# Trajectory Prediction of Marine Moving Target Using Deep Neural Networks with Trajectory Data
## 3 Materials and Methods
### Network Architecture  
The movement of objects has a local correlation in the time domain. The spatial-temporal correlations of adjacent moments are mined through convolution kernels based on the CNN model. Compared with the BP network, CNN retains the time domain correlation of navigation features and extracts abstract features more effectively.  
The network structure is shown in Figure 2. The model can be divided into three parts: features extraction, features integration, and results output. The network structure includes three convolution layers and two full connection layers. The convolution kernel size of the convolution layer is \(1\times 3\times 32\), \(1\times 3\times 64\), and \(1\times 1\times 64\), respectively. The number of neurons of the full connections layer is, respectively, 20 and 2, in which the output layer dimension is 2, representing the longitude and latitude information.  
As mentioned above, the convolution kernel extracts local correlation features. The larger the size of the convolution kernel is, the larger the perceptive field of feature extraction will be, whereas the more the parameters and computations will be [30]. Research [28] shows that in the case that the same perceptive field is reached, the smaller the convolution kernel is, the less the parameters and computation will be required. For example, the perceptive field of the convolution operation of a three-layer with the size \(3\times 3\) is the same as that of the convolution operation of one layer with size \(7\times 7\), but the parameters are greatly reduced. In this paper, the sizes of the convolution kernel of the former layers are all \(1\times 3\), and the channels of the convolution kernel are, respectively, 32 and 64. Considered the sparsity of the time interval, the pooling layer is not applied after the convolution layer to prevent the reduction in the temporal resolution. Through two convolution layers with size \(1\times 3\), an equivalent perceptive field \(1\times 5\), namely joint perception of five  
Figure 2: The architecture of the network.  
adjacent moments, is achieved. This part of the network realizes the feature extraction of spatiotemporal information and forms new feature maps.  
Then, the convolution kernel of size \(1\times 1\) implements information integration. The convolution kernel of size \(1\times 1\) does not change the size of the input feature maps; that is, without decreasing the temporal resolution, it increases the linear combination of multiple feature maps, realizes interaction and integration of cross-channel information, and plays a role in feature dimensionality reduction. At the same time, the nonlinear characteristics of the model are further increased by using the activation function.  
Finally, the full connection layer outputs the prediction results. Two full connection layers are connected in the last part of CNN and convert the feature maps into a one-dimensional vector so as to map the learned features to label space. Full connection layers are fully connected; namely, each node is connected to all nodes of the previous layer to combine all features. There are two nodes in the final output layer to output longitude and latitude. The tanh activation function is used for the nonlinear processing of the model. The expression of the tanh activation function is as Equation (14):  
\[f(z)=\tanh(z)=\frac{e^{z}-e^{-z}}{e^{z}+e^{-z}},\ \ \ \ f(z)\in(-1,1) \tag{14}\]