## 3 Methodology  
### Problem Definition  
The management of vessel traffic in port waters primarily involves three core factors: berths, channels, and anchorages. As shown in Figure 1, for entry vessels, there are generally two scenarios: if the vessel meets the entry conditions upon arrival at the port waters, VTS (Vessel Traffic Service) operators will direct it into the channel for berthing; if the vessel does not meet the entry conditions, it will be directed to the anchorage to wait. For exit vessels, after cargo loading or unloading is completed, the vessel must apply to the VTS center for departure based on the existing scheduling plan. If the departure conditions are met, the vessel will depart with the assistance of tugs and pilots; if there are conflicts or the conditions are not met, the vessel will wait at the dock until the conditions are satisfied. VTS operators need to evaluate berth availability, channel vessel density, and port entry and exit schedules in real-time to determine whether a vessel can use the channel and the order of usage. The behavior of vessels within the channel is crucial for assessing channel risks and ensuring safe and efficient vessel scheduling. The SOLAS Convention mandates that by 31 December 2004, all cargo ships of 300 gross tonnage and above engaged in international voyages, cargo ships of 500 gross tonnage and above engaged in domestic voyages, and all passenger ships must be equipped with AIS. AIS data is categorized into two types: dynamic information, which includes the vessel's position, course, speed, etc., and static information, which encompasses the vessel's name, call sign, length, width, and voyage-related details such as draft, destination, and estimated time of arrival. These two sets of information can be correlated using the MMSI (Maritime Mobile Service Identity) number. AIS data serves as a foundational dataset for learning vessel behavior within channels. The problem of ship behavior modeling in fairways can be formulated through a supervised learning task based on historical AIS data to capture the behavior of vessels in  
Figure 1: VTS workflow diagram. the entire port area. As show in Equation (1), we hope to obtain model \(f\) through supervised learning based on historical AIS data. So, we can obtain any ship's position, COG, and SOG at the corresponding time when we know the ship's berth position, the position of the ship entering or leaving the channel, the length of the ship, the width of the ship, the draft of the ship, the type of the ship, and the time interval between the start of the operation. \[lon_{i},lat_{i},cog_{i},sog_{i}=f(lon_{s},lat_{s},lon_{e},lat_{e},l,b,dm,st,t_{i}) \tag{1}\]  
where \(lon_{i}\) represents the vessel's longitude at time \(t_{i}\), \(lat_{i}\) represents the vessel's latitude at time \(t_{i}\), \(cog_{i}\) represents the vessel's course at time \(t_{i}\), \(sog_{i}\) represents the vessel's speed at time \(t_{i}\), \(lon_{s}\) represents the start position's longitude, \(lat_{0}\) represents the start position's latitude, \(lon_{e}\) represents the longitude of the end position. \(lat_{e}\) represents the latitude of the end position. \(l\) represents the vessel's length. \(b\) represents the vessel's width. \(dm\) represents the vessel's draft. \(st\) represents the vessel type. \(t_{i}\) represents the time interval between the corresponding time and the time when the vessel enters the channel or leaves the berth. As shown in Figure 2, whether for incoming or outgoing vessels, the vessel's attributes, the Channel Location, and the berth location are known. For incoming vessels, the starting point is the Channel Location, and the endpoint is the berth. For outgoing vessels, the starting point is the berth, and the endpoint is the Channel Location. The problem we aim to solve is accurately predicting the vessel's position, heading, and speed at times \(t_{0},t_{1},\dots,t_{n}\) within the channel based on the known information.