Multi-target detection method and system based on sparse reconstruction and expectation maximization clustering

Abstract

The invention belongs to the technical field of underwater target detection, and relates to a multi-target detection method and system based on sparse reconstruction and expectation maximization clustering, and the method comprises the steps: carrying out the preprocessing of echoes received by a linear array in a detection region, and obtaining K independent sample vectors meeting the zero-mean multivariate complex Gaussian distribution; the method comprises the following steps: carrying out uniform and equal-interval sampling on a space sector of a detection area to obtain K theta alternative angles, constructing a K theta-dimensional airspace sparse vector based on the K theta alternative angles, establishing a sparse model for judging whether a target exists in an independent sample vector, and obtaining a joint probability density function; a joint method of expectation maximization clustering based on a sparse model is adopted, and classification and estimation results of parameters in the multi-target scene are obtained through loop iteration; and obtaining an adaptive detector based on likelihood ratio test according to classification and estimation results, and realizing accurate multi-target detection. The method can automatically adapt to different target conditions, and the accuracy and reliability of detection are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater target detection, and in particular relates to a multi-target detection method and system based on sparse reconstruction and expectation maximization clustering. Background Art

[0002] In the field of underwater sonar detection, in order to effectively cope with complex marine environments and improve the accuracy of target detection, scientists have been exploring more advanced signal processing technologies. Among them, space-time adaptive detection (STAD) technology has attracted much attention due to its excellent performance. The core of STAD technology is that it can realize the integration of reverberation suppression and target detection. Compared with the traditional STAP method of reverberation suppression before detection, STAD can make more effective use of observation data, thereby providing better detection performance. In recent years, STAD technology has been widely studied and applied in the field of motion sonar, especially in dealing with point target detection problems in the background of Gaussian distribution reverberation. In this field, a variety of classic detection methods such as maximum likelihood ratio test (GLRT), adaptive matched filter and adaptive coherence estimator have been applied.

[0003] However, in underwater multi-target detection scenarios, traditional STAD methods face some challenges. First, during sonar detection, when the echo signals of multiple targets overlap within the detection window, it is difficult for the sonar to distinguish these signals, which reduces the accuracy and reliability of detection. Second, many existing detection algorithms assume that the target echo signals will appear at a specific arrival angle. However, this assumption is often not true in practical applications because the distribution and motion characteristics of the targets can be very complex and changeable. This results in the algorithm being unable to accurately estimate the arrival angles of multiple targets.

[0004] Existing technical solutions

[0005] With the rise of machine learning and data mining industries, machine learning and artificial neural network algorithms have gradually been applied in the field of target detection and recognition in recent years. Methods such as EM algorithm and sparse reconstruction have been integrated into STAD to improve target classification and feature extraction. The team of the Institute of Acoustics, Chinese Academy of Sciences, used the latent variable model method based on the EM algorithm to achieve joint interference classification and detection of multiple point targets in heterogeneous environments with different interference characteristics. This method can classify each sample unit in the data, identify areas with different interference characteristics, and detect multiple targets that may exist without knowing the number and location of the targets in advance. However, this method has certain technical limitations. In particular, it relies on the cluster assumption when dealing with multi-target arrival angle estimation, assuming that the echo angles of multiple targets are the same. This assumption ignores the complexity of the actual scene that targets may come from different directions, limiting the accuracy of the algorithm in estimating the arrival angle of each independent target.

[0006] Disadvantages of existing technology

[0007] The shortcomings of the existing technology are mainly manifested in that the estimation of the arrival angle of multiple targets relies on the cluster assumption, ignoring the diversity and independence of the target echo angles in actual scenes, which limits the accuracy and applicability of the algorithm. In addition, when dealing with multi-target detection, traditional STAD often relies on spatial guidance vector information, which reflects the distribution characteristics of the target signal in space. However, obtaining accurate spatial guidance vector information can be very difficult in practical applications, especially when there are a large number of targets, fast movement speeds, or high environmental noise. More importantly, it is difficult for existing technologies to effectively deal with the problem of strong signal shielding in a multi-target environment, which increases the risk of missed target detection. Summary of the invention

[0008] The purpose of the present invention is to overcome the defects of the prior art and propose a multi-target detection method and system based on sparse reconstruction and expectation maximization clustering.

[0009] In order to achieve the above object, the present invention proposes a multi-target detection method based on sparse reconstruction and expectation maximization clustering, comprising:

[0010] Step 1) preprocessing the echoes received by the linear array in the detection area to obtain K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution;

[0011] Step 2) Perform uniform and equidistant sampling on the spatial sectors of the detection area to obtain K θ Alternative angles, based on K θ Alternative angles, construct K θ Dimensional spatial domain sparse vector, establish a sparse model of whether the independent sample vector exists in the target, and obtain the joint probability density function;

[0012] Step 3) adopting a joint method of expectation maximization clustering based on a sparse model to obtain the classification and estimation results of parameters in a multi-target scenario through cyclic iteration;

[0013] Step 4) According to the classification and estimation results, an adaptive detector based on likelihood ratio test is obtained to achieve accurate multi-target detection.

[0014] Preferably, the linear array in step 1) includes N array elements, and after preprocessing the echoes of the N array elements, K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution are obtained. in Represents an N-dimensional complex number.

[0015] Preferably, the K in step 2) θ The alternative angle is

[0016] The process of establishing a sparse model of whether an independent sample vector exists in the target includes:

[0017] make Indicates the K in the sector θ The normalized steering vector corresponding to the candidate angles, represents K based on the target complex amplitude factor θ dimensional spatial sparse vector, the superscript T indicates transposition; the independent sample vector z k It is expressed as the following binary hypothesis based on the sparse model:

[0018]

[0019] Among them, α k The non-zero elements of correspond to k∈Ω T region, indicating that there is a target echo in the region; in the target-free region k∈Ω\Ω T Inside, α k =0; Ω = {1,…,K} represents the sample vector z k , k=1,…,K subscript set, Ω T A subscript set indicating that the target component does not exist.

[0020] Preferably, the joint probability density function of step 2) is:

[0021]

[0022] Among them, (z k |iα k ; M) is z k The conditional probability density function of is:

[0023]

[0024] h(α k ; b) is α k A sparsity-enhancing prior function based on the sparsity tuning parameter b∈(0,1], represents the conjugate transpose of (.); M is the interference covariance matrix M = σ 2 I+R,σ 2 I represents the noise component of interference, represents the covariance matrix of the reverberation, M r is the Toeplitz matrix, is the reverberation energy value at a given reverberation-to-noise ratio.

[0025] Preferably, the step 3) comprises:

[0026] Step 3-1) introduce potential random variables and obtain the probability density function of independent sample vectors based on the unknown probability distribution function;

[0027] Step 3-2) Using Jensen inequality to obtain the logarithmic joint probability density function of the echo data matrix under the H1 assumption, the E-step calculation result of the EM algorithm is obtained;

[0028] Step 3-3) Use the maximum likelihood estimation method to solve the unknown parameters in the E step and obtain the M step estimation result.

[0029] Preferably, the step 3-1) comprises:

[0030] Introducing the latent random variable c k , k=1,…,K, the corresponding unknown probability distribution function is P(c k =s) = p s ,s=0,1;

[0031] Apply the total probability formula to convert the independent sample vector z k The probability density function f(z k ; Φ k ) is expressed as:

[0032] f(z k ; Φ k )=f(z k |c k =0,0;M)p0+f(z k |c k =1,α k ; M)h(α k ; b) p1 where p0 and p1 represent z k The probability of having and without a target, Φ k =P k ∪{p s :s=0,1} represents the set of parameters to be estimated, P k ={M,α k ,b},k∈Ω T , P k ={M},k∈Ω\Ω T ;

[0033] Preferably, the step 3-2) comprises:

[0034] Using Jensen's inequality to obtain the echo data matrix under the H1 assumption The logarithmic joint probability density function L(Z;Φ) is expressed as:

[0035]

[0036] In the formula, q k (s), s=0,1 means given zk Next k = the posterior probability function of s, ∑(.) represents the accumulation operation, and log(.) represents the logarithmic operation;

[0037] Apply the E-step optimization process in the EM algorithm and use the generalized information criterion to add a penalty term to improve the (m-1)th iteration q k (s) is expressed as:

[0038]

[0039] Among them, u(s)=(N 2 +3s)(1+ρ) / 2 is the penalty function, ρ≥1, (.) (m-1) represents the estimated result after the (m-1)th outer loop iteration (.), represents the estimated value of the parameter.

[0040] Preferably, the estimation result of step 3-3)M includes:

[0041] Using the Lagrange operator, we can get p s ,s=0,1Estimation results:

[0042]

[0043] Set the initial value of the (n-1)th inner loop It is known that in the (m)th EM iteration, the (n)th inner loop iteration Results for:

[0044]

[0045] in,(.) (m)(n) It represents the estimated result after the (n)th inner loop iteration of the (m)th outer loop (.);

[0046] based on As a result, we get and The estimated results are:

[0047]

[0048] in,

[0049]

[0050] Select an appropriate maximum number of iterations m = m max , n=n max Until the EM iteration ends, the final estimation result of EM is obtained:

[0051] Preferably, the adaptive detector of the likelihood ratio test in step 4) is:

[0052]

[0053] in,

[0054] Respectively represent p s , M, α k , b is the estimated value under the H1 hypothesis, is the estimated value of M under the H0 hypothesis. ∏(.) represents the cumulative multiplication operation, H0 and H1 represent the no-target hypothesis and the target existence hypothesis respectively, and η represents the set detection threshold.

[0055] On the other hand, the present invention also provides a multi-target detection system based on sparse reconstruction and expectation maximization clustering, comprising:

[0056] A preprocessing module is used to preprocess the echoes received by the linear array in the detection area to obtain K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution;

[0057] The sparse model building module is used to implement uniform and equidistant sampling of the spatial sectors of the detection area to obtain K θ Alternative angles, based on K θ Alternative angles, construct K θ Dimensional spatial domain sparse vector, establish a sparse model of whether the independent sample vector exists in the target, and obtain the joint probability density function;

[0058] An expectation maximization clustering module, which is used to obtain the classification and estimation results of parameters in a multi-target scenario through cyclic iteration by using a joint method of expectation maximization clustering based on a sparse model; and

[0059] The adaptive detection module is used to obtain an adaptive detector based on likelihood ratio test according to the classification and estimation results to achieve accurate multi-target detection.

[0060] Compared with the prior art, the advantages of the present invention are:

[0061] 1. This method abandons the traditional clustering assumption and no longer assumes that the arrival angles of multiple targets are consistent. Instead, it assumes that they are different and independent within the sonar detection sector. This model is more in line with the actual application scenarios of sonar, making the multi-target detection results of sonar more reliable;

[0062] 2. The present invention does not rely on the traditional multi-target spatial guidance vector information to estimate the arrival angle. This means that even in the absence of accurate target direction information, multi-target detection can be effectively performed, thereby reducing the reliance on prior knowledge and improving the applicability and flexibility of the algorithm;

[0063] 3. The present invention uses spatial sparse recovery technology to estimate the arrival angle of multiple targets. This method can accurately separate and estimate the arrival angle of the target echo from the complex sonar signal. The advantage of this technology is that it can improve the algorithm's computational efficiency and the accuracy of angle estimation without sacrificing detection performance;

[0064] 4. The method of the present invention combines the EM clustering algorithm with the sparse recovery technology to achieve adaptive detection of multiple targets. The EM algorithm is used to classify and identify the target echoes contained in the received signal, while the sparse reconstruction technology is used to estimate the specific arrival angles of these targets. The design of this joint algorithm enables the detector to automatically adapt to different target conditions, improving the accuracy and reliability of detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a flow chart of the multi-target detection method based on sparse reconstruction and expectation maximization clustering of the present invention;

[0066] Figure 2 is a three-dimensional real sparse amplitude matrix;

[0067] Figure 3 is the three-dimensional reconstructed sparse amplitude matrix;

[0068] Figure 4 is the probability of correct classification of the sample;

[0069] Figure 5 It is the curve of target detection probability changing with SINR. DETAILED DESCRIPTION

[0070] The purpose of the present invention is to provide a more efficient and accurate multi-target detection method. By abandoning the traditional cluster hypothesis and adopting a sparse reconstruction and classification-assisted joint method, not only can the arrival angle of each target be estimated independently, but also there is no need to rely on complex multi-target spatial guidance vector information. By utilizing the EM clustering algorithm and the sparse reconstruction algorithm under the compressed sensing system, the present invention can effectively solve the multi-target sample classification problem and arrival angle estimation, thereby realizing adaptive multi-target detection. This method improves the accuracy of detection, especially when dealing with multi-target scenes, it can better avoid strong signal shielding, and while accurately estimating the arrival angle of multi-target signals, reduce target missed detection, and provide a new technical solution for the field of multi-target detection.

[0071] like Figure 1 As shown, the method includes:

[0072] Step 1) preprocessing the echoes received by the linear array in the detection area to obtain K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution;

[0073] Step 2) Perform uniform and equidistant sampling on the spatial sectors of the detection area to obtain K θ Alternative angles, based on K θ Alternative angles, construct K θ Dimensional spatial domain sparse vector, establish a sparse model of whether the independent sample vector exists in the target, and obtain the joint probability density function;

[0074] Step 3) adopting a joint method of expectation maximization clustering based on a sparse model to obtain the classification and estimation results of parameters in a multi-target scenario through cyclic iteration;

[0075] Step 4) According to the classification and estimation results, an adaptive detector based on likelihood ratio test is obtained to achieve accurate multi-target detection.

[0076] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0077] Example 1

[0078] Embodiment 1 of the present invention proposes a multi-target detection method based on sparse reconstruction and expectation maximization clustering. This method is particularly good at handling the problem of multi-target signal recognition in sonar systems. Its advantage is that it can accurately estimate the sample units and arrival angles corresponding to multiple targets, and does not need to rely on complex multi-target spatial guidance vector information. Specifically, this technology realizes the estimation of multi-target arrival angles through spatial sparse recovery technology. Spatial sparse recovery is an advanced signal processing technology that can extract key information from complex signals. In the present invention, this method is used to identify and locate the echo signals of multiple targets. In addition, the present invention also cleverly combines the EM classification algorithm for processing data containing hidden variables. Through the EM algorithm, the detector can adaptively identify and classify multi-target echoes, and maintain high accuracy even when the target signals overlap or are interfered by noise. The detailed design process of the present invention is as follows:

[0079] 1 Scenario Statistical Modeling

[0080] Assume that the echo in the detection area is received by a linear array composed of N array elements, and after preprocessing, K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution are obtained: Considering that the reflected signals of multiple targets arrive at the detection sector of the array through different wave arrival directions, it is assumed that the interference and noise in the background are statistically consistent and follow the statistical assumption of uniformity.

[0081]

[0082] in

[0083] H0 and H1 represent the hypothesis of no target and the hypothesis of target existence, respectively;

[0084] Interference covariance matrix M = σ 2 I+R,σ 2 I represents the noise component of interference; represents the covariance matrix of the reverberation, and M r is the Toeplitz matrix, is the reverberation energy value under a given reverberation-to-noise ratio (RNR);

[0085] α k 、v k The target complex amplitude factor and normalized steering vector in the kth sample unit where the target exists;

[0086] Ω={1,…,K} represents the sample vector z k , k = 1, ..., K, let T represent the number of multi-target echoes, then the subscript set of target components can be further expressed as Ω T ={k t,1 ,…,k t,T},Ω\Ω T Indicates that the target component does not exist.

[0087] The spatial sectors of the monitoring area are sampled evenly and at equal intervals to obtain the candidate angles in the detection sector. Based on this, represents the normalized steering vector corresponding to each discrete angle point in the sector, represents K based on the target complex amplitude factor θ dimensional spatial sparse vector. From a spatial perspective, using the inherent sparsity of multiple targets, z under H1 k It can be reformulated as the following sparse model:

[0088]

[0089] Among them, α k The non-zero elements of correspond to k∈Ω T region, indicating that there is a target echo in the region; and in the target-free region k∈Ω\Ω T Inside, α k = 0. Since α kis sparse, we model it as a random vector subject to a sparsity-promoting prior. Therefore, under the h1 assumption, z k and α k The expression of the joint probability density function (PDF) is:

[0090]

[0091] Among them, z k The conditional probability density function of is:

[0092] h(α k ; b) is α k A sparsity-promoting prior function based on the sparsity tuning parameter b∈(0,1]. In the next stage, we consider combining the Laplace prior with the EM algorithm to complete the estimation of the corresponding parameters. Finally, we design a joint adaptive detector based on sparse reconstruction and expectation-maximization clustering through an LRT-based design procedure.

[0093] 2 Algorithm Design

[0094] Introducing the latent random variable c k , k = 1, ..., K, the corresponding unknown probability distribution function can be expressed as P(c k =s) = p s ,s=0,1. Applying the total probability formula, the unit sample z k The probability density function of is expressed as:

[0095] f(z k ; Φ k )=f(z k |c k =0,0;M)p0+f(z k |c k =1,α k ; M)h(α k ; b) p1. (5)

[0096] Among them, p0 and p1 represent unit samples z respectively. k The probability of having and without a target, Φ k =P k ∪{p s :s=0,1} represents the set of parameters to be estimated, P k ={M,α k ,b},k∈Ω T , P k ={M},k∈Ω\Ω T .make in represents an N-dimensional complex number. Then the logarithmic joint probability density function is expressed as:

[0097]

[0098] In the formula, q k (s), s=0,1 means a given sample unit z k Next k = s's posterior probability function. Apply the E-step optimization process in the EM algorithm and use the generalized information criterion to add a penalty term to improve it. In the (m-1)th iteration, q k (s) can be expressed as:

[0099]

[0100] Among them, u(s)=(N 2 +3s)(1+ρ) / 2 is the penalty function, ρ≥1. (.) (m-1) represents the estimated result after the (m-1)th outer loop iteration (.), Represents the estimated value of the parameter. Applying the M-step optimization process can obtain the optimized estimate of the unknown parameters:

[0101]

[0102] First, estimate p s ,s=0,1, using Lagrange operator to optimize Item, we can get:

[0103]

[0104] Assume that the initial value of the (n-1)th inner loop is It is known that based on (8), the result of the (n)th inner loop iteration in the (m)th EM iteration can be obtained:

[0105]

[0106] here,(.) (m)(n) represents the estimated result after the (m)th outer loop and the (n)th inner loop iteration (.). Substituting (10) into (8) yields:

[0107]

[0108] Consider the Laplace prior:

[0109]

[0110] in Indicates that it belongs to the kth distance unit, the kth θ The target echo amplitude of the wave arrival angle (when , indicating that there is no target here). Substituting it into (11), taking the derivative and setting it to zero, we can get and The estimated results are:

[0111]

[0112] in,

[0113]

[0114] Select an appropriate maximum number of iterations m = m max , n=n max Until the EM iteration ends, the final estimation result of EM is obtained: Combining the obtained estimates, the adaptive detector based on likelihood ratio test (LRT) can be obtained as follows:

[0115]

[0116] in,

[0117] Respectively represent p s , M, α k , b is the estimated value under the H1 hypothesis, is the estimated value of M under the H0 hypothesis. ∏(.) represents the cumulative multiplication operation, H0 and H1 represent the no-target hypothesis and the target existence hypothesis respectively, and η represents the set detection threshold.

[0118] Example 2

[0119] Embodiment 2 of the present invention proposes a multi-target detection system based on sparse reconstruction and expectation maximization clustering, which is implemented based on the method of embodiment 1 and includes:

[0120] A preprocessing module is used to preprocess the echoes received by the linear array in the detection area to obtain K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution;

[0121] The sparse model building module is used to implement uniform and equidistant sampling of the spatial sectors of the detection area to obtain K θ Alternative angles, based on K θ Alternative angles, construct K θ Dimensional spatial domain sparse vector, establish a sparse model of whether the independent sample vector exists in the target, and obtain the joint probability density function;

[0122] The expectation maximization clustering module is used to adopt a joint method of expectation maximization clustering based on a sparse model to obtain the classification and estimation results of parameters in a multi-target scenario through cyclic iteration;

[0123] The adaptive detection module is used to obtain an adaptive detector based on likelihood ratio test according to the classification and estimation results to achieve accurate multi-target detection.

[0124] Simulation analysis:

[0125] We use Monte Carlo simulation method to verify the classification effectiveness of the invention in multi-target scenarios and the estimation accuracy of target arrival angle. We consider the following conditions: there are 6 targets in the scene, the number of unit samples K = 50, and the number of spatial channels N = 8. The signal-to-interference-noise ratio of the target echo (k=1,...,K;k θ =1,...,K θ ), take the noise energy σ 2 =1, RNR = 20dB, The array detection sector range is [-20°, 20°]. Take the maximum number of iterations n of the inner and outer loops of EM max =5,m max =10.

[0126] In order to verify the sparse matrix α=[α1,...,α K ], Figure 2 and Figure 3 The real α and the reconstruction are plotted separately The three-dimensional sparse matrix amplitude image is obtained. The six target echoes are set to appear in the 6th sample unit, with an arrival angle of -20°; the 6th sample unit, with an arrival angle of 20°; the 30th sample unit, with an arrival angle of -10°; the 30th sample unit, with an arrival angle of 20°; the 47th sample unit, with an arrival angle of -20°; and the 47th sample unit, with an arrival angle of 10°. It can be seen that the reconstruction result based on the proposed method is highly consistent with the real matrix. In terms of the estimation of target components, the present invention can obtain the precise positions of multiple targets and accurately calculate the unit samples and arrival angles corresponding to them.

[0127] Under the condition of SINR = 10dB, Figure 4 The correct classification percentage of the proposed classifier in 1000 Monte Carlo tests on whether there is a target in the sample unit is shown. It can be seen that the correct rate of the classifier in the classification stage is at least 88%, and the classification effect is satisfactory; in order to verify the effectiveness of the proposed algorithm in detecting targets, Figure 5 The detection probability curves based on the proposed detector and the GLRT detector (six targets) are shown after 1000 independent trials. The expression of the GLRT detector is as follows:

[0128]

[0129] in, Set p fa =10 -3 , detection threshold η, η GLRT From 100 / p fa In the same way, the number of unit samples considered by the GLRT detector is K GLRT =50, number of spatial channels N GLRT = 8. Compared with the traditional GLRT detector, the present invention shows superior detection performance.

[0130] Compared with the prior art, the method of the present invention not only excels in estimating the arrival angles of multiple targets, but more importantly, it does not need to rely on complex multi-target spatial guidance vector information to achieve target detection. By adopting spatial sparse recovery technology, the invention can accurately estimate the arrival angles of each target within the sonar detection sector, even if the echo azimuths of these targets are scattered and independent of each other. In addition, the method also cleverly combines the EM clustering algorithm to make the detection process more adaptive, and can intelligently distinguish and process the echo signals of multiple targets, thereby effectively avoiding the strong signal shielding problem common in traditional methods and improving the accuracy and efficiency of detection. This method that combines sparse reconstruction and classification assistance enhances the algorithm's adaptability to multi-target scenarios, making target detection more accurate and reliable.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A multi-target detection method based on sparse reconstruction and expectation maximization clustering, comprising: Step 1) preprocessing the echoes received by the linear array in the detection area to obtain K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution; Step 2) Perform uniform and equidistant sampling on the spatial sectors of the detection area to obtain K θ Alternative angles, based on K θ Alternative angles, construct K θ Dimensional spatial domain sparse vector, establish a sparse model of whether the independent sample vector exists in the target, and obtain the joint probability density function; Step 3) adopting a joint method of expectation maximization clustering based on a sparse model to obtain the classification and estimation results of parameters in a multi-target scenario through cyclic iteration; Step 4) According to the classification and estimation results, an adaptive detector based on likelihood ratio test is obtained to achieve accurate multi-target detection.

2. The multi-target detection method based on sparse reconstruction and expectation maximization clustering according to claim 1 is characterized in that: The linear array in step 1) includes N array elements. After preprocessing the echoes of the N array elements, K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution are obtained. in Represents an N-dimensional complex number.

3. The multi-target detection method based on sparse reconstruction and expectation maximization clustering according to claim 2 is characterized in that: K in step 2) θ The alternative angle is The process of establishing a sparse model of whether an independent sample vector exists in the target includes: make represents the normalized steering vector corresponding to Kθ candidate angles in the sector, represents K based on the target complex amplitude factor θ dimensional spatial sparse vector, the superscript T indicates transposition; the independent sample vector z k It is expressed as the following binary hypothesis based on the sparse model: Among them, α k The non-zero elements of correspond to k∈n T region, indicating that there is a target echo in the region; in the target-free region k∈Ω\Ω T Inside, α k = 0; Ω = {1, ..., K} represents the sample vector z k , k=1,..., the subscript set of K, Ω T Indicates that the target component does not exist.

4. The multi-target detection method based on sparse reconstruction and expectation maximization clustering according to claim 3 is characterized in that: The joint probability density function of step 2) is: Among them, (z k |iα k ; M) is z k The conditional probability density function of is: h(α k ; b) is α k Based on the sparsity-promoting prior function with sparse tuning parameter b∈(0,1], represents the conjugate transpose of (.); M is the interference covariance matrix M = σ 2 I+R,σ 2 I represents the noise component of the interference, represents the covariance matrix of the reverberation, M r is the Toeplitz matrix, is the reverberation energy value at a given reverberation-to-noise ratio.

5. The multi-target detection method based on sparse reconstruction and expectation maximization clustering according to claim 4 is characterized in that: The step 3) comprises: Step 3-1) introduce potential random variables and obtain the probability density function of independent sample vectors based on the unknown probability distribution function; Step 3-2) Using Jensen inequality to obtain the logarithmic joint probability density function of the echo data matrix under the H1 assumption, the E-step calculation result of the EM algorithm is obtained; Step 3-3) Use the maximum likelihood estimation method to solve the unknown parameters in the E step and obtain the M step estimation result.

6. The multi-target detection method based on sparse reconstruction and expectation maximization clustering according to claim 5, characterized in that: The step 3-1) comprises: Introducing the latent random variable c k , k = 1, ..., K, the corresponding unknown probability distribution function is P(c k =s) = p s , s=0,1; Apply the total probability formula to convert the independent sample vector z k The probability density function f(z k ; Φ k ) is expressed as: f(z k ;Φ k )=f(z k |c k =0,0;M)p0+f(z k |c k =1,α k ;M)h(α k ;b)p1# Among them, p0 and p1 represent z k The probability of having and without a target, Φ k =P k ∪{p s : s = 0, 1} represents the set of parameters to be estimated, P k ={M, α k ,b},k∈Ω T , P k ={M}, k∈Ω\Ω T .

7. The multi-target detection method based on sparse reconstruction and expectation maximization clustering according to claim 6, characterized in that: The step 3-2) comprises: Using Jensen's inequality to obtain the echo data matrix under the H1 assumption The logarithmic joint probability density function L(Z;Φ) is expressed as: In the formula, q k (s), s=0,1 means given z k Next k = the posterior probability function of s, ∑(.) represents the accumulation operation, and log(.) represents the logarithmic operation; Apply the E-step optimization process in the EM algorithm and use the generalized information criterion to add a penalty term to improve the (m-1)th iteration q k (s) is expressed as: Among them, u(s)=(N 2 +3s)(1+ρ) / 2 is the penalty function, ρ≥1, (.) (m-1) represents the estimated result after the (m-1)th outer loop iteration (.), represents the estimated value of the parameter.

8. The multi-target detection method based on sparse reconstruction and expectation maximization clustering according to claim 7, characterized in that: The estimation results of step 3-3)M include: Using the Lagrange operator, we can get the estimated results for ps, s = 0, 1: Set the initial value of the (n-1)th inner loop It is known that in the (m)th EM iteration, the (n)th inner loop iteration Results for: in,(.) (m)(n) It represents the estimated result after the (n)th inner loop iteration of the (m)th outer loop (.); based on As a result, we get and The estimated results are: in, Select an appropriate maximum number of iterations m = m max , n=n max Until the EM iteration ends, the final estimation result of EM is obtained:

9. The multi-target detection method based on sparse reconstruction and expectation maximization clustering according to claim 8, characterized in that: The adaptive detector of the likelihood ratio test in step 4) is: in, Respectively represent p s , M, α k , b is the estimated value under the H1 hypothesis, is the estimated value of M under the H0 hypothesis; Π(.) represents the cumulative multiplication operation, H0 and H1 represent the no-target hypothesis and the target existence hypothesis respectively, and η represents the set detection threshold.

10. A multi-target detection system based on sparse reconstruction and expectation maximization clustering, characterized in that: include: A preprocessing module is used to preprocess the echoes received by the linear array in the detection area to obtain K independent sample vectors satisfying zero-mean multivariate complex Gaussian distribution; The sparse model building module is used to implement uniform and equidistant sampling of the spatial sectors of the detection area to obtain K θ Alternative angles, based on K θ Alternative angles, construct K θ Dimensional spatial domain sparse vector, establish a sparse model of whether the independent sample vector exists in the target, and obtain the joint probability density function; The expectation maximization clustering module is used to adopt a joint method of expectation maximization clustering based on a sparse model to obtain the classification and estimation results of parameters in a multi-target scenario through cyclic iteration; and The adaptive detection module is used to obtain an adaptive detector based on likelihood ratio test according to the classification and estimation results to achieve accurate multi-target detection.

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