# Trajectory Prediction of Marine Moving Target Using Deep Neural Networks with Trajectory Data
## 1 Introduction  
Space-based observations are an essential tool for monitoring marine ships. Research on the analysis of marine moving targets for satellite resource scheduling is of great application value in some domains, such as marine rescues, anti-smuggling, and situation assessment. However, due to the orbital regression period of the satellite, it is difficult to achieve long-term and continuous observation of specific ships [1]. Moreover, given the vastness of the sea, searching blindly at sea is tantamount to finding a needle in a haystack. In order to search the moving ships effectively by satellites, it is necessary to combine satellite orbit circulate rules with ship motion prediction [1]. Due to the wide range of maritime activities, high freedom of navigation, and strong maneuverability of ships, the position prediction of marine ships, especially long-term predictions, is a challenging problem [1]. Position prediction needs to forecast successive positions based on historical trajectories. Satellite observation data provide observation time and locations of observed objects consisting of latitude and longitude. Compared with the near-real-time observation of land-based observation methods, the time interval of the hour-scale for satellite observation brings about the extreme sparsity of trajectory data. At the same time, the time interval is quite non-uniform, which increases the prediction difficulty. In addition, since the transit time of satellite revisit is not fixed, it is often necessary to predict the target location of an unequal interval in the future. In some extreme cases, there may be a practical problem in which the satellite fails to capture the target's location in its first revisit cycle, so it is required to forecast again in the second revisit cycle. Therefore, the prediction method should be able to adapt to the sparse and uneven characteristics of observation data. Moreover, it needs to meet the demand for variable duration prediction. Many scholars have carried out a lot of research on mobility pattern mining [2; 3; 4; 5; 6] and trajectory prediction [1; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. However, most methods are proposed for a specific domain under some assumptions only applicable to specific problems. In this paper, 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 methods [9; 11] firstly 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. In addition, the time-series prediction methods represented by grey prediction and autoregressive model can only deal with the equal-interval time prediction, which is hard to satisfy the prediction demand of non-equidistant time. Nowadays, the deep learning method [23] has achieved great success and wide application in the fields represented by computer vision, showing strong feature learning ability [24]. Many researchers are trying to use deep learning to solve problems in their fields [25; 26; 27]. However, towards many practical problems in the non-visual field, there is still a large research space. It is of great value to take the powerful feature representation and data prediction capabilities of deep learning into specific fields to solve practical problems. Trajectory prediction can be regarded as a problem of pattern learning and generalization; thus, deep learning method is feasible. In this paper, based on space-based observation trajectory data with great sparsity and inhomogeneity and targeted for  
knowledge, this is the first study in which local connection characteristics of the CNN have been applied to the time domain to solve ship trajectory prediction problems.