# Roll Motion Prediction of Unmanned Surface Vehicle Based on Coupled CNN and LSTM
## 1 Introduction  
Unmanned surface vehicles (USVs) [1] are small unmanned marine vehicles that travel on water in a remote or autonomous manner. USVs are characterized by small size, fast movement, and high flexibility. In recent years, they have been adopted to conduct missions such as marine rescue, environmental monitoring [2], island reef mapping [3], and resource exploration [4]. The safety of USVs is critical when conducting missions, and the roll motion is directly related to the safety and operating performance [5]. In order to ensure that USVs conduct their missions safely, it is necessary to predict the USV roll motion, so that the operator or automatic control system has sufficient time to avoid serious accidents. The USV roll motion at sea is a time-varying, nonlinear, and uncertain complex dynamic system. It is affected by control systems such as steering and propulsion systems, as well as external disturbances produced by wind, waves, and sea current [6, 7]. Moreover, the USV roll motion and the movements in other degrees of freedom (e.g., leave and pitch motions) are coupled with each other. Therefore, it is difficult to establish precise mathematical models to represent the USV roll motion at sea. Over the past decades, many methods have been developed to model and predict ship motion. [PERSON] et al. [8] applied an available mathematical model with concentrated parameters tothe roll-sloshing problem. [PERSON] et al. (2019) formulated a differential equation model (a Mathieu-type equation) for modeling the roll dynamics of a ship sailing in large-amplitude head waves. [PERSON] et al. (2018) described a time-domain non-linear strip theory model of ship motions in six degrees of freedom based on a potential flow strip theory using [PERSON]'s close fit method. These methods require mechanical analysis and mathematical modeling of the hull, so there are some difficulties in practical application. Later, scholars proposed some simple and practical methods. According to the theoretical differences, these methods can be classified into three types: Kalman filtering, time series methods, and neural-network-based methods ([PERSON], 1999). Kalman filtering is a recursive linear minimum variance filter for online forecasting ([PERSON], 1999). [PERSON] et al. (2018) proposed a Kalman filtering model for ship motion prediction and applied it to a DD-963 destroyer. In implementing the Kalman filtering, accurate state-space equations and noise statistics are necessary. However, in practical engineering applications, these are difficult to obtain. Therefore, although Kalman filtering is simple in calculation, its use is difficult in practical applications. Time series methods provide a feasible solution, which only requires the history and current ship motion status data for prediction. These methods are suitable for practical engineering applications, as they do not require a comprehensive understanding of the ship's dynamic system. Classic time series prediction methods which are widely used include autoregressive (AR) and moving average (MA) models, as well as many extended models based on them ([PERSON], 1999; [PERSON], 1999; [PERSON], 1999). [PERSON] et al. (2018) proposed a time domain model based on autoregressive moving average (ARMA) to predict real-time ship motion. This model best fitted an input wave sensor time history to the ship response time history and was applied to aircraft landing on the ship. However, as ship motion is non-stationary, it conflicts with the stationary assumption of classic time series methods. Therefore, many improved methods based on classic time series methods have been proposed. [PERSON] et al. (2018) conducted a nonlinear autoregressive (NAR) model using an orthogonalization technique, and the experimental results indicated that the NAR model gave better prediction accuracy than the AR model. [PERSON] et al. (2019) combined empirical mode decomposition (EMD) and discrete wavelet transform decomposition (DWT) to improve the AR model for ship motion prediction.