Investigations of Anomalies in Ship Movement During a Voyage

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript presents a method of automated detection of anomalous ship behavior using AIS data and LSTM-based trajectory prediction. This study is of significant importance for maritime safety and the protection of critical infrastructure. This manuscript is, for the most part, clearly written and methodologically sound and a fair contribution to the field. However, several major and minor points should be addressed to improve the manuscript’s clarity, robustness.

1. The literature review is poor and has not presented obviously the latest research achievements and the gap of the automated detection of anomalous ship behavior. It’s well-known that the ship behavior anomaly has been extensively studied and many excellent algorithms have been proposed. A proper literature review of this topic will justify the novelty of this study and highlight its contributions more effectively.
2. Definition of an "Anomaly". What is the definition of anomaly of ship behaviour? The claims of anomaly appear in lines 472-473, age 16 and lines 648-649, page 24. These definitions of anomaly are not clear and operational. This definition should be explicitly stated in the "Materials and Methods" section (Section 2 or 3.2) to set clear expectations for the reader before the results are presented. Furthermore, the rationale of setting of threshold values for anomaly should be discussed.
3. The model/method to detect the anomalous ship behavior is obscure. Section ‘2. Materials and Methods’ did not cover the method to detect the anomaly. The author claims ‘The authors proposed an approach for anomaly identification based on the analysis of differences between the actual and predicted ship positions, courses, and speeds’ in section ‘3.2 Anomaly identification process’. This part expounds the process to detect the anomaly along with illustrative examples. It is recommended to provide the model/method to detect the anomalous ship behavior in a more academic way. A logical and knowledgeable framework/chart flow of the study is advised for a clearer presentation.
4. Thresholds for anomaly detection: The thresholds for anomaly detection (e.g., ±0.5 L for distance, ±0.2 knots for speed, ±30° for course, ± 110 m for distance) are stated empirically without any further explanations. The manuscript would be significantly strengthened by providing a more rigorous justification for these values. Were these thresholds validated against a larger, labeled dataset of "normal" and "anomalous" behaviors? A brief sensitivity analysis or a reference to navigational standards/regulations would bolster the credibility of these critical parameters.
5. Clarity on trajectory prediction model training and generalization. The author did not provide enough information about the training and validating of trajectory prediction model based on LSTM. What about the performance of this LSTM model? This has significant implications for the method's generalizability and the anomaly detection. The manuscript should clarify this point. The statement in Section 2.2.1, "Separate test vessels were excluded from training and used exclusively for evaluation," is positive. However, it should be specified if Ships A and B were part of this held-out test set or if they were used as illustrative examples after the model was finalized.
6. the Abstract, Discussion and Conclusion are poorly composed and are advised to be rewritten according to the academic paradigms. For example, about 80% of abstract introduce the background of the topic. The most important point, the method/model of anomaly detection is missing. Some texts in the two last paragraphs of Discussion and Conclusion are repetitious and recommended written to be more concise and impactful.

Comments on the Quality of English Language

1) Repetitive Text:  the last paragraph of page 25 is repeated in lines 707-712 page 26. This repetition should be eliminated.

2) a full stop is missed in line 2 page 1.

Author Response

Pls. find ourr response in attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript explores maritime vessel trajectory prediction using AIS (Automatic Identification System) data and a unidirectional LSTM neural network. The study focuses on analyzing vessel movement patterns in the Danish Straits using AIS-derived positional, speed, and course data sampled at varying temporal resolutions. The topic is timely and relevant, as AIS-based predictive modeling contributes significantly to maritime navigation safety, collision avoidance, and traffic management. Here are some concerns that need to be addressed before the manuscript can be accepted. 

@ The LSTM network architecture is fixed at 64 hidden units, but there is no justification for this choice. It would be beneficial to provide an explanation (like, hyperparameter tuning, validation experiments) to demonstrate that this configuration offers optimal performance. Moreover, no comparison is made with simpler baselines (like, linear regression, feedforward network) or other temporal models (GRU, BiLSTM), making it difficult to assess the true merit of the chosen design.

@ The resampling at 5-, 10-, 15-, and 20-minute intervals is described as “down sampling at fixed index steps,” but this may introduce time irregularities if AIS transmissions are not perfectly periodic. The authors should clarify whether interpolation was used to enforce exact time spacing and how missing timestamps were handled during this process.

@ The transformation from geodetic (latitude, longitude) to local Cartesian coordinates using a “first-order approximation” of Earth curvature requires mathematical formulation. The projection’s accuracy depends on latitude, and without precise parameters (e.g., reference point, scale factor), spatial displacement errors may occur. A validation step comparing projected distances with true geodesic distances should be reported.

@ The construction of five-dimensional feature vectors (Δx, Δy, cos(COG), sin(COG), ΔSOG) should be formally expressed with equations. This would clarify whether Δx and Δy are computed as finite differences between consecutive time steps or as absolute displacements. Moreover, normalization or standardization procedures for each feature dimension must be explicitly stated, as they directly affect LSTM training stability.

@ The LSTM model has a single hidden layer with 64 units, but no sensitivity analysis or hyperparameter tuning procedure is discussed. Without comparing different hidden sizes or layer depths, the chosen configuration appears arbitrary. Experiments showing the effect of varying hidden units or sequence length on validation error would strengthen the architectural justification.

@ The paper mentions that “test vessels were excluded from training,” but the exact split ratio like, number of vessels in train vs. test is not provided. The criteria for test selection (random, route-based, or vessel-type-based) must be defined, as this choice can bias model evaluation and overestimate generalization performance.

@ The manuscript would benefit from incorporating a discussion of recent advancements in vessel trajectory modeling, anomaly detection, and AIS-based monitoring. Relevant studies addressing ice–ship interactions, mooring dynamics, moving target detection, trajectory optimization, and time-evolving anomaly detection include: 10.1109/TIM.2025.3550616, 10.1016/j.cja.2025.103426, . Integrating these recent technical contributions would improve the scholarly depth, provide a stronger justification for the proposed anomaly assessment criteria, and better situate the study within current research trends in maritime safety and autonomous vessel monitoring.

Author Response

Please find our response in attached file.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper suggests a quantitative method for anomaly identification in ship movements, designed to detect potential safety threats or non-compliant behavior. The method performs a quantitative analysis of deviations in key AIS-derived motion parameters (position, speed, course) from reference passages. By tracking the differences and difference increments between predicted and actual values, the approach generates interpretable indicators for effective maritime traffic monitoring.

The paper is nice and interesting; however, I have several concerns:

1. There is no related work section and the survey of related work is included in the introduction. I would encourage the author to split out the related work section.
2. The heading on line 143 appears to be out of context and somewhat disconnected from the subsection’s content. First, the numbering seems incorrect. Furthermore, the heading itself, 'Machine learning,' is too general and may not be the most appropriate title for this section.
3. The structure of the document currently presents a logical inconsistency, as several subsections within Section 2 have been incorrectly numbered as if they belong to Section 1, creating an error in the hierarchical organization and flow of the paper's second main chapter.
4. Iמ Figure 1, the solid red line is currently used to represent two distinct elements or concepts. To ensure the visual integrity and accurate interpretation of the data presented in the figure, it is recommended to select a separate, unique color for each of the two different features currently symbolized by that single solid red line. Distinguishing these elements visually will significantly enhance the clarity and professionalism of the figure.
5. The data in Table 1 would be much more accessible if presented in a graph. A graphical format would allow for a more immediate and clear understanding of the comparisons. The equivalent values should be moved from inside the table and placed within the main text instead.
6. It seems that the green arrow and the second red arrow in Figure 18 are redundant as they indicate the identical element. For the sake of clarity, would it be possible to use only one of these indicators?
7. The authors write in line 714 “Future research should include the analysis of other shipping routes and the integration of additional information sources, such as radar and satellite observations, to enhance the robustness of the method.”. In Rakhmanov A. and Wiseman Y., "Compression of GNSS Data with the Aim of Speeding up Communication to Autonomous Vehicles", Remote Sensing, 2023, Vol. 15(8), paper no. 2165. Available online at: https://www.mdpi.com/2072-4292/15/8/2165 the authors write: "The use of NMEA in ships is very significant and important because in the sea we do not have signs, and one of the options to navigate at sea in the modern world is through GNSS, in contrast with other transportation such as vehicles that can navigate the roads thanks to road signs and directions". I would encourage the authors to cite this paper and explain the rationale for omitting GNSS data from this study, despite its common use and utility in contemporary maritime operations. A clarification on how the authors plan to incorporate GNSS into future work to address this gap would be appreciated.
8. In Zhang, Y., Tu, P., Zhao, Z., & Chen, X. Y. (2025). Incorporating prior knowledge of collision risk into deep learning networks for ship trajectory prediction in the maritime Internet of Things industry. Engineering Applications of Artificial Intelligence, 146, 110311, the authors enhance the accuracy and reliability of ship trajectory predictions by incorporating collision risk modeling into the prediction framework. How can this model be incorporated into this paper?
9. The manuscript only emphasizes the advantages of the work done, but does not elaborate on the shortcomings of the work done and the follow-up prospects.

Author Response

Please find our response in attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

the comments are addressed.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed all my concerns. The revised manuscript is ready for publication.