A Radar Target Recognition Method Based on Improved Temporal Convolutional Network
Through the TCNA model combining causal convolution and multi-level attention mechanism, the problem of feature extraction and sequence correlation in radar target recognition is solved, and a more comprehensive feature extraction and recognition accuracy is achieved.
Patent Information
- Application Number
- CN202210413812.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-04-14
- Publication Date
- 2025-07-22
- Estimated Expiration
- 2042-04-14
AI Technical Summary
The existing radar target recognition algorithms have problems such as information loss and sequence correlation neglect during feature extraction. Traditional methods are unsupervised and lossy. Deep learning models such as AE, CNN and RNN have limitations in HRRP recognition, such as the inability to capture physical structural features or long-term dependence decay.
The TCNA model based on the time convolution network is adopted, combined with causal convolution and expanded convolution to expand the receptive field, and adaptively adjust the feature importance through a multi-level attention mechanism to extract the global and local features of HRRP.
Effectively extracting the feature information of HRRP solves the problems of insufficient timing modeling of traditional models and long-term dependence degradation of RNNs, and improves the accuracy and generalization ability of radar target recognition.
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Figure CN114861712B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of radar target recognition, and specifically relates to a radar target recognition method based on an improved temporal convolutional network. Background Art
[0002] With the development of radar technology, the distance resolution of modern broadband radars is much smaller than the size of the target along the radar line of sight. The radar observation target changes from a "point" target to a "surface" target in the echo. The target echo is the sum of the echoes of the scattered points on the "surface", that is, the sum of the echoes of the important components of the target. In fact, the reflected echoes of targets such as ships and aircraft can be regarded as composed of multiple independent distance units, and each distance unit is a superposition of scattering points of different intensities. Usually, the echo signal received by this type of high-resolution broadband radar is called the high-resolution one-dimensional range profile (High Resolution Range Profile, HRRP) of the target.
[0003] In the field of target recognition based on one-dimensional high-resolution range profile (HRRP), feature extraction has always been a difficult and key point in research. The existing recognition algorithm models are mainly divided into traditional methods and deep learning methods. In the early stage of HRRP research, most of them used traditional methods, such as using various spectral features to identify targets, using relaxation algorithms to extract the significant features of HRRP for identification, using polarization information for identification, etc. In general, although these traditional methods can achieve good recognition performance, since their modeling methods are mostly unsupervised and lossy, some separable information will be lost in the feature extraction process, thereby limiting the recognition performance of the model. The deep neural network model can automatically extract features from samples and identify them, and has achieved brilliant achievements in the fields of image and speech recognition. With its deep nonlinear end-to-end structure, deep learning has greatly enhanced the ability to express data. It can not only automatically mine effective classification features from data but also has good automatic recognition performance. Therefore, this technology has also attracted much attention in the field of radar target recognition. In the past few years, many excellent works have emerged in HRRP target recognition based on deep learning methods. According to the different network structures, they can be roughly divided into three categories: autoencoder (AE), convolutional neural network (CNN) and recurrent neural network (RNN).
[0004] Deep neural network models such as AE, CNN, and RNN have all achieved fruitful research results in the field of Radar Automatic Target Recognition (RATR). These end-to-end models automatically extract analyzable features of HRRP, improving the deficiencies of traditional models in feature extraction, but still have their own drawbacks. The AE model is constructed based on a fully connected network, so it cannot capture the physical structure features of the scattering points distributed along the target size in HRRP data; the local connection characteristics of the CNN model can effectively extract the structure features in HRRP targets, but ignore the overall sequence correlation of HRRP samples; and the RNN model based on temporal modeling needs to perform time-domain segmentation on HRRP samples through a sliding window, resulting in a highly redundant input sequence, and the problem of historical memory information dissipation occurs as the number of time steps in RNN increases, which is not conducive to subsequent recognition. Summary of the Invention
[0005] To solve the above problems, we propose a Temporal Convolutional Network with Attention (TCNA) model based on the sequence characteristics of HRRP, the temporal convolutional network, and the multi-level attention mechanism. Rich target physical structure information is contained in HRRP samples, and its effective features can be quickly extracted through convolution. At the same time, we use the temporal convolutional network to solve the problem that traditional convolutional network models cannot perform temporal modeling on HRRP samples and make up for the problem of long-term dependence decay existing in the RNN model. In addition, the dual attention mechanism can adaptively scale the feature importance to enhance the feature extraction ability of the model.
[0006] A radar target recognition method based on an improved temporal convolutional network includes the following steps:
[0007] S1: Preprocess the original HRRP sample set.
[0008] Process the original HRRP echo data using L2 norm normalization to divide the amplitude into a unified scale to eliminate the amplitude sensitivity of HRRP. Use the centroid alignment method to improve the translation sensitivity of HRRP.
[0009] S2: Use the TCN model to extract the data features of HRRP;
[0010] The TCN model is obtained by stacking 3 residual modules. The residual module consists of two core modules: causal dilated convolution and residual connection. To improve the recognition accuracy, batch normalization and activation functions are added after each causal dilated convolution. At the same time, to prevent overfitting, the Dropout method is introduced to improve the generalization ability of the model. The output of the model adopts a cross-layer output mechanism to obtain more complete feature information.
[0011] S3: Adopt a multi-level attention module to adaptively scale the feature importance of different segments of the data, so that the output features at different levels all affect the recognition result.
[0012] S4: Retain more effective features through a fully connected layer, and finally use softmax to classify the output of the network;
[0013] Preferably, the specific steps of the said step S1 are as follows:
[0014] S1.1: L2 norm normalization. Divide the amplitude into a unified scale. Represent the original radar HRRP data as X = [x1, x2,..., x M , then the X obtained after L2 norm normalization is norm as follows:
[0015]
[0016] where X represents the original HRRP data, M represents the number of range cells included in the HRRP, and x m represents the amplitude in the m-th range cell. After norm normalization,
[0017] S1.2: Centroid alignment method. The centroid alignment method is divided into two steps: First, it is necessary to calculate the centroid position of the HRRP, and then translate it so that its centroid is located at the center position of the HRRP range cell. The radar HRRP data is represented as then the calculation of the centroid G is as follows:
[0018]
[0019] After translation, the data
[0020] Preferably, the detailed steps of the said S2 are:
[0021] S2.1: Causal dilated convolution.
[0022] Causal dilated convolution increases the receptive field of the convolution kernel by interval sampling, and enables the output to contain rich long-term retrospective information without relying on the model depth. The convolution kernel After preprocessing, the HRRP input sample sequence is Where M is the number of range cells. Then, the output after the calculation of HRRP through causal dilated convolution is defined as:
[0023]
[0024] Where d represents the dilation coefficient, and d increases exponentially with base 2 as the convolutional layer deepens. ker is the convolution kernel size, and f(r) represents the value of the convolution kernel at position r, where 0 ≤ r ≤ ker - 1. The size of the receptive field is as follows:
[0025] field = (ker - 1)·d
[0026] S2.2: Batch normalization.
[0027] Trainable parameters are added to normalize the data for each mini - batch. Each mini - batch contains num data: Define the output after the causal dilated convolution operation on the data of this batch as F o denotes the causal dilated convolution output corresponding to the o - th data in the mini - batch. Then, the batch normalization for can be defined as:
[0028]
[0029] Where F o (k, l), are the l - th values of the k - th channel of the o - th data before and after the batch normalization operation respectively, γ k , β k are trainable parameters, and ε is defined as an extremely small value to prevent the denominator from being 0. μ BN , are the mean and variance respectively, and the calculation process is expressed as:
[0030]
[0031] Where L represents the sequence length. Then, a non - linear transformation is performed on the features after batch normalization, that is, the features are input to the activation function to obtain
[0032]
[0033] S2.3: Activation function.
[0034] The ReLU function is used, and its formula is as follows:
[0035] ReLU(x) = max(0, x)
[0036] S2.4: Residual connection.
[0037] The residual connection uses an identity mapping to enable the residual module to transmit shallow information to the deep layers in a cross-layer manner, solving the degradation problem that occurs when the TCN model is too deep. When X input is the input value of the residual module and F(·) is the mapped output of the residual module, the output X res of the residual module is expressed as:
[0038] X res = Activation(X input + F(X input ))
[0039] S2.5: Cross-layer output mechanism;
[0040] The cross-layer output mechanism is adopted, that is, the output of each residual module in the TCN model is divided into two parts: the first output is the output of the residual connection, which continues to propagate backward after passing through the activation function and serves as the input of the next residual module; the second output is the feature extraction part, and the results are output according to the stacking order of the residual modules and serve as the input of the multi-level attention module to calculate the subsequent attention distribution. The cross-layer output mechanism can extract features with different degrees of abstraction, which is beneficial to improving the recognition accuracy.
[0041] Preferably, the detailed steps of S3 are as follows:
[0042] There are j residual modules in the TCN model; represents the feature output of the j-th residual module, where D represents the number of channels and B represents the number of range cells of the HRRP. The output feature of the d-th channel in the j-th residual module is represented as H dj . The multi-level attention module weights and sums the output features of each residual module in the TCN at different channels as the finally extracted feature F att :
[0043]
[0044] where J is the total number of residual modules, and α dj is the weight coefficient of each channel, representing the contribution made by H dj in the recognition. The solution calculation formula is as follows:
[0045]
[0046] where e dj is the energy of H dj , and the calculation formula is as follows:
[0047] e dj = Uj tanh(W j H dj )
[0048] Among them, U j and W j are trainable parameter matrices corresponding to the residual module j. By training the parameters U j and W j , the model can automatically assign different weights α dj to the features H dj of different channels, and adaptively scale the feature weights that play a role in recognition. The F att obtained through multi-level attention calculation is used as the finally extracted feature for the classifier to perform recognition.
[0049] Preferably, the detailed steps of S4 are as follows:
[0050] S4.1: Fully connected layer. The fully connected layer maps the F att obtained through multi-level attention calculation to the label space, reduces the dimension of the features to obtain the prediction vector y = [y1, y2,..., y C , where C is the total number of target categories of HRRP.
[0051] S4.2: Softmax.
[0052] Use the Softmax function to map the prediction vector y to the probability distribution y′ = [y′1, y′2,..., y′ C , where y′ c represents the probability that the target sample belongs to the c-th category, and its calculation method is:
[0053]
[0054] Classify the HRRP target through the following formula:
[0055]
[0056] where represents the value of the c variable corresponding to when the function in the parentheses takes the maximum value.
[0057] The beneficial effects of the present invention are:
[0058] 1. Causal sequence modeling is applied in the present invention. Aiming at the deficiencies that traditional convolutional networks cannot perform temporal modeling on HRRP samples, and the sequences obtained by the RNN through the time-domain segmentation method are highly redundant and there is a long-term dependence decay, the present invention proposes a TCNA model based on a temporal convolutional network to establish the causal sequence characteristics of HRRP through causal convolution, and expands the receptive field of the model by dilated convolution and stacking the model depth to extract more comprehensive feature information.
[0059] 2. The present invention applies a multi-level attention mechanism. To enable the TCNA model to utilize the structural features of different segments and different levels in the HRRP target, the present invention proposes a multi-level attention mechanism for a multi-layer temporal convolutional network to adjust the importance of the structural features of the target reflected at different levels, highlight the hierarchical features with strong separability, suppress useless features, and adaptively adjust the influence of the outputs of each level on the recognition result. BRIEF DESCRIPTION OF THE DRAWINGS
[0060] Figure 1 : Flowchart of the steps of a radar target recognition method based on an improved temporal convolutional network. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0061] The technical solution of the present invention will be further described below in conjunction with the drawings and embodiments.
[0062] Refer to Figure 1 , which is a flowchart of a radar target recognition method based on an improved temporal convolutional network of the present invention. The specific implementation steps are as follows:
[0063] Training stage:
[0064] S1: Collect the data set. Merge the HRRP data sets collected by the radar according to the types of targets. For each type of sample, select training samples and test samples in different data segments. During the selection process of the training set and the test set, ensure that the selected training set samples cover the poses of the test set samples with respect to the radar. The ratio of the number of training set and test set samples for each type of target is 8:2. Denote the selected data set as T = {(x n , y c )} n∈[1,N],c∈[1,C] , where x n represents the nth sample, and y c represents that the sample belongs to the cth class. A total of C types of targets are collected, and N represents the total number of samples.
[0065] S2: Preprocess the samples in the data set extracted in S1. The specific operation steps are as follows:
[0066] The L2 norm normalization is used to process the original HRRP echo data, and the amplitude is divided into a unified scale to eliminate the amplitude sensitivity of HRRP. The centroid alignment method is used to improve the translation sensitivity of HRRP.
[0067] S2.1:: L2 norm normalization. Divide the amplitude into a unified scale. The original radar HRRP data is represented as X = [x1, x2,..., x M , then the normalized X norm is as follows:
[0068]
[0069] where X represents the original HRRP data, M represents the number of range cells included in HRRP, and x m represents the amplitude in the m-th range cell. After normalization by the norm, we get
[0070] S2.2: Centroid alignment method. The centroid alignment method is divided into two steps: First, the centroid position of HRRP needs to be calculated, and then it is translated so that its centroid is located at the center position of the HRRP range cell. The radar HRRP data is represented as then the calculation of the centroid G is as follows:
[0071]
[0072] After translation, we get the data
[0073] S3: Use the TCN model to extract the data features of HRRP. The specific steps are as follows:
[0074] The TCN model is obtained by stacking 3 residual modules. The described residual module consists of two core modules, causal dilated convolution and residual connection. It not only has the ability to process data in parallel on a large scale like CNN, but also integrates the temporal modeling ability similar to RNN. To improve the recognition accuracy, batch normalization and activation functions are added after each causal dilated convolution. At the same time, to prevent overfitting, the Dropout method is introduced to improve the generalization ability of the model. The output of the model uses a cross-layer output mechanism to obtain more complete feature information.
[0075] S3.1: Causal dilated convolution.
[0076] Causal dilated convolution increases the receptive field of the convolution kernel by interval sampling, enabling the output to contain rich long-term retrospective information without relying on the model depth. The convolution kernel After preprocessing, the HRRP input sample sequence is Where M is the number of range cells. Then, the output of the HRRP after the causal dilated convolution calculation is defined as:
[0077]
[0078] Where d represents the dilation coefficient, and d increases as the power of 2 with the deepening of the convolutional layer. ker is the convolutional kernel size, and f(r) represents the value of the convolutional kernel at position r, where 0 ≤ r ≤ ker - 1. The size of the receptive field is as follows:
[0079] field = (ker - 1)·d
[0080] S3.2: Batch Normalization.
[0081] Trainable parameters are added to normalize the data of each mini - batch. Different from ordinary data normalization, adding trainable parameters can enhance the expressive power of the network. Each mini - batch contains num data: Define the output of the data in this batch after the causal dilated convolution operation as F o representing the causal dilated convolution output corresponding to the o - th data in the mini - batch. Then, the batch normalization of can be defined as:
[0082]
[0083] Where F o (k, l), are the l - th values of the k - th channel of the o - th data before and after the batch normalization operation respectively, γ k , β k are trainable parameters, and ε is defined as a very small value to prevent the denominator from being 0. μ BN , are the mean and variance respectively, and the calculation process is expressed as:
[0084]
[0085] Where L represents the sequence length. Then, a non - linear transformation is performed on the features after batch normalization, that is, the features are input into the activation function to obtain
[0086]
[0087] S3.3: Activation Function.
[0088] The main function of the activation function is to add non - linear expression ability to the model, improve the scalability of the network, and enhance the generalization ability of the model. The most commonly used activation functions are the Sigmoid and ReLU functions. We use the ReLU function, which has a faster convergence speed and alleviates the problem of vanishing gradients that is prone to occur in the Sigmoid function. Its formula is as follows:
[0089] ReLU(x) = max(0, x)
[0090] S3.4: Residual connection.
[0091] The residual connection allows the residual module to pass shallow - layer information to the deep layer in a cross - layer manner through an identity mapping, solving the degradation problem that occurs when the TCN model is too deep. When X input is the input value of the residual module and F(·) is the mapped output of the residual module, the output X res of the residual module is expressed as:
[0092] X res = Activation(X input + F(X input ))
[0093] S3.5: Cross - layer output mechanism. Each residual module of the TCN model extracts features at different levels of abstraction. The features extracted by the last one are often highly abstract. Using the features of this layer directly as the final classification basis may lose some information from the intermediate layers.
[0094] To avoid the impact of information loss on the recognition accuracy, the TCN model adopts a cross - layer output mechanism, that is, the output of each residual module in the TCN model is divided into two parts: the first output is the output of the residual connection, which continues to propagate backward after passing through the activation function and serves as the input for the next residual module; the second output is the feature extraction part, which outputs the results according to the stacking order of the residual modules and serves as the input for the multi - level attention module to calculate the subsequent attention distribution. The cross - layer output mechanism can extract features with different degrees of abstraction, which is beneficial to improving the recognition accuracy.
[0095] S4: Adopt a multi - level attention module to adaptively scale the feature importance of different segments of the data, so that the output features at different levels all affect the recognition result. The specific steps are as follows:
[0096] Different segments in the HRRP data reflect different structural features of the target, so they have different effects on the recognition result. Therefore, a multi - level attention mechanism is introduced into the model, which can not only adaptively scale the feature importance of different segments of the data, but also make the output features at different levels all affect the recognition result.
[0097] There are j residual modules in the TCN model; represents the feature output of the j-th residual module, where D represents the number of channels, B represents the number of range cells of HRRP, and the output feature of the d-th channel in the j-th residual module is represented as H dj The multi-level attention module weights and sums the output features of each residual module in the TCN at different channels as the finally extracted feature F att :
[0098]
[0099] where J is the total number of residual modules, and α dj is the weight coefficient of each channel, indicating the contribution made by H dj in recognition. The calculation formula for solving is as follows:
[0100]
[0101] where e dj is the energy of H dj . The calculation formula is as follows:
[0102] e dj = U j tanh(W j H dj )
[0103] where U j and W j are trainable parameter matrices corresponding to the residual module j. By training the parameters U j and W j , the model can automatically assign different weights α dj to the features H dj of different channels, and adaptively scale the feature weights that play a role in recognition. The F att obtained through multi-level attention calculation is used as the finally extracted feature for the classifier to perform recognition.
[0104] S5: Retain the more effective features through the fully connected layer, and finally use softmax to classify the output of the network. The specific steps are as follows:
[0105] S5.1: Fully connected layer. The fully connected layer maps the F att obtained through multi-level attention calculation to the label space, reduces the dimension of the features to obtain the prediction vector y = [y1, y2,..., y C , where C is the total number of target categories of HRRP.
[0106] S5.2: Softmax.
[0107] Use the Softmax function to map the predicted vector y to a probability distribution y′ = [y′1, y′2,..., y′ C , where y′ c represents the probability that the target sample belongs to the c-th class, and its calculation method is:
[0108]
[0109] Classify the HRRP target through the following formula:
[0110]
[0111] where represents the value of the c variable corresponding to when the function in the parentheses takes the maximum value.
[0112] S6: Feed the HRRP samples processed by S2 into the TCNA model composed of S3, S4, and S5 for training and testing.
[0113] It should be understood that the exemplary embodiments described herein are illustrative rather than restrictive. Although one or more embodiments of the present invention have been described in conjunction with the accompanying drawings, those of ordinary skill in the art should understand that various changes in form and detail can be made without departing from the spirit and scope of the present invention as defined by the appended claims.
Claims
1. A radar target recognition method based on an improved temporal convolutional network, characterized in that, It includes the following steps: S1: Preprocess the original HRRP sample set; Process the original HRRP echo data using L2 norm normalization to divide the amplitude into a unified scale to eliminate the amplitude sensitivity of HRRP; Adopt the centroid alignment method to improve the translation sensitivity of HRRP; S2: Use the TCN model to extract the data features of HRRP; The TCN model is obtained by stacking 3 residual modules; the residual module is composed of two core modules: causal dilated convolution and residual connection; in order to improve the recognition accuracy, batch normalization and activation function are added after each causal dilated convolution; at the same time, in order to prevent overfitting, the Dropout method is introduced to improve the generalization ability of the model; the output of the model adopts a cross-layer output mechanism to obtain more perfect feature information; S3: Adopt a multi-level attention module to adaptively scale the feature importance of different segments of the data; make the output features at different levels all affect the recognition result; S4: Retain the more effective features through the fully connected layer, and finally use softmax to classify the output of the network; The specific steps of the said step S1 are as follows: S1.1: L2 norm normalization; dividing the amplitude into a unified scale; representing the original radar HRRP data as X = [x1, x2,..., x M , then the X obtained after L2 norm normalization is norm as follows: Wherein, X represents the original HRRP data, M represents the number of range cells included in the HRRP, and x m represents the amplitude within the m-th range cell; after being normalized by the norm, we get S1.2: Centroid alignment method; The centroid alignment method is divided into two steps: First, it is necessary to calculate the centroid position of the HRRP, and then translate it so that its centroid is located at the center position of the HRRP range cell; The radar HRRP data is expressed as Then the calculation of the centroid G is as follows: Obtain data by translation The detailed steps of S2 are: S2.1: Causal dilated convolution; Causal dilated convolution increases the receptive field of the convolutional kernel by spaced sampling, enabling the output to contain rich long-term retrospective information without relying on the model depth; the convolutional kernel After preprocessing, the HRRP input sample sequence is where M is the number of range cells; then, the output after the calculation of HRRP through causal dilated convolution is defined as: Among them, d represents the dilation coefficient, and d increases in the exponential power of 2 as the convolutional layer deepens; ker is the convolutional kernel size, and f(r) represents the value of the convolutional kernel at position r, 0 ≤ r ≤ ker - 1; the size of the receptive field is as follows: field = (ker - 1)·d S2.2: Batch normalization; Add trainable parameters to normalize the data for each mini - batch; each mini - batch contains num pieces of data: Define the output after the causal dilated convolution operation on this batch of data as F o Denote the causal dilated convolution output corresponding to the o - th piece of data in the mini - batch; then, for Batch normalization can be defined as: Among them, F o (k, l), are respectively the l-th value of the k-th channel of the o-th data before and after the batch normalization operation, γ k , β k are trainable parameters, ε is defined as an extremely small value to prevent the denominator from being 0; μ BN , are respectively the mean and variance, and the calculation process is expressed as: where L represents the sequence length; then, a non-linear transformation is performed on the batch-normalized features, that is, the features are input into an activation function to obtain S2.3: Activation function; The ReLU function is used, and its formula is as follows: ReLU(x) = max(0, x) S2.4: Residual connection; The residual connection uses the identity mapping to enable the residual module to pass shallow information to deep layers in a cross-layer manner, solving the degradation problem that occurs when the TCN model is too deep; when X input is the input value of the residual module and F(·) is the mapped output of the residual module, then the output X res is expressed as: X res = Activation(X input + F(X input )) S2.5: Cross-layer output mechanism; The cross-layer output mechanism is adopted, that is, the output of each residual module in the TCN model is divided into two parts: the first output is the residual connection output, which continues to propagate backward after passing through the activation function and serves as the input of the next residual module; the second output is the feature extraction part, and the results are output according to the stacking order of the residual modules and serve as the input of the multi-level attention module for subsequent attention distribution calculation; the cross-layer output mechanism can extract features with different degrees of abstraction, which is beneficial to improving the recognition accuracy.
2. The radar target recognition method based on an improved temporal convolutional network according to claim 1, characterized in that, The detailed steps of the said S3 are: There are j residual modules in the TCN model; represents the feature output of the j-th residual module, where D represents the number of channels, B represents the number of range cells of HRRP, and the output feature of the d-th channel in the j-th residual module is denoted as H dj ; The multi-level attention module weights and sums the output features of each residual module in the TCN at different channels as the finally extracted feature F att : Among them, J is the total number of residual modules, and α dj is the weight coefficient of each channel, indicating the contribution made by H dj in the recognition. The solution calculation formula is as follows: where e dj is the energy of H dj and the calculation formula is as follows: e dj = U j tanh(W j H dj ) Among them, U j and W j are trainable parameter matrices corresponding to the residual module j; by training the parameters U j and W j , the model can automatically assign different weights α dj to the features H dj of different channels, adaptively scaling the feature weights that play a role in recognition; F att obtained through multi-level attention calculation is used as the finally extracted feature for the classifier to perform recognition.
3. A radar target recognition method based on an improved temporal convolutional network according to claim 2, characterized in that The detailed steps of the said S4 are: S4.1: Fully connected layer; the fully connected layer maps F obtained by multi-level attention calculation to the token space, reduces the dimension of the features to obtain the prediction vector y = [y1, y2,..., y att , where C is the total number of target categories of HRRP; C S4.2: Softmax; Use the Softmax function to map the predicted vector y to a probability distribution y′ = [y′1, y′2,..., y′ C , where y′ c represents the probability that the target sample belongs to the c-th class, and its calculation method is as follows: Classify the HRRP target through the following formula: Among them represents the value of the c variable corresponding to when the function in the parentheses takes the maximum value.
Citation Information
Patent Citations
Radar HRRP target identification method based on N2N and Bert
CN112699782A