# A Method for Underwater Acoustic Target Recognition Based on the Delay-Doppler Joint Feature
## 4 Experiment
### Results and Analysis
#### 4.4.1 Joint Feature Recognition Experiment  
Experiment 1 verified the effectiveness of Delay-Doppler domain features for target recognition. The joint features were obtained based on the Feature Fusion method in Figure 12, which takes the Time-Frequency feature and Delay-Doppler feature of the signal as inputs and uses the Feature Fusion method to obtain the joint features. This experiment could verify that the joint features can effectively improve the accuracy of target recognition compared to a single Time-Frequency feature. Figure 19 shows the overall image of the loss function obtained from all nine groups of the experiments. The icon represents the combination of network structure and input features. The term \"VGG-TF\" refers to the outcome of employing the VGG model with Time-Frequency feature recognition. Similarly, \"VGG-DD\" denotes the result of using the VGG model with Delay-Doppler feature recognition. Lastly, \"VGG-TF-DD\" signifies the outcome of utilizing the VGG model with joint feature recognition. Each set of experiments conducted 70 rounds of training. The learning rate was set to 0.001, and the ratio of training sets to test sets was defined as 5:1. Table 4 displays the outcomes of Acc, Pre, Rec, and F1 achieved by each experimental group. The table shows the results of \"Training set results/ Testing set results\", and Figure 20 exhibits the recognition accuracy outcomes of the three models on the training set. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Actually Positive** & **Actually Negative** \\ \hline Predicted as positive & PP & PN \\ Predicted as negative & NP & NN \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Confusion matrix of multiple categories. The findings of experiment 1 confirm that the use of Delay-Doppler features significantly enhances the accuracy of ship target detection. Figure 19 shows that the three models' accuracy is best after 30 training iterations. Table 4 shows that the recognition accuracy of several models is between 60% and 80%, among which the ResNet model has the best recognition effect. Figure 20 displays the distribution of identification accuracy for various recognition models and input characteristics. Figure 20 demonstrates that the ResNet network has the highest recognition accuracy, and the recognition results obtained by analyzing the different feature inputs of each model with joint features as the basis are the highest, followed by Time-Frequency domain features. The lowest recognition accuracy is the Delay-Doppler feature, which also reflects the idea proposed in Section 3.1 of this paper. To a certain extent, the result distribution of Figure 20 proves the analysis of Figure 10 because Delay-Doppler may contain multiple overlapping target features, and the corresponding recognition accuracy will be lower than the Time-Frequency domain features. However, by combining the two features, the recognition accuracy of the final model will be greatly enhanced. By analyzing the results of Figure 20 and Table 4, the use \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **Acc (\%)** & **Pre (\%)** & **Rec (\%)** & **F1 (\%)** \\ \hline VGG-TF & 63.94/72.83 & 63.42/72.83 & 63.94/72.83 & 63.23/72.40 \\ VGG-DD & 61.60/68.58 & 60.78/70.60 & 61.59/68.57 & 60.51/67.15 \\ VGG-TF-DD & 69.60/77.08 & 69.10/78.32 & 69.60/77.08 & 69.14/76.26 \\ ResNet-TF & 75.84/72.09 & 75.58/72.39 & 75.84/72.09 & 75.48/71.98 \\ ResNet-DD & 71.06/67.95 & 70.60/67.42 & 71.06/67.95 & 70.38/67.31 \\ ResNet-TF-DD & 80.37/79.30 & 80.08/79.09 & 80.37/79.30 & 80.09/79.12 \\ GoogleNet-TF & 70.53/70.73 & 70.27/70.82 & 70.53/70.73 & 70.01/70.71 \\ GoogleNet-DD & 64.07/64.21 & 63.20/64.79 & 64.07/64.21 & 62.93/62.60 \\ GoogleNet-TF-DD & 72.86/73.79 & 72.34/74.66 & 72.86/73.79 & 72.23/73.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental identification results of each group. Figure 19: Distribution of the loss function. Figure 20: Distribution of the prediction accuracy of the three models.