Radar high-resolution range profile recognition method based on multi-scale group fusion convolution

Abstract

The invention discloses a radar high-resolution range profile recognition method based on multi-scale group fusion convolution, comprising the following steps: step 1: constructing a HRRP recognition network based on a multi-scale group fusion one-dimensional convolution layer (MSGF-1D-CNN); step 2: initializing the recognition network; step 3: forward propagation; step 4: back propagation; step 5: repeating steps 3 and 4, training T batches of data one by one, completing a cycle of training, then using the model trained in the current cycle in combination with a formula to predict samples in a test data set, and performing statistics on the prediction results; step 6: repeating step 5 until τ cycles of training are completed, and saving the model parameters when the recognition accuracy of the test set is the highest.

Description

Technical Field

[0001] The invention belongs to the technical field of radar automatic target recognition, and in particular relates to a radar high-resolution range image recognition method based on multi-scale grouping fusion convolution. Background Art

[0002] Radar automatic target recognition technology has important application value in military and civilian fields, and has attracted extensive attention from scholars at home and abroad. High-resolution Range Profile (HRRP) is the superposition of radar echoes of broadband radar along the radar line of sight at each distance unit. Compared with RCS, it has richer target structure information, and compared with SAR images, it has the advantages of being easy to obtain, store and process. Therefore, domestic and foreign scholars have conducted a lot of algorithm research on radar automatic target recognition technology based on HRRP.

[0003] Common radar target recognition methods based on HRRP include template matching, decision tree, support vector machine, k-nearest neighbor algorithm, linear discriminant analysis, principal component analysis and random forest, etc. However, the features extracted by these methods are shallow, and the generalization performance and robustness of the algorithms are generally low in practical applications. In recent years, with the rapid development of deep learning, HRRP recognition methods based on deep neural networks have become a research hotspot in the field of radar automatic target recognition. Deep neural networks have a multi-layer neuron superposition structure. The parameter values ​​of each layer of neurons can be automatically learned through the stochastic gradient descent algorithm. The neurons in each layer can extract different levels of abstract features of the original data, realizing the feature extraction and classification of data without the need for prior experience of professionals.

[0004] Convolutional Neural Networks (CNN) is a neural network that uses local receptive fields to fuse spatial information and channel information to achieve effective feature extraction. Compared with the above neural networks, its local receptive field has a stronger ability to express the local features of the target, and the alternating convolutional layer and pooling layer structure can achieve invariance to translation, rotation and scale, thereby effectively extracting the target structure information contained in HRRP. Therefore, the features extracted by CNN are more robust.

[0005] The core module of the CNN used for HRRP recognition is a standard convolution layer. Due to the limited computing and storage resources of computers, this standard convolution layer generally tends to use a single convolution kernel with a smaller scale in the actual network structure design, because the larger the convolution kernel, the more trainable parameters it contains. Increasing the scale of the convolution kernel will inevitably make the network training more difficult. At the same time, in order to make up for the fact that a single standard convolution layer uses a smaller convolution kernel and cannot effectively extract a larger range of spatial information from the input data, CNN alternately connects the standard convolution layer and the pooling layer to form a deep CNN (DeepCNN, DCNN), which reduces the size of the input data layer by layer and thus increases the network's receptive field. However, existing studies have shown that the single-scale standard convolution layer in DCNN cannot effectively extract the correlation of different spatial ranges in the feature map, which will cause the actual receptive field to be reduced and the effective spatial information to be lost, thereby affecting the recognition effect. Summary of the invention

[0006] In view of the above problems, the present invention attempts to improve the standard convolution and proposes a multi-scale group fusion one-dimensional convolution to replace the standard one-dimensional convolution. In the design process of multi-scale group fusion one-dimensional convolution, the disadvantage that large-scale convolution kernels will increase the computational complexity of the network is taken into consideration, and the method for determining the optimal number of channels is studied to significantly reduce the overall parameter amount of the network.

[0007] The technical solution adopted by the present invention is:

[0008] The radar high-resolution range profile recognition method based on multi-scale group fusion convolution includes the following steps:

[0009] Step 1: Construct a HRRP recognition network based on multi-scale group fusion one-dimensional convolutional layer (MSGF-1D-CNN)

[0010] First, given a one-dimensional array containing the number of channels of each one-dimensional convolutional layer To represent different model structures, the value of each element in C is an integer power of 2 and gradually increases. Given Ω and determining the corresponding and G (l) , thereby completing the specific configuration of the network structure;

[0011] Step 2: Initialize the recognition network: initialize the trainable parameters θ of the network;

[0012] Step 3: Forward Propagation

[0013] Constructing a multi-scale group fusion one-dimensional convolutional layer (MSGF-1D-CNN) on the HRRP training dataset The cross entropy loss function on the data is used to calculate the loss function value of each batch of data;

[0014] Step 4: Back propagation: Use the stochastic gradient descent algorithm to update the parameters of each batch;

[0015] Step 5: Repeat steps 3 and 4 to train T batches of data one by one to complete a training cycle. Then, use the model trained in the current cycle combined with the formula to predict the samples in the test data set and perform statistics on the prediction results.

[0016] Step 6: Repeat step 5 until τ cycles of training are completed, and save the model parameters when the test set recognition accuracy is the highest.

[0017] Preferably, the HRRP recognition network comprises an input layer, a convolution module, a flat layer and a Softmax classifier;

[0018] Input layer: raw input data Where D (1) =E, C (1) =1;

[0019] Convolutional module: The convolution modules are repeatedly connected for feature extraction;

[0020] Flat layer and Softmax classifier: If the output of the last convolution module The feature map size Then after the flattening operation of the flat layer All feature maps in are arranged into a one-dimensional vector u as the input of the Softmax classifier, which performs target classification.

[0021] Preferably, the convolution module includes a multi-scale group fusion one-dimensional convolution layer, a batch normalization layer, a nonlinear activation layer and a pooling layer; wherein,

[0022] Multi-scale group fusion one-dimensional convolution layer: Use multi-scale group one-dimensional convolution and point-by-point convolution to replace the standard one-dimensional convolution layer, and use H (l) represents the window size of the convolution kernel of the lth standard one-dimensional convolution layer, X (l) All single-scale one-dimensional convolution kernels of this layer Perform convolution operations to generate output feature maps equal to the number of convolution kernels Where D (l+1) and C (l+1) Respectively represent the feature map size and the number of channels after convolution;

[0023] Batch Normalization Layer: Use batch normalization to normalize each batch output of the convolutional layer to a distribution with a mean of 0 and a standard deviation of 1.

[0024] Nonlinear activation layer: Use a nonlinear activation function to activate the output of the one-dimensional convolutional layer; the expression of the nonlinear activation function is δ(x) = x·tanh(ln(1+e x ));

[0025] Pooling layer: Using the maximum pooling method, for the k-th output feature map X of the l-th one-dimensional convolutional layer k (l) , the value at position i of the output feature map after maximum pooling is given by the following formula

[0026]

[0027] where H′ (l) and S′ (l) Represent the window size and step size of the maximum pooling respectively. After the maximum pooling, the number of feature maps remains unchanged, and the size of the feature map becomes

[0028]

[0029] in, Indicates rounding down.

[0030] Preferably, the specific process of the convolution operation is:

[0031] Each multi-scale group fusion one-dimensional convolutional layer performs convolution operations with all input feature maps, and the kth (k∈{1, 2, ..., C (l+1)}) one-dimensional convolution kernel With X (l) The resulting one-dimensional feature map is

[0032]

[0033] Among them, the operator * represents the convolution operation, represents the bias of the kth convolution kernel, δ(·) is the activation function of the nonlinear activation layer, and the input feature map of each layer is firstly padded with zeros. Let the number of zeros padded on one side of each input feature map of the lth layer be P (l) , the size of the input feature map first becomes D (l) +2P (l) , and then with a step length of S (l) The convolution operation is performed with the convolution kernel of , then the k-th output feature map is at position i (i∈D (l+1) ) is

[0034]

[0035] Where ⊙ represents the Hadamard product, from which the output feature map size can be calculated as

[0036]

[0037] In order to allow the convolutional layer to extract different scale information of the input feature map, group convolutions with different scales are used. Replace the single-scale convolution W (l) , generating Ω groups of different outputs use G (ω；l) and denote the scale of the convolution kernel, the number of groups, and the number of output feature maps in the ω(ω∈{1,2,...,Ω})th grouped convolution, respectively. And the number of output feature maps of each group convolution satisfies From the calculation formula of the output feature map size, we can know that the output feature map size obtained by the ω-th group convolution is

[0038]

[0039] in, and They represent the number of zero padding of the input feature map and the step size of the convolution kernel when performing the ω-th grouped convolution operation. In practice, the subsequent convolutional layers require that all input feature maps have the same size, that is, make Take a positive odd number, Make That is, the output feature map has the same size as the input feature map, so the multi-scale group convolution output is

[0040]

[0041] Among them, concat(·) means merging the feature map matrix along the channel direction, so

[0042] Preferably, the specific process of using the Softmax classifier for target classification is as follows:

[0043] The parameters of the Softmax classifier are denoted as θ sm = {W sm ,b sm}, for each HRRP sample (x(n), y(n)), x(n) and y(n) represent the HRRP sample data and the corresponding true label respectively, then the output of the qth neuron of the Softmax classifier represents the probability of judging the sample x(n) as the qth category, that is,

[0044]

[0045] in, represents the multidimensional features extracted by all layers before the Softmax classifier, θ* is the parameter of all feature extraction layers except the Softmax classifier, Flatten(·) represents the flattening operation, θ={θ*,θ sm} represents all trainable parameters of the network. The prediction process of sample x(n) is to maximize the posterior probability, that is,

[0046]

[0047] Preferably, in step 3, the cross entropy loss function is:

[0048]

[0049] Where N is the total number of samples in the training set M; 1{·} is the indicator function, that is, 1{true}=1, 1{false}=0.

[0050] Preferably, in step 4, network training is the process of updating network parameters using training data, which is essentially the minimization of the cross entropy loss function and the empirical risk loss function, that is,

[0051]

[0052] Solving the above formula using all training data requires a lot of computing power and memory. Therefore, the stochastic gradient descent algorithm is generally used to randomly extract B samples each time to update the parameters. The entire training data set is randomly divided into Batches( means rounding up to an integer), that is For the tth iteration (t∈{1,2,…,T}), the update formula of the stochastic gradient descent algorithm is

[0053] θ t+1 =θ t -αg t

[0054] Where α is the learning rate, g t is the loss function with respect to θ t The gradient of

[0055]

[0056] Beneficial effects of the present invention: The multi-scale group fusion one-dimensional convolutional layer (MSGF-1D-CNN) proposed in the present invention has fewer parameters, less computation and higher recognition accuracy. Experimental comparison with other deep neural networks shows that the multi-scale group fusion one-dimensional convolutional layer (MSGF-1D-CNN) is superior in recognition accuracy, recall rate and overall recognition accuracy of each mid-trajectory target, and has higher noise robustness than other deep methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0058] Figure 1 The figure shows the overall structure of the HRRP recognition network based on MSGF-1D-CNN in this embodiment;

[0059] Figure 2 Schematic diagram of group convolution in this embodiment; (a) G = 1 (standard convolution); (b) G = 2; (c) G = 4;

[0060] Figure 3 The following are the physical characteristics of the simulated target in this embodiment; (a) warhead; (b) spherical decoy; (c) mother cabin; (d) high-imitation decoy; (e) simple decoy;

[0061] Figure 4 Shown is the overall recognition accuracy of the test set for each deep learning algorithm at different SNR values. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0063] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] HRRP is the vector sum of the complex sub-echoes of the target scattering points obtained by broadband radar signals projected on the radar line of sight (LOS). Compared with the "point" targets presented by conventional narrowband radars, HRRP provides one-dimensional distribution information of the target scattering points along the distance direction, which has important structural characteristics of the target and can be used as a basis for distinguishing different radar targets. HRRP is based on the scattering center model, and the echo of the jth range unit is equal to the superposition of the echoes of all scattering centers in this range unit, that is,

[0065]

[0066] In the above formula, I n,j represents the number of scattering centers corresponding to the jth distance unit, R n,i (j) represents the distance from the i-th scattering center to the radar in the echo of the j-th range unit, σ n,i and Respectively represent the amplitude and initial phase of the i-th scattering center echo signal. The n-th HRRP sample data is recorded as

[0067] x(n)=[|x1(n)|,|x2(n)|,...,|x E (n)|] (2)

[0068] Where E is the total number of HRRP distance units.

[0069] Based on this, the present invention proposes a radar high-resolution range profile recognition method based on multi-scale grouping fusion convolution.

[0070] Overall design of network structure

[0071] The HRRP recognition network based on multi-scale group fusion 1D-CNN (MSGF-1D-CNN) proposed in this paper is as follows Figure 1 As shown in the figure, the network as a whole can be divided into seven parts: input layer, one-dimensional convolution layer, batch normalization layer, non-linear activation layer, pooling layer, flat layer and Softmax classifier. Among them, one-dimensional convolution layer, batch normalization layer, non-linear activation layer and pooling layer constitute convolution module. The repeatedly connected convolution module in MSGF-1D-CNN is used for feature extraction, and the flat layer and Softmax classifier are mainly used for target classification.

[0072] The functions of each part in MSGF-1D-CNN are as follows:

[0073] (1) Input layer: The target recognition method based on neural network is generally divided into two stages: model training and model testing. Model training is the process of adjusting the parameters of the model according to the input data, while model testing is the process of predicting the input data using the model with adjusted parameters. These two processes require that the dimensions of the input data are consistent, so the original data input to the input layer Where D (1) =E, C (1) = 1. In addition, considering the amplitude sensitivity of HRRP, the value of each distance unit of HRRP is normalized to the range of [0, 1] using formula (3).

[0074]

[0075] (2) One-dimensional convolution layer: The one-dimensional convolution layer performs convolution operation on the input data and the convolution kernel with a fixed window size (i.e., the scale of the convolution kernel) to automatically extract features. Generally, the scale of the convolution kernel is much smaller than the size of the input data. Therefore, the convolution kernel moves on the input data with a certain step size, and the same convolution kernel is used in each step to achieve weight sharing. Assume that there are a total of convolutional modules, For the The multi-channel input of a standard one-dimensional convolutional layer, each channel corresponds to a one-dimensional feature map (the first convolutional layer input is the original data, which is regarded as having one channel), D (l) and C (l) Represent the size of a single one-dimensional feature map and the total number of one-dimensional feature maps, respectively. The one-dimensional convolutional layer converts multi-channel input into multi-channel output. Where D (l+1) and C (l+1) Respectively represent the feature map size and the number of channels after convolution. Figure 1 In the structure of , this paper sets the number of output feature map channels of each module to double, that is, C (l+1) =2×C (l) At the same time, the standard one-dimensional convolutional layer is replaced by a multi-scale fusion one-dimensional convolutional layer to form MSGF-1D-CNN.

[0076] (3) Batch Normalization Layer: Due to the limitation of computer processing power, all data is not sent to the network for training at the same time, but all data is input in batches. Using batch normalization to normalize each batch output of the convolutional layer to a distribution with a mean of 0 and a standard deviation of 1 can accelerate network training and improve the generalization ability of the model.

[23] .

[0077] (4) Nonlinear activation layer: In order to introduce nonlinear factors into the network structure, a nonlinear activation function is used to activate the output of the one-dimensional convolutional layer. All nonlinear activation functions in MSGF-1D-CNN use the Mish function, which is expressed as

[0078] δ(x)=x·tanh(ln(1+e x )) (4)

[0079] (5) Pooling layer: In order to reduce the dimension of the output of the one-dimensional convolution layer and remove the redundancy of adjacent features, the pooling layer downsamples the output of the one-dimensional convolution layer. The pooling layer of MSGF-1D-CNN uses the maximum pooling method. For the k-th output feature map X of the l-th one-dimensional convolution layer, k (l) , the value at position i of the output feature map after maximum pooling is given by formula (5)

[0080]

[0081] where H′ (l) and S′ (l) Represent the window size and step size of the maximum pooling respectively. Therefore, the number of feature maps remains unchanged after the maximum pooling, and the size of the feature map becomes

[0082]

[0083] in, Indicates rounding down.

[0084] (6) Flat layer and Softmax classifier: If the output of the last convolution module The feature map size Then it needs to be leveled through the flat layer. All feature maps in are arranged into a one-dimensional vector u as the input of the Softmax classifier. The Softmax classifier can be regarded as a special fully connected layer activated by the Softmax function, and its number of neurons is equal to the total number of categories Q of the target to be classified. The parameters of the Softmax classifier are expressed as θ sm = {W sm ,b sm}, for each HRRP sample (x(n), y(n)), x(n) and y(n) represent the HRRP sample data and the corresponding true label respectively, then the output of the qth neuron of the classifier represents the probability of judging the sample x(n) as the qth category, that is,

[0085]

[0086] in, represents the multidimensional features extracted by all layers before the classifier, θ* are the parameters of all feature extraction layers except the classifier, Flatten(·) represents the flattening operation, θ={θ * ,θ sm} represents all trainable parameters of the network. The prediction process of sample x(n) is to maximize the posterior probability, that is,

[0087]

[0088] Multi-scale group fusion one-dimensional convolution

[0089] In order to extract multi-scale information layer by layer, such as Figure 1 As shown in Figure 1, multi-scale grouped one-dimensional convolution and point-by-point convolution are used to replace the standard one-dimensional convolution layer to form a multi-scale grouped fusion one-dimensional convolution layer. (l) represents the window size of the convolution kernel of the lth standard one-dimensional convolution layer, X (l) All single-scale one-dimensional convolution kernels of this layer Perform convolution operations to generate output feature maps equal to the number of convolution kernels Specifically, each convolution kernel performs convolution operations with all the input feature maps, and the kth (k∈{1, 2, ..., C (l+1)}) one-dimensional convolution kernel With X (l) The resulting one-dimensional feature map is

[0090]

[0091] Among them, the operator * represents the convolution operation, represents the bias of the kth convolution kernel, δ(·) is the activation function of the nonlinear activation layer, and the input feature map of each layer is firstly padded with zeros. Let the number of zeros padded on one side of each input feature map of the lth layer be P (l) , the size of the input feature map first becomes D (l) +2P (l) , and then with a step length of S (l) The convolution operation is performed with the convolution kernel of , then the k-th output feature map is at position i (i∈D (l+1) ) is

[0092]

[0093] Where ⊙ represents the Hadamard product. From this, the output feature map size can be calculated as

[0094]

[0095] In order to allow the convolutional layer to extract different scale information of the input feature map, group convolutions with different scales are used. Replace the single-scale convolution W (l) , generating Ω groups of different outputs use G (ω；l) and denote the scale of the convolution kernel, the number of groups, and the number of output feature maps in the ωth (ω∈{1,2,…,Ω}) grouped convolution, respectively. And the number of output feature maps of each group convolution satisfies From the calculation formula of the output feature map size, we can know that the output feature map size obtained by the ω-th group convolution is

[0096]

[0097] in, and They represent the number of zero padding of the input feature map and the step size of the convolution kernel when performing the ω-th grouped convolution operation. In practice, the subsequent convolutional layers require that all input feature maps have the same size, that is, make Take a positive odd number, Make That is, the output feature map has the same size as the input feature map, so the multi-scale group convolution output is

[0098]

[0099] Among them, concat(·) means merging the feature map matrix along the channel direction, so

[0100] In grouped convolution, the input feature map and convolution kernel are divided into G groups of equal number, such as Figure 2 (b) and Figure 2 (c) are examples when G = 2 and G = 4, respectively. In each group, each convolution kernel performs convolution operations with all input feature maps in the corresponding group. Figure 2 As shown in (a), the standard one-dimensional convolution can be regarded as a special grouped convolution when G = 1. Grouped convolution adopts a local connection method. Compared with the full connection method of standard convolution, it only extracts the local features of the previous layer output, making the network unable to effectively use global features for classification. Point-by-point convolution is P (l) =0,H (l) =1 and S (l) = 1, it can be seen from formula (9) that the point-by-point convolution can learn the linear correlation of the output of the multi-scale group convolution. Therefore, after the output of the multi-scale group convolution is activated, the point-by-point convolution is connected to realize the linear fusion of the extracted group features.

[0101] Complexity Analysis

[0102] In order to compare the model complexity of standard one-dimensional convolution and multi-scale group fusion one-dimensional convolution, the total amount of trainable parameters PA of the convolution kernel is used for analysis. For the standard one-dimensional convolution kernel, the total amount of trainable parameters of its l-th one-dimensional convolution layer is for

[0103]

[0104] The multi-scale group fusion one-dimensional convolution layer contains Ω group convolutions of different scales and 1 point-by-point convolution. The total number of parameters is It is composed of these two parts of convolution, specifically

[0105]

[0106] Among them, the part before the "+" is the sub-item of the total number of parameters for point-by-point convolution, and the part after the "+" is the sub-item of the total number of parameters for multi-scale grouped convolution.

[0107] From formula (15), we can see that the multi-scale group fusion one-dimensional convolution layer G (ω；l) The larger the value of Therefore, in order to minimize the number of parameters and computational complexity of the multi-scale group fusion one-dimensional convolutional layer, G (ω；l) The maximum feasible value should be taken. Since group convolution requires dividing the input channel and output channel into G (ω；l) Groups, namely G (ω；l) C must be divisible at the same time (l) and When assigning the number of convolution kernels to each group convolution, we can divide C by (l) of but When the total amount of parameters reaches the minimum value, that is,

[0108]

[0109] From formula (14) and formula (16), we can get

[0110]

[0111] From formula (17), we can see that Figure 1 In the network structure of , for the one-dimensional convolution layer with more output channels, that is, In terms of the number of parameters, the single-scale standard one-dimensional convolutional layer is the proposed multi-scale grouped fusion one-dimensional convolutional layer. Therefore, when the number of channels is large, in theory, multi-scale grouped fusion one-dimensional convolution can effectively reduce the number of parameters of single-scale standard one-dimensional convolution.

[0112] For a given C (l) and C (l+1) , we must ensure Divisible by C (l) , and to satisfy It is relatively difficult and may not exist. A feasible solution is C (l) and C (l+1) If we set it to an integer power of 2, it is easy to find integer powers of 2. As shown in Table 1, a multi-scale group fusion convolution layer design scheme is proposed to meet the above conditions when the number of group convolutions Ω is in {2, 3, 4, 5}, and the convolution kernel scale of each group convolution is in {1, 3, 5, 7, 9}. To simplify the description, the convolution kernel scale of each group convolution, the number of output channels and the number of groups are represented by one-dimensional arrays. and express.

[0113] Table 1 Design of multi-scale group fusion one-dimensional convolutional layer

[0114]

[0115] Network training process

[0116] Training the network first requires building a loss function and constructing MSGF-1D-CNN in the entire HRRP training dataset The cross entropy loss function on

[0117]

[0118] Where N is the total number of samples in the training set M; 1{·} is the indicator function, that is, 1{true}=1, 1{false}=0. Network training is the process of updating network parameters using training data, which is essentially the minimization of the empirical risk loss function of formula (18), that is,

[0119]

[0120] Solving formula (19) using all training data requires a lot of computing power and memory, especially for large data sets and networks with many parameters. Therefore, the stochastic gradient descent algorithm is generally used to randomly extract B samples each time to update the parameters. The entire training data set is randomly divided into Batches( means rounding up to an integer), that is For the tth iteration (t∈{1,2,…,T}), the update formula of the stochastic gradient descent algorithm is

[0121] θt+1 =θ t -αg t (20)

[0122] Where α is the learning rate, g t is the loss function with respect to θ t The gradient of

[0123]

[0124] Assuming the total number of cycles of network training is τ, the specific process of the HRRP recognition method based on MSGF-1D-CNN is as follows:

[0125] Step 1: Build the network: First, give a one-dimensional array containing the number of channels of each one-dimensional convolutional layer. To represent different model structures, the value of each element in C is an integer power of 2 and gradually increases. Given Ω, the corresponding and Thus completing Figure 1 The specific configuration of the network structure shown.

[0126] Step 2: Initialize the network: Use Kaiming initialization method

[24] Initialize the trainable parameters θ of the network.

[0127] Step 3: Forward propagation: Calculate the loss function value of each batch of data according to formula (18).

[0128] Step 4 Backpropagation: Using the diffGrad algorithm

[25] Formula (20) is updated using the chain rule to complete the parameter update for each batch.

[0129] Step 5 repeats step 3 and step 4, training T batches of data one by one to complete a cycle of training. Then, the model trained in the current cycle is used in combination with formula (8) to predict the samples in the test data set, and the prediction results are statistically analyzed.

[0130] Step 6: Repeat step 5 until τ cycles of training are completed, and save the model parameters when the test set recognition accuracy is the highest.

[0131] Experiments and Results

[0132] 1. Experimental data

[0133] The HRRP image recognition method of mid-course ballistic targets based on DCNN was used to simulate the HRRP data of five mid-course ballistic targets, namely, warhead, high-imitation decoy, simple decoy, spherical decoy and mother cabin, i.e., Q = 5. The physical parameters of each target are as follows: Figure 3As shown in the figure, the simulated azimuth range and azimuth accuracy are 0-180° and 0.05° respectively. Therefore, 3601 HRRP samples at different azimuths are simulated for each type of target, and the number of distance units of each HRRP sample is 256, that is, E = 256. 20% of the samples of each type of target are randomly selected to form the test data set, and the remaining 80% of the samples form the training data set.

[0134] 2. Experimental Setup

[0135] In the experiment, MSGF-1D-CNN uses the following parameter configuration: the window size H′ of the maximum pooling layer (l) and step length S′ (l) All convolution kernels are set to 3, and the stride of all convolution kernels is set to 1. In addition to comparing MSGF-1D-CNN with the standard 1D-CNN to verify the improvement effect, MSGF-1D-CNN is also compared with the HRRP recognition method based on stacked denoising sparse autoencoder (Stacked Denoising Sparse AE, sDSAE) and the HRRP recognition method based on bidirectional LSTM (Bidirectional LSTM, Bi-LSTM).

[12] The HRRP recognition method based on bidirectional GRU (Bi-GRU) is compared with the HRRP recognition method based on bidirectional GRU (Bi-GRU). The above HRRP recognition methods based on deep learning are all trained using the diffGrad algorithm, and the parameters of the diffGrad algorithm are all set to: learning rate α = 0.01, number of training cycles τ = 200, and number of samples in each batch B = 64.

[0136] 3. Comparative experiment with standard 1D-CNN

[0137] In order to verify the effectiveness of the proposed MSGF-1D-CNN and determine its optimal hyperparameter configuration scheme, experiments were conducted using the default parameter configuration scheme of the multi-scale group fusion one-dimensional convolution layer given in Table 1 under different model structure settings. The experiments involved 6 model structures: C1 = [8, 16, 32, 64], C2 = [16, 32, 64, 128], C3 = [32, 64, 128, 256], C4 = [64, 128, 256, 512], C5 = [128, 256, 512, 1024] and C6 = [256, 512, 1024, 2048]. While keeping the model structure unchanged, the multi-scale group fusion one-dimensional convolution layer was replaced with a single-scale standard one-dimensional convolution layer to construct a standard 1D-CNN for comparative experiments. The value range of the volume window size H of the standard one-dimensional convolution layer is {1, 3, 5, 7, 9}. Five indicators are used to evaluate the recognition performance and model complexity of MSGF-1D-CNN and standard 1D-CNN: overall recognition accuracy of the test set, total number of parameters (unit: number), floating-point operations (unit: FLOPS), multiplication and accumulation operations (unit: MACs) and memory usage required for running during model testing (unit: B). The results are shown in Table 2. In the table, the overall recognition accuracy of the optimal test set for standard 1D-CNN and MSGF-1D-CNN under different model structures is indicated in bold.

[0138] The results in Table 2 can be analyzed from two perspectives:

[0139] Longitudinal comparison: (1) Under the same convolutional layer configuration, the recognition accuracy of standard 1D-CNN and MSGF-1D-CNN shows an overall trend of increasing first and then decreasing with the increase of the number of channels. This is because the number of channels of the model is positively correlated with the total number of model parameters. Fewer channels will result in fewer model parameters, leading to underfitting, while too many channels will result in more model parameters, leading to overfitting; (2) At the same time, the increase in the total number of parameters will also lead to an increase in the amount of floating-point operations, multiplication-accumulation operations, and memory usage. Taking into account the compromise of the above five indicators, that is, satisfying the premise of having a higher recognition accuracy with fewer parameters, floating-point operations, multiplication-accumulation operations, and memory usage, the optimal model structure of standard 1D-CNN and MSGF-1D-CNN is C4.

[0140] Horizontal comparison: (1) In most cases, the recognition accuracy of MSGF-1D-CNN is higher than that of standard 1D-CNN, especially when the number of channels of each one-dimensional convolution layer is more than 64 (such as C4, C5, and C6). The 1D-CNNs using the four multi-scale grouped fusion one-dimensional convolution layer design schemes in Table 1 are all higher than the single-scale 1D-CNN in terms of recognition accuracy; (2) The total number of parameters of MSGF-1D-CNN is smaller than that of the standard 1D-CNN when H ≥ 3. It can be seen from formula (17) that when the convolution kernel window size remains unchanged, compared with the total number of parameters of the standard 1D-CNN, the more the number of output channels increases, the more obvious the reduction effect of the total number of parameters of MSGF-1D-CNN is; (3) As H and Ω increase, the total number of parameters, floating-point operations, multiplication-accumulation operations, and memory usage of the standard 1D-CNN and MSGF-1D-CNN all show an increasing trend, but the increase in each indicator of the standard 1D-CNN is more obvious. The above three phenomena show that, under different model structures, using multi-scale group fusion one-dimensional convolutional layers instead of standard single-scale one-dimensional convolutional layers has certain effectiveness and versatility in improving the model recognition accuracy and reducing the model complexity. Also considering the compromise of the five indicators, the optimal convolution kernel size H of the standard 1D-CNN is 5, while the optimal number of group convolutions Ω of MSGF-1D-CNN is 3.

[0141] In summary, the optimal hyperparameters of MSGF-1D-CNN are: the optimal model structure is C4 = [64, 128, 256, 512], the design of the multi-scale group fusion one-dimensional convolution layer adopts the default setting when Ω = 3 in Table 1, and the optimal hyperparameters of the standard 1D-CNN are: the optimal model structure is C4 = [64, 128, 256, 512], the optimal convolution kernel size H = 5. Under their respective optimal configurations, the recognition accuracy of MSGF-1D-CNN is improved by more than 0.7% compared with the standard 1D-CNN. From formula (17), it can be seen that the total number of model parameters is reduced by more than 2.4 times, and it has lower floating point, multiplication and accumulation operations and memory usage.

[0142] Table 2 Comparative experimental results of MSGF-1D-CNN and standard 1D-CNN

[0143]

[0144] * The bold font represents the maximum value of the recognition accuracy of each row

[0145] 4. Comparative experiments with other deep learning methods

[0146] In order to evaluate the recognition effect of each target in the test set, the accuracy F of each HRRP recognition method for each target is calculated separately. P, recall rate F R and F M At the same time, the overall recognition accuracy of the test set is still used to evaluate the overall recognition effect. Precision refers to the proportion of samples identified as positive examples that are actually positive examples, and recall refers to the proportion of samples correctly identified as positive examples to all samples that are actually positive examples. M It is an indicator that comprehensively considers precision and recall, and is a weighted harmonic average of precision and recall. The formulas for these three indicators are as follows:

[0147]

[0148] Among them, TP is the number of samples judged as positive in the positive class, FP is the number of samples judged as positive in the negative class, and FN is the number of samples judged as negative in the positive class.

[0149] The comparative experimental results of MSGF-1D-CNN and other deep learning methods on the above four indicators are shown in Table 3. The following three conclusions can be drawn from Table 3:

[0150] (1) For most mid-course targets, MSGF-1D-CNN has a higher accuracy rate F than sDSAE, Bi-LSTM, Bi-GRU and 1D-CNN. P and recall F R , so the F of MSGF-1D-CNN for most targets is M It is higher than other deep learning algorithms and has obvious advantages.

[0151] (2) MSGF-1D-CNN has the highest overall recognition accuracy of 96.69% compared to sDSAE, Bi-LSTM, Bi-GRU and 1D-CNN. This is mainly due to the fact that MSGF-1D-CNN has a higher recall rate for spherical decoys, high-imitation decoys and warheads. R It is higher than other deep learning algorithms, even though the recall rate of MSGF-1D-CNN for the mother cabin and simple bait is sometimes slightly lower than that of Bi-LSTM and Bi-GRU. As shown in Table 2, without considering the trade-off between the recognition accuracy and computational complexity of MSGF-1D-CNN, the recognition accuracy of MSGF-1D-CNN still has room for improvement, and can reach up to 96.92%.

[0152] (3) Although the accuracy of the MSGF-1D-CNN warhead is PCompared with other deep learning algorithms, it is not very high, but its recall rate of warheads has obvious advantages over other deep learning algorithms. Therefore, from a combat perspective, MSGF-1D-CNN has higher practical application value and can effectively distinguish warheads, thus providing a certain reference for further improving the missile interception rate and reducing the damage rate of one's own side.

[0153] Table 3 Comparative experimental results of MSGF-1D-CNN and other deep learning methods

[0154]

[0155]

[0156] Since the model will be affected by noise in the actual process, in order to further compare the recognition accuracy of the model under different signal-to-noise ratio (SNR) environments, Gaussian white noise is added to the samples in the test set. The definition of SNR is as follows:

[0157]

[0158] Where E = 256 represents the number of HRRP distance units, P l represents the original signal strength of the lth distance unit, P Noise Indicates the signal strength of the noise.

[0159] Figure 4 It is the change of the overall recognition accuracy of different deep learning algorithms for the test set when SNR takes values ​​within {10, 15, 20, 25, 30, 35, 40}. Figure 4 It can be seen that compared with Bi-LSTM, MSGF-1D-CNN has a higher overall recognition accuracy of the test set within the range of SNR, and when SNR≥20, the overall recognition accuracy of the test set of MSGF-1D-CNN is better than other deep learning algorithms. Therefore, the proposed method has higher noise robustness than other deep methods to a certain extent.

[0160] The above description is only used to illustrate the technical solution of the present invention rather than to limit it. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in this field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims

1. A radar high-resolution range profile recognition method based on multi-scale group fusion convolution is characterized by: The following steps are involved: Step 1: Construct HRRP recognition network based on MSGF-1D-CNN First, given a one-dimensional array containing the number of channels of each one-dimensional convolutional layer To represent different model structures, the value of each element in C is an integer power of 2 and gradually increases. Given Ω and determining the corresponding and G (l) , thereby completing the specific configuration of the network structure; Step 2: Initialize the recognition network: initialize the trainable parameters θ of the network; Step 3: Forward Propagation Constructing MSGF-1D-CNN on HRRP training dataset The cross entropy loss function on the data is used to calculate the loss function value of each batch of data; Step 4: Back propagation: Use the stochastic gradient descent algorithm to update the parameters of each batch; Step 5: Repeat steps 3 and 4 to train T batches of data one by one to complete a training cycle. Then, use the model trained in the current cycle combined with the formula to predict the samples in the test data set and perform statistics on the prediction results. Step 6: Repeat step 5 until completed After training for 1 cycle, save the model parameters when the recognition accuracy of the test set is the highest; The HRRP recognition network includes an input layer, a convolution module, a flat layer and a Softmax classifier; Input layer: raw input data Where D (1) =E, C (1) =1; Convolutional module: The convolution modules are repeatedly connected for feature extraction; Flat layer and Softmax classifier: If the output of the last convolution module The feature map size Then after the flattening operation of the flat layer All feature maps in are arranged into a one-dimensional vector u as the input of the Softmax classifier, which performs target classification; The convolution module includes a multi-scale group fusion one-dimensional convolution layer, a batch normalization layer, a nonlinear activation layer and a pooling layer; wherein, Multi-scale group fusion one-dimensional convolution layer: Use multi-scale group one-dimensional convolution and point-by-point convolution to replace the standard one-dimensional convolution layer, and use H (l) represents the window size of the convolution kernel of the lth standard one-dimensional convolution layer, X (l) All single-scale one-dimensional convolution kernels of this layer Perform convolution operations to generate output feature maps equal to the number of convolution kernels Where D (l+1) and C (l+1) Respectively represent the feature map size and the number of channels after convolution; Batch Normalization Layer: Use batch normalization to normalize each batch output of the convolutional layer to a distribution with a mean of 0 and a standard deviation of 1. Nonlinear activation layer: Use a nonlinear activation function to activate the output of the one-dimensional convolutional layer; the expression of the nonlinear activation function is δ(x) = x·tanh(ln(1+e x )); Pooling layer: Using the maximum pooling method, for the k-th output feature map X of the l-th one-dimensional convolutional layer k (l) , the value at position i of the output feature map after maximum pooling is given by the following formula where H′ (l) and S′ (l) Represent the window size and step size of the maximum pooling respectively. After the maximum pooling, the number of feature maps remains unchanged, and the size of the feature map becomes in, Indicates rounding down; The specific process of convolution operation is: Each multi-scale group fusion one-dimensional convolutional layer performs convolution operations with all input feature maps, and the kth (k∈{1, 2, ..., C (l+1) }) one-dimensional convolution kernel With X (l) The resulting one-dimensional feature map is Among them, the operator * represents the convolution operation, represents the bias of the kth convolution kernel, δ(·) is the activation function of the nonlinear activation layer, and the input feature map of each layer is firstly padded with zeros. Let the number of zeros padded on one side of each input feature map of the lth layer be P (l) , the size of the input feature map first becomes D (l) +2P (l) , and then with a step length of S (l) The convolution operation is performed with the convolution kernel of , then the k-th output feature map is at position i (i∈D (l+1) ) is Where ⊙ represents the Hadamard product, from which the output feature map size can be calculated as In order to allow the convolutional layer to extract different scale information of the input feature map, group convolutions with different scales are used. Replace the single-scale convolution W (l) , generating Ω groups of different outputs use G (ω；l) and denote the scale of the convolution kernel, the number of groups, and the number of output feature maps in the ω(ω∈{1,2,...,Ω})th grouped convolution, respectively. And the number of output feature maps of each group convolution satisfies From the calculation formula of the output feature map size, we can know that the output feature map size obtained by the ω-th group convolution is in, and They represent the number of zero padding of the input feature map and the step size of the convolution kernel when performing the ω-th grouped convolution operation. In practice, the subsequent convolution layers require that all input feature maps have the same size, that is, make Take a positive odd number, Make That is, the output feature map has the same size as the input feature map, so the multi-scale group convolution output is Among them, concat(·) means merging the feature map matrix along the channel direction, so The specific process of Softmax classifier for target classification is as follows: The parameters of the Softmax classifier are denoted as θ sm = {W sm ,b sm }, for each HRRP sample (x(n), y(n)), x(n) and y(n) represent the HRRP sample data and the corresponding true label respectively, then the output of the qth neuron of the Softmax classifier represents the probability of judging the sample x(n) as the qth category, that is, Among them, φ θ* (·) represents the multidimensional features extracted by all layers before the Softmax classifier, θ* is the parameter of all feature extraction layers except the Softmax classifier, Flatten(·) represents the flattening operation, θ={θ*,θ sm } represents all trainable parameters of the network. The prediction process of sample x(n) is to maximize the posterior probability, that is, 2. The radar high-resolution range profile recognition method based on multi-scale grouping fusion convolution according to claim 1 is characterized in that: In step 3, the cross entropy loss function is: Where N is the total number of samples in the training set M; 1{·} is the indicator function, that is, 1{true}=1, 1{false}=0.

3. The radar high-resolution range profile recognition method based on multi-scale grouping fusion convolution according to claim 2 is characterized in that: In step 4, network training is the process of updating network parameters using training data, which is essentially the minimization of the cross entropy loss function and the empirical risk loss function, that is, Solving the above formula using all training data requires a lot of computing power and memory. Therefore, the stochastic gradient descent algorithm is generally used to randomly extract B samples each time to update the parameters. The entire training data set is randomly divided into batches, It means rounding up to an integer, that is For the tth iteration (t∈{1,2,...,T}), the update formula of the stochastic gradient descent algorithm is i t+1 =θ t -ag t Where α is the learning rate, g t is the loss function with respect to θ t The gradient of

Images