A classification assistance-based anti-coherent interference target detection method and system

Abstract

The application provides a kind of classification auxiliary-based anti-coherent interference target detection method and system, the method comprises: the echo received by linear array in detection area is preprocessed, and the sample vector to be detected and auxiliary sample vector are obtained;Independent and identically distributed discrete random variable is introduced, and the probability density function of the sample vector to be detected is obtained;The posterior probability of the classification to which the sample vector to be detected belongs is calculated using the E step of EM algorithm, and the estimation values of interference covariance matrix, target echo, the signal amplitude of CJ, the posterior probability of the classification to which the sample vector to be detected belongs and incident angle are obtained in M step according to auxiliary sample data set;According to the obtained estimation values, an adaptive detector based on LRT is obtained, and anti-coherent interference target detection is realized.The advantage of the application lies in: single unit sample containing different signal components can be autonomously identified and processed, and the efficiency and accuracy of interference / target detection are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of sonar anti-jamming detection, and particularly relates to a classification-assisted anti-coherent jamming target detection method and system. BACKGROUND

[0002] With the increasing complexity of the marine environment, sonar systems face more challenges in practical applications, which makes the problem of target detection of multi-channel sonar in a complex jamming environment gradually attract attention. The space-time adaptive detection (STAD) technology is often used for target detection in a strong reverberation background because of its excellent reverberation suppression and target detection performance. Based on different detector design criteria, the technology uses the space-time joint data received by the sonar to construct a detection statistic, and simultaneously realizes reverberation suppression and target detection by comparing with a preset threshold, thereby greatly improving the target detection performance in a complex underwater environment. With the development of the STAD theoretical system, the generalized likelihood ratio detector (GLRT), the adaptive matched filter (AMF), the Rao detector, the Wald detector and other detection algorithms with constant false alarm rate (CFAR) characteristics have been proposed and applied.

[0003] In addition to marine reverberation interference, sonar systems also need to cope with the threat of active artificial interference. As a typical artificial countermeasure, coherent jamming (CJ) intercepts sonar transmitted signals through digital radio frequency storage technology, generates deceptive signals highly correlated with real target echoes through waveform modulation and power enhancement processing. Such interference can accurately simulate the acoustic characteristics of the target, so that the real echo is masked by the false signal, and eventually leads to false alarm or missed detection of the detection system. The traditional anti-CJ target detection method based on STAD has the problems of insufficient mining of sample component heterogeneity information and inability to dynamically select the optimal detector according to environmental changes, which makes the detection algorithm performance significantly decrease in a dynamic jamming environment.

[0004] Based on the anti-CJ target detection and information extraction problem of STAD, the existing technical solutions include:

[0005] Solution one: The modified Rao and Wald detector design framework proposed by Sun Mengru et al. solves the key problems of subspace target detection under coherent jamming (including the first derivation of a new Rao detector Rao-SNE-I in a structured non-uniform environment under known interference, the unified subspace generalization form of four types of equivalent detectors as AORD under completely unknown interference, and the proof of the theoretical limitations of the partial known interference without reasonable Rao / Wald solution) by reconstructing the complex parameter set and correcting the Fisher information matrix. The effectiveness of the modified detector is verified through statistical analysis and numerical experiments.

[0006] This scheme only studies the existence of targets in a specific CJ scene, lacks analysis of signal components in the detection scene, and ignores the influence of CJ in the scene on target detection.

[0007] Scheme two: sparse reconstruction architecture based on compressed sensing, by modeling target detection in a joint interference scene as a sparse signal reconstruction problem and applying the SLIM algorithm, solves the detection and classification problem of CJ, first realizes the joint estimation of target response and CJ amplitude, and uses the characteristics of sparse solution to complete signal classification (distinguish targets, CJ and their coexistence scene), replaces the traditional sidelobe blanking (SLB) function, and overcomes the limitation that SLB needs to be shielded when targets and CJ coexist.

[0008] This scheme only relies on the estimated angle characteristics to identify the signal components in the scene, and relies too much on the accuracy of the target angle estimation results of the algorithm, and does not fully mine the information of abnormal values in the sample.

[0009] The common problem of existing CJ scene target detection methods is that they fail to fully exploit and utilize the heterogeneity information of sample components, and have significant performance limitations in dynamic interference environments. SUMMARY

[0010] The present application proposes an anti-coherent interference detection method and system based on a classification auxiliary algorithm to solve the signal component discrimination and target detection problem in a CJ environment. This method constructs a classification model of target echo and coherent jamming (CJ) existence assumption, estimates the noise interference covariance matrix using auxiliary samples, completes sample classification and angle estimation of targets and CJ using grid search and expectation maximization (EM) classification algorithm, and designs an adaptive detector based on likelihood ratio test (LRT) according to the final parameter estimation result, to realize target CFAR detection that can change with the environment.

[0011] The present application proposes an anti-coherent interference target detection method based on classification assistance, comprising:

[0012] Step 1: Preprocess the echo received by the linear array in the detection area to obtain a to-be-detected sample vector and an auxiliary sample vector;

[0013] Step 2: Introduce independent and identically distributed discrete random variables to obtain the probability density function of the to-be-detected sample vector;

[0014] Step 3: Calculate the posterior probability of the classification to which the to-be-detected sample vector belongs using the E step of the EM algorithm, and obtain the estimates of the interference covariance matrix, the target echo, the CJ signal amplitude, the posterior probability of the classification to which the to-be-detected sample vector belongs, and the incident angle in the M step according to the auxiliary sample data set;

[0015] Step 4: Based on the obtained estimates, an adaptive detector based on LRT is obtained to achieve the anti-coherent interference target detection.

[0016] As an improvement of the above method, the probability density function of the sample vector to be detected is expressed as:

[0017] ;

[0018] Wherein, represents the probability density function of the sample vector to be detected; represents the sample vector to be detected; represents an independent and identically distributed discrete random variable introduced, which is equal to the probability ; , , and respectively represent the probabilities of the sample to be detected without target and CJ component, containing CJ, containing target and containing target and CJ component, and ; represents the unknown parameter set of the sample to be detected, when , otherwise when , otherwise ; , , , respectively represent the unknown parameter set of the sample to be detected under the assumption of , , , , , , , respectively represent the alternative hypotheses of no target, existence of CJ, existence of target, existence of target and CJ; represents the interference covariance matrix containing noise and clutter information; represents the target echo; represents the signal amplitude of the target CJ; and represent the incident angle.

[0019] As an improvement of the above method, the step 3 comprises:

[0020] The log-likelihood function of is expressed by using Jensen inequality as:

[0021] ​​;

[0022] wherein, denotes the log-likelihood function of denotes the logarithm operation, denotes the sample to be detected the posterior probability function of when

[0023] The E-step optimization procedure in the EM algorithm is applied and the penalty term is added to the joint model order selection criterion to improve the estimation of in the th iteration as:

[0024] ;

[0025] wherein, denotes the estimation of after the th loop iteration, denotes the interference covariance matrix estimate, the penalty function , and the coefficient ;

[0026] The M-step optimization procedure in the EM algorithm solves the following problem:

[0027] ;

[0028] The estimate of the interference covariance matrix is obtained from the auxiliary sample dataset as:

[0029] ;

[0030] Only considering the second term related to , the estimation of in the th loop optimization is obtained by combining the Lagrange operator optimization method under the constraint as:

[0031] ;

[0032] It is assumed that in the th EM iteration, the estimation result of after the th internal loop is known, and the problem solved by the M-step optimization procedure is taken the partial derivative with respect to and set to zero to obtain the optimization result of as:

[0033] ;

[0034] ​​​Set the first EM iteration, the first internal loop after estimation results Known, get optimization results:

[0035] ;

[0036] Finally through the grid search, the target and CJ incident angle estimation:

[0037] ;

[0038] The final parameter estimation results: , , , , , .

[0039] As an improvement of the above method, the step 4 includes:

[0040] The LRT-based adaptive detector expression is:

[0041] ;

[0042] Wherein, is the estimation result of ; , , is the detection threshold set according to the set false alarm rate

[0043] When the target / interference exists, the probability density function of is expressed as:

[0044] ;

[0045] Wherein, denotes the conjugate transpose; denotes the trace of the matrix; denotes the determinant evaluation; denote the normalized spatial steering vector with incident angle , ;

[0046] When there is no target / interference, the probability density function of is expressed as:

[0047] . ​​​

[0048] This application also provides a classification-assisted anti-coherent interference target detection system, implemented based on the above method, the system comprising:

[0049] The preprocessing module is used to preprocess the echoes received by the linear array within the detection area to obtain the sample vector to be detected and the auxiliary sample vector.

[0050] The probability density function acquisition module is used to introduce independent and identically distributed discrete random variables to obtain the probability density function of the sample vector to be detected.

[0051] The EM algorithm module is used to calculate the posterior probability of the class to which the sample vector to be detected belongs in the E-step of the EM algorithm. In the M-step, the interference covariance matrix, the target echo, the signal amplitude of CJ, the posterior probability of the class to which the sample vector to be detected belongs, and the estimated values ​​of the incident angle are obtained from the auxiliary sample dataset.

[0052] The anti-interference detection module is used to obtain an LRT-based adaptive detector based on the obtained estimated values, thereby achieving anti-coherent interference target detection.

[0053] Compared with existing technologies, the advantages of this application are:

[0054] This application proposes an innovative anti-CJ target detection technique. This technique simultaneously considers the presence and signal characteristics of both CJ and the target within the scene. By introducing latent variables, it remodels the detection scene where CJ and the target exist separately (simultaneously). Based on the EM classification algorithm and the grid search method, it achieves sample classification and joint estimation of the CJ / target incident angles. Specifically, the grid search technique can accurately obtain the incident angles of the CJ and target signals; simultaneously, the fused EM classification algorithm can autonomously identify and process unit samples containing different signal components, improving the efficiency and accuracy of interference / target detection. Attached Figure Description

[0055] Figure 1 The flowchart shown is for a classification-assisted target detection method against coherent interference.

[0056] Figure 2 As shown Classification results of sample units in the scenario (1000 simulation experiments);

[0057] Figure 3 As shown Classification results of sample units in the scenario (1000 simulation experiments);

[0058] Figure 4 As shown Classification results of sample units in the scenario (1000 simulation experiments);

[0059] Figure 5 The detection probability curve shown as the SINR or JNR changes (1000 simulation tests, the false alarm probability is The sample unit classification result under the scene (1000 simulation tests);

[0060] Figure 6 The detection probability curve shown as the SINR or JNR changes (1000 simulation tests, the false alarm probability is ). DETAILED DESCRIPTION

[0061] The technical solutions of the present application will be described in detail below with reference to the accompanying drawings.

[0062] The core principle of the present application is to jointly use the EM classification under the latent variable model and the grid search method, introduce latent variables representing different signal components by using the latent variable model, establish a correlation model between the sample statistical characteristics and the CJ in the unit sample and the existence of the target, use the EM iteration to classify the samples to be detected, realize the preliminary identification of the existence of the target and the CJ in the sample, and on this basis, realize the angle estimation of the two by jointly using the maximum likelihood estimation and the grid search, and finally realize the CFAR decision of the existence of the target based on the classification result of the target components in the scene to guide the selection of the detector under the corresponding scene.

[0063] As Figure 1 shown, the anti-coherent interference target detection method based on classification assistance provided by the present application includes the following specific process:

[0064] Scene statistical modeling:

[0065] Suppose that the receiving array of a sonar detection system is a element equidistant uniform linear array. After pretreatment such as filtering, amplification, analog-to-digital conversion, etc., the received signal is respectively organized into a sample vector to be detected and auxiliary sample vectors . It is assumed that only contains environmental noise and clutter; the sample vector to be detected contains environmental noise, clutter, and possibly existing target echo and CJ components. In order to determine the existence of the target and the CJ in the scene, the following multiple hypothesis testing problem is established:

[0066] (1)

[0067] wherein, , , , respectively represent the alternative hypotheses of no target, existence of CJ, existence of target, and existence of target and CJ; represents is a mean of The covariance matrix is of Gaussian complex vector; This represents the interference covariance matrix, which contains information about noise and clutter. They represent the angles of incidence as... , The normalized spatial steering vector, , These represent the signal amplitudes of the target echo and CJ, respectively.

[0068] make , , , These represent the samples to be tested in... , , , The set of unknown parameters under the above four assumptions. The expression for the probability density function (PDF) is:

[0069] (2)

[0070] in, Indicates exponentiation. This indicates the conjugate transpose. This indicates the evaluation of the determinant. This indicates finding the trace of a matrix.

[0071] Algorithm Design:

[0072] Introducing independent and identically distributed discrete random variables It is equal to probability ,in, , , and These represent the samples to be tested. The probabilities of having no target and CJ components, including CJ, including the target, and including both target and CJ components are given. Applying the law of total probability, the sample to be detected can be... The probability density function can be rewritten as:

[0073] (3)

[0074] in, Represents the set of unknown parameters of the sample to be tested, when hour ,otherwise ,when hour ,otherwise The EM algorithm is then used to solve the sample class determination problem when the target is present. The log-likelihood function of (3) can be expressed as

[0075] (4)

[0076] where denotes the logarithm operation, denotes the sample to be detected, and is the posterior probability function of when the target is present. The E-step optimization procedure in the EM algorithm is applied and a penalty term is added to improve the joint model order selection (MOS) criterion. The estimate of in the th iteration is given by

[0077] (5)

[0078] where denotes the estimate of after the th loop iteration, denotes the interference covariance matrix estimate, the penalty function , and the coefficient . The M-step optimization procedure is to solve the following problem:

[0079] (6)

[0080] The estimate of the interference covariance matrix can be obtained from the auxiliary sample dataset as

[0081] (7)

[0082] where K denotes the number of auxiliary samples.

[0083] Considering only the second term related to and combining the Lagrange operator optimization method under the constraint of , the estimate of in the th loop optimization is given by

[0084] (8)

[0085] Assuming that in the th EM iteration, the estimate of after the th loop iteration is known, the partial derivative of (6) with respect to is taken and set to zero to obtain the optimization result of .

[0086] (9)

[0087] Similarly, assume in the jth EM iteration, the estimation results after the (j-1)th inner loop Given, the optimization results of can be obtained as:

[0088] (10)

[0089] Finally, the target and CJ incident angle estimation is achieved by grid search:

[0090] (11)

[0091] where, is the log-likelihood function of

[0092] The final parameter estimation results are: , , , , , Combining the obtained estimation values, the adaptive detector based on LRT can be obtained as:

[0093] (12)

[0094] where, is the estimation result of , , , is the detection threshold set according to a specific false alarm rate When the target / interference exists, the PDF of can be expressed as:

[0095] (13)

[0096] When no target / interference exists, the PDF of

[0097] (14)

[0098] Simulation analysis:

[0099] ​​​​​​​​Monte Carlo simulation was used to verify the accuracy of the proposed method in signal component discrimination and its effectiveness in detecting CJ and targets. It is assumed that the sonar is equipped with an array of [number of elements]. A uniform linear array, auxiliary sample number .consider , , , In each of the four scenarios where the assumption holds true, the number of sample units to be detected is 1. The first scenario, where no target / CJ signal exists within the sample to be detected, corresponds to... Assume; will The sample unit is assumed to be of type 2, and the sample to be tested contains an interference-to-noise ratio (JNR) of 20 dB and an incident angle of [missing information]. CJ signal; The sample cells are assumed to be of type 3, with a signal-to-interference-to-noise ratio (SINR) of 20 dB and an incident angle of [missing information]. Target echo; The assumption is that the sample cell simultaneously contains CJ in The target signal in the data is of type 4.

[0100] To examine the algorithm's ability to classify samples containing different signal components, 1000 Monte Carlo experiments were conducted to verify the classification accuracy of sample units when a specific hypothesis was valid. Figures 2-5 They respectively showed the assumptions , , , The probability that a sample unit is classified into one of the four categories when the condition is met. As can be seen, In this scenario, the accuracy rate of sample unit classification is approximately 90%. In this scenario, the accuracy rate of sample unit classification is approximately 96%. In this scenario, the accuracy rate of sample unit classification is approximately 98%. In this scenario, the accuracy of sample unit classification is close to 100%. The accuracy of sample discrimination is above 90%, and the classification results are satisfactory.

[0101] To evaluate the detection performance of the proposed invention for CJ / targets in the scene, Figure 6 The results of 1000 Monte Carlo experiments are given. , , The detection probability curves of CJ and the target in three scenarios vary with JNR / SINR, and the false alarm probability is set. It can be observed that, under the same SINR or JNR conditions, compared to the detection results in the first two scenarios, The CJ and target detection probability in the scene is significantly increased. When SINR,JNR When SINR,JNR 16 dB, the detection probabilities of the three curves all tend to 100%, verifying the good detection performance of the application on CJ and target.

[0102] The application is based on a dynamic anti-CJ target detection scene, discards the deterministic interference model used in traditional methods, and introduces a latent variable to re-model the detection scene of the existence of CJ and target (simultaneously). This model is more consistent with the actual scene in electronic countermeasures, making the CJ / target detection more accurate.

[0103] Compared with the traditional method of regarding CJ as fixedly existing, the application realizes the existence evaluation of CJ and target signals by classifying sample units, designs and selects a detector more consistent with the current scene, so that the application has better detection performance in the dynamic CJ scene.

[0104] The method proposed in the application fuses the EM algorithm and the grid search method, analyzes sample data, adopts the maximum posterior probability criterion for judgment, and realizes the identification and information estimation of signal components in unit samples.

[0105] The anti-CJ target detection and information extraction scheme proposed in the application can accurately estimate the signal strength and incident angle of CJ and target in the scene, help the sonar to perceive CJ and target in the scene, and guide it to make correct detection / avoidance selection.

[0106] The application also provides an anti-coherent interference target detection system based on classification assistance, which is realized based on the above method. The system comprises:

[0107] A preprocessing module is configured to pre-process the echo received by the linear array in the detection area to obtain a to-be-detected sample vector and an auxiliary sample vector.

[0108] A probability density function acquisition module is configured to introduce a discrete random variable with independent and identical distribution to obtain a probability density function of the to-be-detected sample vector.

[0109] An EM algorithm module is configured to calculate the posterior probability of the classification to which the to-be-detected sample vector belongs by using the E step of the EM algorithm, and obtain, in the M step, an estimate of the interference covariance matrix, the target echo, the signal amplitude of CJ, the posterior probability of the classification to which the to-be-detected sample vector belongs, and the incident angle based on the auxiliary sample data set.

[0110] An anti-interference detection module is configured to obtain an adaptive detector based on LRT based on the obtained estimate, and realize anti-coherent interference target detection.

[0111] The application can also provide a computer device, comprising at least one processor, memory, at least one network interface and user interface. The various components in the device are coupled together by a bus system. It can be understood that the bus system is used to realize the connection communication between the components. In addition to including a data bus, the bus system also includes a power supply bus, a control bus and a status signal bus.

[0112] The user interface can include a display, a keyboard or a pointing device, for example, a mouse, a trackball, a touchpad or a touch screen.

[0113] It can be understood that the memory in the embodiments of the application can be a volatile memory or a non-volatile memory, or can include both volatile and non-volatile memories. The non-volatile memory can be a Read-Only Memory (ROM), a Programmable ROM (PROM), an Erasable PROM (EPROM), an Electrically EPROM (EEPROM) or a flash memory. The volatile memory can be a Random Access Memory (RAM) used as an external cache. By way of example, but not limitation, many forms of RAM can be used, such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDR SDRAM), Enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM) and Direct Rambus RAM (DRRAM). The memory described herein is intended to include, but not be limited to, these and any other suitable types of memory.

[0114] In some embodiments, the memory stores elements, executable modules or data structures, or a subset thereof, or an extended set thereof: an operating system and an application program.

[0115] The operating system includes various system programs, such as a framework layer, a core library layer, a driver layer, and the like, for implementing various basic services and processing hardware-based tasks. The application programs include various application programs, such as a media player (Media Player), a browser (Browser), and the like, for implementing various application services. The program for implementing the method of the embodiments of the present disclosure can be included in the application programs.

[0116] In the above-described embodiments, the processor can be configured to, by invoking the program or the instruction stored in the memory, specifically, the program or the instruction stored in the application program:

[0117] perform the steps of the above-described method.

[0118] The above-described method can be applied to the processor or implemented by the processor. The processor can be an integrated circuit chip having a signal processing capability. In the implementation process, the steps of the above-described method can be completed by hardware integrated logic circuits in the processor or by the instructions in the form of software. The above-described processor can be a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. The above-described methods, steps and logical block diagrams can be implemented or executed by the above-described processor. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor. The steps of the above-described method in combination with the above-described disclosure can be directly embodied as a hardware code processor to execute, or a combination of hardware and software modules in the code processor to execute. The software module can be located in the random access memory, the flash memory, the read-only memory, the programmable read-only memory or the electrically erasable programmable memory, the register or other mature storage mediums in the art. The storage medium is located in the storage memory, and the processor reads the information in the storage memory to complete the steps of the above-described method in combination with the hardware thereof.

[0119] It can be understood that the embodiments described in the present application can be realized by hardware, software, firmware, middleware, microcode or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), general purpose processors, controllers, micro-controllers, microprocessors, other electronic units designed to perform the functions described in the present application, or a combination thereof.

[0120] For software implementation, the present application can be implemented by executing the functional modules (such as processes, functions, etc.) described in the present application. The software code can be stored in a memory and executed by a processor. The memory can be implemented in the processor or outside the processor.

[0121] The present application also provides a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, each step of the above method embodiments can be implemented.

[0122] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit. Although the present application is described in detail with reference to the embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the present application, and they should be covered in the scope of the claims of the present application.

Claims

1. A classification-assisted target detection method for coherent interference, comprising: Step 1: Preprocess the echo received by the linear array within the detection area to obtain the sample vector to be detected and the auxiliary sample vector; Step 2: Introduce independent and identically distributed discrete random variables to obtain the probability density function of the sample vector to be detected; Step 3: Calculate the posterior probability of the class to which the sample vector to be detected belongs using the E-step of the EM algorithm. In the M-step, obtain the interference covariance matrix, target echo, signal amplitude of CJ, posterior probability of the class to which the sample vector to be detected belongs, and estimated values ​​of the incident angle based on the auxiliary sample dataset. Step 4: Based on the obtained estimates, an LRT-based adaptive detector is obtained to achieve target detection against coherent interference; The probability density function of the sample vector to be detected is expressed as: ； in, The probability density function representing the vector of the sample to be detected; Represents the vector of the sample to be detected; Let represent the introduced independent and identically distributed discrete random variables, which are equal to probability ; , , and These represent the samples to be tested. The probabilities of having no target and CJ components, including CJ, including the target, and including both target and CJ components are given. ; Represents the set of unknown parameters of the sample to be tested, when hour ,otherwise ,when hour ,otherwise ; , , , These represent the samples to be tested in... , , , The set of unknown parameters under the assumption, , , , Let represent alternative hypotheses for no target, existence of CJ, existence of target, and existence of both target and CJ, respectively. This represents the interference covariance matrix, which contains information about noise and clutter. Indicates the target echo; This indicates the signal amplitude of the target CJ; and Indicates the angle of incidence.

2. The classification-assisted anti-coherent interference target detection method according to claim 1, characterized in that, Step 3 includes: Using Jensen's inequality The log-likelihood function is expressed as: ； in, express The log-likelihood function; Represents logarithmic operations. Indicates the sample to be tested exist The posterior probability function at time; By applying the E-step optimization process of the EM algorithm and improving it by adding a penalty term using the joint model order selection criterion, we obtain the... In the next iteration The estimated value Represented as: ； in, Indicates the first After the second iteration The estimation results The penalty function represents the estimated value of the interference covariance matrix. ,coefficient ; The M-step optimization process in the EM algorithm addresses the following issues: ； The estimated value of the interference covariance matrix is ​​obtained from the auxiliary sample dataset: ； Only consider with The second related item, combined The Lagrange operator optimization method under constraints yields the... In the next iteration of optimization The estimated value is: ； Set at In the EM iteration, the first After the second inner loop Estimation results It is known that the problem solved by the M-step optimization process is... Taking the partial derivative and setting it to zero, we get Optimization results: ； Set at In the EM iteration, the first After the second inner loop Estimation results Given, we obtain Optimization results: ； Finally, the incident angle between the target and CJ is estimated through grid search: ； The final parameter estimation results are as follows: , , , , , .

3. The classification-assisted anti-coherent interference target detection method according to claim 2, characterized in that, Step 4 includes: The expression for the LRT-based adaptive detector is: ； in, for The estimation results; , , To determine the false alarm rate The set detection threshold; When the target / interference exists probability density function Represented as: ； in, Indicates conjugate transpose; This indicates finding the trace of a matrix; This indicates the evaluation of a determinant; They represent the angles of incidence as... , Normalized spatial steering vector; When no target / interference exists probability density function Represented as: 。 4. A target detection system for coherent interference based on classification assistance, implemented according to the method of any one of claims 1-3, characterized in that, The system includes: The preprocessing module is used to preprocess the echoes received by the linear array within the detection area to obtain the sample vector to be detected and the auxiliary sample vector. The probability density function acquisition module is used to introduce independent and identically distributed discrete random variables to obtain the probability density function of the sample vector to be detected. The EM algorithm module is used to calculate the posterior probability of the class to which the detected sample vector belongs in the E-step of the EM algorithm. In the M-step, the interference covariance matrix, target echo, CJ signal amplitude, posterior probability of the class to which the detected sample vector belongs, and estimated values ​​of the incident angle are obtained from the auxiliary sample dataset. The anti-interference detection module is used to obtain an LRT-based adaptive detector based on the obtained estimated values, thereby achieving anti-coherent interference target detection.

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