# Roll Motion Prediction of Unmanned Surface Vehicle Based on Coupled CNN and LSTM
## 1 Introduction
Compared with the conventional AR model, this model is more capable of handling nonlinear and non-stationary signals. [PERSON] et al. (2018) adapted a hybrid methodology to combine autoregressive integrated moving average (ARIMA) and deep neural network (DNN) models for predicting the roll motion. The hybrid model had a good ability to capture the linear and nonlinear patterns. Although these improved methods have shown their effectiveness, they are still limited in nonlinear ship motion prediction, as explicit relationships between input and output variables for the data sets have to be hypothesized. Neural networks are a simulation of the biological nervous system ([PERSON], 2018). In contrast to time series methods, neural networks are more capable of modeling nonlinear systems without a priori knowledge of the relationships between input and output variables. In recent decades, neural networks have been successfully applied in various fields, such as natural language processing ([PERSON] et al., 2018), computer vision ([PERSON] et al., 2018), and autonomous driving ([PERSON] et al., 2018). There are also some USV applications. [PERSON] et al. (2018) presented a path-following controller based on a radial basis function neural network (RBFNN) for formation control in single unmanned surface vehicles. In theory, a neural network can approximate any nonlinear system with arbitrary accuracy ([PERSON] et al., 2018). Accordingly, they have been used to model the nonlinear ship motion dynastic system for prediction. [PERSON] et al. (2018) obtained a ship motion prediction model based on a BP neural network by training the ship motion MATLAB simulation data. Their experimental results showed that the trends of the true and predicted values were consistent. [PERSON] et al. (2018) proposed a coarse and fine-tuning fixed-grid wavelet network model to predict ship roll motion, which is trained by simulated ship roll motion data in regular waves. These neural network models are trained by MATLAB simulation data instead of actual measured sensor data, and therefore the applicability of these models in the real world remains to be verified. [PERSON] et al. (2018) constructed an ensemble prediction scheme by combining the discrete wavelet transform (DWT) method with a variable-structure radial basis function (RBF) network for real-timeship roll motion prediction. [PERSON] et al. [30] constructed a variable-structure RBF network sequentially by an adaptive sliding data window (SDW) learning scheme to predict ship roll motion online. The two references adopted a variable-structure RBF neural network as the prediction model. In their model, an innovative algorithm was proposed to adjust the data sliding window online. Both the structure and parameters of RBF neural network were tuned according to the data of the current window in order to achieve real-time prediction. However, in the process of training the neural network, they used real-time data, making the training set relatively small. In this way, the neural network model could be overfitting and its generalization ability was poor. Moreover, they only used ship roll motion time series data to train the neural network model, and ignored the coupling characteristics between the ship movements in six degrees of freedom [31; 32], as well as the influence of the control system on the ship's movements. With the rise of deep learning (DL) [33], data-driven prediction methods are increasingly applied in various fields [34; 35]. In maritime applications, [PERSON] [36] proposed a deep-learning-based dynamic model identification method. The long short-term memory (LSTM) [37] based dynamic model extracted patterns of USV dynamics from free-running test data, and outperformed conventional simplified maneuvering models. However, the data-driven method requires a large amount of data for training. Fortunately, there are normally many sensors installed on the ship at various positions.