A Method to Infer Customary Routes via Analysis of the Movement Importance of Ship Trajectories Calculated Using TF-IDF

Abstract

Ship positional data are widely used for route inference, yet most existing studies rely on automatic identification system data, which contain irregular transmission intervals and limit the ability to capture vessel-specific operational habits and subtle route choices. This study addresses these limitations by proposing a methodology to infer customary routes using periodic 3 s ship position data collected through the Korean e-Navigation system based on long-term evolution maritime communication. The method comprises three main steps: constructing a sea-area grid with an associated weight map, determining data-driven importance and updating weights, and performing pathfinding. Domestic waters are divided into 100 m grids, and navigable and non-navigable areas are binarized to establish a framework for route exploration. Ship positional data are processed to extract inter-port trajectories, which are then classified by ship size and tidal time zone to account for navigational differences arising from vessel characteristics and tide-dependent accessibility. These trajectories are combined with spatial grids and transformed into a document–word structure, enabling the calculation of movement importance between grid cells using a modified term frequency–inverse document frequency measure. The resulting weights are applied to a pathfinding graph to derive routes that reflect vessel size and tidal conditions. The effectiveness of the proposed method is evaluated by computing cosine similarity between the inferred routes and actual trajectories.

1. Introduction

The International Maritime Organization (IMO) has established and is globally disseminating the e-Navigation strategy to improve maritime safety, security, operational efficiency, and digitalization [1,2,3]. This trend is laying the foundation for a faster integration of maritime traffic information services and digitization of ship operations. The Korean e-Navigation service has developed the world’s first periodic (3 s) trajectory network based on the long-term evolution for maritime (LTE-M) communication protocol to complement the irregular transmission cycles and gaps in existing automatic identification system (AIS) data [4]. This uniform high-frequency data provides a foundation for detailed analysis of the actual operational characteristics of coastal vessels, and thus provides higher reliability compared to traditional AIS data.

The development of e-navigation services and maritime autonomous surface ships (MASS) [1,5] has sparked interest in technologies that infer ship routes based on data. Researchers are also investigating path-following control methods for MASS [6]. Conventional methods to provide ship routes have focused on presenting uniform routes based on navigational safety regulations. However, coastal vessels tend to select habitual routes based on factors such as weather, tide, and experience, which are known as “customary routes.” In this study, we propose a method to infer customary routes from real navigation data.

The proposed method calculates the movement importance for each ship size using LTE-M positional data from the Korean e-Navigation system, and then applies this to a pathfinding algorithm to infer customary routes. Specifically, trajectory data between ports are generated, and the movement importance between grid cells is calculated by applying a modified term frequency–inverse document frequency (TF-IDF) algorithm, which is typically used in information retrieval. Subsequently, the calculated movement importance is combined with navigational constraints such as coastlines, fishing grounds, aquaculture farms, and electronic chart objects to construct a weight map for pathfinding. Finally, the customary route inference results are evaluated using the A* algorithm [7] and Dijkstra’s algorithm [8].

The main contributions of this study are summarized as follows:

• More precise trajectory-based customary routes can be inferred using LTE-M positional data, which allows for uniform data collection compared to AIS.
• The proposed method quantifies movement importance in pathfinding by utilizing TF-IDF, a statistical weighting technique, to analyze trajectory data.
• The outputs of the proposed customary route inference method exhibited high similarity with actual trajectories, and the feasibility of the proposed approach was verified in that no significant reduction in calculation speed was observed compared to an existing method.

2. Research Related to Route Search

2.1. Research on Trajectory Prediction

AIS data are a representative example of trajectory data that can collect real-time information such as the position, speed, and course of a ship. According to the International Telecommunication Union Technical Standard [4], for Class-A vessels, the AIS data transmission rate is determined by the dynamic information status and speed, as listed in

Table 1. Transmission rates of AIS data for Class A vessels.

Ship Status and Speed	Reporting Interval
Ships anchored or moored and not moving faster than 3 knots	3 min
Ships anchored or moored and moving faster than 3 knots	10 s
Ships with speeds ranging from 0 to 14 knots	10 s
Ships with speeds ranging from 0 to 14 knots currently changing course	3 1/3 s
Ships with speeds ranging from 14 to 23 knots	6 s
Ships with speeds ranging from 14 to 23 knots currently changing course	2 s
Ship speed > 23 knots	2 s
Ship speed > 23 knots and changing course	2 s

.

AIS has been reported to exhibit irregular transmission cycles, gaps in shaded areas, and reduced reliability owing to human manual input errors or equipment configuration issues [9]. Numerous prediction techniques have been proposed to address these issues.

Gao, D. et al. [10] developed a multi-point long short-term memory (LSTM) model for ship trajectory prediction and demonstrated that deep recurrent neural network architectures can effectively capture the nonlinear spatiotemporal patterns of vessel movements. Sun, Y. et al. [11] showed that denoising AIS data and normalizing temporal intervals can significantly improve the performance of trajectory prediction models. In addition to deep-learning-based methods, Liu, J. et al. [12] utilized an improved support vector machine (SVM), a traditional machine-learning technique, for vessel trajectory prediction. More recently, Zaman, U. et al. [13] compared the performance of various neural network models, including convolutional neural networks (CNN), deep neural networks (DNN), LSTM, and gated recurrent units (GRU), using AIS data collected from Korean coastal waters.

2.2. Research on Route Calculation

Previous studies on route generation based on electronic charts have applied various pathfinding algorithms, as listed in

Table 2. Summary of representative studies on route calculation algorithms.

Reference	Algorithm Used	Main Features	Performance Evaluation
Liu et al., 2024 [14]	A*	Route planning considering depth and obstacle information	Route safety, suitability of avoidance path
Li et al., 2024 [15]	Improved D* Lite	Enhanced version of D* Lite with improved computational efficiency and avoidance path quality	Computation time, path quality
Gu et al., 2023 [16]	Improved RRT	RRT planning using AIS/DP-based advance information	Path length, number of nodes, computation time
Charalambopoulos et al., 2023 [17]	PRM	PRM for vessel route navigation using weather and oceanographic information	sailing time, fuel consumption, weather hazards
Zhai et al., 2025 [18]	Sparse A*	Reducing the search space with sparse A* using only important points as nodes	Number of nodes, computation time, path quality
Liu et al., 2025 [19]	Informed-RRT*	Informed-RRT* adjusts step size according to environment complexity	Path length, number of sampling nodes, computation time
He et al., 2019 [20]	Dijkstra + ACO	Graph-based route optimization after AIS turning point clustering	Path length, avoidance of hazardous waters, safety

.

Liu et al. [14] proposed an A*-based pathfinding method that reflected depth and obstacle information. Li et al. [15] improved computational efficiency and the quality of avoidance paths by improving the D* Lite algorithm, while Gu et al. [16] presented an improved rapidly exploring random tree (RRT) based route-planning method that uses representative routes extracted from AIS trajectories and compressed via the Douglas-Peucker algorithm as prior information. Charalambopoulos et al. [17] proposed a ship weather-routing method that incorporates meteorological and oceanographic forecasts into the cost function within a probabilistic roadmap (PRM) framework. Zhai et al. [18] introduced a sparse A* algorithm that reduces the search space by using only key points as nodes while maintaining path quality. Liu et al. [19] proposed an intelligent route-planning method based on an adaptive step-size Informed-RRT* that adjusts the extension step according to environmental complexity, thereby reducing path length and the number of sampled nodes. He et al. [20] computed optimal ship routes that reflect actual sailing patterns by extracting and clustering turning points from AIS trajectories and then applying Dijkstra’s algorithm and ant colony optimization (ACO).

2.3. Research on Clustering

Approaches to generalize patterns in trajectory data to derive representative paths have also been actively pursued. Yuan et al. [21] organized the routes of inland waterway vessels using ordering points to identify the clustering structure (OPTICS) clustering and Douglas-Peucker simplification. Huang et al. [22] proposed a trajectory framework based on density-based spatial clustering of applications with noise (DBSCAN) to extract representative trajectories for each cluster. Oh et al. [23] classified the passage characteristics of large vessels by analyzing their operational patterns and berthing characteristics based on k-means clustering.

However, methods based on clustering average multiple trajectories to derive representative paths, which makes it difficult to fully reflect the actual choices and preferences of operators or differences based on conditions. To overcome these limitations, we propose a method to calculate the importance of specific intervals.

2.4. Research on Importance Calculation

To improve the accuracy of route inference, it is necessary not only to perform pathfinding, but also to quantify the relative importance of each grid cell or segment. In network analysis, graph-centrality measures such as closeness and betweenness have been widely used [24], and PageRank is another representative approach that evaluates the importance of nodes based on information about link structures [25]. To infer customary routes, higher importance values must be assigned to grid cells that are frequently selected across many trajectories. Therefore, we adopt TF-IDF as an information retrieval method to compute relative importance [26].

3. Problem Definition and Data Collection

Prior research on route inference has focused on deriving mathematically optimal routes considering factors such as operational safety, fuel efficiency, and computational performance. However, this method fails to reflect customary routes based on ship size. Therefore, the proposed method infers a route that reflects actual operational characteristics based on ship specifications and historical trajectory data. To specify the direction of operation, we compiled data on port areas to be used as points of origin and destination. Obstacle data such as coastlines, fishing grounds, fish farms, and electronic chart objects were used to identify nonnavigable areas. In addition, depth and tide data were reflected in the obstacle data while considering the differences in operating areas based on the size of a given vessel.

3.1. Static Data from Vessels

Static data were collected from vessels using the Korean e-Navigation service. We also collected data linked to the Korea Research Institute of Ships and Ocean Engineering (KRISO). As listed in

Table 3. Static Data from Vessels.

Table	Filed	Description
Ship Detail	MRN	This is used as a unique identifier and address for data transmission and reception in the Korean e-Navigation service and as a foreign key to match with other tables.
	Vessel type code	The vessel type can be identified by matching this code with the Common Code table.
	Tonnage	Gross Tonnage of the vessel.
	Length	Length Overall of the vessel.
	Width	Width of the vessel.
	Draft	Draft of the vessel.
Common Code	Code identifier	This code is used as a foreign key to link with the Ship Detail table.
	Code name	This indicates the classification types of vessels, such as passenger ships, fishing boats, and cargo ships.
Ship Master	MRN	This is used as a foreign key to link to the Ship Detail table.
	MMSI	The Maritime Mobile Service Identity is used as a unique identification number for ships.
	Vessel usage status	This indicates whether the ship is operational.
Router Master	MRN	This is used as a foreign key to link to the Ship Detail table.
	Router usage status	This indicates whether or not to use a router for service communication.
ECS Master	MRN	This is used as a foreign key to link to the Ship Detail table.
	ECS usage status	This indicates whether or not the service terminal is used.

, tables containing ship specifications and ship type data were collected along with a status table to confirm the normal collection of ship operation data. However, the Maritime Resource Name (MRN) and Maritime Mobile Service Identity (MMSI) were pseudonymized using a hash.

3.2. LTE-M Positional Data

LTE-M-based ship positional data obtained from the Korean e-Navigation service were collected. We developed a data pipeline at KRISO to collect data from January 2022 to February 2023. A total of 4,541,753,073 LTE-M positional data points were collected, including dynamic data such as hourly coordinates, speed, and heading, as listed in

Table 4. LTE-M Positional Data.

Column	Data Type	Description
Message Send Date Time	string	Timestamp when the position message was sent (YYYYMMDDHHmmssSSS)
Message Source ID	string	MRN of the message source (unique vessel identifier)
SOG	float	Vessel speed over ground in knots
COG	float	Vessel course over ground in degrees (0–359°)
Latitude	float	Latitude of vessel position (WGS84)
Longitude	float	Longitude of vessel position (WGS84)

.

3.3. Port Area Data

As shown in Figure 1, areas identifiable as ports within the study area such as harbors and piers were labeled as polygons. We compiled 1502 area data points for ports, as listed in

Table 5. Port area data.

Column	Data Type	Description
Port Identifier	integer	Unique numeric identifier for the port or pier
Port Name	string	Name of the port or pier
Geometry	polygon	Geospatial polygon representing the spatial extent of the port or pier

, using Naver Maps [27] and Google Maps [28].

3.4. Navigation Obstacles

Object data from electronic charts (S-101) based on the S-100 framework used in Korean e-Navigation services were collected. Datasets linked to KRISO were also collected (

Table 6. Object data from electronic charts.

Category	Features
Navigation Aids	Beacon cardinal, Beacon isolated danger, Beacon lateral, Beacon special purpose general, Daymark, Pile, Pylon bridge support
Anchorage & Mooring	Anchorage area, Floating dock, Mooring warping facility, Pontoon
Buoys	Buoy artificial, Buoy cardinal, Buoy installation, Buoy isolated danger, Buoy lateral, Buoy safe water, Buoy special purpose general
Bridges & Structures	Bridge, Span fixed, Span opening, Conveyor, Pipeline overhead, Shoreline construction
Fishing & Facilities	Fishing facility, Offshore platform, Offshore production area, Oil barrier, Hulk
Traffic Management	Traffic separation zone

).

In addition, data related to nonnavigable waters were further collected through the Public Data Portal. This study collected data on coastlines (

Table 7. Coastline data.

Column	Data Type	Description
City/County/District Group	integer	Administrative region code for city, county, or district group
Island Group	integer	Group identifier for associated islands
Source Date	integer	Year of the source data (2022)
Geometry	line string	Geospatial line string representing the coastline (WGS84)

), fishing grounds (

Table 8. Fishing ground data.

Column	Data Type	Description
Geometric Identifier	integer	Unique numeric identifier for the geometric feature
Category Code	integer	Code representing the category or type of the fishery area
Revision Year	integer	Year when the data or boundaries were last revised (2022)
Area	float	Area size of the fishery
Longitude	float	Longitude of a representative point in the fishery area (WGS84)
Latitude	float	Latitude of a representative point in the fishery area (WGS84)
Geometry	polygon	Geospatial polygon defining the spatial extent of the fishery area

), and aquaculture farms (

Table 9. Aquaculture farm data.

Column	Data Type	Description
Object Number	integer	Unique numeric identifier for the aquaculture site
Electronic Navigational Chart Level	integer	Chart scale or level classification according to electronic navigational charts
Source Date	string	Date when the source data was recorded (YYYYMMDD)
Geometry	polygon	Geospatial polygon representing the boundary of the aquaculture site

) from the Korea Hydrographic and Oceanographic Agency.

3.5. Depth and Tidal Data

Depth and tidal data for domestic waters were collected. This study collected depth data linked to KRISO (

Table 10. Depth data.

Column	Data Type	Description
Origin Latitude	float	Latitude of the data starting point (WGS84)
Origin Longitude	float	Longitude of the data starting point (WGS84)
Spacing Latitudinal	float	Grid spacing in the latitudinal direction, in degrees (0.001)
Spacing Longitude	float	Grid spacing in the longitudinal direction, in degrees (0.001)
Depth	float	Measured water depth at the location (meters; negative = below sea level)

) and tidal data from the Korea Hydrographic and Oceanographic Agency (

Table 11. Tidal data.

Column	Data Type	Description
Station Name	String	Unique name of the observation station
Latitude	Float	Latitude of observation station
Longitude	Float	Longitude of observation station
Record Time	String	Observation time (YYYYMMDDHHmm)
Tide Type	String	MAX for highest tide, MIN for lowest tide
Tide Height	Integer	Tide height (in centimeters)

).

4. Constructing Sea Area Grids for the Pathfinding Algorithm

The study areas were divided into grid cells for use by a pathfinding algorithm. Subsequently, navigable areas were determined by removing grids that overlapped with obstacle data. The grid size was selected by comprehensively considering both calculation speed and route accuracy. Reducing the grid size further could increase the accuracy of route calculations, but would also reduce processing speed owing to the increased computational load. In this work, we generated a total of 40,157,334 grid cells by dividing the sea area bounded by 33.120581° N to 38.726809° N and 124.896901° E to 132.058734° E into cells measuring 100 m each. The grid resolution of 100 m was selected based on prior algorithm design studies conducted within the Korean e-Navigation R&D framework [29].

4.1. Reflecting Obstacle Data

Obstacle data were compiled to designate areas where ships could not navigate. Obstacle areas were extracted by combining the geometric values of coastline, fishing grounds, fish farms, and electronic chart object data as shown in Figure 2. Subsequently, the obstacle area was excluded from the pathfinding target.

Our results revealed that some LTE-M positional data passed through fishing grounds and aquaculture areas while reflecting obstacle data. This indicated a need to reflect the navigable grid more precisely for small vessels because the grid size was 100 m, whereas the width of small vessels is approximately 4 m. Therefore, the location was corrected to a navigable area for small vessels when LTE-M positional data points of small vessels overlapped with obstacle data, as shown in Figure 3.

4.2. Reflecting Depth by Ship Size

The grids of nonnavigable depths for each vessel size are reflected in the obstacle data. Nonnavigable grid cells were identified by considering the draft and under keel clearance (UKC) of the vessel. Referring to the UKC coefficient from Lee [30], we modeled the UKC at 30% of the draft and established the depth of navigable water for each ship size group, as listed in

Table 12. Setting the navigable water depth by ship size group.

LOA (Length Overall)	Draft	UKC (Under-Keel Clearance)	Navigable Water Depth (Draft + UKC)
1–20 m	1 m	0.3 m	1.3 m
21–40 m	3 m	0.9 m	3.9 m
41–80 m	5 m	1.5 m	6.5 m
81–200 m	7 m	2.1 m	9.1 m
200 m	9 m	2.7 m	11.7 m

.

4.3. Grid Binarization

For each ship size, the grid cells were represented by binarizing the grid into navigable and nonnavigable cells to reflect the obstacle data as shown in Figure 4. In addition, a weighted map was created in which the Euclidean distance between grid cells served as the movement weight to provide a foundation to apply a pathfinding algorithm. Generally, pathfinding uses an 8-directional weight map that moves up, down, left, right, and diagonally. However, in this study, we considered 32 directions by subdividing the path as shown in Figure 5. Consequently, a total of five pairs of grid cells and weight maps were generated for each ship size group.

5. Calculating and Reflecting Weights for Trajectory-Based Movement Importance

The vessel table was compiled using static vessel data. The vessel table refines LTE-M positional data and processes it for easy analysis. LTE-M positional data was processed into trajectory data by sorting it chronologically by vessel, and trajectory data was extracted between ports. The importance of movement between grid cells was calculated by applying a modified TF-IDF technique to port-to-port trajectories.

5.1. Constructing the Ship Table

Among the collected static ship data, defective data with missing dimensions or duplicate key identifiers such as MRN and MMSI were removed. In addition, vessels that were out of operation and those that lacked LTE-M positional data transmission were excluded. We obtained static data for a total of 3829 vessels, including their dimensions, type, and position. A set of rules for assigning ship codes were established as listed in

Table 13. Rules for assigning ship code.

Prefix of Ship Code	Ship Length Overall	Second Segment of the Ship Code	Ship Type
A	1–20 m	Axx	Passenger ship
B	21–40 m	Bxx	Fishing
C	41–80 m	Cxx	Cargo ship
D	81–200 m	Dxx	Official vessel
E	200 m	Exx	Miscellaneous
		Fxx	Oil tanker

to analyze LTE-M positional data considering the specifications and ship types of the target vessels. The first code was assigned based on size, and the second to fourth codes were assigned based on the detailed ship type.

Subsequently, hexadecimal numbers were sequentially assigned to the 5th to 8th codes to compile a table of vessels similar to

Table 14. Example ship table.

SHIP_CODE	MRN	MMSI	GT	LOA	Width	Draft	Ship Type
CA010000	(HASH)	(HASH)	388	53	11	3	Passenger ship
AB01008e	(HASH)	(HASH)	10	15	5	1	Fishing
AB020313	(HASH)	(HASH)	9	15	4	1	Fishing (Drift Net)
CA01001c	(HASH)	(HASH)	494	44	12	4	Passenger ship
CA050038	(HASH)	(HASH)	225	44	9	5	Passenger ship (Car Ferry)

, which allowed us to estimate vessel specifications using an 8-digit ship code.

5.2. Extracting Trajectory Data Between Ports

The ship table processes the LTE-M positional data using

Table 15. Processed positional data.

Column	Definition
szMsgSendDT	Message Send Date Time
SHIP_CODE	Size-and-type-based vessel identifier
dSOG	Speed over ground
dCOG	Course over ground
dLat	Latitude
dLon	Longitude

to provide information on the size, type, and position of the ship.

The processed positional data were categorized by ship code and sorted chronologically to allow for tracking of vessel movements. Using the speed of ground (SOG), we removed the stopping points of each ship to extract the trajectory data from the origin of the ship to its destination. We assumed that the point of cessation was when the SOG was two or less. Finally, as shown in Figure 6, the trajectory data between ports where both the origin and destination were within the port area were extracted from the trajectory data. Consequently, 118,039 trajectory data points between ports were extracted.

Given the nature of fishing vessels, the trajectories from fishing operations were not appropriate to be reflected in the importance of movement between ports. In this study, as shown in Figure 7, the fishing trajectories of the fishing vessel were refined during the trajectory data extraction process between ports, and only the trajectories for movement were extracted.

5.3. Importance Calculation Using Modified TF-IDF

The movement importance of each grid cell during port-to-port travel is calculated by applying the $TF-IDF$ equation to trajectory data between ports and grid cells. $TF-IDF$ is a statistical method that calculates the importance of each word $t$ within a document $d$ (1). $TF$ refers to how frequently a word appears (2), and $IDF$ refers to how rarely a word appears in other documents (3). That is, words that appear frequently in one document but not in another are considered more important.

$$TF-IDF\left(t,d\right)=TF\left(t,d\right)\times IDF\left(t\right),$$

(1)

$$TF\left(t,d\right)={\displaystyle \frac{f\left(t,d\right)}{{\sum }_{w^{\prime }\in d}f\left(t,d\right)}},$$

(2)

$$IDF\left(t\right)=\mathit{log}{\displaystyle \frac{N}{df\left(t\right)}}$$

(3)

After the ports of origin and destination were designated, the movement importance between grid cells during port-to-port travel was calculated by substituting the trajectory data between ports for $d$ and the grid numbers between ports for $t$. However, to reflect frequency rather than rarity across other trajectories, we employed $DF$ (4), the inverse of $IDF$.

$$DF\left(t\right)={\displaystyle \frac{1}{\log \frac{N}{df\left(t\right)}}}$$

(4)

Consequently, the movement importance between grid cells was calculated for 12,039 origin-destination pairs using the $TF-DF$ equation (5), a variant of the $TF-IDF$ technique.

$$TF-DF\left(t,d\right)=TF(t,d)\times DF\left(t\right)$$

(5)

5.4. Reflecting Pathfinding Movement Weight

The calculated inter-grid movement importance is reflected in a weight map and used as the movement weight when pathfinding between specific origins and destinations. Conventional weight maps assign movement weights between each grid cell based only on Euclidean distance values. The grid cells with higher importance are prioritized during pathfinding by reducing the movement weight by the inter-grid movement importance (6).

$$D_W\left(t_1,t_2\right)=D_E\left(t_1,t_2\right)-(TF-DF\left(t_2\right))$$

(6)

To reflect significant importance, the Euclidean distance of 100 m was normalized to a value of one, and a scaling factor was applied to the movement importance between grid cells. The scaling factor was empirically selected as 1000 to balance the magnitude between the Euclidean distance and the $TF-IDF$ score.

Furthermore, the minimum value for the travel weight was constrained to 0.001 to prevent negative values (7). Consequently, the 32-directional movement weights, reflecting the importance of movement between grid cells, range from 0.001 to √13.

$$D_W\left(t_1,t_2\right)=\max \left(0.001,D_E\left(t_1,t_2\right)-\mathsf{\lambda }\times \left(TF-DF\left(t_2\right)\right)\right), \mathsf{\lambda }=1000$$

(7)

To reflect the differences in route usage characteristics by ship size and the navigable area based on tide height conditions, five weight maps were calculated for each ship size group for a single origin-destination pair as shown in Figure 8. Subsequently, each weight map was divided into maximum and minimum tide height conditions as shown in Figure 9, resulting in 10 maps with refined weights. To calculate the importance of movement between grid cells, only the size and trajectory of the tide height corresponding to each weight map condition were used.

6. Results of Identifying Customary Routes

To verify the effectiveness of the weighted map reflecting trajectory-based movement importance, a pathfinding algorithm is executed between ports to infer customary routes. In this work, we applied the A* algorithm, which is known for its excellent computational speed. The validity of the proposed customary route inference method was verified by measuring the similarity between the derived customary routes and the trajectory data between ports. In addition, we verified whether the proposed method degraded pathfinding speed.

6.1. Measurement of Cosine Similarity Between Customary Routes and Port-to-Port Trajectories

The cosine similarity between the derived customary route and the trajectory data between ports was measured to quantitatively evaluate the validity of the proposed customary route inference method (8). For the similarity evaluation of the inferred routes, sea areas with more than 100 available port-to-port trajectory records were selected. Among the extracted port-to-port trajectory data, 90% were used as training data to construct the weighted map, while the remaining 10% were used as independent test data (Vector $A$) for similarity measurement.

$$\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{e} \mathrm{s}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{y}\left(A, B\right)={\displaystyle \frac{A·B}{\Vert A\Vert \Vert B\Vert }}$$

(8)

Cosine similarity was measured by substituting the trajectory between ports into vector $A$ and the predicted customary route into vector $B$ (9). In this formulation, $V_{tr}$ and $V_{pr}$ denote grid-based binary vectors representing the spatial footprint of the trajectory data and the predicted customary route, respectively.

$$\begin{gathered} \cos sim\left(V_{tr}, V_{pr}\right)={\displaystyle \frac{V_{tr}·V_{pr}}{\Vert V_{tr}\Vert \Vert V_{pr}\Vert }}, \\ {V}_{tr}=\mathrm{T}\mathrm{r}\mathrm{a}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y} \mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}, \\ {V}_{pr}=\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{c}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{y} \mathrm{r}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{e} \mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r} \end{gathered}$$

(9)

The measurement results indicated that the cosine similarity between the customary route and the trajectory was approximately 0.8, as listed in

Table 16. Results of cosine similarity measurement.

Origin	Destination	LOA	Cosine Similarity
Gamdo Harbor, Yeosu	Sinwol Harbor, Yeosu	1 m~20 m	0.7602
Seogwi Port	Jeju Port	21 m~40 m	0.8644
Jeonjangpo Harbor, Sinan	Songdo Harbor, Sinan	1 m~20 m	0.8954
Jindo Port, Jindo	Sangchujah Port, Jindo	1 m~20 m	0.8897

. This confirms that the proposed customary route inference method largely reflects the actual trajectory-based operational characteristics. Specifically, the cosine similarity was higher when there was sufficient trajectory data between ports and the deviation between trajectories was small. As visualized in Figure 10, the inferred customary routes are shown to follow the underlying port-to-port trajectory data.

Because the similarity evaluation is based on grid inclusion rather than point-to-point correspondence, the proposed method is robust to differences in trajectory length and sampling density. The grid-based representation may introduce a spatial deviation on the order of the grid resolution (approximately 100 m). However, in this study, the similarity evaluation focuses on spatial consistency at the route level rather than precise point-to-point positional accuracy.

6.2. Comparison of Pathfinding Speed

Even if a valid customary route is inferred, a decrease in route calculation speed can limit the practical applications of a computational method in realistic service. Therefore, the pathfinding time required to execute the proposed method was compared with that of an existing distance-based weight map method. For evaluation, the most widely used A* and Dijkstra algorithms were applied, as listed in

Table 17. Comparison of pathfinding times.

Origin	Destination	Elapsed Time for Pathfinding by Algorithm (s)
		A*		Dijkstra
		Distance Based	Movement Importance Based	Distance Based	Movement Importance Based
Gamdo Harbor	Sinwol Harbor	0.73 s	1.41 s	9.10 s	17.34 s
Seogwi Port	Jeju Port	2.03 s	5.29 s	149.64 s	86.34 s
Jeonjangpo Harbor	Songdo Harbor	0.57 s	0.34 s	2.45 s	15.59 s
Jindo Port,	Sangchujah Port	0.62 s	1.23 s	197.46 s	38.06 s

.

Based on the results of the comparison results, the A* algorithm demonstrated superior computational speed compared with the Dijkstra algorithm. Within the same algorithm, the results of the comparison based on the weight map showed both cases where the speed decreased and increased. This is attributed to the movement weights being distributed more diversely, which causes the pathfinding algorithm to explore more candidate grid cells and thus results in an increase in search time for shorter routes. In contrast, when the route was long, the grid cells with higher importance were selected first, reducing unnecessary search space and actually shortening the search time. Consequently, in the A* algorithm, which has excellent pathfinding speed, the time difference between distance-based route inference and customary route inference was not significant.

6.3. Comparison Between Low and High Tide

We verified the effect of the segmented weight map by comparing the inferred customary routes between low and high tide conditions. In this study, we targeted island areas strongly affected by tides and major container ports, and compared inference results for time windows around the minimum and maximum tidal levels. As shown in Figure 11, different routes are inferred between low and high tide, which confirms the validity of applying condition-specific weight maps.

7. Discussion

In this study, we have proposed a method to infer the customary route of a ship using positional data collected every 3 s and validated its effectiveness. However, several concerns must be addressed before applying it to real systems such as e-Navigation services.

7.1. Requirements When Applying the Service

The customary route inference method proposed in this study assumes sea areas where port-to-port trajectory data are available. In areas without sufficient trajectory data, distance-based routes relying on Euclidean distance are provided instead. Therefore, to enable the practical deployment of the proposed method, a database for port areas must be established, and ship trajectories should be continuously collected to create an environment in which port-to-port trajectory data can be efficiently extracted. In this study, positional data points collected over a one-year period from vessels using the Korean e-Navigation service were processed to construct port-to-port trajectory data. Accordingly, the validity of the proposed method was evaluated only in sea areas where more than 100 port-to-port trajectories were available. If trajectory data collected over a longer period are utilized, it would be possible to analyze the impact of trajectory length and density on inferred customary routes and to construct weighted maps that reflect additional factors, such as seasonal operational characteristics. Moreover, in areas where shipping routes frequently change owing to environmental factors such as shallow waters, there is a need to establish an auxiliary system that can collect and reflect real-time environmental information.

7.2. Compliance with Laws and Regulations

The purpose of this study was to infer customary routes based on the operational trajectories of vessels. Although obstacle data are reflected, the route is inferred based on the actual trajectories of vessels; therefore, trajectories that do not comply with regulations may be included. In particular, the obligation to comply with traffic separation schemes (TSS) does not apply for small fishing vessels given their relatively independent operations. Therefore, the weight map derived from their trajectories cannot guarantee compliance with TSS (Figure 12). To infer routes that comply with regulations, compliance with regulations should be reviewed in the process of constructing trajectory data between ports, and preprocessing procedures must be applied to remove noncompliant routes.

7.3. Convention on the International Regulations for Preventing Collisions at Sea (COLREGs) and Operational Constraints

The route inference method proposed in this study aims to analyze and estimate customary vessel movement patterns based on historical trajectory data and is not intended to directly implement real-time collision avoidance or the enforcement of navigational regulations prescribed by the COLREGs [31]. In real-world maritime operations, navigational safety rules such as COLREGs must always take precedence over efficiency or route optimality [32,33]. Accordingly, the routes derived in this study are intended to serve as strategic-level baseline routes, rather than as direct substitutes for rule-based or real-time navigational decision-making systems.

8. Conclusions

In this study, we have proposed a method to infer customary routes that reflect operational characteristics between ports using periodically collected ship position data. To achieve this, the research area was divided into grid cells, and a weight map of navigable grid cells was developed as input for the pathfinding algorithm. In addition, port area data were compiled to extract trajectory data between ports from vessel static data and LTE-M positional data. The importance of movement was then calculated for each of several ship size classes and tide height conditions during navigation based on the compiled data. Our results show that customary routes could be determined effectively by reflecting this information in a weight map.

To verify the efficacy of the proposed approach, we applied the method to infer routes using the A* algorithm and measured the cosine similarity with trajectory data between actual ports. Consequently, high cosine similarity was observed in areas with sufficient trajectory data between ports, which confirms that the weight map of movement importance across grid cells reflected the operational characteristics of actual vessels accurately. Furthermore, there was no significant decrease in computational speed during the process of inferring customary routes compared to an existing state-of-the-art method relying on a distance-based weight map.

This study differs from previous research in that the proposed method quantifies operational importance using actual ship positional data and incorporates it into route inference. Our results are significant as an empirical foundation for further research on techniques that rely on e-Navigation and MASS systems to improve the accuracy of route planning. Future investigations should refine the inference of customary routes based on seasons and weather conditions and consider long-term trajectory data as well as various marine environmental factors. The proposed approach should then be expanded into a real-time route recommendation service to allow for verification in actual sea areas.

The movement-importance-based weighted map proposed in this study can be utilized in combination with real-time navigational decision-making or collision avoidance algorithms. In practical maritime operations, rule-based safety constraints—such as TSS, regulated areas, and collision-risk situations—must be given priority over route optimality. Future research should focus on integrating COLREGs and navigational regulations as hard constraints within the pathfinding process, thereby extending the proposed approach toward a safer and more practical route recommendation framework.