A model fusion recognition method based on SAR image azimuth characteristics

Abstract

The invention discloses a model fusion recognition method based on azimuth characteristics of SAR images, comprising the following steps: dividing sub-data sets and a total data set according to the azimuth characteristics of SAR images, namely, azimuth sensitivity and azimuth 180° image symmetry, training corresponding total models and sub-models with the total undivided data set and the sub-data set; when testing, putting a picture to be tested into each model to obtain a preliminary result, performing azimuth estimation on the picture to be tested, and then performing decision fusion of the model, namely, performing different weighted summations on the preliminary results of each model according to different situations of azimuth estimation to obtain a final prediction result, thereby improving the accuracy compared with the prediction result obtained by training the total model with a single total data set and compared with other SAR image recognition methods.

Description

Technical Field

[0001] The invention belongs to the field of radar technology and relates to a SAR image target classification method, in particular to a model fusion recognition method based on SAR image azimuth characteristics. Background Art

[0002] SAR, or Synthetic Aperture Radar, is a radar that uses the principle of synthetic aperture to achieve high-resolution microwave imaging. It has many characteristics such as all-day, all-weather, high resolution, and wide bandwidth. Its many advantages make it widely used in civil and military fields. SAR image recognition, as an important part of SAR application, has always been a hot research topic. However, the imaging characteristics of SAR images make it difficult to judge them by simple manual methods like optical images. Therefore, how to extract effective feature information from SAR images to make quick and accurate judgments is one of the issues in the development and research of SAR. In 2012, AlexNet won the championship in the Imagenet competition with its 15.3% Top5 error rate, which set off a wave of target recognition and detection based on deep learning. Since then, convolutional neural networks, one of the most popular deep learning, have continued to shine in image recognition. In 2014, Szegedy et al. won the championship with a Top5 error rate of 6.67% with their Google Inception network, and greatly reduced the number of parameters and calculations. In 2015, the emergence of Resnet reduced the error rate directly to 3.57%, proving the superiority of convolutional neural networks.

[0003] At present, image recognition based on deep learning has also been widely used in the recognition of SAR images, and has always had a high recognition accuracy, namely, Probability of Correct Cognition, PCC. Deep convolutional neural networks have been used to recognize SAR image targets and have achieved good results. However, unlike natural optical images, SAR images are extremely sensitive to the azimuth of imaging. There are certain differences in SAR images of the same target at different azimuths, that is, the target characteristics will change more dramatically with the change of azimuth. Previous research methods only tested the overall data set and did not take into account the sensitivity of SAR images in specific azimuths. Training and testing SAR images of all azimuths together inevitably has limitations. Therefore, the present invention proposes a model fusion recognition method based on the azimuth characteristics of SAR images. Summary of the invention

[0004] The purpose of the present invention is to provide a model fusion recognition method for SAR image azimuth characteristics and based on the SAR image azimuth characteristics, which solves the shortcomings of insufficient consideration of SAR image azimuth characteristics under a single model, is comprehensive and can improve the target recognition accuracy to a certain extent.

[0005] To achieve the above object, the present invention provides the following technical solution: a model fusion recognition method based on SAR image azimuth characteristics, comprising the following steps:

[0006] Step 1: Analyze the azimuth characteristics of the SAR image and divide the data set according to the azimuth characteristics. First, obtain the training set and the test set. The obtained sample data set contains multiple types of targets. Each type of target contains multiple SAR images with azimuth angles from 0 to 360°. According to the analyzed azimuth characteristics, namely sensitivity and the 180° symmetrical similarity of the image azimuth angle, the data set is divided into two sub-datasets S1S2. The overall data set without azimuth division is the total data set G.

[0007] Step 2: Train each data set to obtain each convolutional neural network model, pre-train the sub-data set S1S2 through the convolutional neural network to obtain the sub-model S1S2, pre-train the total data set G through the convolutional neural network to obtain the total model G, and save the three trained models for later use;

[0008] Step 3: Add and average all the pixels of the training set images in the sub-datasets S1 and S2 to obtain the average images P1 and P2, and the two average images are regarded as containing the approximate azimuth information of the two corresponding sub-datasets;

[0009] Step 4: Estimate the azimuth of the image to be tested, calculate the Euclidean distance C1 C2 between the image to be classified and P1 P2, and find the difference between the two. Since the average image contains the azimuth information of the corresponding sub-dataset, the image to be classified with a smaller Euclidean distance between P1 P2 is considered to have an azimuth that is close to the overall data set corresponding to its average image, so that the model corresponding to this data set has more weight in the subsequent weighting of model results;

[0010] Step 5: Input the image to be tested into the model trained in step 2 to obtain the output result in the Softmax layer. Determine the weighting coefficients of the three results according to the different relationships between C1 and C2 in step 4. Weight the results of each model according to the weighting coefficients to obtain the final classification result.

[0011] Furthermore, in step 1, a SAR image with a known actual azimuth is used to calculate the Euclidean distance between it and sample images of the same and different categories containing various azimuths to express the similarity between images. The Euclidean distance is the actual distance between two points in n-dimensional space. Given two points A = (a1, a2, ..., a n ), point B = (b1, b2, ..., b n ) then the distance between AB is:

[0012]

[0013] Among them, the smaller the Euclidean distance, the greater the surface similarity; the azimuth characteristics of the SAR image are observed through the relationship curve; first, the azimuth sensitivity of the SAR image, that is, the SAR images with similar azimuths show a higher correlation and second, the azimuth 180° symmetry of the SAR image, that is, the images with azimuths from 0 to 90° are highly correlated with the images with azimuths from 180° to 270°; the images with azimuths from 90° to 180° are highly correlated with the images with azimuths from 270° to 360°. Therefore, the images with higher correlation are put together to form sub-datasets S1 and S2, and the total data set is G.

[0014] Furthermore, in the step 2, the network model includes an input layer, a convolutional layer, a maximum pooling layer, a fully connected layer and finally an output layer after Softmax.

[0015] Furthermore, in the step 2, since the overall G dataset is divided into S1 and S2 sub-datasets according to the azimuth angle, the latter two datasets are even more insufficient in quantity. In order to compensate for this deficiency, the S1 and S2 datasets are artificially expanded to twice the original quantity through data enhancement to achieve a quantity close to the original overall dataset.

[0016] Furthermore, in the step four, considering that the azimuth of the image to be tested is near the critical angle, i.e., 90°, 180°, and 270°, it will be closer when calculating the Euclidean distance with P1 and P2, i.e., C1 and C2 will be closer, and it will be vague when judging the weight of the model to which it belongs, so a threshold is set, that is, when the distance between C1 and C2 is less than this threshold, the azimuth of these images is regarded as belonging to the critical angle, when C1-C2 is greater than this threshold or C2-C1 is greater than this threshold, the azimuth of the image to be tested is regarded as being closer to the azimuth contained in the corresponding sub-data set of the smaller one between C1 and C2, so in summary, the azimuth includes three cases.

[0017] Furthermore, in step 5, the Softmax layer output of the image to be tested in each model is obtained. The Softmax layer converts the output result of the neural network and expresses the output result in the form of probability. When the output of the neural network is sent to the fully connected layer, the score z in the range of K categories (-∞, +∞) is obtained. j In order to obtain the probability of belonging to each category, first use e zj Mapping the score to (0, +∞) and then normalizing it to (0, 1) is called the Softmax idea:

[0018]

[0019] After obtaining the ten categories of probabilities, the probability of each category of the model output is fused with different weights according to the azimuth estimation results obtained in step 4, and finally the category with the largest probability is obtained, which is the final prediction result of the fusion model.

[0020] Compared with the prior art, the invention has the following beneficial effects: the whole method is tested in many aspects based on the MSTAR data set, and the experimental results show that due to the unique characteristics of the azimuth of the SAR image, the azimuth is used as a factor for SAR target recognition, taking into account the azimuth sensitivity of the SAR image, that is, the SAR images with similar azimuths show a higher correlation and the azimuth 180° symmetry of the SAR image, so when the sub-data set is subsequently trained with a sub-model, the model is more sensitive to these images corresponding to a specific azimuth range, that is, the accuracy is higher. By estimating the azimuth of the image to be tested, putting it into each model to obtain the result, and by setting the weighted values ​​of the results of different models, the final prediction result is obtained, which has a higher accuracy than the prediction result obtained by training the total model with a single total data set, and the accuracy is also greatly improved compared with other SAR image recognition methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0022] In the attached picture:

[0023] Figure 1 is a diagram showing the azimuth characteristics of SAR images according to the present invention: Figure 1 (a) shows the Euclidean distance curve between the actual image and BMP2. Figure 1 (b) represents the Euclidean distance curve between the actual image and BTR70;

[0024] Figure 2 is a flow chart of the model fusion recognition method based on the azimuth characteristics of SAR images of the present invention: Figure 2 (a) represents the training process of each model. Figure 2 (b) shows the testing process of the fusion model;

[0025] Figure 3 It is a convolutional neural network model diagram used in the present invention;

[0026] Figure 4 It is a schematic diagram showing data enhancement in the present invention;

[0027] Figure 5 It is a diagram of the change process of relevant parameters during the training of each model in the present invention: Figure 5 (a) The accuracy change diagram of model G during training process, Figure 5 (b) shows the learning rate change diagram of the model G training process. Figure 5 (c) The accuracy change diagram of model S1 during training process. Figure 5 (d) The accuracy change diagram of model S2 during training process;

[0028] Figure 6 is the average graph used for azimuth estimation in the present invention: Figure 6 (a) is the average graph P1 of the training set in sub-dataset S1. Figure 6 (b) is the average graph P2 of the training set in sub-dataset S2;

[0029] Figure 7 It is a confusion matrix diagram used in the present invention to compare the classification results of a single model and a fusion model. DETAILED DESCRIPTION

[0030] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0031] Embodiment: A model fusion recognition method based on SAR image azimuth characteristics includes two stages: a training process of each model and a testing process of the fusion model. The specific steps are as follows:

[0032] Step 1: Analyze the azimuth characteristics of the SAR image and divide the data set according to the azimuth characteristics. First, obtain the training set and the test set.

[0033] This experiment uses the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset published by the United States, and selects SAR images of ten types of vehicle targets under standard operating conditions (SOC) as experimental data. These vehicle targets are: 2S1, BMP2, BRDM2, BTR60, BTR70, D7, T62, T72, ZIL131, and ZSU_23_4. All types of SAR data contain targets with azimuth angles of 0° to 360°. This experiment selects SAR images taken at a pitch angle of 17° as the training set, and SAR images taken at a pitch angle of 15° as the test set. The total data set is shown in the following table. The following table shows the data set used in the experiment. This selection can verify the generalization ability of the feature extraction method.

[0034]

[0035] According to the analyzed azimuth characteristics, namely sensitivity and the 180° symmetry of the image azimuth, the data set is divided into two sub-datasets S1 and S2, and the overall data set without azimuth division is the total data set G.

[0036] like Figure 1 As shown in the figure, taking a BMP2_SN_9563 SAR image with an actual azimuth angle of 81° as an example, the Euclidean distance between it and all the images in the training set samples of the two types of targets, BMP2_SN_9563 and BTR70, is calculated. From the relationship curve between the Euclidean distance and the image azimuth angle, it can be found that an image has the same or different targets. 1. The SAR image only maintains a low Euclidean distance with samples with a particularly close azimuth angle, that is, sensitivity. 2. The SAR image has a similar Euclidean distance with samples that are symmetrical at an azimuth angle of 180 degrees, that is, symmetry.

[0037] Therefore, in order to put SAR images with high similarity together, considering that the dataset used contains all images with azimuth angles from 0° to 360°, that is, the overall distribution is from 0° to 360°, and there is a lack of some angles in the middle. The distribution of other angles introduced later also has this meaning. The dataset is divided into four parts according to the azimuth interval of 90°, namely 0° to 90°, 90° to 180°, 180° to 270°, and 270° to 360°. Considering the 180° symmetrical similarity of the image, the two datasets with angles of 0 to 90° and 180° to 270° are merged into sub-dataset S1, and the two datasets with angles of 90° to 180° and 270° to 360° are merged into sub-dataset S2. The overall undivided dataset is called dataset G.

[0038] Step 2: Train each data set to obtain each convolutional neural network model. The network model includes input layer, convolution layer, maximum pooling layer, fully connected layer and finally output layer after Softmax. Sub-data sets S1 and S2 are pre-trained through convolutional neural network to obtain sub-models S1 and S2, and the total data set G is pre-trained through convolutional neural network to obtain the total model G. The three trained models are saved for later use. The convolutional neural network structure is as follows: Figure 2 As shown, the specific parameters are set as follows:

[0039] Input layer: Input SAR image of 100×100. The data set is grayscale image, which can be treated as RGB image and processed as 100×100×3 image.

[0040] Convolutional layer 1 has 96 convolution kernels, the convolution kernel size is 11×11, the stride is 4, and the activation function is the ReLU function;

[0041] Pooling layer 1, window size 2, stride 4;

[0042] Convolutional layer 2, with 256 convolution kernels, the convolution kernel size is 5×5, and the activation function is the ReLU function;

[0043] Pooling layer 2, window size is 3, stride is 1;

[0044] Convolution layer 3, including 384 convolution kernels, the convolution kernel size is 3×3, and the activation function is the ReLU function;

[0045] Convolutional layer 4, including 384 convolution kernels, the convolution kernel size is 3×3, and the activation function is the ReLU function;

[0046] Convolution layer 5, including 256 convolution kernels, the convolution kernel size is 3×3, and the activation function is the ReLU function;

[0047] Pooling layer 3, window size is 3×3, stride is 1;

[0048] Fully connected layer 1, with 1024 neuron nodes;

[0049] Dropout layer, 0.5;

[0050] Fully connected layer 2, with 1024 neuron nodes;

[0051] Dropout layer, 0.5;

[0052] The output layer uses the Softmax activation function to classify SAR images and includes 10 neuron nodes.

[0053] Data enhancement is used in two places during training. Data enhancement is to make limited data generate more data, increase the number and diversity of training samples, and improve model robustness. It is generally used for training sets. Data enhancement is used in two places in the present invention. 1. Since the overall G data set is divided into S1 and S2 data sets according to the azimuth angle, the latter two data sets are even more insufficient in quantity. In order to make up for this deficiency, the S1 and S2 data sets are artificially expanded to twice the original quantity through data enhancement to achieve a quantity close to the original overall data set; 2. In the model training process, data enhancement is used in the network. Although the number of the three data sets is not increased on the surface, the diversity of the data is actually increased. The data enhancement methods used in the present invention mainly include 1. Random shearing; 2. Random scaling; 3. Random rotation angle; 4. Random horizontal flipping. Such as Figure 3 shown.

[0054] The three data sets are trained into three models respectively, where the G data set is trained as the overall model G, and the sub-data sets S1 S2 are trained as sub-models S1 S2 respectively, as shown in Figure 2 The hyperparameter settings for the three models during training are shown in the following table:

[0055] Hyperparameters Model G <![CDATA[Model S1]]> <![CDATA[Model S2]]> Epoch 600 600 600 Learning Rate <![CDATA[Initial 8e -3 , decreasing by half every 100 rounds]]> <![CDATA[1×e -3 ]]> <![CDATA[1×e -3 ]]> Optimizer SGD SGD SGD Momentum 0.9 0.9 0.9 Batchsize 16 16 16 Activation Function Relu / Softmax Relu / Softmax Relu / Softmax Regularization coefficient <![CDATA[5×10 -4 ]]> <![CDATA[5×10 -4 ]]> <![CDATA[5×10 -4 ]]>

[0056] In terms of training strategy, for the original overall data set G, during training, the learning rate is initially set to 8e -3 , the learning rate is reduced to half of the original rate after every 100 training rounds. In order to suppress overfitting, dropout is added to all networks during training, and L2 regularization is added to each convolutional layer. The optimizer uses stochastic gradient descent (SGD) to train the entire network, and uses a momentum parameter of 0.9 to maintain the inertial direction of the gradient descent to enhance the stability of network training.

[0057] The final result model of the three models is then saved and further called by the method of the present invention. Figure 5 shown.

[0058] Step 3: Get the average images P1 and P2. Add and average all the pixels of the training sets in the sub-datasets S1 and S2 to get the average images P1 and P2, as shown in Figure 6 As shown in . It can be considered that the average map contains the azimuth information of this corresponding sub-dataset.

[0059] Step 4: Estimate the azimuth of the image to be tested. Calculate the Euclidean distance C1 C2 between the image to be classified and P1P2, and find the difference between the two. Since the average image contains the azimuth information of the corresponding sub-dataset, the image to be classified with the smaller Euclidean distance between P1 P2 can be regarded as the azimuth of the image being similar to the overall data set corresponding to its average image, so that the model corresponding to the data set has more weight in the subsequent weighting of the model results.

[0060] Step 5: Weighted fusion of the results of each model to obtain the final classification result. Input the image to be tested into the trained model in step 2 to obtain the output result in the Softmax layer. Determine the weight coefficients of the three results according to the different relationships between C1 and C2 in step 4. Weight the results of each model according to the weight coefficient to obtain the final classification result. That is, when C2>C1, it means that the Euclidean distance between the image to be tested and P1 is smaller, which means that the azimuth of the image to be tested is closer to the azimuth contained in the sub-dataset S1. In other words, it can be determined that the image to be tested has a better result in the corresponding sub-model S1. The total model G contains data sets of all azimuths during training, so the prediction results of the image to be tested in the total model can also be considered as part of the weighting. Therefore, when C2>C1, the results of the image to be tested in the C1 model and the G model are generally weighted. Similarly, when C1>C2, the results of the image to be tested in the C2 model and the G model are generally weighted. However, considering that when the azimuth angle of the image to be tested is near the critical angle, that is, 90°, 180°, and 270°, P1 and P2 will be closer when calculating the Euclidean distance, that is, the difference between C1 and C2 is small, which will be vague when judging our model, so the threshold is set to 1, that is,

[0061] 1. When |C1-C2|<1, the azimuth angles of these images are considered to be critical angles, and these images are directly put into the overall model G to obtain the classification results. That is, the weighted coefficient of the overall model result is 1, and the weighted coefficients of the two sub-models are 0.

[0062] For images that are not at the critical angle, according to the accuracy curve of the model training results, it is found that sub-model S1 has a slightly higher accuracy in azimuth classification than sub-model S2, that is, it is more sensitive to azimuth classification. Therefore, in the prediction results, the weights are slightly adjusted.

[0063] 2. When C2-C1>1, the sub-model S1 result and the total model G result are weighted for the graph to be tested, and the weighting coefficients are 0.6 and 0.4 respectively; the weighting coefficient of the S2 result is 0.

[0064] 3. When C1-C2>1, the sub-model S2 results and the total model G results are weighted for the graph to be tested, and the weighting coefficients are 0.4 and 0.6 respectively, and the S1 weighting coefficient is 0.

[0065] The above weighting is implemented in the Softmax layer. Softmax maps the classification results into 10 numbers, which represent the probability of the model predicting the class to which the test image belongs. After weighted fusion, the class with the highest probability is also the class predicted by this fusion model. For example, if a picture to be tested is of the second category, after this picture passes through our fusion model, when the azimuth angle is estimated and judged by the Euclidean distance, it is found that C2-C1>1. The picture is put into the overall model G. If the output result of the Softmax layer is a=[0.5,0.4,……,0.0125], the prediction result of the model G is the first category. The picture is put into the sub-model S1. If the output result of the Softmax layer is b=[0.3,0.5,……,0.02], the two results are weightedly fused, and the final result is c=[0.38,0.46,……,0.017]. The fused prediction result is the second category. This avoids the inaccuracy of single model prediction and reflects the sensitivity of model prediction at specific azimuth angles.

[0066] All the above steps are implemented for all the images to be tested to obtain the final prediction results. The confusion matrix of each classification result using only a single overall model and the fusion model of the present invention is as follows: Figure 7 As shown in the figure, the bold part is the fusion model used in this paper; Figure 4 As shown in the figure, the original SAR image used and the image after data enhancement, it can be seen that the G model after adopting training strategies such as data enhancement, learning rate decay, Dropout, L2 regularization, etc. has a very high accuracy rate, which can reach 99.13%. However, in the SAR image classification after using the fusion model based on azimuth characteristics, the accuracy rate of each type of target recognition is very high, and the recognition rate of several types of targets reaches 100%. Compared with a single model, the accuracy rate is also improved to 99.34%, which fully proves the feasibility of using the characteristics of SAR image sensitivity to azimuth to divide the data set and perform sub-model training, and also illustrates that the method of model fusion for azimuth characteristics in the present invention is more comprehensive than a single overall model.

[0067] Finally, it should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A model fusion recognition method based on SAR image azimuth characteristics, characterized in that: The following steps are involved: Step 1: Analyze the azimuth characteristics of the SAR image and divide the data set according to the azimuth characteristics. First, obtain the training set and the test set. The obtained sample data set contains multiple types of targets. Each type of target contains multiple SAR images with azimuth angles from 0 to 360°. According to the analyzed azimuth characteristics, namely sensitivity and the 180° symmetrical similarity of the image azimuth angle, the data set is divided into two sub-datasets S1S2. The overall data set without azimuth division is the total data set G. Step 2: Train each data set to obtain each convolutional neural network model, pre-train the sub-data set S1S2 through the convolutional neural network to obtain the sub-model S1S2, pre-train the total data set G through the convolutional neural network to obtain the total model G, and save the three trained models for later use; Step 3: Add and average all the pixels of the training set images in the sub-datasets S1 and S2 to obtain the average images P1 and P2, and the two average images are deemed to contain the approximate azimuth information of the two corresponding sub-datasets; Step 4: Estimate the azimuth of the image to be tested, calculate the Euclidean distance C1 C2 between the image to be classified and P1 P2, and find the difference between the two. Since the average image contains the azimuth information of the corresponding sub-dataset, the image to be classified with a smaller Euclidean distance between P1 P2 is considered to have an azimuth that is close to the overall data set corresponding to its average image, so that the model corresponding to this data set has more weight in the subsequent weighting of model results; Step 5: Input the image to be tested into the model trained in step 2 to obtain the output result in the Softmax layer. Determine the weighting coefficients of the three results according to the different relationships between C1 and C2 in step 4. Weight the results of each model according to the weighting coefficients to obtain the final classification result.

2. The model fusion recognition method based on SAR image azimuth characteristics according to claim 1, characterized in that: In the step 1, a SAR image with a known actual azimuth is used to calculate the Euclidean distance between the image and sample images of the same or different categories including various azimuths to express the similarity between the images.

3. The model fusion recognition method based on SAR image azimuth characteristics according to claim 1, characterized in that: In the step 2, the network model includes an input layer, a convolutional layer, a maximum pooling layer, a fully connected layer and finally an output layer after Softmax.

4. The model fusion recognition method based on SAR image azimuth characteristics according to claim 1, characterized in that: In the step 2, since the overall G dataset is divided into S1 and S2 sub-datasets according to the azimuth angle, the latter two datasets are even more insufficient in quantity. In order to compensate for this deficiency, the S1 and S2 datasets are artificially expanded to twice the original quantity through data enhancement to achieve a quantity close to the original overall dataset.

5. The model fusion recognition method based on SAR image azimuth characteristics according to claim 1, characterized in that: In the step 4, considering that the azimuth of the image to be tested is near the critical angle, i.e., 90°, 180°, and 270°, it will be relatively close when calculating the Euclidean distance with P1 and P2, i.e., C1 and C2 will be relatively close, and it will be relatively vague when judging the weight of the model to which it belongs, so a threshold is set, that is, when the distance between C1 and C2 is less than this threshold, the azimuth of these images is regarded as belonging to the critical angle, when C1-C2 is greater than this threshold or C2-C1 is greater than this threshold, the azimuth of the image to be tested is regarded as being close to the azimuth contained in the corresponding sub-data set of the smaller one between C1 and C2. Therefore, in summary, there are three cases for azimuth estimation.

6. The model fusion recognition method based on SAR image azimuth characteristics according to claim 1, characterized in that: In step 5, the Softmax layer output of the image to be tested in each model is obtained. The Softmax layer converts the output result of the neural network and expresses the output result in the form of probability. When the output of the neural network is sent to the fully connected layer, the score z in the range of K categories (-∞, +∞) is obtained. j In order to obtain the probability of belonging to each category, first use e zj Mapping the score to (0, +∞) and then normalizing it to (0,1) is called the Softmax idea: After obtaining the ten categories of probabilities, the probability of each category of the model output is fused with different weights according to the azimuth estimation results obtained in step 4, and finally the category with the largest probability is obtained, which is the final prediction result of the fusion model.

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