Long-term Ship Position Prediction using
Automatic Identification System (AIS) and Deep Learning(AIS ɏόɇǽɏȫόɟɱόɓɻȸȧ⭘ǙǴ㡩㡦ȃ䮧ᵏⲴս㖞Ҹ⑜Ȁ䯒ǮȠ⹄ウ)

Ibadurrahman
D 190785

DISSERTATION
Submitted to the Graduate School of Engineering, Hiroshima University

September 2022
Higashi-Hiroshima

Abstract
Predicting a ship’s long-term position can be game-changing in maritime industries. Ship
position prediction for maritime situational awareness (MSA), as a critical aspect of maritime
safety and security, requires a longer time interval than collision avoidance and maritime trafficmonitoring. However, previous studies focused mainly on shorter time-interval predictions
ranging from 30 min to 10 h. A longer time-interval ship position prediction is required for
MSA and efficient allocation of ships or business objectives. This study used an end-to-end
tracking method that inputs the previous position of a vessel to a trained deep learning model
to predict its next position with an average 24-h interval, up to the 96-h interval. An AIS datasetwith a long-time-interval distribution in nine years for Capesize bulk carriers worldwide wasused.
The dissertation is constructed from two main parts of the study: each consists of threeexperiments followed by constructing discussions. From the former, a deep learning model ofthe Indian Ocean was examined, and subsequently, the model performance was compared forsix different oceans and six primary maritime chokepoints. In the third experiment, a sample
location within the Malacca Strait area was selected, and the number of ships was counted daily.
The results indicate that the ship position can be predicted accurately with an average timeinterval of 24 h using deep learning systems with AIS data. From the latter, larger networks of
DL models were trained on different observation area sizes with magnified time intervals. Then,
more observation size variations were conducted in the next experiment, increasing 4 and 3.2
degrees on longitude and latitude, respectively. Finally, in the last experiment, five DL models
were built for five major locations of maritime shipping routes focused on Capesize bulk
carriers. The result reveals that the locations where importers of bulk shipments constitute thelargest portion appear to be harder to predict than those that constitute bulk export regions.
Keywords: deep learning; AIS; ship position prediction; long-term; end-to-end

iiContents
Abstract ..................................................................................................................................... ii
Contents ................................................................................................................................... iii
List of Figures ........................................................................................................................... vi
List of Tables ............................................................................................................................. ix
Chapter 1 Introduction ............................................................................................................ 1
1.1. The Importance of Long-term Prediction of Ship Position ............................................ 1
1.2. Objective of this Study.................................................................................................... 2
1.3. Organization of this Dissertation .................................................................................... 3
Chapter 2 Related Studies ....................................................................................................... 5
2.1. Methods of Vessel Position Prediction ........................................................................... 5
2.1.1. Trajectory-based Method ......................................................................................... 6
2.1.2. Point-based Method ................................................................................................. 7
2.1.3. Motion-based Method .............................................................................................. 8
2.2. Characteristics of Trajectory-based and Motion-based Methods.................................... 92.3. Characteristics of this Study ......................................................................................... 10
Chapter 3 Basic Concept and Data Used in This Study ..................................................... 13
3.1. AIS Data ........................................................................................................................ 13
3.2. Ship Data....................................................................................................................... 14
3.3. Deep Learning Model for Position Prediction .............................................................. 14
3.4. Procedure of This Research .......................................................................................... 16
Chapter 4 One-day Interval of Ship Position Prediction ................................................... 18
4.1. Overview of One-day Interval of Ship Position Prediction .......................................... 18
4.2. Methodology ................................................................................................................. 18
4.2.1. Model Structure and Properties ............................................................................. 19
4.2.2. Input and Target Features ....................................................................................... 20
4.2.3. Performance Evaluation Metrics............................................................................ 224.3. Baseline Model ............................................................................................................. 23
4.4. First Experiment: DL Model for the Indian Ocean ....................................................... 25iii

4.4.1. Experimental Setup ................................................................................................ 25
4.4.2. Error and Sensitivity Analyses ............................................................................... 26
4.4.3. Results and Discussions ......................................................................................... 27
4.5. Second Experiment: DL Models for the International Open Waters ............................ 29
4.5.1. Experimental Setup ................................................................................................ 29
4.5.2. Results and Discussions ......................................................................................... 30
4.5.3. Discussions: Influence of the Area ........................................................................ 33
4.5.4. Discussions: Influence of Data Size ...................................................................... 35
4.6. Third Experiment: Application of the DL Model ......................................................... 37
4.6.1. Experimental Setup ................................................................................................ 37
4.6.2. Results and Discussions ......................................................................................... 38
4.7. Discussions on Performance of End-to-end Deep Learning Models ............................ 40
4.7.1. Comparison of End-to-end DL Models ................................................................. 40
4.7.2. Comparison of End-to-end DL Models on Small Dataset ..................................... 42
4.8. Conclusions on one-day interval of ship position prediction........................................ 44
Chapter 5 Several-day Intervals of Ship Position Prediction ............................................ 46
5.1. Overview of Several-day Intervals of Ship Position Prediction ................................... 46
5.2. Methodology ................................................................................................................. 47
5.2.1. Model Structure and Properties ............................................................................. 47
5.2.2. Input and Target Features ....................................................................................... 47
5.2.3. Performance Evaluation Metrics............................................................................ 49
5.3. Baseline Model ............................................................................................................. 50
5.4. First Experiment: Time-Interval Magnification ............................................................ 50
5.4.1. Experimental Setup ................................................................................................ 50
5.4.2 Results and Discussions .......................................................................................... 52
5.5. Second Experiment: Coverage Size Variations............................................................. 60
5.5.1. Experimental Setup ................................................................................................ 60
5.5.2. Results .................................................................................................................... 62
5.5.3. Discussion: coverage size expansion ..................................................................... 64
5.5.4. Discussion: the optimum coverage size for long-term position prediction ........... 65
5.6. Third Experiment: Comparison of Observation Area Worldwide ................................ 68
5.6.1. Experimental Setup ................................................................................................ 68
5.6.2. Results and Discussions ......................................................................................... 70iv

5.7. Discussions on Single-Worldwide Model and Limitations of the Prediction Models .. 72
5.7.1. Single-Worldwide DL Model ................................................................................. 72
5.7.2. Limitations: Outliers and AIS Data Uncertainty .................................................... 73
5.8. Conclusions on several-day intervals of ship position prediction ................................ 75
Chapter 6 Conclusions and Future Works .......................................................................... 77
6.1. Conclusions ................................................................................................................... 77
6.2. Future Works ................................................................................................................. 78
References ............................................................................................................................... 80
Acknowledgements ................................................................................................................ 87v

List of Figures
Figure 1-1. Structure of the dissertation .................................................................................... 4
Figure 2-1. An example of decomposed highly dense routes extracted from historical vessel
voyages in the North Adriatic Sea [3] ........................................................................................ 6
Figure 2-2. An example of short trajectory reconstruction by interpolation represented withboth data structures: the original AIS data (blue), and the new interpolated points (red) [17] .. 7
Figure 2-3. An example of a grid ranges definition set on a designated area [22] .................... 8
Figure 2-4. An example of two conventional approaches to compute future position from thecurrent geographical position and movements [26] ................................................................... 8
Figure 2-5. Uncertain trajectory reconstruction of long-time-interval data with uneven
distribution ............................................................................................................................... 11
Figure 3-1. Time-interval distribution of the AIS dataset ........................................................ 13
Figure 3-2. Overview of data exploration ................................................................................ 14
Figure 3-3. (a) The building block of each unit in the MLP (b) The network architecture ..... 15
Figure 3-4. MLP architectures for regression .......................................................................... 15
Figure 3-5. Overview of vessel prediction model with AIS and deep learning ....................... 16
Figure 3-6. Overview of the research’s procedure................................................................... 17
Figure 4-1. Hold-out validation split of the dataset (non-proportional scale) ......................... 20
Figure 4-2. Relation between the distance error and the angular error .................................... 23
Figure 4-3. Normalized density distribution of AIS data in the observed Indian Ocean area . 25
Figure 4-4. Sensitivity analysis of the DL model .................................................................... 27
Figure 4-5. Normalized plot distribution of the result in the Indian Ocean area from 10,888
vessel positions ........................................................................................................................ 29
Figure 4-6. Location of the observed areas: (a) open oceans and (b) maritime chokepoints .. 30
Figure 4-7. Normalized plot distribution of the result in Malacca Strait (MS) from 22,745
vessel positions ........................................................................................................................ 32
Figure 4-8. Distance-interval distribution of AIS data on the ocean and chokepoint areas..... 33vi

Figure 4-9. Distance error distribution of the predicted positions based on the distanceinterval on ocean areas (left) and chokepoint areas (right): DL model (top) and geodesic
calculation (below)................................................................................................................... 34
Figure 4-10. Mean PFI score of the DL models on the ocean areas (left) and chokepoint areas(right) ....................................................................................................................................... 35
Figure 4-11. Size distribution of the training set and dev-test sets for each area .................... 36
Figure 4-12. Effect of dataset size on the deep learning performance in Malacca Strait (MS).................................................................................................................................................. 36
Figure 4-13. Location of the observation area (red-filled square): the Malacca Strait; thenormalized density distribution is calculated based on the test set .......................................... 37
Figure 4-14. Hold-out validation split for the third experiment (non-proportional scale)....... 38
Figure 4-15. Fitted plots of the daily prediction of the number of ships in the Malacca Straitfrom October to December 2018: (a) DL model and (b) geodesic calculation ........................ 38
Figure 4-16. Daily prediction of the number of ships in the Malacca strait in November 2018.................................................................................................................................................. 39
Figure 4-17. Ship positions in the Malacca strait on three consecutive days in November
2018: TP is the true position (left), DL is the deep learning prediction (center), and GC is thegeodesic calculation (right) ...................................................................................................... 40
Figure 4-18. The small dataset properties: (a) Time-interval distribution; (b) Normalized
density distribution................................................................................................................... 43
Figure 5-1. Size variations of the observed area with 24-h time-interval average (thenormalized density distribution of AIS data is based on the largest area) ............................... 52
Figure 5-2. Comparison of the DL model performance with the previous model andcharacteristics of each observed area dataset in 24-h average time interval ............................ 53
Figure 5-3. Size variations of the observed area with 48-h time-interval average (normalized
density distribution of AIS data is based on the largest area) .................................................. 54
Figure 5-4. Comparison of the DL model performance with the previous model andcharacteristics of each observed area dataset in 48-h average time interval ............................ 55
Figure 5-5. Size variations of the observed area with 72-h time-interval average (normalized
density distribution of AIS data is based on the largest area) .................................................. 56
Figure 5-6. Comparison of the DL model performance with the previous model andcharacteristics of each observed area dataset in 72-h average time interval ............................ 57

vii

Figure 5-7. Size variations of the observed area with 96-h time-interval average (normalized
density distribution of AIS data is based on the largest area) .................................................. 58
Figure 5-8. Comparison of the DL model performance with the previous model andcharacteristics of each observed area dataset in 96-h average time interval ............................ 59
Figure 5-9. Size variations of the observed area for four-different time intervals (thenormalized density distribution of AIS data is based on the largest area by the 24-h averagetime interval) ............................................................................................................................ 61
Figure 5-10. The DL model performance on area size variations in four-different time interval.................................................................................................................................................. 63
Figure 5-11. Expanded size variations of the coverage area with doubled size interval (thenormalized density distribution of AIS data is based on the largest area) ............................... 64
Figure 5-12. The DL model performance on the expanded coverage variations in fourdifferent time interval .............................................................................................................. 65
Figure 5-13. DL model performance and dataset characteristics comparison across different
time intervals and coverage size variation ............................................................................... 67
Figure 5-14. Location of the observed area ............................................................................. 69
Figure 5-15. Comparison of DL model performance across observed location and timeintervals .................................................................................................................................... 71
Figure 5-16. Single-worldwide model performance across time intervals: mean distance error(left y-axis) and error ratio (right y-axis) ................................................................................. 73
Figure 5-17. Dataset characteristics comparison of the location-based and worldwide models:coefficient of variation across time interval magnification (a) and number of training data (b).................................................................................................................................................. 75

viii

List of Tables
Table 2-1. Vessel position prediction studies ............................................................................. 5
Table 2-2. Primary differences between trajectory-based and motion-based methods for vessel
position prediction ................................................................................................. 10
Table 4-1. Error analysis of the DL model ............................................................................... 26
Table 4-2. Comparison of the model performance .................................................................. 28
Table 4-3. Comparison of the loss and metric scores of the DL model and baseline model oneach observed area ................................................................................................. 31
Table 4-4. Comparison of the deep learning model performance ............................................ 41
Table 4-5. Comparison of the model performance on the small dataset .................................. 44
Table 5-1. Variation of time intervals and its coverage size .................................................... 51
Table 5-2. Comparison of model performance in 24-h average time interval ......................... 53
Table 5-3. Comparison of model performance in 48-h average time interval ......................... 55
Table 5-4. Comparison of model performance in 72-h average time interval ......................... 57
Table 5-5. Comparison of model performance in 96-h average time interval ......................... 59
Table 5-6. Size variation of observation coverage ................................................................... 62
Table 5-7. Comparison of model performance in all area size and time interval variations ... 63ix

Chapter 1
Introduction
1.1. The Importance of Long-term Prediction of Ship Position
Maritime transportation is recognized for its central role in the global supply chain
considering it accounts for 90% of international trade by volume and 70% by value [1]. The
United Nations predicted that the total volume of seaborne trade worldwide would increase by
3.2% from 2019 to 2022 [2]. Therefore, establishing safety and security in maritime
transportation is essential. Maritime situational awareness (MSA) is a critical aspect ofmaritime safety and security that can be achieved through tracking, surveillance, and position
prediction of ships [3]. Once a prediction of the ship position is obtained, decision making andaction planning can be supported at different information levels. However, ship position
prediction for MSA requires a longer time interval than other tasks such as collision avoidance
and maritime traffic monitoring, which mainly use a short-term prediction from a highprecision real-time forecast spanning less than one hour [4]. Accordingly, we considered a
prediction with a time interval ∆t longer than 12 h as a long-term prediction, and a prediction
with a time interval between short- and long-term threshold as a medium-term prediction [5].
Studies on the long-term prediction of vessel position remain scarce despite its
considerable potential for maritime applications, while almost all previous studies have focusedon either near real-time predictions (short-term prediction) or predictions with a time interval
lesser than 12 h (medium-term predictions). Long-term ship position prediction is required not
only for MSA but also for efficient allocation of ships by shipping companies in accordancewith global freight demand. It can be utilized to monitor and assist the fleet, specifically, whencommunication with a ship operator breaks down owing to poor weather conditions or when aship is in distress. It can also be implemented by shipping insurance and maritime investigatorsfor investigation purposes. The ability to predict the long-term position of a fleet could prove
not merely necessary but vital for strategy formulation in the fast-changing dynamics ofmaritime industries.
Maximizing the potential of maritime big data is essential for predicting vessel positions.
The automatic identification system (AIS) is a self-reporting message system on board a vesselthat records its position and condition [6]. Each record of the AIS message contains the staticand voyage-related information of the vessel and its dynamic information such as longitude,1

latitude, speed over ground, course over ground, and heading. As of July 2008, all commercial
vessels above 300 GT serving international routes were regulated to be outfitted with an AISClass A device by the International Maritime Organization (IMO) [7]. Prior to the widespreaduse of maritime big data (i.e., AIS data), studies on vessel position prediction were conductedusing data from radar or laser sensors, such as in the work of Perera et al. (2012) [8]. Since
2015, studies in the field have started using AIS as a historical data source for ship position
information. Czapiewska and Sadowski (2015) conducted position prediction experiments
using linear and nonlinear motion functions for location data compression of AIS records [9].
The high volume of AIS data accumulated over the years is a potential asset that needs to be
explored, especially in the current age of artificial intelligence. With this big data of vessel
position records, it is possible to predict vessel position by applying advanced machine learning(ML) techniques such as deep learning.

1.2. Objective of this Study
This study aims to achieve a 24 h interval and more ship position prediction for MSA.
Predicting a ship’s long-term position can be game-changing in maritime industries. The
application of the long-term position prediction may not be the end goal. The results can be fed
to another machine learning system, along with many other signals. Then, a business objectiveof the machine learning pipeline can be established broadly, such as for ship allocation,
shipping investment, or global economic projection. For instance, with the objective ofshipping investment, this downstream system will determine whether it is worth investing in acertain area and future time or not by predicting direct components to the measurement of theBaltic Dry Index (BDI), which has a predictive ability for a range of stock markets [10]. The
accurate results of the application are critical, as it directly affects revenue. This work provides
a valuable benchmark for future studies.
Previous studies focused mainly on short- and medium-term prediction, ranging from 30
min to 10 h intervals as the AIS data were dense (closely packed between short time intervals)
but in a limited period or timespan. Naturally, a vessel position prediction with long timeintervals (e.g., 24 h) requires data with a long timespan, given that state-of-the-art ML
algorithms, such as deep learning, require large amounts of data to make accurate predictions
for longer intervals [11]. Accordingly, nine-year AIS data for capesize bulk carriers worldwide
and deep learning (DL) were used to accomplish long-term prediction. End-to-end learningrefers to training a learning system represented by a single deep network model that supersedes2the preprocessing stages typically present in traditional pipeline designs. By using extensive
fleet data and computing power, the model can learn robustness to noise and generalization todata variation; this result confirms that an accurate long-term prediction of vessel position canbe generated with the straightforward method. The utilization of nine years of AIS dataworldwide and the development of a generalized DL model from an uneven time-interval
dataset for the long-term prediction of ship positions constitute the novelty of this study.

1.3. Organization of this Dissertation
Each chapter in this thesis is organized as follows.
Chapter 1 overviews the long-term prediction of ship position and its importance. The
objective of this study is also presented.
In Chapter 2, studies on vessel position prediction are compiled and described based on
the prediction methods. The different characteristics between trajectory-based and motionbased methods are also described. The characteristics of this study are further discussed.
Chapter 3 outlines the basic concept and data used in this study. The AIS and ship data
used are described. The basic concept of the deep learning model for position prediction is also
explained.
In Chapter 4, the first part of the research, a one-day interval of ship position prediction
is carried out. In the first experiment, the model performance was demonstrated for the Indian
Ocean, followed by a comparison of the performance for six different oceans and six primary
maritime chokepoints to investigate the influence of each area. Finally, the model performancefor a sample area within the Malacca Strait was analyzed to simulate a practical application.
In Chapter 5, as the second part of the research, the time interval prediction was magnified
up to several days; a larger network was proposed where the previous model was used as thebaseline, and the observation coverage was also enlarged. DL models were trained on different
observation area sizes with magnified time intervals in the first experiment. More observation
size variations were conducted in the subsequent experiment, increasing 4 and 3.2 degrees on
longitude and latitude, respectively. In the last experiment, five DL models were built for five
major locations of maritime shipping routes focused on Capesize bulk carriers.
Finally, Chapter 6 presents conclusions, and some future works are proposed.
The structure of this thesis is depicted in Figure 1-1.

3

Figure 1-1. Structure of the dissertation

4

Chapter 2
Related Studies
2.1. Methods of Vessel Position Prediction
The methods for forecasting vessel positions can be classified into three categories:
trajectory-based, point-based, and motion-based methods. Overall, studies concerning shipposition prediction are summarized in Table 2-1; only studies focused on predicting vessel
position are listed. The results of one method are not equivalent to those of another method
because each method is specifically developed for the desired objective and the data used.
Table 2-1. Vessel position prediction studies
Prediction
Method1

Authors∆t∆t

Threshold Prediction

Objective2

AIS Data

ML

TargetTarget Unrestricted(Range) Algorithm3

Vessel4

Area5

Trajectory

T-b
T-b
T-b
T-b
T-b

[18]
[20]
[17]
[21]
[19]

MediumMediumShort
Short
Medium8h
10 h
15 min
5 min
1h

MSA
MSA
CA
MTM
MSA

5m
1m
1y
2m
nr

kNN
ELM

Cg,Tg,Tk
Cg
nr
nr
nr

OW
OW
RW
RW
nr

Yes
No
Yes
No
Yes

P-b
P-b
P-b

[23]
[24]
[25]

Medium
Short
Short

1h
50 min
5 min

MTM
MTM
MTM

1m
2y
1m

kNN
CNN
CNN,LSTM

Fs,Cg,Tk
Cg, Tk
nr

RW
RW
RW

Yes
Yes
Yes

[8]
Short
[9]
Short
[28]
Short
[27]
Short
[30]
Short
[32]
Short
[31]
Medium
[29]
Short
[33]
Short
[34]
Short
this study Long

< 1 min5 min
40 min8 min
3 min
15 min4h
20 min10 min< 1 min
24 h

MTM
DC
AD,MSA
MTM
MTM
CA
MSA
CA,MSACACA
MSA,SA

nr
1m
3m
nr
nr
nr
1y
nr
9y

ELM
MLP
MLP
MLP
MLP
bLSTM
LSTM
MLP

nr
Cg
nr
nr
Tk
Fe
Ps
nr
nr
Fe
BC

RW
RW
OW
RW
RW
nr
RW
RW
RW
RW
OW

No
No
No
Yes
No
No
No
Yes
Yes
No
Yes

M-b
M-b
M-b
M-b
M-b
M-b
M-b
M-b
M-b
M-b
M-b
1

Prediction methods: T-b, trajectory-based; P-b, point-based; M-b, motion-based
Prediction objectives: CA, collision avoidance; MSA, maritime situational awareness; SA., ship allocation; DC, datacompression; MTM, maritime traffic monitoring; AD, anomaly detection.
3
ML algorithm or DL architecture used for vessel position prediction: SVM, support vector machine; ELM, extreme learning
machine; kNN, k-nearest neighbors; MLP, multilayer perceptron; RNN, recurrent neural network; LSTM, long short-term
memory; CNN, convolutional neural network; bLSTM, bidirectional long short-term memory.
4 Target vessel type: Cg, cargo, Tk, tanker, Tg, tugboat, BC, bulk carrier, Fs, fishing vessel, Fe, ferry, Ps, passenger ship.
5
Target area: OW, open water; RW, restricted water.
nr, not reported.
25

2.1.1. Trajectory-based Method
In the trajectory-based prediction method, clusters of vessel trajectories must be initiallycreated and classified based on shipping routes from historical voyage patterns [12]. A
trajectory is defined as a structure of polygon or matrix that forms one shipping route, createdfrom AIS data points of particular ships or vessels entering a coverage area. A waypoint
detection is utilized to detect new or existing routes once vessels enter the coverage.
Trajectories can also be decomposed from a cluster or classification of AIS data points basedon dense points in shipping routes or other criteria from all historical voyage patterns inside an
examined area [13]. The route decomposition extracts similar vessel behaviors into a cluster;to accurately estimate vessel trajectory, different features are identified to decompose it into
different sub-routes [14]. Figure 2-1 demonstrated a sample of trajectories extracted from a
trajectory deonposition of AIS data points in the North Adriatic Sea.

Figure 2-1. An example of decomposed highly dense routes extracted from historical vessel
voyages in the North Adriatic Sea [3]As a set of trajectories creates a trajectory database, each trajectory must have a similar
structure. It generally undergoes a trajectory reconstruction such as interpolation or othermeans (see Figure 2-2 for an example of trajectory reconstruction by interpolation AIS data
points). The ship position that is wanted to be predicted is first matched to the database basedon its historical trajectory. The reconstruction of trajectories requires intensive preprocessing
regarding the varying density of data points, abnormal behavior, trajectory anomaly, noise,
missing points, the assumption regarding status, and the trade-off between similarity thresholds[15, 16].

6

Figure 2-2. An example of short trajectory reconstruction by interpolation represented withboth data structures: the original AIS data (blue), and the new interpolated points (red) [17]A position prediction can then be derived by formulating or interpolating the trajectory
structure. Because vessels' entire trajectories (such as port-to-port trajectories) are required in
an observed area, this method has been implemented mainly for large areas (e.g., open waters,
oceans, and straits).
Several studies have developed unique route extraction algorithms to be used before thevessel position is predicted by deriving from its routes, such as in the work of Pallotta et al.
(2014), Tu et al. (2020), and Mazzarella et al. (2015) [18-20]. We considered ∆t of Mazarella
et al. (2016) to be effective for only 10 h because they merely demonstrated their trajectorybased algorithm on a particular target and route, where the 10 h threshold exhibited the mostsignificant performance compared to those of the other algorithms. Dalsnes et al. (2018)
conducted predictions using a Gaussian mixture model combined with the neighbor course
distribution method [17]. Using k-nearest neighbor (kNN), Virjonen et al. (2018) compared the
trajectories of a new ship and historical ships within the Gulf of Finland [21].
2.1.2. Point-based Method
In the point-based method, the examined area is first transformed into non-overlappingcells or grids. The position of a ship inside the area is converted into a grid reference anddefined by the occupied cells. Once a vessel enters the coverage, its movement is captured bythese occupied cells. Figure 2-3 illustrates a grid ranges definition to be tested on a selected
rectangular shipping area. As a fixed time interval must be maintained inside the observed
coverage, the AIS points or trajectories must undergo a trajectory reconstruction such as
interpolation or other means. An ML model then calculates the prediction of the next positionof the ship, trained from historical movement data inside the grid. Some researchers used CNNs
by converting vessel positions from AIS data into a gridded ocean floor model as the input.

7

Figure 2-3. An example of a grid ranges definition set on a designated area [22]Several studies have utilized this method for vessel position prediction for various
objectives. Duca et al. (2017) employed a kNN classifier for ship route prediction [23]. Kim etal. (2018) employed a combined hierarchical architecture of a convolutional neural network(CNN) for feature extraction with five separate fully connected neural networks (NNs) topredict the number of ships around the Korean port Yeosu up to 50 min ahead with initial AIS
points reconstructed by interpolation [24]. Zhou et al. (2020) used three different architectures,
including CNN, long short-term memory (LSTM), and bi-directional LSTM (bLSTM)
integrated with CNN, to predict the inflow and outflow of gridded Singapore waters [25].
2.1.3. Motion-based Method
The motion-based method estimates the future vessel position using motion functions fromthe current geographical position and movements (see Figure 2-4) or a trained ML model using
historical information as input. Table 2-2 shows the main differences between trajectory-based
and motion-based methods for vessel position prediction. This method is relatively more
flexible than the other methods and can be effectively generalized for data variation. Most
researchers have used this method for short- and medium-term predictions within a small area
(e.g., near ports, waterways, and restricted water areas) and particular trajectories.

Figure 2-4. An example of two conventional approaches to compute future position from thecurrent geographical position and movements [26]8Several studies have utilized this method with many approaches. Juraszek et al. (2020)
used an extended Kalman filter for fast short-term prediction in the distributed processing
system Apache Flink [27]. Mao et al. (2017) generated ship position predictions 20 and 40 min
ahead for the west coast of the US using an extreme learning machine (ELM) [28]. Duca et al.
(2017) employed a kNN classifier to forecast ship movements around Malta [23]. Using an NN,
Simsir and Ertugrul (2009) and Zhou et al. (2019) conducted predictions with intervals of 3
and 20 min, respectively, targeting vessels in narrow waterways [29, 30]. Meanwhile, Zissis etal. (2016) attempted predictions in Greek waters up to 4 h ahead, focusing on the regular sea
trips of passenger ships around the Aegean Islands [31]. Borkowski (2017) combined AIS
location data and sensor data onboard a vessel to predict its subsequent position, aiming at
collision avoidance [32]. Gao et al. (2018) used a bidirectional recurrent neural network(bRNN) with an LSTM unit seeking short-term predictions [33], and another study by Gao etal. (2021) combined the TPNet framework and LSTM for multi-step ship trajectory prediction
based on four types of navigation stages [34].

2.2. Characteristics of Trajectory-based and Motion-based Methods
As long-term vessel position predictions have not been performed yet, determining asuitable method is vital for achieving long-term prediction. Consequently, the observed
location (and dataset) must be considerably larger than the ship distance intervals toaccommodate and capture their long-term movements; a small observation area limits longterm movement. The point-based method inevitably involves computing the entire cell
information in each computation cycle, and thus the observed area cannot be too large because
the computational costs would be exorbitant. Meanwhile, utilization of the trajectory-based
method is expected to result in high accuracy for any time-interval threshold and area size;
however, this method is not sufficiently flexible for adaptation to factors other than theobserved variable. It also involves arduous work on route clustering and classification andtrajectory reconstructions, in addition to anomaly detection owing to the partially incomplete
and noisy AIS data. Furthermore, although we can create a database for millions of historicaltrajectories, ship trajectories are not fixed but quickly adapt to the weather and other conditions;ship routes evolve owing to various factors such as climate change and the emergence of newports and new routes [35]. In contrast, the motion-based method is relatively more flexible,
efficient, and practical than the other methods, and, notably, can be effectively generalized for9data variation. Table 2-2 shows the main differences between trajectory-based and motionbased methods for vessel position prediction.
Table 2-2. Primary differences between trajectory-based and motion-based methods for vessel
position prediction

MeritsDemerits

Trajectory-based

Motion-based

high accuracy for any time-interval

flexible, efficient, and can bethreshold and area size

generalized for data variation

requires arduous work on pre-requires machine learning where

processing such as trajectory definition,

developing a model involves a CPU-

classification, and reconstruction

intensive and specialized expertise

Therefore, from the perspective of long-term position prediction on large international
open waters without the consent of any restricted trajectory, a more general and updatablemodel with generalization to data variation and robustness to noise needs to be constructed thatincorporates a fast prediction generation for predicting the long-term position of a vessel. In
this study, a motion-based method was used to develop a generalized deep learning model for
long-term vessel position prediction to overcome these challenges.

2.3. Characteristics of this Study
In previous studies, such as in Zhang et al. (2020), trajectories with missing records over
one day and lasting less than one day were excluded from the training and testing process [35].
However, this study does not execute this pre-processing because eliminating the routes or
trajectories with missing data can be applied when trajectories have been defined, only whenusing other methods (see Table 2-2). Because of the nature of our dataset, we consider an AIS
message to be an outlier when its time interval from the previous messages is more than twice
the observed time interval. For instance, in a 24-h time interval prediction, AIS data with morethan 48 h intervals are considered outliers. These outliers (individual AIS messages, not theentire trajectories) are removed from the training process, but are retained in the testing process.
An end-to-end DL model was developed to supersede a vessel position prediction modelthat requires arduous preprocessing steps (e.g., trajectory reconstruction) since the timeintervals of the AIS data vary considerably. A trajectory reconstruction becomes impractical as
the time intervals have an uneven distribution. The asynchronous nature of AIS messages withtime intervals of less than 3 min allows the application of a trajectory reconstruction from a10

short-interval to a long-interval dataset without a significant error. This satisfactory outcome isbecause the AIS points can be aligned using a simple method of sampling the nearest point in
the time dimension that satisfies the x interval condition as  ȁο‫ ݐ‬െ ‫ݔ‬ȁ ൌ Ͳ. Nonetheless, thisο௧՜௫

preprocessing destroys information regarding latent variables [36]; it causes distortion (thetrajectory becomes compressed or simplified), causing the acceleration (derived from speed
over ground) and rate of turn to become unusable [37].

Figure 2-5. Uncertain trajectory reconstruction of long-time-interval data with uneven
distribution
However, if the values of the time interval ∆t are relatively large with uneven distribution,
the interpolation can cause a considerable error in the aligned positions [38]. In this study, thedataset has ∆t values ranging between almost zero and 48 h (in the absence of outliers),
indicating that although the dataset consists of daily AIS messages (averaging 24 h), their exact
time interval can be longer than 24 h. The large gap in time intervals between two consecutive
AIS messages signifies that the interpolation to create an evenly-spaced dataset time series
would result in large errors. For instance, in a time window of 24 h, a moving ship generally
has an average distance interval of more than 400 km. Consequently, interpolating the shipposition in this extended time window is expected to result in a significant error in the aligned
positions, thus accumulating additional errors when predicting the subsequent position. Figure
2-5 illustrates the uncertainty of trajectory reconstruction of the long-time-interval data with
uneven distribution; the aligned data are prone to result in a large error. Therefore, any
application or method that requires trajectory reconstruction is considered impractical.
Based on the nature of the AIS dataset used while achieving the objective (which
eventually focuses on the long-time interval data and large observation area), performing a
trajectory reconstruction is unattainable. Therefore, in this study, deep feed forward network

11was employed to solve the long-term position prediction. Previous studies have also attempted
to use this basic architecture but have been limited to shallow networks with limited timeintervals and area sizes. We aimed for a larger-scale and longer timespan of the AIS dataset,and more importantly, developed a more general and updatable model from a long-timeinterval dataset with uneven distribution, which has not been achieved thus far. By leveraging
the advantages of deep learning systems supported by extensive fleet data and computing power,
the model was developed to learn robustness to noise from extensive data with unrestrictedtrajectories in international open waters and realize generalization to data variation of timeintervals, vessel activities, statuses, and locations.

12

Chapter 3
Basic Concept and Data Used in This Study
3.1. AIS Data
We processed AIS data from exactEarth [39], considering that it was established as an AISdata-service company that started deploying AIS receivers on satellites soon after the IMO
regulation was implemented. As exactEarth offers the untapped potential of extensive AIS dataof SOLAS-compliant ships, we took advantage of the capacity provided by deep learning
systems to learn from large datasets to improve the overall performance.
The dataset comprises nine years of archived AIS messages of global capesize bulk carriers,
from July 2010 to December 2018. This type of vessel exhibits proper records with lessirregularity compared to those of smaller vessel types and more diverse shipping routes thancontainers and tankers [40]. The dataset alone is composed of over 3.5 million archived AIS
messages from 1698 different IMO numbers (vessels).

Figure 3-1. Time-interval distribution of the AIS dataset
Daily archived AIS messages have random time intervals ∆t between less than 1 h and up
to 48 h, averaging 24-h intervals; the time-interval distribution is depicted in Figure 3-1. The
fitted probability density function (PDF) of the overall dataset showed a standard Gaussian
distribution. The data proliferated from 2010 to 2014 when satellite-based AIS became astandard practice. Although the dataset has an uneven time-interval distribution, it is consideredadequate for long-term prediction because it contains years of extensive fleet data worldwide.
13

3.2. Ship Data
Ship specification data from IHS SeaWeb's fleet data [41] were utilized to organize andvalidate the capesize bulk carrier vessels from billions of raw exactEarth data records. Thisdataset was also used to rectify the static information in each AIS message.

Figure 3-2. Overview of data exploration
Figure 3-2 illustrates the overview of data handling from retrieval to processing for a DL
model. All datasets were collected independently from each source and stored in a single SQL
relational database for easy access and management. An IMO number identifies every vessel,each of which is related to another piece of information in the dynamic and static data. Whena model needs to be generated, a specified chunk of the AIS dataset is retrieved from therelational database and subsequently processed into a DL model. All scripts from preprocessing
to postprocessing were written in Python.

3.3. Deep Learning Model for Position Prediction
A DL model refers to the process of training and testing multilayered NNs that can learncomplex structures and achieve high levels of abstraction [42]. Building a DL model to performa specified task satisfactorily requires hours of iterative prototyping; the process is not a trivial
task, even for a simple small model. Keras, an open-source high-level API framework capableof running on GPU clusters was used to facilitate rapid model prototyping [43]. The decision
regarding the structure of the model and its input-target features was determined through our
extensive experimentation and evaluation, focusing on the model objectives: performance andgeneralization on the observed areas.
In this study, we employed a deep feed-forward Neural Network, or can be called a deep
Multi-Layer Perception (MLP). The building block of each neuron or unit is shown in Figure
3-3(a), and the overall network architecture is presented in Figure 3-3(b). For each unit in thehidden layer ݈ , an activation function ߪ is applied to the input’s weighted sum (‫) ݖ‬. The

14

information is then propagated through the network up to the output layer ‫ܮ‬, where the lastlayer end has no activation (a linear layer).

(a)

(b)
Figure 3-3. (a) The building block of each unit in the MLP (b) The network architecture

Figure 3-4. MLP architectures for regression
The model was constructed as a DL model to solve regression problems. Compared withthe classification problem that treats portions of the covered area as classes, regression
problems can achieve a higher location resolution and, therefore, higher prediction accuracy[27]. The option of MLP architecture for regression is depicted in Figure 3-4. Scalar regression
model of the MLP architecture outputs one scalar value, where vector regression yields twovalue at once; multi-output (or multihead) model has more parameters to be computed but cansolve the imbalanced loss caused by the different scales of the target. In this investigation, the15

target is longitude-interval and latitude-interval value between the current and the next timestep,and hence both vector regression and multihead model would produce similar result.
A straightforward method that takes advantage of the capacity provided by deep learning
systems with sufficient data and computing power is proposed to produce long-term shipposition prediction. Fast result generation and generalization from the trained model make theproposed method suitable for practical use. The flowchart in Figure 3-5 summarizes the overall
method for long-term vessel position prediction. Given a selected location and time range, asizeable chunk of the AIS dataset is queried from the database. Next, a set of input features ܺ௜and a set of target features ‫ݕ‬௜ comprising vessel positions at the next time step are created. Eachset is standardized and then input for training into DL model(s). The model generates a
prediction of the displacements of the positions. Then, the results are passed through inverse
standardization using the standardization parameters of the target features. Finally, thepredicted ship position (i.e., latitude and longitude) is systematically evaluated and analyzed.

Figure 3-5. Overview of vessel prediction model with AIS and deep learning

3.4. Procedure of This ResearchThis study explores AIS data and deep learning potential for vessel position prediction by
conducting three experiments on 1-d intervals followed by another three on several-day
intervals. An overview of the study flow is illustrated in Figure 3-6
In the first part of the research, a model definition was utilized. The model's objectives areto accurately predict the next-1-d position and make a generalization. The first experimentexamines a DL model for the Indian Ocean. Subsequently, DL models were assessed for six
open oceans and six near-port global primary chokepoints. The target area is the international
open waters; we specified a worldwide observation into these twelve areas to avoid building
an excessively large model. Finally, a simulation of practical application was carried out insidea sample area of the Malacca Strait.
In the second part of the research, a new model was defined with deeper layers and larger
networks. The objectives of this new model are to predict up to the next 4-d position andconsequently more extensive coverage with the same procedure as the previous experiments.
16

The first experiment examines this new model compared with the previous model in four
different coverage sizes and time intervals from 1-d to 4-d intervals; each time-interval model
has a different coverage size due to the nature of moving ship characteristics. Afterward, theDL model was performed on more detailed size variation to capture the fluctuation of the model
performance in more detail in order to find the optimum coverage size requirement for eachtime interval. Finally, five DL models for five major locations of maritime shipping routes
focused on Capesize bulk carriers were assessed to further assess the area's influence.

Figure 3-6. Overview of the research’s procedure

17Chapter 4
One-day Interval of Ship Position Prediction
4.1. Overview of One-day Interval of Ship Position Prediction
Study on long-term prediction of ship position (i.e., more than 12-h interval) is scarce,
despite many advantages that can be attained. However, as machine learning algorithm thrives
nowadays, supported by abundant maritime big data (i.e., AIS), the lofty aspiration isachievable. Deep learning, one of the most popular machine learning algorithms, craves
enormous data for training to effectively produce accurate results. This criterion fits perfectlywith maritime transportation as nowadays, AIS data has become mandatory for international
shipping.
This research is the first to predict vessel position for around 24-h intervals (on average).
The long-term prediction aims to establish additional safety and security in maritime
transportation, which benefits all relevant stakeholders. The motion-based method implies
building a generalized model that can generate fast results suitable for practical use.
This research consists of three experiments followed by discussions regarding theperformance of end-to-end DL models. In the first experiment, a model for the Indian Ocean
area was examined, and in the subsequent experiment, 12 models were investigated on open
oceans and maritime chokepoints. In the last experiment, a selected sample location within the
Malacca Strait area was examined, resembling a simulation of practical application. In thediscussion section, the DL model was compared to other end-to-end models with sequencebased architectures (i.e., RNN, LSTM), and then they were tested on a small dataset. Finally,
the conclusion of this research is presented.
The detail of the one-day interval of ship position prediction in this dissertation ispresented in the following chapter.

4.2. Methodology
The overview of the prediction model is explained in the previous chapter.
We performed the regression task by setting the target as a scalar value for analysis andobjective evaluation in the prototyping process at the expense of running it twice; the target
features are the displacements of longitude ∆λ and latitude ∆φ directions. Accordingly, the18input and target features were fed into two independent DL models with the same model
properties. The model predicts the displacements in longitude and latitude directions that areuncorrelated.
4.2.1. Model Structure and Properties
During the prototyping process, the most salient input features were selected by evaluating
permutation feature importance (PFI) based on Fischer et al. (2018) [44]. After a model wastrained and the model score ‫ ݏ‬was computed, a corrupted matrix ܺ௞ǡ௝ was generated bypermuting feature ݆ in the original matrix ܺ . Subsequently, a new score ‫ݏ‬௞ǡ௝ was computed
based on the prediction of the permuted data ܺ௞ǡ௝ . Finally, the PFI score ‫ܫ‬௝ was calculated asfollows:ͳ ௄σ௞ୀଵ ‫ݏ‬௞ǡ௝ െ ‫ݏ‬‫ܭ‬ൈ ͳͲͲΨ
‫ܫ‬௝ ൌ
‫ݏ‬ሺͳሻThe permuted data ܺ௞ǡ௝ were then returned to the original order. This step was repeated for all
the features of the input data.
The PFI evaluation was conducted using the dev set at the prototyping stage to determine
the extent to which the model relied on each input feature to generate predictions [45]. All
irrelevant and insignificant features with minimum PFI scores were removed, and subsequently,
a new feature was extracted and re-evaluated until the final set of features was established.
Thus, any timestep-based information added to the final inputs would not improve the model
performance; instead, it would overfit the model.
The proposed model uses a deep network with six layers: five hidden layers with a sigmoid
activation function and a one-unit linear output layer [64, 64, 32, 32, 16, 1]. The mean absolute
error (MAE) was employed as the loss function since it is less sensitive to outliers than the root
mean square error (RMSE), and mini-batch gradient descent with a mini-batch size of 64 wasused for training. We used an adaptive learning rate method involving the adaptive moment
estimation optimization algorithm (Adam), an update to the RMSProp with momentum [39];the learning rate was automatically reduced by a factor of 0.5 once the validation loss stagnatedfor 50 epochs. Moreover, to accommodate areas with low AIS data coverage (to avoid
overfitting caused by deep networks), a validation-based early stopping was set to interrupt
training once the validation stopped improving for 100 epochs. These in-training validationbased methods were solely used for the experiment and were not used in the prototyping stage
[40].

19

A hold-out validation split was conducted to prevent information leakage from the test data.
An overview of the hold-out validation split for the dataset is depicted in Figure 4-1. AIS datafrom July 2010 to December 2017 were randomly shuffled into a training set, and the dataset
was disrupted with data from other vessels and timelines. Meanwhile, a dev set was randomly
sampled from half of the 2018 data. The remainder was retained as a test set that had neverbeen used for model prototyping. The split was designed to reflect the dev/test set as the recent
AIS data. The dev set was used to validate the training set while having the same distribution
as the test set. The randomly shuffled data combined with mini-batch training ensured rapid
convergence of the gradient descent with minimal disturbances. Moreover, this combination
prevented deep networks from conspiring to memorize the chronological sequences of vessel
locations.

Figure 4-1. Hold-out validation split of the dataset (non-proportional scale)
4.2.2. Input and Target Features
A set of AIS messages was first retrieved from the SQL database, given a boundary
condition of location and time. The specified input and output features were then extracted
from the dataset with vessel states at the current time step ‫ ݐ‬as the input matrix ܺ௜ and its
location at the next time step ‫ ݐ‬൅ ͳ as the target vector ‫ݕ‬௜ . The input ܺ is composed of 10
features: longitude ߣ, latitude ߮, speed over ground ܷ௢௚ , course over ground ߰௢௚ , heading ߰௛ ,time interval ο‫ ݐ‬, distance ݀ , haversine distance 1 ݀௛ , Manhattan distance 2 ݀௠ , and average
speed ܷ௔௩௚ . Meanwhile, the component of the target ‫ ݕ‬follows the DL model output that targets
particularly one of the two variables: the displacements of longitude οߣ and latitude ο߮

1great-circle distance calculation between two points on a sphere given their coordinates.

2

distance between two points measured along axes at right angles.

20

between the current time step ‫ ݐ‬and the next time step ‫ ݐ‬൅ ͳ. The input matrix and target vectors
are expressed as follows:ܺ௜ ൌ ቄߣ௜௧ ǡ ߮௧௜ ǡ ܷ௢௚ ௜ ǡ ߰௢௚ ௜ ǡ ߰௛ ௜௧ ǡ ο‫ݐ‬௧௜ ǡ ݀௧௜ ǡ ݀௛ ௜௧ ǡ ݀௠ ௜௧ ǡ ܷ௔௩௚ ௜ ቅሺʹሻ‫ݕ‬௜ ఒ ൌ ൛οߣ௜௧ ൟǢ‫ݕ‬௜ ఝ ൌ ൛ο߮௧௜ ൟ

ሺ͵ሻ

௧

௧

௧

where ݅ ൌ ሼͲǡͳǡ ǥ ǡ ݉ሽ , the subscript ‫ ݐ‬represents the time step, οߣ௧ ൌ ߣ௧ାଵ െ ߣ௧ is thelongitude interval, and ο߮௧ ൌ ߮௧ାଵ െ ߮௧ is the latitude interval.
Input features of ߣ , ߮ , ܷ௢௚ , ߰௢௚ , and ߰௛ are extracted directly from the archived AIS
messages, whereas some of the remaining inputs provide implicit information on the position
history at the previous time step ‫ ݐ‬െ ͳ. Further, the target timestamp (at the next time step ‫ ݐ‬൅ͳ) is represented as a time interval ο‫ ݐ‬and a rough distance to the target ݀௧ . They are defined
as follows:݀௛ ௧ ൌ ݀௛ ൫ሺఝ݀௠ ௧ ൌ ݀௛ ൫ሺఝο‫ݐ‬௧ ൌ ܶ௧ାଵ െ ܶ௧ሺͶሻ݀௧ ൌ ο‫ݐ‬௧ ܷ௢௚ሺͷሻ೟షభ ǡఒ೟షభ ሻǡሺఝ೟ ǡఒ೟ ሻ൯௧‫߮݁ݎ݄݁ݓ‬ǡ ߣ݅݊‫ݏ݊ܽ݅݀ܽݎ‬೟షభ ǡఒ೟షభ ሻǡሺఝ೟షభ ǡఒ೟ ሻ൯൅ ݀௛ ൫ሺఝ೟షభ ǡఒ೟షభ ሻǡሺఝ೟ ǡఒ೟షభ ሻ൯ܷ௔௩௚ ൌ ݀௛ ௧ Ȁο‫ݐ‬௧
௧

ሺ͸ሻ
ሺ͹ሻ
ሺͺሻ

where ܶ is the timestamp of the AIS message, and ܶ௧ାଵ is referred to as the prediction
timestamp. We utilized implicit information because it enables the DL model to generatepredictions while using less information, rather than employing every possible explicit
information directly from the AIS messages (the selection is described in Section 4.1.2). The
above calculations (Eq. (3)–(7)) are empirical formulas such that the extraction is performed at
a high speed.
After retrieving the input and target, all input features ܺ௜ are standardized, similar to thetarget feature standardization shown in Eq. (9). The standard score of the target feature ‫ݕ‬௜ iscalculated as follows:‫ ݕ‬ᇱ ௜ ൌ ‫݀ݐݏ‬ሺ‫ݕ‬௜ ሻ ൌ ሺ‫ݕ‬௜ െ ‫ݕ‬ഥሻȀߪ
ప
௬೔

ሺͻሻ

where ‫ݕ‬௜ is the target feature containing ‫ݕ‬௜ ఒ and ‫ݕ‬௜ ఝ , ‫ݕ‬ഥప is the mean of ‫ݕ‬௜ , ߪ௬೔ is the standard
deviation of ‫ݕ‬௜ , and ‫ݕ‬Ԣ௜ is the standard score of ‫ݕ‬௜ . The standardization of the input and output
features avoids any imbalance in the network parameters and loss calculations during training.

21

Two sets of standardized input and target features, ሺܺԢ௜ ǡ ‫ݕ‬Ԣ௜ ఒ ሻ and ሺܺԢ௜ ǡ ‫ݕ‬Ԣ௜ ఝ ሻ, are then fed
separately into two independent DL models with the same model properties.
4.2.3. Performance Evaluation Metrics
Loss Score
Two separate models were trained for each standardized target feature ‫ݕ‬Ԣ௜ of οߣ௧ and ο߮௧values (scalar regression model). Subsequently, each value was discretely predicted. The
predicted vessel position was then generated by inverse standardization using thestandardization parameters of the target features as follows:‫ݕ‬ො௜ ൌ ‫ି݀ݐݏ‬ଵ ሺ‫ݕ‬ොԢ௜ ሻሺͳͲሻwhere ‫ݕ‬ො௜ is the prediction vector after inverse normalization, and ‫ݕ‬ොԢ௜ is the prediction vector
that combines the outputs of the two separate models (‫ݕ‬ොԢ௜ ఒ and ‫ݕ‬ොԢ௜ ఝ ). Both results (‫ݕ‬ොఒ and ‫ݕ‬ොఝ )are then transformed into latitude ߮ො௧ାଵ and longitude ߣመ௧ାଵ by the addition of each component
in the input (i.e., ߣ௧ , ߮௧ ). Finally, a new loss score for each result is calculated as follows:‫ܧܣܯ‬ఒ ൌ௠ͳ෍ หߣመ௜௧ାଵ െ ߣ௜௧ାଵ ห
݉
௜ୀଵ

ሺͳͳሻ

‫ܧܣܯ‬ఝ ൌ௠ͳ௜௜෍ ห߮ො௧ାଵെ ߮௧ାଵ
ห
݉
௜ୀଵ

ሺͳʹሻ

௜
where ߣመ௜௧ାଵ ൌ ൫‫ݕ‬ො௜ ఒ ൅ ߣ௜௧ ൯ is the prediction longitude, ߮ො௧ାଵൌ ቀ‫ݕ‬ො௜ ఝ ൅ ߮௧௜ ቁ is the prediction௜latitude, ߣ௜௧ାଵ is the target longitude, and ߮௧ାଵis the target latitude.

Metric Score
The metric scores for the combined results (i.e., location) were defined as the mean
distance error (MDE) and mean angular error (MaE). The distance error is the haversine
distance between the prediction and target (true position) in kilometers, signifying the extent
to which the result (prediction) deviates from the true position (target). MDE can be a single
evaluation metric for the long-term prediction of vessel location; however, in cases where thedistance between previous positions and target positions is remarkably diverse (owing to timeinterval variation), another evaluation metric is required.
The MaE as the second evaluation metric was calculated based on the three known pointsof the base, target, and predicted positions. The angular error between the target and theprediction is a spherical triangle that can be solved using the law of haversines [46]. Because
the haversine distance between the prediction and the target is small, the formula is derived in22

combination with the spherical law of cosine. Accordingly, these metric scores were calculated
as follows:‫ ܧܦܯ‬ൌ௠ͳ෍ ݀௛ ௜ሺ௩ǡ௪ሻ
݉
௜ୀଵ

ሺͳ͵ሻ

௠

ͳ
௜
‫ ܧܽܯ‬ൌ ෍ ‫ܥ‬ሺ௨ǡ௩ǡ௪ሻ݉ሺͳͶሻܿ‫ ݏ݋‬ቀ݀௛ ሺ௩ǡ௪ሻ ቁ െ ܿ‫ ݏ݋‬ቀ݀௛ ሺ௨ǡ௩ሻ ቁ ܿ‫ ݏ݋‬ቀ݀௛ ሺ௨ǡ௪ሻ ቁ‫ܥ‬ሺ௨ǡ௩ǡ௪ሻ ൌ   ቌቍ‫ ݊݅ݏ‬ቀ݀௛ ሺ௨ǡ௩ሻ ቁ ‫ ݊݅ݏ‬ቀ݀௛ ሺ௨ǡ௪ሻ ቁ

ሺͳͷሻ

௜ୀଵ

where ‫ ݑ‬is the base point ሺ߮௧ ǡ ߣ௧ ሻ, ‫ ݒ‬is the true position ሺ߮௧ାଵ ǡ ߣ௧ାଵ ሻ, and ‫ ݓ‬is the predicted
point ൫߮ො௧ାଵ ǡ ߣመ௧ାଵ ൯. The predicted position is in a vector space, and consequently, its distanceerror relative to the current position may not be proportional to its angular error. Figure 4-2
illustrates the relationship between distance and angular errors. Furthermore, the distance andangular errors can reflect the accuracy and precision of the prediction from the target,
respectively.

Figure 4-2. Relation between the distance error and the angular error

4.3. Baseline Model
A non-ML baseline and a sanity check were used as model-building guidelines to conduct
error analysis on bias and variance, gaining confidence in the overall performance of the DL
models. The baseline replicates a human-level performance as a proxy for the Bayes optimalerror in the classification problem [47].

23The predicted positions were defined as the next timestep positions averaging 24-hintervals, and consequently, a conventional formula for the dead reckoning position3 of the ship
could not be adopted as the baseline. The dead reckoning calculation is too simple for two
distant points; while it is accurate in the Euclidian space, it fails to map the Earth as a great
circle4. An equation for the geodesic on a spherical surface, namely the great circle equation,is more accurate for planning routes [48].
Therefore, the geodesic calculation was established as a baseline model, computed basedon the shortest distance on a spherical earth. Given a starting position (߮௧ and ߣ௧ ), current
course ߰௛ ௧ , and distance to the target (next position) ݀௧ , the destination point along a (shortest
distance) great circle arc is computed as follows:߮ු௧ାଵ ൌ ൫ሺ߮௧ ሻ ሺߜ௧ ሻ ൅ ሺ߮௧ ሻ ሺߜ௧ ሻ ൫߰௛ ௧ ൯൯ߣሙ௧ାଵ ൌ ߣ௧ ൅ ʹ൫൫߰௛ ௧ ൯ ሺߜ௧ ሻ ሺ߮௧ ሻ ǡ ሺߜ௧ ሻ െ ሺ߮௧ ሻ ሺ߮ු௧ାଵ ሻ൯

ሺͳ͸ሻ
ሺͳ͹ሻ

where ߮௧ ǡ ߣ௧ ǡ ߰௛ ௧ are in radians, ߜ௧ ൌ ݀௧ Ȁ‫ݎ‬௘௔௥௧௛ is the angular distance, and ‫ݎ‬௘௔௥௧௛ is the earth
diameter [49]. The results from Eq. (16) and (17) were subjected to normalization to degrees.
Additionally, the average distance interval of the ships was adopted as a sanity check,assuming that the next position always equals the present state. This approach is adopted to
examine the performance evaluation metrics between the current position ሺ߮௧ ǡ ߣ௧ ሻ and the next
position ሺ߮௧ାଵ ǡ ߣ௧ାଵ ሻ, calculated as follows:തതത௛ ൌ݀௠ͳ෍ ݀௛ ௜൫ሺఝ ǡఒ ሻǡሺఝ ǡఒ ሻ൯ ‫߮݁ݎ݄݁ݓ‬ǡ ߣ݅݊‫ݏ݊ܽ݅݀ܽݎ‬೟ ೟೟శభ ೟శభ
݉
௜ୀଵ

ሺͳͺሻ

where ሺ߮௧ ǡ ߣ௧ ሻ is the base point, and ሺ߮௧ାଵ ǡ ߣ௧ାଵ ሻ is the next position at 1-d interval.

3

in seamanship, a position determined by plotting courses and speeds from a known position.

4

also known as an orthodrome, is the largest circle that can be drawn around a sphere. Earth is

not a perfect sphere, but as long as the Arctic and Antarctic Circles are not included, allmeridians on Earth can be treated as great circles.
24

4.4. First Experiment: DL Model for the Indian Ocean
4.4.1. Experimental Setup
In the first experiment, a DL model was built for the Indian Ocean. The observed area iswithin 60°E–90°E longitude and 24°S–0°N latitude boundaries, covering 8.6 million square
kilometers5. Compared to all previous studies, the boundaries were relatively larger, adequately
capturing the continuous long-term movements of the vessels. Figure 4-3 presents thenormalized density distributions of the dataset in the observed area from nine years of AIS
messages involving 1531 different IMO numbers (vessels). This distribution was calculatedusing kernel density estimation (KDE), adopting a Gaussian kernel [50], in which thebackground geography was visualized using an open-source Python library Matplotlib
Basemap toolkit for geospatial data processing [51].

Figure 4-3. Normalized density distribution of AIS data in the observed Indian Ocean area
The dataset was split into a training set and dev-test sets according to the hold-out
validation split described in Section 4.1.3. The training set comprised more than 122,000 data
records after omitting AIS messages with missing values and abnormalities, whereas each dev
and test set contained more than 10,000 data records. The size of these sets was consideredsufficiently large, thus providing high confidence in the model performance.

5

calculated by geodesic area assuming the earth is a perfect sphere with a radius defined in

WGS84 as 6,378,137 m.
25

4.4.2. Error and Sensitivity Analyses
The MAE, as the performance evaluation metric of the model, is shown in Table 4-1; thesevalues correspond to the absolute deviation between the prediction point and the target point indegrees (longitude ߣ and latitude ߮). The results from the geodesic calculations were computed
based on the training set.
Interestingly, the DL model performance on the training set and dev set surpassed thegeodesic calculation as the baseline model. The model displayed minimal bias, fitting thetraining and dev sets satisfactorily. In practice, the sole focus of a regression model is not thedeviation between the training loss and dev loss (i.e., variance), but rather its prediction
performance, that is, the dev loss. Nevertheless, the variance in the model was insignificant,indicating that the model generalized very well to the dev set without overfitting.
Table 4-1. Error analysis of the DL model
Model

ࡹ࡭ࡱࣅ

ࡹ࡭ࡱ࣐

Geodesic calculation

0.225

0.226

Training set

0.163

0.145

Dev set

0.169

0.147

Moreover, hyperparameters sensitivity of the DL model was carried out while also
applying regularization techniques to confirm further that the model generalized very well tothe dev set. All hyperparameters combinations were permutated except the structure of hidden
layers and their units to see the effect on prediction performance from hyperparameters'
influence. This permutation was repeated for other models with regularization: 20% and 40%
dropout on all hidden layers and a model with batch normalization.
Figure 4-4 shows the hyperparameters sensitivity of all models. The selected
hyperparameter proved to be the best combination for the standard DL model. The model withno regularization achieved the most optimum error compared to other models withregularization, confirming that the model was already generalized well without overfitting.
Applying dropout worsened the model performances than applying batch normalization.
Naturally, predictions of longitude values would have accuracy less than latitude values since
the longitude values have a distribution twice as large as latitude. This natural divergenceappears to negatively affect the model with batch normalization but with the expense of
accuracy.

26

Figure 4-4. Sensitivity analysis of the DL model
Based on these error and sensitivity analyses, we determined that the proposed deeplearning model achieved an optimal error with generalization to the dev set and was ready forthe evaluation on the unseen test set resembling a practical scenario.
4.4.3. Results and Discussions
The performance evaluation metrics of the DL and baseline models are presented in Table
4-2. All results were computed using the test set. The average distance interval indicates thedifference between the current vessel position and the subsequent position. Compared withthese average values, the geodesic calculation appears to be reasonably accurate for long-term
predictions.
The DL model adequately outperformed the baseline model and almost doubled its
performance based on the metric scores. Given that the distance between the current positionof a vessel and its position the next day was approximately 486 km, the geodesic calculation
might be accurate for long route planning, yielding an average distance error of 40 km. However,the DL model generated more accurate and precise predictions with a slight mean distance errorof approximately 25 km and a mean angular error of 1.8°. If we assume that the evaluation
metric (i.e., ‫ ) ܧܦܯ‬of the average distance interval created an error of 100%, simulating amodel performance similar to the classification problem, the geodesic calculation and DL
model predicted the vessel positions with 8% and 5% error, respectively.
Moreover, several ensemble-based ML regressors have been investigated, including
random forest, gradient boosted decision trees, and extreme gradient boosting algorithm(XGBoost) [52, 53]. The hyperparameters were tuned using the exhaustive grid search method,
and therefore, all hyperparameters were optimized for each ML model in this manner. With the27same input, output, and validation splits, the performances across all the models were broadly
comparable. Nevertheless, despite performing more accurately than the geodesic calculation,
their performances were not significantly different from each other, among which the DL model
still achieved the best performance (13% better than the ML models).
Table 4-2. Comparison of the model performance
Methods

Loss

ࡹࡰࡱ

ࡹࢇࡱ

ࡹ࡭ࡱࣅ

ࡹ࡭ࡱ࣐

(km)

(degree)Average distance interval
Geodesic calculation
Deep learning

3.553
0.239
0.174

2.564
0.239
0.149

486.1
40.6
27.0

3.3
1.7

Random forest
Gradient boosted decision tree
XGBoost

0.197
0.198
0.197

0.174
0.171
0.175

31.3
31.4
31.6

2.1
2.3
2.2

Results from the DL model compared with the baseline model can be analyzed further by
its distribution, which is plotted in Figure 4-5. The 2D plot represents more than ten thousand
test data of vessels' previous position, plus their next position predicted by geodesic calculationand the DL model with axis in degrees longitude and latitude. To demonstrate the accuracy ofthe predictions, all plotted points were normalized relative to the true position (target)
positioned at (0,0). The sparsely distributed plots of vessels' previous position (blue dots) werecaused by the time interval of AIS messages, affecting their distance intervals between theprevious position and target (next position). Their dense plot past Southwest-Northeast
direction was due to the typical pattern of shipping lanes in the Indian Ocean (see Figure 4-3).
Nevertheless, the geodesic calculation and DL model generated precise predictions, atwhich the model confirmed better accuracy and precision, converging on the target: thestandard deviation of the model predictions was slightly lower than the geodesic calculation
with 0.40 and 0.43, respectively; 92% of the predictions were within one standard deviationfrom the mean, more precise than the geodesic calculation with only 87%.

28

Figure 4-5. Normalized plot distribution of the result in the Indian Ocean area from 10,888
vessel positions

4.5. Second Experiment: DL Models for the International Open Waters
4.5.1. Experimental Setup
In the second experiment, 12 DL models were built for six open oceans and six maritime
chokepoints with the same model properties to assess the influence of the respective areas.
Open waters of the North Pacific Ocean (NPO), South Pacific Ocean (SPO), North Atlantic
Ocean (NAO), South Atlantic Ocean (SAO), Indian Ocean (IO), and Philippine Sea (PS) wereselected considering that vessels generally sail across these deep oceans without stopping.
According to Rodrigue (2020), the primary maritime shipping chokepoints were selected torepresent long-term vessel behavior near the ports and congested (high-traffic) waters, namely,
Gibraltar Strait (GS), South Africa Coast (SAC), Bab al-Mandab Strait (BMS), Strait of
Hurmuz (HS), Laccadive Sea (LS), and Malacca Strait (MS) [54]. Altogether, the ocean andchokepoint areas correspond to the simple and complex movement of ships, respectively.
Figure 4-6 shows the location and size of each area (red rectangles). The size of theobserved maritime chokepoint area was as large as that of the open ocean. Each has the sameobservation area size: within 30-interval longitude and 24-interval latitude, covering more thaneight million square kilometers. The same procedure as in the first experiment was applied tothe models: each used the same model properties and followed a similar hold-out validation
split. We limited the worldwide observation to these 12 areas to avoid building an excessively
large model. A large model is prone to fit noise from inferior-quality data and random vessel

29behavior contained in the massive AIS dataset. Regularization methods might be a constructive
solution; however, they require an extremely large model to fit all nonlinear problems.

(a)

(b)
NPO, North Pacific Ocean; SPO, South Pacific Ocean; NAO, North Atlantic Ocean; SAO, South Atlantic
Ocean; IO, Indian Ocean; PS, Philippine Sea; GS, Gibraltar Strait; SAC, South Africa Coast; BMS, Bab alMandab Strait; HS, Strait of Hurmuz; LS, Laccadive Sea; MS, Malacca Strait.

Figure 4-6. Location of the observed areas: (a) open oceans and (b) maritime chokepoints
4.5.2. Results and Discussions
The performance evaluation metrics of the models for each examined area are listed inTable 4-3. Again, the DL models substantially outperformed the geodesic calculation as thebaseline model in all areas, especially in the chokepoint areas. The improvement score (‫ܫ‬௦ ) was
the only inference to determine the extent to which the DL model outperformed its counterpart
baseline model based on the MDE scores. The improvement scores were notably higher in the
chokepoint areas than in the open ocean areas, scoring more than a 50% improvement over thebaseline model for almost all the chokepoint areas. The geodesic calculation appears accurateenough to predict moving vessels; however, it fails to predict vessel behavior near the ports
and high-traffic areas (i.e., the chokepoint areas). With no information regarding vessel status,
historical trajectory, or destination, conventional calculations would fail.
The effect of a high improvement score can be seen by the normalized results distribution
plot from Malacca Strait’s model (see Figure 4-7), where the DL model was vastly superior togeodesic calculation. Vessel behavior in this area was widely dispersed in terms of voyage
direction and time interval. The scattered results of the geodesic calculation from the target30

demonstrated the failure of the conventional method to estimate vessel position in this area.
Nevertheless, supported by a considerable amount of training data, the model could learn
intricate and high-level structures in its deep layers, generating predictions with significant
performance than the baseline model.
Table 4-3. Comparison of the loss and metric scores of the DL model and baseline model oneach observed area
DL Model
Loss

Area

ࡹࡰࡱ

ࡹࢇࡱ

ࡹ࡭ࡱࣅ

ࡹ࡭ࡱ࣐

(km)

(deg)

NPO
SPO
NAO
SAO
IO
PS

0.18
0.13
0.30
0.13
0.17
0.25

0.13
0.11
0.22
0.11
0.15
0.31

27
20
41
19
27
48

1.8
1.5
3.7
1.7
1.7
8.0

GS
SAC
BMS
HS
LS
MS

0.54
0.35
0.28
0.34
0.26
0.37

0.27
0.23
0.31
0.27
0.33
0.34

63
46
51
52
51
63

21.7
15.4
4.3
39.8
37.4
16.7

Geodesic Calculation

Number Average

Loss

ࡵ࢙
(%)

ࡹࡰࡱ

ࡹࢇࡱ

of TestDistance

ࡹ࡭ࡱࣅ

ࡹ࡭ࡱ࣐

(km)

(deg)

Data

Interval

27
15
15
24
33
37

0.20
0.13
0.33
0.15
0.24
0.48

0.23
0.15
0.28
0.15
0.24
0.46

37
24
48
26
41
77

3.1
2.1
4.5
2.5
3.3
10.5

471
499
2474
4672
10888
9206

485
484
467
491
486
453

38
50
55
58
50
60

0.78
0.59
0.56
0.77
0.57
0.88

0.53
0.54
0.75
0.70
0.63
0.93

102
92
113
123
102
158

20.2
15.0
10.9
31.0
27.8
19.5

4263
13337
1251
3734
5975
22745

355
389
473
259
273
417

In Figure 4-7, Gaussian KDE was computed to approximate the probability density
function of each three different vessel positions: previous position, geodesic calculation, andmodel prediction. The results are plotted in their normalized density by each latitude andlongitude. A 1D plot of each vessel's position is also plotted to explain each distribution. The
superior accuracy and precision of the model compared to the geodesic calculation wereconfirmed by the standard deviation of 0.89 and 2.06 and the population within one standard
deviation from the mean of 92% and 87%, respectively.
Both the DL model and geodesic calculation showed more accurate predictions for theocean areas than the chokepoint areas, but not in the average distance intervals between thecurrent position and the next position, indicating that more vessels have shorter distanceintervals in the chokepoint areas. Almost all vessels were moving in the ocean areas, whereas
in the chokepoint areas, many vessels were idle for berthing or resting at anchorages. These31

activities resulted in an extremely short distance interval between two consecutive AIS
messages at any time interval.

Figure 4-7. Normalized plot distribution of the result in Malacca Strait (MS) from 22,745
vessel positions
Figure 4-8 shows the distance-interval distribution of AIS data on both areas; the distanceintervals were calculated from the haversine distance between the base point ሺ߮௧ ǡ ߣ௧ ሻ and thenext position ሺ߮௧ାଵ ǡ ߣ௧ାଵ ሻ . Many vessel activities have very low distance intervals in the
chokepoint areas but not in the ocean areas. Consequently, the average distance intervals in the
chokepoint areas would indicate lower performance evaluation metrics than the ocean areas.
The irregularity of idle vessels and activities other than sailing with minimal distance intervals
renders the MaE unsuitable as a metric score. The angle between the prediction and the target
no longer corresponds to the accuracy of the prediction because the distance interval between
two consecutive positions is extremely short. Accordingly, for the evaluation of the chokepoint
areas, the MDE alone suffices as a single metric score.

32

Figure 4-8. Distance-interval distribution of AIS data on the ocean and chokepoint areas
4.5.3. Discussions: Influence of the Area
Figure 4-9 presents the distance error distribution of the predicted positions based on the
distance interval, where the distance errors are the haversine distance between the true positionሺ߮௧ାଵ ǡ ߣ௧ାଵ ሻ and the predicted point ൫߮ො௧ାଵ ǡ ߣመ௧ାଵ ൯.
In the ocean areas, as most data have distance intervals between 400 and 600 km, the DL
models generated continuous accurate predictions with a distance error below 40 km for 80%of the population over the entire test set. For the same 80% population, the geodesic calculation
generated a distance error below 60 km with a more diverse distribution, where its standard
deviation was twice as high as that of the DL models.
In the chokepoint areas, as most data have distance intervals distributed between 400 km
and near zero, the DL models constantly generated accurate predictions with a distance error
below 65 km for 80% of the population. In contrast, the geodesic calculation generated
projections with distance errors below 100 km for only 65% of the population. Its projections
resulted in grave errors when the distance intervals were broad, but the errors became lesssevere when the distance intervals were near zero. Overall, the geodesic calculation fails to
make accurate projections for the complex movements of vessels in chokepoint areas.
Deep learning systems can learn from large datasets to effectively improve theirperformance to generate accurate predictions by discovering complex variations across all
input features [55]. Accordingly, we computed the mean PFI score of the DL models on theocean areas and chokepoint areas to determine which features play a vital role in improving theoverall performance (shown in Figure 4-10). The scores were calculated based on the test setof each area and were grouped by ocean and chokepoint areas and then averaged. The input
features were classified into five components: distance, speed, angle, time, and position.

33

Figure 4-9. Distance error distribution of the predicted positions based on the distanceinterval on ocean areas (left) and chokepoint areas (right): DL model (top) and geodesic
calculation (below).
Based on the results for both the chokepoint and ocean areas, the speed component of thevessel (i.e., ܷ௢௚ , ܷ௔௩௚ ) does not appear to be essential because the distance ݀ alreadyrepresents it, whereas the course over ground ߰௢௚ proves vital for making predictions.
Models in the ocean areas rely primarily on input features of angle and distancecomponents but not on speed and position components; this is similar to the geodesic
calculation, which generally proved accurate for position projections of vessels moving in adefinite straight direction or making simple movements.
Meanwhile, models in the chokepoint areas rely more on the current position (i.e., ߣ௧ , ߮௧ ),implying that they can be used to develop high-level abstraction to alternatively predict thenext position when vessels deviate from a simple trajectory. Furthermore, focusing on the
distance component, they also rely more on the distance ݀ as a rough estimate of the distanceinterval to the next position than the haversine distance ݀௛ and Manhattan distance ݀௠ as the
distance interval between the current position and the previous position, suggesting that theprevious position of the vessel at ‫ ݐ‬െ ͳ is not as important as its current position at ‫ ݐ‬and arough estimate projection at ‫ ݐ‬൅ ͳ. Nonetheless, the utilization of all input features may not34

suffice to cover the entire range of unexpected vessel behavior near ports or with complex
movements.

Figure 4-10. Mean PFI score of the DL models on the ocean areas (left) and chokepoint areas(right)
The model performance can be enhanced by incorporating additional information
regarding the vessel status, destination, or historical trajectory without a trajectory definition;
thus, this approach remains a topic to explore in our future work.
4.5.4. Discussions: Influence of Data Size
The proportion of AIS messages varied widely according to the area location. Thisvariability among different areas is a general characteristic of AIS data: rarely passed areas
contributed only a limited amount of data, whereas congested areas contained a substantial
quantity of information. Figure 4-11 presents the size distribution of the training and dev-test
sets in each observed area based on the same hold-out validation split.
The proportion of the dev-test sets to the training set increased in the areas with the busiest
shipping routes; for instance, the Malacca Strait (MS) area encompasses half of South East
Asian waters, including the most congested maritime primary chokepoints and three secondary
chokepoints in Indonesian waters [54]. The proportion was drastically reduced in the rarelytransited areas, such as the Pacific Ocean. Consequently, areas with a small amount of test data
would indicate lower confidence in the overall performance of the model than areas withextensive data. The K-fold validation split can solve this problem; nonetheless, it would
produce non-comparable models.

35

Figure 4-11. Size distribution of the training set and dev-test sets for each area
The dataset size affects deep learning performance, as a small amount of training data may
degrade the performance [56]. We recreated the DL model for the Malacca Strait (the area withthe most extensive dataset size) for each variation in the training set to show the effect of thedata size on the model performance (see Figure 4-12). The most significant improvement in
the performance occurred when the training set size exceeded 25,000. The model performance
began to stabilize when the training set reached approximately 200,000. This effect may not
represent all areas because three areas have a small dataset of less than 25,000 thresholds (i.e.,
NPO, SPO, BMS); however, all the models were trained with eight years of data, and are thus
still capable of producing accurate predictions.

Figure 4-12. Effect of dataset size on the deep learning performance in Malacca Strait (MS)36

4.6. Third Experiment: Application of the DL Model
4.6.1. Experimental Setup
In the third experiment, a DL model was built for the Malacca Strait (MS) area, and asample location was selected in which the number of ships was counted each day consecutively,
resembling a simulation of practical application. In the MS area, ships traveled approximately
417 km daily on average (see Table 4-3). Thus, the Malacca Strait itself, between Malaysia andIndonesia (95.2°E–103.2°E longitude and 0.5°N–6°N latitude), was selected as the sample
location, covering an area of half a million square kilometers. Figure 4-13 shows the sample
locations in the MS area. As the highest density area, Singapore waters were not included in
the sample because there would be many outliers in the northeast and southeast portions thatenter the observed sample location. Nonetheless, long-term ship behavior near ports can beobserved on Malaysia’s Teluk Rubiah port inside the location.

Figure 4-13. Location of the observation area (red-filled square): the Malacca Strait; thenormalized density distribution is calculated based on the test set
For the application, uninterrupted AIS data for a period of time were required as the test
set. Consequently, the previous hold-out validation split cannot be applied because the test anddev sets are equivalently derived from shuffled 2018 data; in addition, the training and dev sets
have to be generated in the same manner as the models in the previous experiment to produce
a generalized DL model similar to the previous experiment.
Accordingly, a different scheme for the hold-out validation split was developed. Randomly
shuffled AIS data from July 2010 to September 2017 were used as the training set, while
randomly shuffled data between October 2017 and September 2018 were used as the dev set.
The last three-month data were not randomized and were retained chronologically as the test37

set, as shown in Figure 4-14; the predictions were processed sequentially, day by day, rather
than instantaneously. Subsequently, the number of ships was counted at the selected locations
every day.

Figure 4-14. Hold-out validation split for the third experiment (non-proportional scale)
4.6.2. Results and Discussions

(a)

(b)
Figure 4-15. Fitted plots of the daily prediction of the number of ships in the Malacca Straitfrom October to December 2018: (a) DL model and (b) geodesic calculation
The fitted plots of the overall results from the DL models and geodesic calculations werecompared to the actual data, as shown in Figure 4-15. The results are the daily prediction of thenumber of ships inside the Malacca Strait from October to December 2018. The r-value
measures the linear relationship between the predictions and actual values. Compared to theactual data, a strong relationship with the r-value of 0.83 from the DL model confirms that38

predictions with an average time interval of 24 h using deep learning are possible, which iscontrary to the belief that the motion-based method is not effective for long-term vessel location
prediction. By using proper DL systems and massive data, this result confirms that an accurate
long-term prediction of the vessel position can be generated with the straightforward motionbased method. In contrast, the geodesic calculation showed a weak relationship with an r-valueof 0.51, suggesting that conventional calculations cannot be used for the long-term position
projection of a vessel moving in congested waters or near the ports.

Figure 4-16. Daily prediction of the number of ships in the Malacca strait in November 2018
Moreover, Figure 4-16 shows the daily prediction of the number of ships inside the sample
location for the entire month of November 2018; the estimated target values from the DL modeland geodesic calculations were compared to the ground truth target values. The DL model
proved that it can accurately predict the quantity inside the location for an entire day without
additional information regarding historical navigational status. Meanwhile, as the geodesic
calculation failed to predict the long-term position of a vessel moving in congested waters ornear the ports, it also failed to predict the number of ships.
Detailed ship position predictions inside the sample location are shown in Figure 4-17.
The ship position prediction from the DL model and geodesic calculation in the Malacca Strait
was compared with the actual position on November 10 and 11, 2018. In this location, mostships were moving, and some were idle near Malaysia’s Teluk Rubiah port. Examining theactual data on November 9, there was a line of ships moving from the northwest to thesouthwest, three of which were separated at the rear. These three ships moved to the southwest
the next day, and another line of ships appeared from the northwest, which eventually was thestart of a congested line of moving ships that appeared on the 11th. The DL model closely
mimicked the position of these ships and the movement of the ground truth targets on
November 10 and 11, even for ships idling at the port. The number of ships and their positions
39

were reliably predicted by the model. From these results, the dl model appears to have a senseof the dimension of the geographic coordinate system that can be or is often passed. In contrast,
geodesic calculation failed to predict the position of the ships either in the moving position oridle near ports, and also resulted in a poor estimate of the number of ships inside the area.

Figure 4-17. Ship positions in the Malacca strait on three consecutive days in November
2018: TP is the true position (left), DL is the deep learning prediction (center), and GC is thegeodesic calculation (right)

4.7. Discussions on Performance of End-to-end Deep Learning Models
4.7.1. Comparison of End-to-end DL Models
The MLP model shows a remarkable performance compared to the ensemble-based ML
models and conventional approach from the dataset with the long-time-interval distribution.
End-to-end means that the approach does not need a trajectory reconstruction and otherpreprocessing/postprocessing steps for making a prediction.
To further clarify the robustness of end-to-end DL-based models, we built two DL-basedmodels: Deep RNN and LSTM. These sequence-based DL architectures were built with thesame input, output, and validation splits to the MLP model so that their performances arebroadly comparable (the structure was also constructed as closely as possible to the MLP model
40

while also tuned to the most optimized). The input does not go through an interpolation or
trajectory reconstruction to ensure an equivalent model; it already carries information regarding
time interval ο‫ ݐ‬and a rough distance ݀௧ to the target. The Deep RNN and LSTM models have
five hidden recurrent layers with recurrent units of [64, 64, 32, 32, 16] and a one-unit linear
output layer; the model was trained in mini-batch with the loss function of mean absolute error(MAE) optimized by Adam. The stacked deep recurrent layers were easily prone to overfit thetraining set (LSTMs are much easier), which was alleviated using a combination of recurrent
dropout and recurrent layer normalization.
The Indian Ocean and Malacca Straits areas similar to the second experiment, representing
the simple and complex movement of ships on the ocean and chokepoint areas, respectively,
were selected as a definitive test for the DL-based models. The overall prediction methodologyof these two recurrent models is similar to the second experiment. The models were also set togeneralize on the data at which the training set was shuffled. The number of steps wasconsidered one-time steps: the input only contains information at time step‫( ݐ‬the implicit
information of ‫ ݐ‬െ ͳ is included) to make a prediction at ‫ ݐ‬൅ ͳ , and thus this resembles amultivariate time series with a single time step.
Table 4-4. Comparison of the deep learning model performance
Areas

Methods

Indian Ocean(IO)

Malacca Strait
(MS)

Loss

ࡹࡰࡱ

ࡹࢇࡱ

Training

ࡹ࡭ࡱࣅ

ࡹ࡭ࡱ࣐

(km)

(degree)Time (s)

MLP
RNN
LSTM

0.174
0.176
0.177

0.149
0.150
0.148

27.0
27.4
27.3

1.7
1.7
1.7

1,699
2,758
1,845

MLP
RNN
LSTM

0.376
0.384
0.381

0.337
0.335
0.336

62.8
63.6
63.4

16.9
16.6
16.2

4,257
6,561
6,243

The performance of the DL-based models is presented in Table 4-4. The results of the
proposed MLP model in the ocean and chokepoint areas are slightly more accurate than theother DL architectures. However, with only a 1% improvement, the performance of the feedforward model is considered similar to the recurrent models (RNN and LSTM) that have moretrainable parameters; applying more computational cost and complex models appear tonegatively improve the performance. The MLP model took the fastest total training times onboth areas with the least parameters than the other DL models. These results were obtained ona single Intel i7-9700K processor (8 CPU @3.60 GHz).
41

The patterns observed result from the small sequences (time steps), at which the regularfeed-forward network is sufficient for this task. This is confirmed as the application of the
LSTM model did not deliver better performance than the RNN model since LSTMs capability
is much better at handling long sequential data than simple RNNs with limited short-term
memory. The results correspond to Gers et al. (2002) that tested RNNs and LSTMs for timeseries predictions, but the results were poor as simple multilayer perceptrons (MLPs) often
outperformed LSTMs when applied to the same data [57].
4.7.2. Comparison of End-to-end DL Models on Small Dataset
A small dataset with short-time intervals near the ports was used to further analyze therobustness of the end-to-end DL models. The dataset was retrieved from the ATD2019
challenge dataset6. All AIS training and challenge data with different properties were combined
and used to construct a dataset with varying time-interval distribution. Figure 4-18(a) shows
the short-time-interval distribution of the small dataset averaging around 10 seconds intervals;
most of the data have near-real-time intervals, and the rest varies up to 60 seconds. The dataset
consisted of ships movements near ports located around north of Norfolk, Virginia, North
America (see Figure 4-18(b)). In this dataset, course over ground ߰௢௚ is given but not heading߰௛ , and therefore, to accommodate the same 10 input features as the previous experiments, theheading was copied from the course over ground.
The dataset was split into a training set and dev-test sets according to the hold-out
validation split with 80% data for training and the rest 20% for validation and test. The training
set comprised more than 90,000 data records, whereas each dev and test set contained morethan 10,000 data records. The size of these sets was considered sufficiently large, thus
providing high confidence to the overall result.

6

https://gitlab.com/algorithms-for-threat-detection/2019/atd2019.

42

(a)

(b)
Figure 4-18. The small dataset properties: (a) Time-interval distribution; (b) Normalized
density distribution
The results show that compared to the conventional approach, the DL-based models are
not as effective as on the long-term prediction task, and the LSTM model delivers the same
performance as the feed-forward networks since the time steps are limited (single time steps
with 10 dimensions). This limited sequence allows the feed-forward networks to deliver
optimum performance but would not maximize the potential of the sequence-based recurrent
networks. Moreover, on the dataset with varying time-interval distribution and without
trajectory reconstruction, the feed-forward networks generated predictions as accurate as of the
LSTM with faster training times and less trainable parameters.
Table 4-5 shows the results from the DL models and geodesic calculation on the small
dataset. According to the second experiment results, the pattern of MaE on the small dataset
confirms that the dataset consists of vessel behavior near ports with short-distance intervals
such as berthing, idling, and maneuvering. The average distance interval between two
consecutive AIS points is 24.6 meters. At this small distance, the geodesic calculation isqualitatively similar to the dead reckoning calculation with an error of around 3.5 meters. The
DL models are 8% better than the geodesic calculation. Naturally, LSTMs can generate the43most accurate short-term predictions of vessel position; however, on this dataset with theuneven distribution and without trajectory reconstruction, the MLP model generated
predictions as accurate as of the LSTM with almost half of the training times.
The results show that compared to the conventional approach, the DL-based models are
not as effective as on the long-term prediction task, and the LSTM model delivers the same
performance as the feed-forward networks since the time steps are limited (single time steps
with 10 dimensions). This limited sequence allows the feed-forward networks to deliver
optimum performance but would not maximize the potential of the sequence-based recurrent
networks. Moreover, on the dataset with varying time-interval distribution and without
trajectory reconstruction, the feed-forward networks generated predictions as accurate as of the
LSTM with faster training times and less trainable parameters.
Table 4-5. Comparison of the model performance on the small dataset
Methods

Loss

ࡹࡰࡱ

ࡹࢇࡱ

Training

Totalࡹ࡭ࡱࣅ (10-5) ࡹ࡭ࡱ࣐ (10-5)(m)(degree)Time (s)ParamsAverage distance int.
Geodesic calculation

19.7
2.4

12.1
2.1

24.6
3.5

29.2

-

-

MLP
RNN
LSTM

2.3
2.4
2.3

1.8
1.8
1.7

3.2
3.3
3.2

31.5
31.4
31.4

922
2,537
1,693

8,545
19,041
76,1134.8. Conclusions on one-day interval of ship position prediction
This research demonstrated that predictions with an average time interval of 24 h arepossible, confirming that the straightforward motion-based method can generate an accurate
long-term prediction of the vessel position. The DL models generated more accurate
predictions than the geodesic calculation as the baseline model in all areas. Predictions in the
open ocean areas yielded higher accuracy than in the chokepoint areas; however, compared to
the geodesic calculation, the improvement scores were higher in the chokepoint areas than in
the ocean areas since the geodesic calculation failed to predict vessel behavior near the ports
and congested waters. The DL model can predict the complex movement of ships near ports
and congested routes, whereas conventional calculations fail, with no information regarding
vessel status, historical trajectory, or destination. The last experiment demonstrated that the DL
model appears to have a sense of the dimension of the geographic coordinate system that canbe or is often passed, wherein the chokepoint areas rely more on the input features of the current
44

latitude and longitude of the vessels. Moreover, on the dataset with varying and uneven timeinterval distribution and without a trajectory reconstruction, the proposed MLP model
generated predictions as accurate as the LSTM with faster training times.
This research can be a basis for future research for further improvement or even longer
time intervals. Additionally, the generated predictions can be directly utilized for any further
actions depending on the maximum error threshold the prediction model allows; the final model
can then be launched into production. After launching, the model can be trained incrementallywith new data on the fly in line with the growth of AIS data over time, further improving themodel.

45

Chapter 5
Several-day Intervals of Ship Position Prediction
5.1. Overview of Several-day Intervals of Ship Position Prediction
The previous chapter demonstrates that a one-day interval prediction of vessel position
using the straightforward motion-based method is feasible with deep learning, more accurate
than another machine learning algorithm, and much more accurate than the conventional
approach. In the previous chapter, the selected observation size is large enough to capture thelong-term movement of ships, with the time interval averaging 24 h. However, the optimum or
minimum coverage size to capture the long-term ship movement according to the respective
time intervals is not yet established.
This research continues the work in the previous chapter, utilizing deep learning and AIS
data to predict ship position at four different time intervals: from 24 h to 96 h. This chapter
aims to achieve up to a 4-d interval of ship position prediction and resolve the topics regarding
optimum coverage size on each magnified time interval. As the distance traveled by moving
ships in a straight line is proportional to the time interval, if the time interval is magnified, theobservation area size must also be expanded or magnified. Additionally, to cope with theextensive coverage, hence data handled, we utilized a new deep learning model with deeper
layers and bigger networks than the model used in the previous chapter.
This research consists of three experiments followed by discussions regarding the singleworldwide model and the limitations of the prediction models. In the first experiment, larger
networks of DL models were trained on different observation area sizes with magnified timeintervals. We focused more on observation size variations in the next experiment, increasing 4
and 3.2 degrees on longitude and latitude, respectively. In the last experiment, five DL models
were built for five major locations of maritime shipping routes focused on Capesize bulk
carriers. In the discussion section, a single-worldwide model was executed, and research
limitations such as outliers and AIS data uncertainty are discussed. Finally, the research's
conclusion is presented at the end of this chapter.
The several-day intervals of ship position prediction in this thesis is detailed in thefollowing chapter.

46

5.2. Methodology
The overall method for this research is almost similar to the previous chapter. The
differences are that the set of input features ܺ௜ and target features ‫ݕ‬௜ comprising vessel
positions were created based on the next time step ‫ ݐ‬൅ ‫ݐ‬௧ , where ‫ݐ‬௧ is the time-interval target(in days). Moreover, a larger deep learning model was utilized as a vector regression model,
generating both the displacements in longitude and latitude directions at the same time.
5.2.1. Model Structure and Properties
Through extensive experimentation and evaluation based on the previous research, wedeveloped a deep feed-forward model with the objectives of performance and generalizationon the wider observation area and time intervals. The deep MLP architecture was constructed
as a vector regression model to solve regression problems by setting the target as two scalar
outputs (vector): the displacements of longitude ∆λ and latitude ∆φ directions. Compared tothe previous research that set the target as a scalar value, hence one model for each target, thismodel can solve the same problem with half of the running time.
The model used a deeper and bigger network with eleven layers: triangle-shaped ten
hidden layers with selu activation function and LeCun initialization and a two-unit linear output
layer [98, 98, 88, 58, 44, 43, 32, 28, 26, 16, 2]. The mean absolute error (MAE) was still
employed as the loss function since it is less sensitive to outliers, particularly when used in thelarger observation area. A larger mini-batch size of 256 was used for training to fasten
computation time with GPU as more training data were utilized extensively. Similarly, we used
an adaptive learning rate method involving the adaptive moment estimation optimization
algorithm (Adam); the learning rate was automatically reduced by a factor of 0.5 once thevalidation loss stagnated for 20 epochs. A validation-based early stopping was set to interrupt
training once the validation stopped improving for 100 epochs. Moreover, a hold-out validation
split was applied similar to the previous research.
5.2.2. Input and Target Features
As the overall method of ship position prediction with several-day intervals is similar tothe previous research with one-day intervals, the input matrix ܺ௜ is still composed of the same
10 features or vessel states at the current time step ‫ ݐ‬. Meanwhile, the target vector ‫ݕ‬௜ iscomposed of the displacements of longitude οߣ and latitude ο߮ between the current time step‫ ݐ‬and the next time step ‫ ݐ‬൅ ‫ݐ‬௧ , following the DL output as a vector regression model. The input

47

matrix and target vectors are retrieved from the SQL database given a boundary condition oflocation and time, expressed as follows:ܺ௜ ൌ ቄߣ௜௧ ǡ ߮௧௜ ǡ ܷ௢௚ ௜ ǡ ߰௢௚ ௜ ǡ ߰௛ ௜௧ ǡ ο‫ݐ‬௧௜ ǡ ݀௧௜ ǡ ݀௛ ௜௧ ǡ ݀௠ ௜௧ ǡ ܷ௔௩௚ ௜ ቅሺͳሻ‫ݕ‬௜ ൌ ൛οߣ௜௧ ǡ ο߮௧௜ ൟ

ሺʹሻ

௧

௧

௧

where ݅ ൌ ሼͲǡͳǡ ǥ ǡ ݉ሽ , οߣ௧ ൌ ߣ௧ା௧೟ െ ߣ௧ is the longitude interval, ο߮௧ ൌ ߮௧ା௧೟ െ ߮௧ is thelatitude interval, subscript ‫ ݐ‬represents the time step, and subscript ‫ݐ‬௧ represents the target
interval in day(s).
Similarly, input features of ߣ, ߮, ܷ௢௚ , ߰௢௚ , and ߰௛ are extracted directly from the archived
AIS messages at the current time step ‫ ݐ‬. Some of the remaining inputs provide implicit
information on the position history at the previous time step ‫ ݐ‬െ ‫ݐ‬௧ . The target timestamp (atthe next time step ‫ ݐ‬൅ ‫ݐ‬௧ ) is represented as a time interval ο‫ ݐ‬and a rough distance to the target݀௧ . They are defined as follows:݀௛ ௧ ൌ ݀௛ ቀ൫ఝ݀௠ ௧ ൌ ݀௛ ቀ൫ఝο‫ݐ‬௧ ൌ ܶ௧ା௧೟ െ ܶ௧ሺ͵ሻ݀௧ ൌ ο‫ݐ‬௧ ܷ௢௚ሺͶሻ೟ష೟೟ ǡఒ೟ష೟೟ ൯ǡሺఝ೟ ǡఒ೟ ሻቁ௧‫߮݁ݎ݄݁ݓ‬ǡ ߣ݅݊‫ݏ݊ܽ݅݀ܽݎ‬ሺͷሻ൅ ݀௛ ቀ൫ఝ

ሺ͸ሻ೟ష೟೟ ǡఒ೟ష೟೟ ൯ǡ൫ఝ೟ష೟೟ ǡఒ೟ ൯ቁ೟ష೟೟ ǡఒ೟ష೟೟ ൯ǡ൫ఝ೟ ǡఒ೟ష೟೟ ൯ቁܷ௔௩௚ ൌ ݀௛ ௧ Ȁο‫ݐ‬௧௧ሺ͹ሻwhere ܶ is the timestamp of the AIS message, and ܶ௧ା௧೟ is referred to as the prediction
timestamp.
After extracting the input and target at high speed, all input features ܺ௜ and target features‫ݕ‬௜ are standardized. The standard scores are calculated as follows:ܺ ᇱ ௜ ൌ ‫݀ݐݏ‬ሺܺ௜ ሻ ൌ ܺ௜ െ ܺഥప Ȁߪ௑೔ሺͺሻ‫ ݕ‬ᇱ ௜ ൌ ‫݀ݐݏ‬ሺ‫ݕ‬௜ ሻ ൌ ‫ݕ‬௜ െ ‫ݕ‬ഥȀߪ
ప ௬೔

ሺͻሻ

where according to the corresponding features, the accent ҧ is the mean, ߪ is the standard
deviation, and the superscript Ԣ is the standard score. The standardized input and target featuresሺܺԢ௜ ǡ ‫ݕ‬Ԣ௜ ሻ are then fed into a DL model.

485.2.3. Performance Evaluation Metrics
Loss Score
After the DL model generated vessel position, the prediction was inversed using thestandardization parameters of the target features as follows:‫ݕ‬ො௜ ൌ ‫ି݀ݐݏ‬ଵ ሺ‫ݕ‬ොԢ௜ ሻሺͳͲሻwhere ‫ݕ‬ො௜ is the prediction vector after inverse normalization, and ‫ݕ‬ොԢ௜ is the prediction vector.
The results (οߣመ௧ and ο߮ො௧ ) are then transformed into latitude ߮ො௧ା௧೟ and longitude ߣመ௧ା௧೟ byadding each component to the input (i.e., ߣ௧ , ߮௧ ). Finally, a new loss score for each result is
calculated as follows:‫ܧܣܯ‬ఒ ൌ௠ͳ෍ หߣመ௜௧ା௧೟ െ ߣ௜௧ା௧೟ ห
݉
௜ୀଵ

ሺͳͳሻ

‫ܧܣܯ‬ఝ ൌ௠ͳ௜௜෍ ห߮ො௧ା௧െ ߮௧ା௧
ห
೟
೟
݉
௜ୀଵ

ሺͳʹሻ

௜
where ߣመ௜௧ା௧೟ ൌ ൫οߣመ௧ ൅ ߣ௜௧ ൯ is the prediction longitude, ߮ො௧ା௧ൌ ൫ο߮ො௧ ൅ ߮௧௜ ൯ is the prediction೟௜
latitude, ߣ௜௧ା௧೟ is the target longitude, and ߮௧ା௧is the target latitude.
೟

Metric Score
We used the same metric scores from the previous research, defined as the mean distanceerror (MDE) and mean angular error (MaE). The distance error is the haversine distance
between the prediction and target (true position) in kilometers, signifying the deviation of theresult (prediction) from the true position (target). The MaE as the second evaluation metric was
calculated based on the three known points of the base, target, and predicted positions,signifying precision of the prediction from the target. These metric scores were calculated asfollows:‫ ܧܦܯ‬ൌ௠ͳ෍ ݀௛ ௜ሺ௩ǡ௪ሻ
݉
௜ୀଵ

ሺͳ͵ሻ

௠

ͳ
௜
‫ ܧܽܯ‬ൌ ෍ ‫ܥ‬ሺ௨ǡ௩ǡ௪ሻ݉ሺͳͶሻܿ‫ ݏ݋‬ቀ݀௛ ሺ௩ǡ௪ሻ ቁ െ ܿ‫ ݏ݋‬ቀ݀௛ ሺ௨ǡ௩ሻ ቁ ܿ‫ ݏ݋‬ቀ݀௛ ሺ௨ǡ௪ሻ ቁቍ‫ܥ‬ሺ௨ǡ௩ǡ௪ሻ ൌ   ቌ
‫ ݊݅ݏ‬ቀ݀௛ ሺ௨ǡ௩ሻ ቁ ‫ ݊݅ݏ‬ቀ݀௛ ሺ௨ǡ௪ሻ ቁ

ሺͳͷሻ

௜ୀଵ

49

where ‫ ݑ‬is the base point ሺ߮௧ ǡ ߣ௧ ሻ, ‫ ݒ‬is the true position ൫߮௧ା௧೟ ǡ ߣ௧ା௧೟ ൯, and ‫ ݓ‬is the predicted
point ൫߮ො௧ା௧೟ ǡ ߣመ௧ା௧೟ ൯.

5.3. Baseline Model
The previous research is used as a baseline of this research for model-building guidelines
especially in the prototyping process. The baseline was defined as a DL model with the samestructure and hyperparameters as the previous research, presented in the previous chapter [58].
We also utilized a naive baseline, geodesic calculation, as a non-ML baseline, computed asfollows:߮ු௧ା௧೟ ൌ ൫ሺ߮௧ ሻ ሺߜ௧ ሻ ൅ ሺ߮௧ ሻ ሺߜ௧ ሻ ൫߰௛ ௧ ൯൯ߣሙ௧ା௧೟ ൌ ߣ௧ ൅ ʹ൫൫߰௛ ௧ ൯ ሺߜ௧ ሻ ሺ߮௧ ሻ ǡ ሺߜ௧ ሻ െ ሺ߮௧ ሻ ൫߮ු௧ା௧೟ ൯൯

ሺͳ͸ሻ
ሺͳ͹ሻ

where ߮௧ ǡ ߣ௧ ǡ ߰௛ ௧ are in radians, ߜ௧ ൌ ݀௧ Ȁ‫ݎ‬௘௔௥௧௛ is the angular distance, ‫ݎ‬௘௔௥௧௛ is the earth
diameter, ߮ු௧ା௧೟ and ߣሙ௧ା௧೟ are subjected to normalization to degrees [49]. These baselinemodels were used to conduct error analysis on bias and variance.
Likewise, the average distance interval of the ships was adopted as a sanity check. Thisapproach examines the performance evaluation metrics between the current position and thenext position, calculated as follows:
തതത
݀
௛ ൌ

௠
ͳ
௜
෍ ݀௛ ቀሺఝ
‫߮݁ݎ݄݁ݓ‬ǡ ߣ݅݊‫ݏ݊ܽ݅݀ܽݎ‬೟ ǡఒ೟ ሻǡ൫ఝ೟శ೟೟ ǡఒ೟శ೟೟ ൯ቁ
݉
௜ୀଵ

ሺͳͺሻ

where ሺ߮௧ ǡ ߣ௧ ሻ is the base point, and ൫߮௧ା௧೟ ǡ ߣ௧ା௧೟ ൯ is the next position at the designated timeinterval.

5.4. First Experiment: Time-Interval Magnification
5.4.1. Experimental Setup
In the first experiment, we trained the DL model on four different time intervals prediction:from averaging 24 h to 96 h. The model was trained on four different variations of observation
area size at each time interval. Naturally, the distance traveled by moving ships in a straightline is proportional to the time interval. Therefore, the variation in the observation area size isincreased twofold as the time interval doubles, and so on. Table 5-1 shows the size variation of
the observation area at each time interval.

50

We focused our observation on Malacca Strait and its surrounding area. The strait is themost congested primary chokepoint, where it is one of the core routes of the main maritime
shipping route [59]. The observed area covers from 1 to 204 million square kilometers fromthe smallest observation area at 24-h average time intervals ο‫ݐ‬௧ to the largest observation area
at 96-h average time intervals, respectively, adequately capturing the continuous long-term
movements of the vessels conformed to its time intervals.
Table 5-1. Variation of time intervals and its coverage size
Time intervals Index

Longitude

LatitudeArea size7 Train set Dev/test set(106 km2) size (103) size (103)(in average)

area

24 h

1
2
3
4

95°E–105°E 0°S–8°N
90°E–110°E 4°S–12°N
85°E–115°E 8°S–16°N
80°E–120°E 12°S–20°N

1
4
9
16

48
107
172
367

5
10
15
33

48 h

1
2
3
4

90°E–110°E
80°E–120°E
70°E–130°E
60°E–140°E

4°S–12°N
12°S–20°N
20°S–28°N
28°S–36°N

4
16
35
60

82
316
763
1352

7
28
77
138

72 h

1
2
3
4

85°E–115°E
70°E–130°E
55°E–145°E
40°E–160°E

8°S–16°N
20°S–28°N
32°S–40°N
44°S–52°N

9
35
75
126

123
700
1544
1892

11
71
158
190

1

80°E–120°E 12°S–20°N

16

222

20

2
3
4

60°E–140°E 28°S–36°N
40°E–160°E 44°S–52°N
20°E–180°E 60°S–68°N

60
126
204

1280
1878
2039

133
189
204

96 h

According to the hold-out validation scheme, the dataset was split into a training set anddev-test sets. In the smallest observation area, the training set comprised more than 48 thousand
data records after omitting AIS messages with missing values and abnormalities; each dev and7

calculated by geodesic area assuming the earth is a perfect sphere with a radius defined in

WGS84.
51

test set contained more than five thousand data records. Meanwhile, more than 2 million AIS
data for training was used in the largest observation area, with 200 thousand more for testing.
The size of these sets was considered sufficiently large for each condition, where the smallest
area is already above the 25,000 thresholds, thus providing high confidence in the overall model
performance [58].
5.4.2 Results and Discussions
Time interval = 24-h average
Figure 5-1 demonstrates four size variations of the observed area with a 24-h average timeinterval. The normalized density distributions were calculated using Gaussian kernel density
estimation (KDE) with the largest observed area dataset from nine years of AIS messages
involving 1662 different IMO numbers (vessels). For geospatial data processing, thebackground geography was visualized using an open-source Python library, the Matplotlib
Basemap Toolkit [51]. The smallest observation area captures the densest region, the narrowbottom-end of Malacca Strait and around Singapore Strait. Meanwhile, the largest observation
area covers Makassar Strait, a secondary maritime chokepoint or the second densest region.

Figure 5-1. Size variations of the observed area with 24-h time-interval average (thenormalized density distribution of AIS data is based on the largest area)
The performance evaluation metrics of the DL and baseline models are given in Table 5-2;
all results were computed using the test set. The average distance interval indicates the average
distance between ships’ current and subsequent positions in their corresponding time-interval
window. Similar to the geodesic calculation performance on the maritime chokepoint areasfrom the previous research, the geodesic calculation fails to make predictions of vessel behavior
52

in this high-traffic area. Both DL models effectively outperformed (accuracy and precision) the
non-ML baseline on all area size variations.
Table 5-2. Comparison of model performance in 24-h average time interval
DL modelIndex

Previous model

Geodesic calc.

Average

Loss

ࡹࡰࡱ

ࡹࢇࡱ

ࡹࡰࡱ

ࡹࢇࡱ

ࡹࡰࡱ

ࡹࢇࡱ

distanceࡹ࡭ࡱࣅ ࡹ࡭ࡱ࣐

(km)

(deg)

(km)

(deg)

(km)

(deg)

interval (km)

1

0.40

0.26

55

23.7

56

24.5

182

39.7

288

2

0.48

0.35

72

17.9

75

18.8

202

31.3

377

3

0.42

0.31

63

16.1

64

16.4

162

26.0

403

4

0.29

0.27

49

13.3

50

13.2

128

20.3

424

area

Figure 5-2. Comparison of the DL model performance with the previous model andcharacteristics of each observed area dataset in 24-h average time interval
53

Figure 5-2 reveals the mean distance error from the results of the DL model with deeper
and larger networks and the previous research’s model, along with the dataset characteristics
in each area. The DL model constantly generated more accurate and precise predictions thanthe previous model on all area size variations, which exceeded 2.5% and 2.3% on accuracy andprecision, respectively. Generally, the models’ performance improves with larger covered areas.
The irregularity of the smallest area compared to other areas corresponds to the surprisingly
higher data related to ships near ports and high-traffic areas in the surrounding Singapore Strait
than ships in normal sailing movement, indicated by the high ratio of the low-distance interval.
Time interval = 48-h average
Figure 5-3 depicts four size variations of the observed area with a 48-h average timeinterval. The normalized density distributions were calculated with the largest observed area
dataset from AIS messages involving 1693 vessels over nine years. By the third-largest
observation area (index area number 3), the Indian Ocean surrounding Port Hedland, the siteof the highest tonnage port in Australia, becomes the densest zone eclipsing Malacca Strait.
This transition is caused since the observed AIS data were taken from only Capesize bulk
carriers that mainly transport coal, ore, and other commodity raw materials, the largest ships
dedicated to ore transportation [60]. This particular fit perfectly with the fact that it is theworld’s largest bulk export port and a major iron ore exporting port in Western Australia [61].
Following the densest region, the East China Sea surrounding China, South Korea, and Japanas the second place was covered in the largest observation area.

Figure 5-3. Size variations of the observed area with 48-h time-interval average (normalized
density distribution of AIS data is based on the largest area)
54

Table 5-3. Comparison of model performance in 48-h average time interval
DL modelIndex

Previous model

Geodesic calc.

Average

Loss

ࡹࡰࡱ

ࡹࢇࡱ

ࡹࡰࡱ

ࡹࢇࡱ

ࡹࡰࡱ

ࡹࢇࡱ

distanceࡹ࡭ࡱࣅ ࡹ࡭ࡱ࣐

(km)

(deg)

(km)

(deg)

(km)

(deg)

interval (km)

1

1.04

0.73

151

16.8

150

16.8

563

42.6

686

2

0.67

0.66

116

14.0

119

15.4

354

26.8

842

3

0.61

0.66

111

14.9

115

15.4

286

23.1

870

4

0.65

0.76

122

27.0

128

27.3

294

34.3

697

area

Figure 5-4. Comparison of the DL model performance with the previous model andcharacteristics of each observed area dataset in 48-h average time interval
The performance evaluation metrics of the DL and baseline models computed using thetest set are presented in Table 5-3. Again, the geodesic calculation fails (both in accuracy and55

precision) to predict vessel positions in this high-traffic area; both DL models tremendously
outperformed the non-ML baseline on all area size variations. The average distance between
ships’ successive positions was normally increased twofold in this doubled time-interval
average window (48-h average time interval with index area 1 and 2 compared to 24-h averagetime interval with index area 2 and 4, respectively). However, predictions from geodesic
calculation grew worse dramatically than the results at the same area size with half time interval,
indicating that the geodesic calculation is bound to fail for ship position prediction at this longinterval.
Figure 5-4 shows the performance of the DL model and the previous model and the datacharacteristics in each area. The DL model generated more accurate and precise predictions
than the previous model on almost all area size variations, with more than 2.5% accuracy
and 3.1% precision on average. The performance improves relative to the size of the area until
drastically altered when the covered area at the largest. The patterns observed in the largest
area may be caused by the surprisingly high low-distance interval ratio, leading to the low
average distance interval compared to other areas.
Time interval = 72-h average

Figure 5-5. Size variations of the observed area with 72-h time-interval average (normalized
density distribution of AIS data is based on the largest area)
Figure 5-5 reveals the area size variations with a 72-h average time interval. The
normalized density distributions were calculated with the largest observed area dataset
involving the same number of vessels at the largest area with a 48-h average time interval. The
56

Indian Ocean was captured completely by the largest observation area, including waters
surrounding Australia, Japan, China, and Indonesia. The East China Sea and the Yellow Sea
surrounding China were the second densest regions after Northwest Australia waters.
Table 5-4. Comparison of model performance in 72-h average time interval
DL modelIndex

Previous model

Geodesic calc.

Average

Loss

ࡹࡰࡱ

ࡹࢇࡱ

ࡹࡰࡱ

ࡹࢇࡱ

ࡹࡰࡱ

ࡹࢇࡱ

distanceࡹ࡭ࡱࣅ ࡹ࡭ࡱ࣐

(km)

(deg)

(km)

(deg)

(km)

(deg)

interval (km)

1

1.58

1.18

235

18.2

237

18.0

890

45.1

1081

2

1.02

1.12

188

16.0

195

16.0

522

27.1

1283

3

1.11

1.40

218

28.4

227

29.1

544

38.9

1024

4

1.10

1.35

211

28.3

225

29.2

521

38.2

1020

area

Figure 5-6. Comparison of the DL model performance with the previous model andcharacteristics of each observed area dataset in 72-h average time interval

57

Table 5-4 gives an overview of the performance of the DL and baseline models. Similar
performance of geodesic calculation was generated, which is bound to fail at time intervals
longer than 24 h. The DL models far exceeded the non-ML baseline performance, althoughnaturally, the model's performance decreased as the time interval increased. As the average
distance interval reached more than one thousand kilometers at this large time interval, themodel performance degraded to more than one-degree error in both longitude and latitude
directions.
Figure 5-6 demonstrates the performance comparison of the DL models, including thedataset characteristics in each area. Again, the DL model generated more accuracy andprecision with 3.6% and 1.1% on average than the previous model on all area size variations,
respectively. At this large time interval, the performance appears to accumulate the total errors
as the coverage area expanded, indicated by the distancing performance of both models.
Consequently, the larger networks improve steadily relative to the size of the area.
Time interval = 96-h average

Figure 5-7. Size variations of the observed area with 96-h time-interval average (normalized
density distribution of AIS data is based on the largest area)
Figure 5-7 depicts the variations of the coverage area with a 96-h average time interval.
Almost all capsize bulk carriers were captured with 1695 vessels over nine years and used to
calculate density distributions by the largest observation area. Almost all regions in the eastern
hemisphere were covered at this most extensive coverage, including 6 out of 8 primary58

chokepoints and 8 out of 13 secondary chokepoints in main maritime shipping routes [59].
Eastern Parts of the North Pacific and South Pacific Oceans were covered, including Southernparts of the Mediterranean Sea.
Table 5-5. Comparison of model performance in 96-h average time interval
DL modelIndex

Previous model

Geodesic calc.

Average

Loss

ࡹࡰࡱ

ࡹࢇࡱ

ࡹࡰࡱ

ࡹࢇࡱ

ࡹࡰࡱ

ࡹࢇࡱ

distanceࡹ࡭ࡱࣅ ࡹ࡭ࡱ࣐

(km)

(deg)

(km)

(deg)

(km)

(deg)

interval (km)

1

1.77

1.61

293

18.1

296

18.6

1024

39.5

1484

2

1.51

1.95

304

27.1

314

27.1

813

40.6

1364

3

1.55

2.02

309

27.9

328

28.9

793

40.8

1350

4

1.57

1.99

308

28.0

322

28.0

767

39.4

1367

area

Figure 5-8. Comparison of the DL model performance with the previous model andcharacteristics of each observed area dataset in 96-h average time interval

59

Table 5-5 presents the performance evaluation metrics of the DL and baseline models using
the test set. At this longest time interval, based on the total average distance interval between
two AIS points, the DL models still delivered good performance, especially compared to thecomplete failure of the non-ML baseline. However, this result may not be reasonably
acceptable since the performance degraded steadily relative to the time interval magnification.
Figure 5-8 demonstrates the comparison of DL models’ performance and the dataset
characteristics of each area. The model generated a steady improvement from the previous
model with 3.5% more accuracy and 1.5% more precision on average. Additionally, theaccumulation of the prediction performance in the large areas appears to distance the total
average performance of both models.

5.5. Second Experiment: Coverage Size Variations
5.5.1. Experimental Setup
In the previous experiment, the coverage area variation was different between time interval
dimensions since the dimension naturally modulated the extent of vessel movement, which is
directly related to the minimal coverage area to observe the objects completely. Thus, theresults from each time interval dimension could not be compared. However, from the previous
experiment, the geodesic calculation as a non-ML baseline failed when the time interval
average was beyond 24 h, and the performance of the previous DL model as the baseline wasgetting worse in large coverage areas compared to the new larger networks. The DL model
delivered a satisfactory performance compared to the baseline models and succeeded in
responding to the task of an increasingly large time interval dimension and thus coverage area;
thus, the larger networks generalized better. As the optimization was carried out with no explicit
regularization such as dropout or batch normalization, this phenomenon is allegedly caused by
the optimization algorithm that remains largely unexplained [62].
In the second experiment, we trained only the proven DL model on observation size
variations based on the first experiment. We focused more on the coverage area, increasing 4
and 3.2 degrees on longitude and latitude, respectively. The coverage variation was from 90°E–
110°E to 60°E–140°E longitude and from 4°S–12°N to 28°S–36°N latitude based on the firstexperiment where the fluctuation occurred before the models’ performance settled down. The
more detailed size variation was expected to capture the fluctuation of the model performancein more detail. The model was then trained on each of four different time interval ο‫ݐ‬௧dimensions.
60

Figure 5-9. Size variations of the observed area for four-different time intervals (thenormalized density distribution of AIS data is based on the largest area by the 24-h averagetime interval)
Figure 5-9 reveals the size variations of the observed area for four-different time interval
dimensions. The normalized density distributions were calculated using Gaussian kernel
density estimation (KDE) with the dataset at the largest observation area by the 24-h averagetime interval dimension involving 1693 different IMO numbers. Meanwhile, the smallest
observation area at 96-h time interval dimension covered 1590 vessels. The most extensive
coverage was similar to the largest observation area at a 48-h time interval in the second
experiment. The Indian Ocean surrounding Northwest Australia, followed by the East China
Sea surrounding China, South Korea, and Japan, became the densest zone eclipsing Malacca
Strait.
Table 5-6 gives the overview of size variation of the observation area. The observation
area covers from 4 to 60 million square kilometers. The dataset was split into training and devtest sets with the same hold-out validation scheme as the first experiment. Separate training
and dev-test sets were prepared due to the differences in time interval dimensions. The longest
time interval suffers from the size limitation because the starting point at ‫ ݐ‬and the target pointat ‫ݐ‬௧ ൌ ͻ͸݄ have to be in the coverage area, at which vessels traveled by more than 1300 km
on average (see Table 5-5). Still, the size of these sets was sufficient where the smallest area atthe largest time interval was already above the 25,000 thresholds, thus providing highconfidence in the overall model performance.

61

Table 5-6. Size variation of observation coverage
Index
area

Longitude

LatitudeArea size(106 km2)

Training; dev/test size (103)
based on average time intervals
24 h

48 h

72 h

96 h

1
2
3
4

90°E–110°E
88°E–112°E
86°E–114°E
84°E–116°E

4.0°S–12.0°N
5.6°S–13.6°N
7.2°S–15.2°N
8.8°S–16.8°N

4
6
8
10

107; 10132; 12157; 14185; 1682; 7107; 9132; 12161; 14

61; 6
84; 7
108; 10137; 12

43; 4
64; 6
86; 7
114; 10567
882°E–118°E
80°E–120°E
78°E–122°E
76°E–124°E

10.4°S–18.4°N
12.0°S–20.0°N
13.6°S–21.6°N
15.2°S–23.2°N

13
16
19
22

235; 21367; 33
516; 47
585; 54

194; 17316; 28
457; 41
522; 48

169; 15271; 25
399; 37
465; 44

146; 13222; 20342; 32
410; 39

9
10
11
12

74°E–126°E
72°E–128°E
70°E–130°E
68°E–132°E

16.8°S–24.8°N
18.4°S–26.4°N
20.0°S–28.0°N
21.6°S–29.6°N

26
30
35
39

663; 63761; 76
832; 83
1044; 101

593; 56
692; 69
763; 77
997; 96527; 50
626; 64700; 71952; 92

471; 46
563; 58
641; 67
908; 89

13
14
15
16

66°E–134°E
64°E–136°E
62°E–138°E
60°E–140°E

23.2°S–31.2°N
24.8°S–32.8°N
26.4°S–34.4°N
28.0°S–36.0°N

44
49
54
60

1147; 113
1223; 123
1278; 129
1393; 142

1098; 109
1176; 118
1230; 125
1352; 138

1053; 105
1131; 115
1184; 121
1314; 135

1013; 101
1091; 111
1142; 118
1280; 133

5.5.2. Results
Table 5-7 presents the performance evaluation metrics of the DL models across area size
variations at four-different time intervals; results were computed using each test set by theirrespective trained models. On average, across all coverage size variations, the accuracy
difference (based on ‫ )ܧܦܯ‬between DL models with different long-time intervals was directly
proportional to the difference in average distance interval. Each has a performance baselinethat is almost equidistant from the others as the time intervals (thus the distance intervals) have
uniform magnification. Meanwhile, models with shorter time intervals were just more precise(based on ‫ ) ܧܽܯ‬than longer-time interval models in general without any correlation.
Figure 5-10 gives an overview of the model performance across the coverage variations
for each time interval dimension. All models generated comparable performances based on thetime intervals, fluctuating from the initial coverage size until reaching around 20 million square
kilometers. The fluctuation appears to be more intense for models with longer intervals. At thispoint, the performances improved from the initial coverage size and became stable. Then, aweak fluctuation was generated between this point and 30 million square kilometers of62

coverage for models with the longest-time intervals (i.e., 72 h, 96 h). Eventually, allperformances experienced a gradual increase on over 40 million square kilometers of coverage.
Table 5-7. Comparison of model performance in all area size and time interval variations
Index

ࡹࡰࡱ(km)Average distance interval (km)ࡹࢇࡱ(deg)area ο‫ݐ‬௧ =1d ο‫ݐ‬௧ =2d ο‫ݐ‬௧ =3d ο‫ݐ‬௧ =4d ο‫ݐ‬௧ =1d ο‫ݐ‬௧ =2d ο‫ݐ‬௧ =3d ο‫ݐ‬௧ =4d ο‫ݐ‬௧ =1d ο‫ݐ‬௧ =2d ο‫ݐ‬௧ =3d ο‫ݐ‬௧ =4d
1

73

149

211

247

18.2

17.3

19.2

18.6

377

686

912

1078

2

68

155

230

281

16.8

16.0

18.0

18.4

396

745

991

1192

3
4

65
60

154
145

243
240

307
327

14.7
15.7

15.6
16.3

17.7
17.7

17.9
19.2

411
411

783
797

1070
1108

1300
1356

5

55

135

235

332

16.2

18.0

19.1

20.9

395

788

1111

1371

6

49

116

199

293

13.2

14.3

15.8

18.3

424

842

1208

1484

7
8

45
46

105
113

184
193

271
284

14.7
15.7

15.4
16.6

16.8
18.0

17.5
18.7

422
419

839
835

1226
1229

1558
1581

9

46

113

197

287

15.4

16.7

17.6

18.6

420

841

1240

1604

10

46

111

187

276

13.8

15.3

16.6

16.8

432

867

1282

1656

11
12

45
46

111
110

188
185

278
276

14.1
19.6

14.7
18.9

15.6
19.8

17.4
20.9

430
391

870
783

1283
1161

1658
1521

13

47

113

191

285

23.3

22.4

22.0

23.6

373

747

1114

1459

14

49

116

197

290

25.5

24.8

25.3

24.8

364

727

1076

1416

15

50

119

201

295

25.7

25.1

26.2

25.8

361

721

1070

1403

16

50

123

206

303

28.4

27.0

27.4

26.6

347

697

1037

1364

Figure 5-10. The DL model performance on area size variations in four-different time interval

635.5.3. Discussion: coverage size expansion
From the experiment result, the performances across long time intervals became stable
after the coverage size reached 20 million square kilometers but increased gradually on 40
million square kilometers of coverage. After that range, the performance tendency leads touncertainty about whether to remain in a gradual increase or become stable.
On that account, we trained the DL model on the expanded variations of the coverage size.
The coverage area was increased in size, continuing from beyond 60 million to 204 million
square kilometers as the widest coverage area in the first experiment (from 56°E–144°E to
20°E–180°E longitude and 31.2°S–39.2°N to 60°S–68°N latitude). As the performance was
expected to be steady at this more extensive coverage, the size interval was doubled: expanded
by 8 and 6.4 degrees on longitude and latitude, respectively.

Figure 5-11. Expanded size variations of the coverage area with doubled size interval (thenormalized density distribution of AIS data is based on the largest area)
Figure 5-11 portrays the expanded variations of the coverage area, whereby the largest
observation area, almost all 1695 capsize bulk carriers, was captured over nine years andcalculated for the density distribution. Identical to the most extensive coverage in the firstexperiment, almost all regions in the earth’s eastern hemisphere were covered.
Figure 5-12 reveals the model performance across the expanded coverage variations foreach time interval dimension. Overall, DL models across multiple time intervals deliver stable64

performance and generate a proportional magnitude to the time intervals (predicted distanceintervals). The performances remained steady from the initial to the end of the observed area.
The observed performance stability across the size range may result from no high-density lowdistance-interval region dominating beyond the initial coverage.

Figure 5-12. The DL model performance on the expanded coverage variations in fourdifferent time interval
5.5.4. Discussion: the optimum coverage size for long-term position prediction
As the stability is different in each time-interval model, the observed performance patterns
may not result from only enlarging the coverage area. The shortest-interval model produced a
direct result, but models with time intervals longer than 24 h produced different patterns,
although the amount of training data is roughly equivalent. The optimum coverage size needed
to be answered whether it is influenced more by its size or possibly the dataset characteristicsof the area.
Accordingly, we compare the dataset properties used to train the models across the timeinterval dimension and coverage size. The dispersion for continuous data can be measured bystandard deviation, but comparing the variability when the coverage size and time intervals aredifferent is tricky [63]. Therefore, we compare the number of training sets and AIS datacharacteristics on each observed area size and time interval represented by the dispersion ofvessels distance interval (the haversine distance between two AIS messages). We calculated thecoefficient of variation (CV), a measure of relative variability or dispersion of frequency
distribution, to compare the distribution of ships’ distance intervals across different timeintervals as follows [64]:65‫ܸܥ‬ௗ೓ ൌ

ߪௗ೓
ൈ ͳͲͲ
തതത
݀௛

ሺͳͻሻ

തതത௛ are the standard deviation and the mean of ships’ distance interval between
where ߪௗ೓ and ݀
the base and true positions, respectively (see Equation 18).
Figure 5-13 compares the model performance and dataset characteristics across observed
time intervals and covered area size variations. The dataset size may not directly influence theperformance since the observed area is already large and contains sufficient data for themachine learning algorithm. The coverage size affects the data size until the coverage reaches
the furthest of the northern and southern hemispheres. As the coverage size reaches 100 million
square kilometers, AIS data is no longer significantly captured.
Based on the coefficient of variation, the dataset with a time interval of 24 h average hasa similar pattern but different magnitude from other datasets with magnified time intervals. Its
magnitude is relatively larger than the others across the coverage size, indicating that it has agreater variability to the ships' average distance interval despite having an almost equal amountof data at each coverage. This profound distinction may result from using the daily archived
AIS messages with natural time intervals averaging 24-h. The dataset sampling in the time
dimension satisfies the ο‫ ݐ‬՜ ‫ݐ‬௧ interval condition as ο‫ א ݐ‬ሺͲǡ ʹ‫ݐ‬௧ ሻ , destroying information
regarding latent variables and causing distortion, indicated by the low dispersion compared to
the raw AIS dataset with daily interval (i.e., averaging 24 h). Consequently, the transformed
dataset became unbalanced or skewed, hindering the machine learning model's performance[65]. The unbalanced dataset may also be caused by a new formation of outliers that are notstrictly defined when the time interval was magnified.
The model performance with 24 h time interval is already stable at 19 million square
kilometers. Malacca Strait is the densest region in this coverage, followed by the Makassarstrait. Meanwhile, the performance of magnified-interval models fluctuated until 39 million
square kilometers of coverage. In this coverage, the Northwest Australian waters as the densest
region are completely captured, at which the CV soared to around 60 percent. The sharp
increase of CV corresponds to capturing the densest region, indicating that dataset
characteristics influenced these model performances more than the observed area size.
However, after this point, the model performances increase gradually and become stable when
the coverage reaches around 72 million square kilometers, corresponding to dispersion ratestability. This coverage completely captured the waters surrounding China, the second densest
region.

66

Figure 5-13. DL model performance and dataset characteristics comparison across different
time intervals and coverage size variation
Therefore, according to the observed location, 19 million kilometers of coverage is optimalfor the prediction model with 24-h intervals but not for the other DL models with magnifiedtime intervals. Meanwhile, the optimum coverage size for all models is 39 million square
kilometers, corresponding to the dataset's high dispersion rate. The subsequent gradual increase67

observed from the longest-time interval models appears insignificant, resulting from capturing
the second densest region degrees by degrees. Thus, by capturing the densest region on theobserved location, which leads to a proportional ratio of the low-distance to the high-distanceintervals, optimum coverage for long-term position prediction can be achieved. Enlarging thecoverage area size may eventually solve the prerequisite of partial coverage.

5.6. Third Experiment: Comparison of Observation Area Worldwide
5.6.1. Experimental Setup
Predictive performance is directly proportional to the time interval dimension based on
performance evaluation metrics. Meanwhile, the observation area size is not only the main
determinant in optimizing prediction performance but also a dataset characteristic shaped basedon its location. To further assess the influence of the area, in the third experiment, five DL
models were built for five major locations of maritime shipping routes focused on Capesize
bulk carriers. The same procedure was applied to the models as in the previous experiments:
each used the same model properties and followed a similar hold-out validation split.
The observed locations shared the same longitude and latitude length based on the
optimum coverage size from the previous experiment: within 64-interval longitude and 52interval latitude. Each area's size varies despite having the same geographical boundaries since
the geographic coordinate measurements are angles and are not on a planar surface [66]. Eachwas named after the crossed region of the continent due to its large size, namely, Europe (EUR),South America (SAM), Southern Region of Africa (SRA), South and Southeast Asia (SAS),and East Asia (EAS).
Figure 5‑14 illustrates the location and size of each area (red rectangles) based on theequidistant cylindrical projection, which neither covers equal-area nor conformal, a standard
for imaging the relationship between the observed location on the map and its corresponding
geographic location on Earth [67]. Each observed location is further depicted based on the
Mercator projection, which inflates the area size away from the equator [68]8. The normalized

8

Despite large distortion at high latitude, it is commonly used in nautical and aerial use and ispractical for visual mapping the Earth’s globe (without polar areas).
68density distribution on each observed location reveals the complete capture of the densest
region, not partial, complying with the recommendations for the optimum coverage of longterm position prediction.

Europe (EUR), South America (SAM), Southern Region of Africa (SRA),South and Southeast Asia (SAS), East Asia (EAS)

Figure 5-14. Location of the observed area
Capesize bulkcarriers are one-way cargo transport, where round trips between the
countries are a common pattern. China, Australia, and Brazil are the top players with Capesize
ships’ iron ore shipments [69]. From the normalized density distribution, the densest region in
East Asia is located between Shanghai Port and Port of Ningbo in China; combined, they are
the world’s biggest importers of iron ore and bulk shipments [70]. Meanwhile, the densest
region in South and South East Asia is Northwest Australia, where the nearest Port Hedland is
the world’s largest bulk export port [71]. In South America, the densest region is dry bulk cargo
ports around Ponta da Madeira in North Brazil and Sepetiba and Tubarao in South Brazil,
exporting mainly iron ore [72]. In Europe, the densest region is around the port of Rotterdam
in the Netherlands, an important transit point for transport bulk between the European continent69

and other parts of the world [73]. Further, the densest region in the Southern Region of Africa
stretches around the Cape of Good Hope as ships sail between the Pacific and Atlantic oceans,plus additional traffic of iron ore exports around Port of Saldanha on the south-western coastof South Africa [74].
5.6.2. Results and Discussions
The performance evaluation metrics of the models for each examined area are shown in
Figure 5-15. Based on the mean angle error (MaE), model performance in the Southern Regionof Africa (SRA) generated the most precision across time intervals, followed by models inSouth and Southeast Asia and South America. Their precisions gradually fade with the timeinterval magnification scheme. Meanwhile, model performance in Europe followed by East
Asia produced the worse precision, to which magnifying time intervals barely affected them.
All models produced a similar performance pattern based on the mean distance error,
where the accuracy was inversely proportional to the time intervals. At 24-h average intervals,
their magnitude appeared not substantially different from each other. As the time interval was
magnified, the model's distance error in Europe and East Asia closely soared to their highest
levels of more than 300 km at 96-h average intervals, much higher than the models in otherobserved locations. Meanwhile, models on South America, the Southern Region of Africa, andSouth and Southeast Asia generated a more accurate result and similar trends, with a gradualincrease over the time-interval magnification.
As ships’ behavior in each observed location has different observable properties, the error
ratio demonstrates the generated error (MDE) relative to the average movement (i.e., distanceinterval) of the predicted objects per location and time-interval scheme, calculated as follows:
௜
௠ ݀௛
‫ܧܦܯ‬
ሺ௩ǡ௪ ሻൈ ͳͲͲ ൌ ෍ൈ ͳͲͲ݁‫ ݋݅ݐܽݎݎ݋ݎݎ‬ൌ
௜
തതത
݀௛
௜ୀଵ ݀

ሺʹͲሻ

௛ ሺ௨ǡ௩ሻ

where ‫ ݑ‬is the previous or base point ሺ߮௧ ǡ ߣ௧ ሻ , and ‫ ݒ‬and ‫ ݓ‬are the true ൫߮௧ା௧೟ ǡ ߣ௧ା௧೟ ൯ andpredicted positions ൫߮ො௧ା௧೟ ǡ ߣመ௧ା௧೟ ൯ at designated time intervals.

70

Figure 5-15. Comparison of DL model performance across observed location and timeintervals
Based on the error ratio, model performances in Europe and East Asia produced poor
results across the time interval magnification compared to the model performances in otherobserved locations. By 24-h and 96-h average intervals, their error ratio worsened significantly
from around 24% and 18% to 30% and 39%, respectively, double the average of the othermodel performances at the same time intervals. Although their mean distance error is notstatistically significant to the other models, especially at low magnification time intervals, theirerror ratio appears to have a large gap. At 24-h and 96-h average intervals, the error ratio ofSouth America, the Southern Region of Africa, and South and Southeast Asia averaged 9% and15%, respectively. For the case like the Southern Region of Africa, where the dominant AIS
characteristics formed from the common sailing movement of bulk fleet stretching across theCape of Good Hope, an ideal condition for a position prediction model, the DL model generated
the lowest error ratio with the smallest increase over the longest time intervals.
Therefore, the deep learning models generated worse predictions in Europe and East Asia
than in the other observed locations (i.e., South America, the Southern Region of Africa, andSouth and Southeast Asia). The locations where importers of bulk shipments constitute the71largest portion appears to be harder to predict than those that constitute bulk export regions,which corresponds with the fact that Capesize dry bulk carriers' unloading time takes longer
with a wider approximate range than loading time. Based on IHS MARKIT/TheTradeNet
Market Intelligence Network (MINT) data from Muzhoffar, D.A.F., et al. (2022), the averageport-staying time of worldwide Capesize bulkcarriers when loading is around 3 days ± 2 days,
and when unloading is around 5 days ± 3 days [75]. The unloading operations require more
complex procedures in cargo handling treatment than loading operations, which may lead tomore lengthy delays or other uncertainties [76]. More importantly, the divergent state throughunloading conditions is considered unsuitable for long-term position predictions of ships as theprocessed input is only their last movement and geographical position.

5.7. Discussions on Single-Worldwide Model and Limitations of thePrediction Models
5.7.1. Single-Worldwide DL Model
The more accurate performance of the larger networks than the previous DL model can
mitigate the larger observation area, thus a bigger and wider range of data. The larger model
also performs better as the time interval was magnified longer than 24 h average, a more
complex problem than the 24-h interval model. To further assess performances from a muchlarger model, a single worldwide model, we created a DL model trained from the wholeworldwide data, having the same model properties and hold-out validation split. Model
performances from the third experiment provide a baseline for this process.
Figure 5-16 reveals performances from the single-worldwide model across the magnified
time intervals. Compared to the location-based models in the third experiment, the worldwide
model generated poor performance based on the MDE evaluation metric, similar to the inferior
performance of the models with import-dominated regions of bulk shipments (i.e., Europe, East
Asia). However, based on the error ratio, the worldwide model demonstrated output equivalent
to the average between the poor performance models of the import-dominated location andstrong performance models of the export-dominated locations, indicating that the worldwide
model poses more generalized networks. The bigger and wider range of training data of theworldwide model is a way to generalize position prediction from the combinations of specificships' behavior that may be only associated with specific locations.

72

Figure 5-16. Single-worldwide model performance across time intervals: mean distance error(left y-axis) and error ratio (right y-axis)
The worldwide model may be suitable for predicting general responses; however, it will
limit accuracy in certain circumstances or sites previously covered by the less-generalized
location-based models that perform better on the designated observation area [77]. Moreover,this model contains extensive data that can naturally lead to more spurious correlations being
fit undetected across many spots worldwide; consequently, more input features are required togenerate optimal results [78]. Finally, the networks can be either overparameterized (e.g., large
networks trained on small data tasks) or underparmeterized, which are too small for theenormous and complex world-scale model [79].
5.7.2. Limitations: Outliers and AIS Data Uncertainty
Despite a thorough understanding of the data and a deep learning ability that is robust to
outliers, outliers identification and appropriate analytical technique are still hard to be carriedout in preprocessing operations [80]. As our observation covers a relatively larger area and time
range of AIS data with no restrictions on shipping trajectory than other position prediction
studies, defining all outliers would be tremendously difficult had we examined everything at
the micro level. Point or global outliers naturally inhere within AIS data are one thing, but
detecting contextual or conditional outliers related to geographical position requires amonumental work that needs to specify every existing geographical boundary (e.g., polygon)
and practicable definition of the geographical position [81, 82]. This preprocessing,
nonetheless, is not essential in the motion-based method of vessel position prediction studies,
where generalization plays an important role. Additionally, the AIS data used does not require73

a preprocessing of anomalous motion patterns or trajectory outliers found naturally in the low
time-interval data sets [83].
Global outliers from the functions of movement and geographical position explicitly from
AIS data were already omitted earlier in the database handling process, along with the absence
and abnormality of AIS message components. Following the preprocessing, to rationalize on ahuge scale, we further considered the outliers based on the time-interval functions and all theirderivatives, which may affect prediction performances in particular scenarios. Considering thata formation of outliers possibly contributed to data sets when the time interval was magnified
due to the nature of the AIS data used. This problem intensifies for the worldwide model as theCV dropped significantly compared to the location-based models when the time interval was
magnified (see Figure 5-17 (a)). In this extensive coverage, the dispersion rate across timeintervals is affected mainly by data set characteristics, not their size, since the number of AIS
data has no correlation to the magnitude of CV on the respected location (see Figure 5-17 (b)).
Conditional outliers related to ships' navigational status also play notable roles which may
impact the data set's balance. Their identification analysis would reveal the balance of the data
set; ML experts can then choose the most suitable set to be trained so that the prediction results
will be more sensitive and accurate, but only in the specified situation [84]. Instead, we
generalized the deep learning model since we focused only on the last geographical movements
as the input, and it is interesting to incorporate the statuses in future studies.
Moreover, other limitations inherent to the nature of AIS data may add certain deviations
to the data set characteristics, affecting the deep learning performance. The development of
AIS technology and mandatory installation regulation took years to fully implement, leading
to differences in data volume and signal coverage across the observed years (see Figure 3-1)[85]. Some loss reported where it is difficult for satellites to capture all messages emitted,
attributed to the congestion in some spots, such as in China [86, 87]. Nevertheless, theseconcerns are trivial as the observation covers a more extensive zone and time coverage.
The archived and compressed AIS messages with random sampling intervals also inheres
major limitations to the study [88]. Despite being compressed within a one-day interval, therandom sampling renders the data set distribution; having a clear Gaussian distribution will
benefit machine learning building [89]. However, the issue has been minimalized as the timeinterval targets are not strictly defined. The DL model is also improved by replacing sigmoid
functions that work most naturally with normally distributed data with selu activation [90]. For
the same time windows within 24-h intervals, the deep learning generated remarkable good74

performance; however, at the time-intervals magnification, it is possible that the issue
intensifies, especially for the single-worldwide scenario.

(a)

(b)
Figure 5-17. Dataset characteristics comparison of the location-based and worldwide models:coefficient of variation across time interval magnification (a) and number of training data (b)5.8. Conclusions on several-day intervals of ship position prediction
Results from this research show that the geodesic calculation as a non-ML baseline failed
when the time interval average was magnified beyond 24 h, and the performance of theprevious DL model as the baseline became worse in large coverage areas compared to the newlarger networks. The vector regression model is better than the scalar regression model; thus,
the larger networks generalized better. The DL model delivered a satisfactory performancecompared to the baseline models and succeeded in responding to the task of an increasingly
large time interval dimension and coverage area.
Meanwhile, the optimum coverage size for all time-interval models is 39 million square
kilometers, corresponding to the dataset's high dispersion rate. By capturing the densest region75

on the observed location, which leads to a proportional ratio of the low-distance to the highdistance intervals, optimum coverage for long-term position prediction can be achieved. The
deep learning models generated worse predictions in Europe and East Asia than in the otherobserved locations (i.e., South America, the Southern Region of Africa, and South andSoutheast Asia). The locations where importers of bulk shipments constitute the largest portion
appears to be harder to predict than those that constitute bulk export regions, which correspondswith the fact that Capesize dry bulk carriers' unloading time takes longer with a wider
approximate range than loading time.
Moreover, the worldwide model is a way to generalize position prediction and may besuitable for predicting general responses, but it will limit accuracy in certain circumstances orareas where location-based models perform better on them. The deep learning model wastrained based on the last geographical movements; thus, this limitation intensifies at the timeintervals magnification.

76

Chapter 6
Conclusions and Future Works
6.1. Conclusions
This study employed DL models with experimentally defined properties using exactEarthAIS daily data. There are two main chapters: each consist of three experiments and discussions.
In the first experiment of the former, a model for the Indian Ocean area was examined, and in
the subsequent experiment, 12 models were investigated on open oceans and maritime
chokepoints. Then, a selected sample location within the Malacca Strait area was examined,
resembling a simulation of practical application. In the first experiment of the latter, larger
networks of DL models were trained on different observation area sizes with magnified timeintervals. We focused more on observation size variations in the next experiment, increasing 4
and 3.2 degrees on longitude and latitude, respectively. Finally, five DL models were built forfive major locations of maritime shipping routes focused on Capesize bulk carriers.
The conclusions of this dissertation are summarized as follows:
1. Ship position prediction with an average time interval of 24 h was possible with thestraightforward motion-based method, more accurate than the geodesic calculation as
the baseline model in all areas.
2. Predictions in the open ocean areas yielded higher accuracy than in the chokepoint
areas; the improvement compared to the geodesic calculation was higher in the
chokepoint areas than in the ocean areas as the conventional calculation failed to predict
vessel behavior near the ports and congested waters.
3. The DL model can predict the complex movement of ships near ports and congested
routes with no information regarding vessel status, historical trajectory, or destination.
The DL model appears to have a sense of the dimension of the geographic coordinate
system that can be or is often passed, wherein the chokepoint areas rely more on the
input features of the current latitude and longitude of the vessels.
4. The proposed MLP model generated predictions as accurate as of the LSTM with fastertraining times on the dataset with varying and uneven time-interval distribution andwithout a trajectory reconstruction.
5. From the research of several-day intervals of ship position prediction, the DL model
delivered a satisfactory performance compared to the baseline models in increasingly77large time interval dimensions and coverage size; thus, the larger networks generalized
better. The geodesic calculation as a non-ML baseline failed when the time interval
average was beyond 24 h, and the performance of the previous DL model as the baseline
became worse in large coverage areas.
6. The optimum coverage size for all time-interval models is 39 million square kilometers,
corresponding to the dataset's high dispersion rate. To achieve the optimum coveragefor long-term position prediction, the densest region on the observed location must be
captured, leading to a proportional ratio of the low-distance to the high-distanceintervals.
7. The locations where importers of bulk shipments constitute the largest portion appears
to be harder to predict than those that constitute bulk export regions, which correspondswith the fact that Capesize dry bulk carriers' unloading time takes longer with a wider
approximate range than loading time.
8. The worldwide model is a way to generalize position prediction and may be suitablefor predicting general responses, but it will limit accuracy in certain circumstances orareas where location-based models perform better. The deep learning model was trained
based on the last geographical movements; thus, this limitation intensifies at the timeintervals magnification.

6.2. Future Works
This paper is the first study to explore long-term ship position prediction using an AIS
dataset in nine years for Capesize bulk carriers worldwide, providing a valuable benchmark for
future studies. As this is the first study on long-term position prediction, we focused only on
the basics of AIS data as the input features, that is, the last geographical position and movement.
Therefore, it is very possible to incorporate other valuable input features and utilize othertechniques in future studies to improve the prediction performance, such as:xAdding new essential input features regarding the vessel status, destination, or longer
historical trajectory.

x

Adding feature-engineered input processed from AIS data and other data (e.g., Port data,
Country data, etc.).

x

78

Adding input from other data (e.g., Weather data, operation data, etc.).

x

Exploring new thrived architecture specialized for the objective (sequence-based timeseries problems): The neural ordinary differential equation model and Transformer
Neural Networks for regression.

In future studies, we intend to improve the model performance by utilizing thesetechniques and incorporating other types of vessels, thereby increasing the complexity of themodel.

79

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Acknowledgements
The research motivation was formulated together with my supervisor, Professor Kunihiro
Hamada. His valuable suggestion and advice have smoothed out the flow of my research. I am
also thankful for his support in scholarship and administrative matters.
This work was impossible without the supervision and support of Prof. Hamada, Prof.
Hirata, and Dr. Wada. Also, I am very much grateful to the reviewers of this thesis, Prof.
Mitsuru Kitamura and Prof. Eiji Shintaku, for their suggestions and comments.
I am also grateful to my family for supporting me during these three years of hard times:
my long-distance parents, my beloved wife, and my ludicrously entertaining children. At thesame time, I am lucky to be together with them.
Lastly, thanks to my only discussional lab mates, Dimas and Ede, who share the rollerskating experiences for these years, along with the other Laboratory members of Transportation
System Innovation, the office's staff of the Graduate School of Engineering, friends, andcolleagues I cannot mention. I am benefitted from discussing and debating issues with them.
Principally, I am grateful to all.

87