

[0181]

[0182] Among them, due to p K yes The principal vector of the matrix can be obtained:

[0183]

[0184] Multiply equation (46) by get:

[0185]

[0186] Substituting formula (47) into formula (45) we can obtain:

[0187]

[0188] The statistical properties of β have been verified in published papers. 0 Assume that it is independent of M. Next, verify the second half. Definition is a slice unitary matrix.

[0189]

[0190] Note that the columns of the matrix Z in (49) are expanded into the matrix The orthogonal complement space of 0 Assume that R P =JQ+N P , then there is:

[0191]

[0192] here Substituting formula (50) into formula (49), we can obtain:

[0193]

[0194] Using whitening transformation, QR decomposition and block matrix theory, equation (51) can be rewritten as:

[0195]

[0196] in,

[0197]

[0198] is a matrix whose columns are independent and identically distributed complex normal vectors with mean zero and covariance matrix I r ,and N 2B , are all independent random matrices.

[0199] Now it is obvious that in H 0 Assume that η in formula (40) RPD-2Wlad The distribution of is independent of M. It can also be seen that the statistic is composed of two independent random matrices N 2B and The maximum eigenvalue of the matrix determined by , and the distribution of these two matrices is independent of M. This proves that the RPD-2Wald detector derived above has CFAR characteristics.

[0200] (1) The present invention combines the dimension reduction method with the skew symmetry of the clutter covariance matrix to improve the performance of the distance extended target direction detector under the background of subspace interference plus Gaussian clutter; a subspace-based distance extended target signal model under interference plus unknown clutter is established. Based on the GLRT strategy and the Wlad test strategy, a direction detector for the distance extended target under the background of interference plus clutter based on the GLRT test, the two-step GLRT test and the two-step Wald test is derived, which improves the detection performance of the detector while ensuring the constant false alarm rate characteristics, and has a wide range of potential promotion and application value.

[0201] The effect of the present invention can be illustrated by the following simulation experiment:

[0202] The CRAF characteristics and detection performance of RPD-GLRT are analyzed by Monte Carlo simulation. Assuming the probability of false alarm (PFA) is 10 -4 , the number of simulations to obtain the threshold is set to 100 / PFA, and the number of simulations to obtain the probability of detection (PD) is set to 5000. The signal-to-noise ratio SCR is defined as:

[0203] SCR=α H αp H H H M -1 Hp; (55)

[0204] The dry-mix ratio (ICR) is defined as:

[0205] ICR=tr(Q H J H M -1 JQ). (56)

[0206] Without loss of generality, the signal subspace H is selected as:

[0207] H=[t(0.18),t(0.21),...,t(0.18+(r-1)0.03)] (57)

[0208] The interference subspace J is:

[0209] J=[t(-0.03),t(0),...,t(-0.03+(q-1)0.03)] (58)

[0210] When N is an even number, t(f) is:

[0211]

[0212] When N is an odd number, t(f) is:

[0213]

[0214] The element in the mth row and nth column of the clutter covariance matrix is ​​expressed as [M] m,n =σ 2 ρ m-n , σ 2 represents the clutter power, ρ represents the correlation coefficient, and ρ = 0.9. Without loss of generality, the interference coordinate vector q k The zero-mean covariance matrix is The independent and identically distributed complex normal vectors, here is the interference power; p represents the zero mean covariance matrix is ​​I r The complex normal vector of |α k |=α,α k The phase is an independent and identically distributed random variable and follows a uniform distribution of (0,2π).

[0215] Verify the RPD-GLRT detector, RPD-2GLRT detector and RPD-2Wald detector for clutter power σ 2As well as the CFAR characteristics of the clutter covariance matrix, the results are shown in Figure 2(a), Figure 2(b) and Figure 2(c). Figure 2(a), Figure 2(b) and Figure 2(c) show that when the first-order hysteresis coefficient γ is fixed, only the clutter power level σ 2 The false alarm probability under the same threshold remains basically unchanged; the fixed clutter power level σ 2 , only the first-order hysteresis coefficient γ changes, and the false alarm probability under the same threshold is also very close. It can be concluded that the detection performance of the RPD-GLRT detector, the RPD-2GLRT detector and the RPD-2Wald detector is basically not affected by the interference coordinate covariance matrix correlation and the clutter power, thus verifying the detector proposed in the present invention to the clutter power level σ 2 The sum of the clutter covariance matrix has a constant false alarm rate characteristic, which is consistent with the previous theoretical analysis.

[0216] In order to test the anti-interference performance of the detector, a simulation experiment of detection performance under different interference-to-noise ratios was set up, in which the first-order hysteresis coefficient γ was set to 0.9 and the clutter power σ 2 is 1. The results are shown in Figures 3(a), 3(b) and 3(c). It can be seen from Figures 3(a), 3(b) and 3(c) that under different ICRs, the detection performances of the RPD-GLRT detector, the RPD-2GLRT detector and the RPD-2Wald detector are almost the same, which shows that the above detectors have good anti-interference performance.

[0217] The following is an analysis of the effect of the change in the number of master data on the detection performance of the detector. The results are shown in Figure 4(a), Figure 4(b) and Figure 4(c). It can be seen from Figure 4(a), Figure 4(b) and Figure 4(c) that the number of master data K P The detection performance of RPD-GLRT detector, RPD-2GLRT detector and RPD-2Wald detector all gradually decreases. The reason may be that the distance unit occupied by the target is fixed and the increase of K P This results in the introduction of too many cells that do not contain targets but contain interference, resulting in reduced detection performance.

[0218] The effect of the amount of auxiliary data on the detection performance of the RPD-GLRT detector, RPD-2GLRT detector and RPD-2Wald detector is further studied, and the results are shown in Figure 5(a), Figure 5(b) and Figure 5(c). It can be seen from Figure 5(a), Figure 5(b) and Figure 5(c) that the detection performance of the RPD-GLRT detector, RPD-2GLRT detector and RPD-2Wald detector improves with the increase of auxiliary data. This is because the increase of auxiliary data improves the accuracy of the corresponding estimated clutter covariance matrix, thereby indirectly improving the detection probability.

[0219] The above-mentioned research on the detector is based on the premise of subspace matching. Since signal subspace mismatch or interference subspace mismatch will inevitably occur in the process of target detection, taking signal mismatch as an example, signal mismatch can be understood as the deviation between the actual subspace steering vector and the nominal steering vector, resulting in different degrees of loss in detection performance. Therefore, the present invention studies the detection performance of the detector under the condition of mismatch between the signal subspace and the interference subspace of the proposed detector.

[0220] Next, we analyze the signal subspace mismatch and interference subspace mismatch. 2 θ represents the nominal signal subspace H and the actual interference subspace H 0 The mismatch degree is expressed as:

[0221]

[0222] Among them, cos 2 θ = 1 means that the nominal signal subspace H is different from the actual signal subspace H 0 In the case of a complete match, cos 2 θ=0 means the nominal signal subspace H is different from the actual signal subspace H 0 Complete mismatch case. In the case of signal subspace mismatch, the specific detection performance loss is shown in Figure 6(a), Figure 6(b) and Figure 6(c).

[0223] Figure 7(a), Figure 7(b) and Figure 7(c) show the detection performance curves compared with different detectors under different auxiliary data. It can be seen from Figure 7(a), Figure 7(b) and Figure 7(c) that due to the limitations of the D-GLRT detector, D-2GLRT detector and D-2Wald structure, the detector does not work when the amount of auxiliary data is less than N, and the limitations of the PD-GLRT detector, PD-2GLRT detector and PD-2Wald detector structure cause the detector to not work when the amount of auxiliary data is less than N / 2. The proposed RPD-GLRT detector, RPD-2GLRT detector and RPD-2Wald detector can detect targets under the condition of lack of auxiliary data, and the effect is better than the same type of PD-GLRT detector, PD-2GLRT detector and PD-2Wald detector. Since auxiliary data is difficult to obtain in actual environments, the proposed RPD-GLRT detector, RPD-2GLRT detector and RPD-2Wald detector have a wide range of potential promotion and application value when the amount of auxiliary data is small and more accurate target detection is required.

[0224] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. A method for detecting extended-range targets in interference and clutter background based on GLRT. It is characterized in that The following steps are involved: Step 1: From K P The detected distance unit obtains the data to be detected as the main data, and obtains K from the target-free distance unit adjacent to the detected unit. S observation data without target signal is used as auxiliary data; subspace modeling is performed on target signal and interference signal, clutter is modeled as a complex Gaussian distribution with zero mean and unknown positive definite covariance matrix, and a binary hypothesis testing model is established; Step 2: Use the skew symmetry of the clutter covariance matrix to transform the constructed binary hypothesis test model, perform dimensionality reduction on the transformed binary hypothesis test model, obtain a new binary hypothesis test model, and then construct the joint probability density function of the primary data and the auxiliary data; Step 3: Perform maximum likelihood estimation on the unknown parameters in the joint probability density function and construct the detection statistic under the GLRT test; Step 4: Set the detection threshold T according to the preset false alarm probability G , the detection statistic and the detection threshold T G If the detection statistic is greater than or equal to the detection threshold, the current K P There is a distance extension target in the distance unit to be detected; otherwise, if the detection statistic is less than the detection threshold, it is determined that the current K P There is no range extension target in the range unit to be detected.

2. According to claim 1, a method for detecting extended-range targets in an interference-plus-clutter background based on GLRT, It is characterized in that In step 1, subspace modeling is performed on the target signal and the interference signal, and the clutter is modeled as a complex Gaussian distribution with a mean of zero and an unknown positive definite covariance matrix, and a binary hypothesis testing model is established, which specifically includes: Among them, H 0 represents the assumption that there is no target signal, H 1 represents the hypothesis that there is a target signal; r k represents the signal received by the kth range unit, represents clutter, p represents the coordinate vector of the unknown target signal in the subspace, q k represents the coordinate vector of the disturbance in the subspace, represents a multi-rank subspace matrix, represents the multi-rank subspace matrix, α k Represents the value of the kth distance unit coordinate vector, k∈Ω P ≡{1,...,K P } represents the number of master data, k∈Ω S ≡{K P +1,...,K P +K S } indicates the number of auxiliary data.

3. According to the GLRT-based method for detecting extended-range targets in interference and clutter backgrounds as described in claim 1, It is characterized in that In step 2, the constructed binary hypothesis test model is transformed by utilizing the skew symmetry of the clutter covariance matrix, and then the transformed binary hypothesis test model is subjected to dimensionality reduction processing to obtain a new binary hypothesis test model, wherein the new binary hypothesis test model is: in, In the above formula, H 0 represents the assumption that there is no target signal, H 1 represents the hypothesis that there is a target signal; x k Indicates The signal received by the kth distance unit after matrix transformation, y k Indicates The signal received by the k-th distance unit after matrix transformation, J represents the interference subspace, represents the coordinate vector of the disturbance in the subspace, n k represents a vector of Gaussian distribution, represents the coordinate vector of the unknown target signal in the subspace, and H represents the signal subspace; Represents the signal subspace with corresponding matrix transformation; represents the interference subspace after the corresponding matrix transformation; Indicates that in the k The signal received by the kth distance unit after matrix transformation; Indicates that in the k The signal received by the kth distance unit after matrix transformation, r k represents the signal received by the kth distance unit; (·) H represents conjugate transpose; represents a set of r×1-dimensional real matrices, represents a set of N×1 dimensional complex matrices, where r∈N, N=N a ×N t , indicating N a The antenna array senses K P distance cells, each antenna collects N t samples.

4. According to claim 1, a method for detecting extended-range targets in interference and clutter background based on GLRT, It is characterized in that The step 2 includes constructing a joint probability density function: H 0 Assume that the joint probability density function f 0 (R; M, Q) is: f 0 (R;M,Q)=(π) -NK M K [exp{-tr[M -1 T 0 ]}] K H 1 Assume that the joint probability density function f 1 (R; p, α, M, Q) is: f 1 (R;p,α,M,Q)=(π) -NK M K [exp{-tr[M -1 T 1 ]}] K In the above formula, Q represents the interference coordinate covariance matrix; M represents the clutter covariance matrix; R = [R P R S ], where R represents the matrix of the main data and auxiliary data, R p is the main data matrix, R s is the auxiliary data matrix; N = N a ×N t , indicating N a The antenna array senses K P distance cells, each antenna collects N t samples; K = K P +K S , K represents the total number of detection distance units, K P Indicates the number of distance units to be detected, K S represents the number of target-free distance units adjacent to the detected unit; M represents the clutter covariance matrix; T 0 Indicates that H 0 Assume that the Gaussian variable, Q represents the interference coordinate covariance matrix, J represents the interference subspace, S represents the covariance matrix of the auxiliary data; α represents the coordinate vector; p represents the coordinate vector of the unknown target signal in the subspace; is the full column rank matrix function of p; is the full row rank matrix function of q; tr(·) represents the trace of the matrix, (·) H represents conjugate transpose; represents a set of N×(q+1)-dimensional complex matrices, represents (q+1)×K P A collection of dimensional complex matrices.

5. According to claim 1, a method for detecting extended-range targets in interference and clutter background based on GLRT, It is characterized in that In step 2, a joint probability density function of the primary data and the auxiliary data is constructed, including a joint probability density function of a two-step method: H 0 Assume that the joint probability density function f 0 (R P ; Q) is: H 1 Assume that the joint probability density function f 1 (R P ; p, α, Q) is: In the above formula, H 0 represents the assumption that there is no target signal, H 1 Indicates the hypothesis that there is a target signal; K P Indicates the number of distance units of the data to be detected; N = N a ×N t , indicating N a The antenna array senses K P distance cells, each antenna collects N t samples; R P is the main data matrix; p represents the coordinate vector of the unknown target signal in the subspace; α represents the coordinate vector; Q represents the interference coordinate covariance matrix; M represents the clutter covariance matrix; is the full column rank matrix function of p, H represents the signal subspace, J represents the interference subspace, q∈N; is the full row rank matrix function of q; tr(·) represents the trace of the matrix, (·) H represents the conjugate transpose, represents a set of N×(q+1)-dimensional complex matrices, represents (q+1)×K P A collection of dimensional complex matrices.

6. A method for detecting extended-range targets in interference and clutter background based on GLRT according to claim 4 or 5, It is characterized in that The step 3 specifically includes: Step 3-1: the unknown parameters in the joint probability density function include a clutter covariance matrix, target coordinates, and an interference coordinate covariance matrix, and maximum likelihood estimation is performed on the clutter covariance matrix, target coordinates, and interference coordinate covariance matrix in the joint probability density function; Step 3-2: Substitute the maximum likelihood estimator of the unknown components in the target coordinates, the transformed interference coordinate covariance estimator, and the estimator of the clutter covariance matrix back into the joint probability density function to construct the detection statistic.

7. The method for detecting extended-range targets in interference and clutter background based on GLRT according to claim 6, It is characterized in that The step 3-2 includes: constructing the test statistic η under the GLRT test RPD-GLRT : In the formula, λ max Indicates finding the maximum eigenvalue of the matrix parameters; H′ S =Z H H S H′ S Indicates H S The matrix obtained by matrix transformation, H S represents the matrix obtained by matrix transformation of H, Z represents the slice unitary matrix, H S ′p’s projection matrix, u belongs to H S ′ is the unit norm vector; R P is the main data matrix; S represents the covariance matrix of auxiliary data; in, In the above formula, represents the identity matrix, I represents the projection matrix projected onto the full column rank matrix; N Represents the identity matrix.

8. The method for detecting extended-range targets in interference and clutter background based on GLRT according to claim 6, It is characterized in that The step 3-2 includes: constructing the test statistic η under the two-step GLRT test RPD-2GLRT : In the formula, λ max Indicates finding the maximum eigenvalue of the matrix parameters; H′ S =Z H H S H′ S Indicates H S The matrix obtained by matrix transformation, H S represents the matrix obtained by matrix transformation of H, Z represents the slice unitary matrix, H S ′p’s projection matrix, u belongs to H S ′ is the unit norm vector; R P is the main data matrix; Represents the auxiliary data estimated covariance matrix.

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