Wideband Radar Target Detection Method Based on Deep Network

Abstract

The present invention discloses a broadband radar target detection method based on a deep network, which mainly solves the problem of low detection probability caused by the mismatch of the detection model due to the artificially set target characteristics and the length of the detection window in the prior art. The solution is as follows: a target scattering point model is established by simulation to obtain the one-dimensional range profile of the target echo, and its training data set is established; a convolutional neural network composed of a cascade of multiple hidden layers and an output decoding layer is constructed, and the binary cross-entropy loss function is set as its cost function; according to the training data set and the cost function, the convolutional neural network is iteratively trained using the mini-batch gradient descent method; the echo of the target to be detected is input into the trained convolutional neural network to obtain the target detection result. The present invention applies deep learning to broadband target detection, avoids the mismatch of the detection model caused by artificially designing the length of the detection window or artificially setting the target characteristics, improves the detection probability of targets with different signal-to-noise ratios, and can be used for broadband radar tracking and early warning.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and further relates to a broadband radar target detection method, which can be used for tracking and warning of broadband radars. Background Art

[0002] Modern high-resolution radars can obtain high range resolution by transmitting broadband signals. At this time, the target size is larger than the size of the radar range resolution unit. Therefore, the target echo will be distributed in multiple range units, forming a high-resolution one-dimensional range profile. In the application of broadband radar target detection, the theoretically optimal detector is the matched filter detector, that is, when the target characteristics are completely known, the radar transmitted waveform is used to perform matched filtering on the target impulse response. Since in the actual detection scenario, all information of the target cannot be accurately known, the matched filter detector cannot be realized in practice. Thus, in the past few decades, several optimal or sub-optimal detectors based on single-pulse echoes have been invented when some or all of the true information of the target is unknown. Since the true information of the target is unknown, these detectors need to artificially set target information such as the position of the target in the echo signal or the length of the support area according to experience. For example, the generalized likelihood ratio detector SSD-GLRT based on the spatial density of scattering centers disclosed by the Naval Research Laboratory of the United States in the paper "Detection of a spatially distributed target in white noise" (Gerlach, K, etc., IEEE Signal Processing Letters, Vol. 4, 1997, pp. 198-200), and a "range extended target detector OS-RSTD based on order statistics" disclosed in the paper published by Dai Fengzhou et al. in the Journal of Electronics and Information Technology, Vol. 31, 2009, pp. 2488-2492. These detectors first design a certain decision criterion based on the artificially set target information, then calculate the corresponding detection threshold, then accumulate the energy of multiple range units in the one-dimensional range profile as the test statistic, and finally compare the test statistic with the test threshold to obtain the decision result. However, in practical applications, these artificially set target information usually has a certain model mismatch with the true information of the target, resulting in additional noise being doped when accumulating the energy of the one-dimensional range profile, making it difficult for the existing technologies to achieve their theoretical performance. Summary of the Invention

[0003] The object of the present invention is to propose a broadband radar target detection method based on a deep network in view of the above deficiencies of the existing technologies, to avoid the detection model mismatch caused by artificially designing the detection window length or artificially setting target characteristics, and to improve the target detection probability.

[0004] The technical solution for achieving the object of the present invention includes the following:

[0005] (1) Construct a training data set:

[0006] (1a) Utilize the parameter information of the target in the wideband radar scenario to simulate and establish a scattering point model of the target;

[0007] (1b) Calculate the echo signal received by the radar from the scattering point model, obtain the one-dimensional range profile of the wideband radar target, and randomly crop the one-dimensional range profile near the target. Take the cropped one-dimensional range profile as a training sample;

[0008] (1c) Repeat steps (1a)-(1b) several times to obtain the training data set D;

[0009] (2) Construct a convolutional deep neural network composed of 2K hidden layers and 1 output decoding layer in cascade, and use the binary cross-entropy loss function as the cost function J(θ) of this network, where K≥1;

[0010] (3) According to the training data set D and the cost function J(θ), use the mini-batch stochastic gradient descent method to train the convolutional neural network to obtain a trained convolutional neural network;

[0011] (4) Wideband radar target detection:

[0012] (4a) Obtain the wideband radar monopulse echo data and perform pulse compression and linear detection processing to obtain the one-dimensional range profile of the target to be detected;

[0013] (4b) Input the one-dimensional range profile into the trained convolutional neural network to obtain the network output sequence of the target to be detected;

[0014] (4c) According to the expected false alarm probability P fa and the average signal-to-noise ratio SNR of the radar, use the Monte Carlo method to calculate the detection threshold γ;

[0015] (4d) Calculate the maximum peak value a of the network output sequence obtained in (4b) at the target to be detected, and compare it with the detection threshold γ to complete the target detection:

[0016] If a≥γ, the target exists,

[0017] Otherwise, the target does not exist.

[0018] The present invention has the following advantages compared with the existing technologies:

[0019] First, the present invention applies deep learning technology to the field of wideband radar target detection, establishes a wideband radar target detector based on a deep network model, trains the deep network using simulated wideband radar target data, automatically extracts some target feature information that is difficult to extract manually by the network, and does not require artificial assumptions about the target prior information during the target detection process, avoiding the additional noise brought by the artificial extraction of target features using the model-driven method in the prior art and improving the detection probability of wideband radar targets.

[0020] Second, the present invention realizes end-to-end target detection by utilizing the modularity and easy integration characteristics of the deep network, that is, after the model is offline trained, only the threshold decision needs to be made on the network output of the online target echo, and the target detection result can be obtained simply and quickly.

[0021] Third, the present invention utilizes the property that one-dimensional convolution can process any long input, making the wideband radar target detector constructed by the present invention have no limit on the sequence length of the input target single-pulse one-dimensional range profile, and has strong adaptability and flexibility in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is the implementation flowchart of the present invention;

[0023] Figure 2 is the structural schematic diagram of the convolutional neural network in the present invention;

[0024] Figure 3 is the comparison diagram of the simulation results of the present invention, the signal-to-noise ratio weighted detector, and the traditional non-coherent integration sliding window detector for wideband radar target detection. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0025] The following further describes the embodiments and effects of the present invention in detail with reference to the drawings.

[0026] This embodiment is for detecting targets in a wideband high-resolution radar. Since the size of the target is larger than the size of the radar range resolution unit, the target can be regarded as composed of a series of scatterers, and the overall echo of the target can be regarded as the synthesis of the echoes of these scatterers, forming a one-dimensional range profile distributed in multiple range units in the range dimension. By simulating and establishing a training data set of single-pulse one-dimensional range profiles of wideband radar targets with different signal-to-noise ratios, training a convolutional neural network to enable it to learn the feature information of wideband radar targets from the simulation data with different signal-to-noise ratios, and then implementing wideband radar target detection to improve the detection probability of targets with different signal-to-noise ratios.

[0027] Referring to Figure 1 , the implementation steps of this embodiment are as follows:

[0028] Step 1, construct a training data set.

[0029] 1.1) Use the parameter information of the target in the wideband radar scenario to establish a scattering point model of the simulation target:

[0030] 1.1.1) Determine the value ranges of the parameters such as the size and the number of scattering points of the simulation target according to the size of the target to be detected;

[0031] 1.1.2) Randomly generate the length L, width W, height H and the number of scattering points N of the simulation target within the value ranges of the parameters of the simulation target, and assign a random scattering coefficient σ to each scattering point i ;

[0032] 1.1.3) Set the distance R of the center of the simulation target relative to the wideband radar, and randomly generate the distance R of each scattering point of the simulation target relative to the wideband radar within the three-dimensional space range of L, W, H with R as the symmetric center i , to obtain the scattering point model of the simulation target {(R i , σ i ) | i = 1, 2,..., N}.

[0033] 1.2) Calculate the echo signal received by the radar from the scattering point model:

[0034] 1.2.1) Obtain the transmitted waveform s w of the wideband radar according to the bandwidth B aup of the wideband radar transmitted signal, the pulse width T s of the wideband radar transmitted pulse, and the set sampling frequency F t of the wideband radar;

[0035] 1.2.2) Based on the established scattering point model of the simulation target {(R i , σ i ) | i = 1, 2,..., N} and the obtained transmitted waveform s t (t) of the wideband radar, calculate the single-pulse echo of each scattering point respectively:

[0036] s r (t) i = Ar i * s t (t - τ i ) + w r (t), i = 1, 2,..., N

[0037] where s r (t) i is the single-pulse echo of the i-th target scattering point, Ar i is the proportionality coefficient of the echo of the i-th target scattering point, τ i is the echo time delay of the i-th target scattering point, wr (t) is the Gaussian white noise in the receiver;

[0038] 1.2.3) Linearly superpose the monopulse echoes of all scattering points in the complex domain to obtain the overall echo signal of this simulated target.

[0039] 1.3) For different signal-to-noise ratios, sequentially add noise, perform pulse compression, and linear detection processing on the echo signals received by the broadband radar to obtain the one-dimensional range profiles of the broadband radar targets at different signal-to-noise ratios;

[0040] 1.4) Randomly crop the obtained one-dimensional range profiles near the target, and use the cropped one-dimensional range profiles as a training sample data;

[0041] 1.5) Repeat steps 1.1)-1.4) several times to obtain the training dataset D.

[0042] Step 2, construct a convolutional neural network.

[0043] Refer to Figure 2 , the implementation of this step is as follows:

[0044] 2.1) Establish a convolutional deep neural network structure cascaded by 2K hidden layers and 1 output decoding layer, where:

[0045] The 2K hidden layers have the same number of channels, and each hidden layer is alternately cascaded by a one-dimensional convolutional layer and a cropping layer. The convolutional kernel sizes of all convolutional layers gradually increase as the network deepens. Each cropping layer is connected after a convolutional layer and is used to crop the output sequence of the one-dimensional convolutional layer to the same length as the input sequence of this one-dimensional convolutional layer.

[0046] Taking K = 16 and the number of channels in the hidden layer being 25 as an example, that is, the convolutional neural network contains a total of 32 hidden layers, where:

[0047] The first layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 3;

[0048] The second layer is a cropping layer with 25 channels;

[0049] The third layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 3;

[0050] The fourth layer is a cropping layer with 25 channels;

[0051] The fifth layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 5;

[0052] The sixth layer is a cropping layer with 25 channels;

[0053] The seventh layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 5;

[0054] The eighth layer is a cropping layer with 25 channels;

[0055] The ninth layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 9;

[0056] The tenth layer is a cropping layer with 25 channels;

[0057] The eleventh layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 9;

[0058] The twelfth layer is a cropping layer with 25 channels;

[0059] The thirteenth layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 17;

[0060] The fourteenth layer is a cropping layer with 25 channels;

[0061] The fifteenth layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 17;

[0062] The sixteenth layer is a cropping layer with 25 channels;

[0063] The seventeenth layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 33;

[0064] The eighteenth layer is a cropping layer with 25 channels;

[0065] The nineteenth layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 33;

[0066] The twentieth layer is a cropping layer with 25 channels;

[0067] The twenty-first layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 65;

[0068] The twenty-second layer is a cropping layer with 25 channels;

[0069] The twenty-third layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 65;

[0070] The twenty-fourth layer is a cropping layer with 25 channels;

[0071] The twenty-fifth layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 129;

[0072] The twenty-sixth layer is a cropping layer with 25 channels;

[0073] The twenty-seventh layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 129;

[0074] The twenty-eighth layer is a cropping layer with 25 channels;

[0075] The twenty-ninth layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 257;

[0076] The thirtieth layer is a cropping layer with 25 channels;

[0077] The thirty-first layer is a one-dimensional convolutional layer with 25 channels and a convolutional kernel size of 257;

[0078] The thirty-second layer is a cropping layer with 25 channels;

[0079] The output decoding layer uses a one-dimensional convolutional layer with an output channel number of 1 and a convolutional kernel size of 1;

[0080] 2.2) Set the cost function of the convolutional neural network to the binary cross-entropy loss function J(θ), which is expressed as follows:

[0081]

[0082] where N T represents the number of training samples in the training dataset, n represents the sample serial number, represents the expected output when the nth training sample is input into the convolutional neural network, y represents the actual output obtained when the nth training sample is input into the convolutional neural network, and θ represents the parameters connecting each layer of the network in the convolutional neural network, which tends to be optimal as the cost function approaches a constant during the training of the convolutional neural network.

[0083] Step 3, according to the training dataset D and the cost function J(θ), use the mini-batch stochastic gradient descent method to train the convolutional neural network.

[0084] 3.1) Set the batch size B of the mini-batch gradient descent method and the network parameter update step size η;

[0085] 3.2) Randomly select B training data from the training dataset D to form a mini-batch, send it into the convolutional neural network and calculate the corresponding cost function J(θ);

[0086] 3.3) Calculate the gradient g of the current convolutional neural network cost function J(θ) with respect to the network parameter θ;

[0087] 3.4) Update the parameter θ of the convolutional neural network to θ - ηg;

[0088] 3.5) Repeat 3.1)-3.4) until the cost function J(θ) of the convolutional neural network approaches a constant, and obtain the trained convolutional neural network;

[0089] Step 4, use the trained convolutional neural network to detect wideband radar targets.

[0090] 4.1) Obtain the broadband radar monopulse echo data, perform pulse compression and linear detection processing to obtain the one-dimensional range profile x of the target to be detected;

[0091] 4.2) Input the one-dimensional range profile x into the trained convolutional neural network to obtain the network output sequence y of the target to be detected;

[0092] 4.3) According to the known false alarm probability P fa of the radar and the average signal-to-noise ratio SNR, use the Monte Carlo method to calculate the detection threshold γ:

[0093] 4.3.1) For the one-dimensional range profile x of the target to be detected, estimate its noise average power σ 2 ;

[0094] 4.3.2) Simulate and generate a complex Gaussian white noise sequence of the same length as x where each noise data is independent of each other and follows a complex Gaussian distribution with a mean of 0 and a variance of σ 2 ;

[0095] 4.3.3) Take the modulus of the complex Gaussian white noise sequence and use it as a noise data set sample w n ;

[0096] 4.3.4) Input the noise sample w n into the trained convolutional neural network to obtain the network predicted output sequence y w ;

[0097] 4.3.5) Repeat 4.3.2)-4.3.4) until a noise network output data set Y w of size M is obtained, where M is the number of Monte Carlo experiments;

[0098] 4.3.6) For each sample y w in the network output data set Y w take the modulus and find its maximum value respectively, and then sort the maximum values of these M samples in descending order to obtain a maximum value sequence A w ;

[0099] 4.3.7) Given the known false alarm rate P fa of the radar and the maximum value sequence A w obtained in 4.3.6), calculate the detection threshold γ:

[0100] γ = A w (n),

[0101] where Aw (n) represents the n-th element of the maximum value sequence A w of represents the ceiling operation;

[0102] 4.4) For the network output sequence y obtained in 4.2), calculate its maximum peak value a at the target to be detected:

[0103] a = max(abs(y))

[0104] where abs(·) represents the modulo operation, and max(·) represents the maximum value among all elements within the parentheses.

[0105] 4.5) Compare the maximum peak value a with the detection threshold γ: If a ≥ γ, the target exists; otherwise, the target does not exist. Thus, the target detection is completed.

[0106] The effects of the present invention will be further described below in conjunction with simulation experiments.

[0107] 1. Experimental conditions for simulation:

[0108] The hardware test platform for the simulation experiment of the present invention is: the processor is CPU Core i7-10700, the main frequency is 2.9GHz, and the memory is 32GB; the software platform is: Windows 10 Professional Edition, 64-bit operating system, Python3.8.

[0109] In the simulation experiment of the present invention, the radar system is set to operate in the C band, and the detection signal it emits is a linear frequency modulation signal with a bandwidth of 400MHz. In the training scenario, it is assumed that the scattering centers of the target are randomly distributed in the region of 3m to 35m, and the target in the test scenario is a certain type of actual measured aircraft target.

[0110] It is assumed that the echo of the target follows the Swerling I distribution, and the noise encountered during the detection process is assumed to be the internal noise of the receiver, which is white noise following the complex Gaussian distribution.

[0111] The average signal-to-noise ratio of the simulation target is -10 to 20dB, and the target echo amplitude follows the Swerling I distribution.

[0112] 2. Simulation content and analysis of simulation results:

[0113] Under the above simulation conditions, the present invention, the existing signal-to-noise ratio weighted detection method, and the traditional non-coherent accumulation sliding window detection method are respectively used to detect broadband radar targets with a false alarm probability P fa = 10 -6 1000 times in the complex Gaussian white noise environment, and the target detection probability with the average signal-to-noise ratio in the range of -10 to 20dB is obtained. The results are as follows Figure 3, where: the horizontal axis is the average signal-to-noise ratio, representing the average value of the signal-to-noise ratio of each range cell in the support area of the wideband radar target; the vertical axis is the target detection probability.

[0114] From Figure 3 It can be seen that for the targets to be detected with different average signal-to-noise ratios in the range of -10 to 20 dB, the detection probability of the present invention is always greater than that of the signal-to-noise ratio weighted detection method and the traditional non-coherent accumulation sliding window detection method, indicating that the present invention can be applied to the detection of targets with different signal-to-noise ratios and can obtain a higher detection probability.

[0115] The above description is only a specific example of the present invention and does not constitute any limitation to the present invention. Obviously, for professionals in the field, after understanding the content and principle of the present invention, various modifications and changes in form and details may be made without departing from the principle and structure of the present invention. However, these corrections and changes based on the idea of the present invention are still within the protection scope of the claims of the present invention.

Claims

1. A broadband radar target detection method based on a deep network, characterized in that, it includes the following: (1) Construct a training data set: (1a) Utilize the parameter information of the target in the broadband radar scenario to establish a scattering point model of the simulated target; (1b) Calculate the echo signal received by the radar from the scattering point model, obtain the one-dimensional range profile of the broadband radar target, and randomly crop the one-dimensional range profile near the target. Take the cropped one-dimensional range profile as a training sample; (1c) Repeat (1a)-(1b) several times to obtain the training data set D; (2) Construct a convolutional deep neural network composed of 2K hidden layers and 1 output decoding layer in cascade, and use the binary cross-entropy loss function as the cost function J(θ) of this network, where K≥1; (3) According to the training data set D and the cost function J(θ), use the mini-batch stochastic gradient descent method to train the convolutional neural network to obtain a trained convolutional neural network; (4) Broadband radar target detection: (4a) Obtain the single-pulse echo data of the broadband radar and perform pulse compression and linear detection processing to obtain the one-dimensional range profile of the target to be detected; (4b) Input the one-dimensional range profile into the trained convolutional neural network to obtain the network output sequence of the target to be detected; (4c) Calculate the detection threshold γ using the Monte Carlo method according to the expected false alarm probability P of the radar fa and the average signal-to-noise ratio SNR; (4d) Calculate the maximum peak a of the network output sequence obtained in (4b) at the target to be detected, and compare it with the detection threshold γ to complete target detection: If a≥γ, the target exists, otherwise, the target does not exist.

2. The method according to claim 1, characterized in that, in (1a), by using the parameter information of the target in the broadband radar scenario, a scattering point model of the target is simulated and established as follows: (1a1) According to the size of the target to be detected, determine the value ranges of the parameters such as the size of the simulated target and the number of scattering points; (1a2) Within the value range of each parameter of the simulation target, randomly generate the length L, width W, height H, and the number of scattering points N of the simulation target, and assign a random scattering coefficient σ to each scattering point i ; (1a3) Set the distance R of the center of the simulation target relative to the wideband radar, and randomly generate the distance R of each scattering point of the simulation target relative to the wideband radar within the three-dimensional space range of L, W, and H with R as the symmetric center. i , to obtain the simulation target scattering point model {(R i , σ i ) | i = 1, 2,..., N}.

3. The method according to claim 1, characterized in that, in (1b), calculating the echo signal received by the radar from the scattering point model is realized as follows: (1b1)According to the bandwidth B of the broadband radar transmitted signal w , the pulse width T of the broadband radar transmitted pulse aup , and the set sampling frequency F of the broadband radar s , the transmitted waveform s t (t) of the broadband radar is obtained; (1b2) Based on the established simulation target scatterer model \(\{(R i ,\sigma i )|i = 1,2,\cdots,N\}\) and the obtained wideband radar transmit waveform \(s t (t)\), calculate the monopulse echo of each scatterer respectively: s r (t) i =Ar i *s t (t - τ i ) + w r (t), i = 1, 2,..., N where s r (t) i is the monopulse echo of the i-th target scatterer, Ar i is the proportionality coefficient of the echo of the i-th target scatterer, τ i is the echo time delay of the i-th target scatterer, w r (t) is the Gaussian white noise in the receiver; (1b3) Linearly superimpose the single-pulse echoes of all scattering points in the complex domain to obtain the overall echo signal of this simulated target.

4. The method according to claim 1, characterized in that, the structural parameters of the 2K hidden layers and one decoding layer of the convolutional deep neural network in (2) are as follows: For the 2K hidden layers, their number of channels is the same, and each hidden layer is composed of a one-dimensional convolutional layer and a cropping layer in alternating cascade. The convolutional kernel sizes of all convolutional layers gradually increase as the network deepens. Each cropping layer is connected after a convolutional layer and is used to crop the output sequence of the one-dimensional convolutional layer to the same length as the input sequence of this one-dimensional convolutional layer; The output decoding layer uses a one-dimensional convolutional layer with an output channel number of 1 and a convolutional kernel size of 1.

5. The method according to claim 1, characterized in that, the cost function J(θ) of the convolutional deep neural network in (2) is expressed as follows: Among them, N T represents the number of training samples in the training dataset, n represents the sample sequence number, represents the expected output when the nth training sample is input into the convolutional neural network, y represents the actual output obtained when the nth training sample is input into the convolutional neural network, and θ represents the parameters connecting each layer of the network in the convolutional neural network, which tend to be optimal as the cost function approaches a constant during the training of the convolutional neural network.

6. The method according to claim 1, characterized in that, in (3), according to the training data set D and the cost function J(θ), using the mini-batch stochastic gradient descent method to train the convolutional neural network is realized as follows: (3a) Set the batch size B of the mini-batch gradient descent method and the network parameter update step size η; (3b) Randomly select B training data from the training data set D to form a mini-batch, send it into the convolutional neural network and calculate the corresponding cost function J(θ); (3c) Calculate the gradient g of the current convolutional neural network cost function J(θ) with respect to the network parameter θ; (3d) Update the parameter θ of the convolutional neural network to θ - ηg; (3e) Repeat (3a)-(3d) until the cost function J(θ) of the convolutional neural network tends to be invariant, and obtain the trained convolutional neural network.

7. The method according to claim 1, wherein, (4c) Use the Monte Carlo method to calculate the detection threshold γ, and the implementation is as follows: (4c1) For the one-dimensional range profile x of the target to be detected, estimate its average noise power σ 2 ; (4c2)Simulate and generate a complex Gaussian white noise sequence that is the same length as x where each noise data is independent of each other and follows a complex Gaussian distribution with a mean of 0 and a variance of σ 2 ; (4c3) Modulo operation is performed on the complex Gaussian white noise sequence and the result is used as a noise data set sample w n ; (4c4) Input the noise sample w n into the trained convolutional neural network to obtain the output sequence y predicted by the network w ; (4c5) Repeat (4c2)-(4c4) until a noisy network output dataset Y of size M is obtained w , where M is the number of Monte Carlo experiments; (4c6) For each sample y in the network output data set Y w take the modulus respectively and find its maximum value, and then sort the maximum values of these M samples in descending order to obtain a maximum value sequence A of length M w w ; (4c7) Substitute the false alarm rate P expected by the known radar fa and the maximum value sequence A obtained in (4c6) w , into the following formula to calculate the detection threshold γ: γ = A w (n), Where A w (n) represents taking the nth element of the maximum value sequence A w , represents the ceiling operation.

8. The method according to claim 1, wherein, Calculate the maximum peak value a of the network output sequence at the target to be detected, and the formula is as follows: a = max(abs(y)) where y is the network output sequence of the target to be detected, abs(·) represents the modulo operation, and max(·) represents the maximum value of all elements in the brackets.

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