# Trajectory Prediction of Marine Moving Target Using Deep Neural Networks with Trajectory Data
## 2 Related Studies
### Ship Trajectory Prediction  
Researchers have proposed plenty of trajectory prediction methods, especially with the help of deep learning algorithms. Based on the movement character of maneuvering targets on the sea, the movement forecasting models are built, such as the interpolation and extrapolation method [11], the grey model [9], the autoregressive model [22], and neural networks [7; 8; 10; 16; 17; 18; 19; 20]. Taking into consideration the error of speed and course, the dead reckoning method [13] predicts the location area of the target at the next moment under the condition that the moving speed and course are known. In order to analyze the characteristics of maritime moving targets and aim at the problem of inconsistent sampling interval of trajectory data, a grey forecasting method with interpolation is developed to improve targets' potential area prediction [9] and forecast long-term location. Aimed at the satellite search problem of moving targets with indefinite motion rules, [PERSON] et al. [1] proposed a target transition probability density function based on Gaussian distribution and updated the target probability distribution based on Bayesian.  
In recent years, the neural network model has been widely used in trajectory prediction. Based on the AIS information of the waters near the Nanpu Bridge in Pudong New Area, Shanghai, the back-propagation (BP) neural network is used to predict the ship's navigational behavior eigenvalues accurately and in real time [16]. [PERSON] et al. [8] employed long short-term memory neural network (LSTM) for prediction based on the targets' positions and motion directions of the previously known time. To avoid collision between the ships and improve the safety of the ships' maritime navigation, a trajectory prediction method based on the LSTM framework is proposed to predict the ship's trajectory [17]. [PERSON] et al. [19] propose a methodology based on bi-LSTM for predicting the ship's trajectory that can be used for an intelligent collision avoidance algorithm at sea. [PERSON] et al. [10] proposed sequence-to-sequence vessel trajectory prediction models based on recurrent neural networks (RNNs) that are trained on historical trajectory data to predict future trajectory samples given previous observations. [PERSON] et al. [18] introduce a deep learning framework and a Gate Recurrent Unit (GRU) model to predict vessel trajectories.  
These above methods are generally proposed for a specific domain under certain assumptions, mainly for shore-based AIS data which produce dense trajectories with time intervals of a few minutes, and are faced with problems of low accuracy and the inability to make long-term predictions.  
In this paper, oriented trajectory prediction is applied to space-based satellite navigation for marine observation. There is a great sparsity and inhomogeneity of space-based observation trajectory data. However, most of the current time-series modeling and forecasting methods require uniform time interval. For non-uniform time series data, the common processing [9; 11; 17] methods first use the interpolation algorithm to fit historical data, then uniformly sample to obtain equal time interval data, and then carry out predictions based on equal interval data. The disadvantage is that the accuracy of the interpolation data will limit the prediction accuracy. Moreover, this paper focuses on long-term and variable time interval prediction, whereas most present methods aim at short-term projections, and the time-series prediction methods represented by grey prediction and autoregressive model can only deal with the equal-interval time prediction.