A Fast Satellite Selection Algorithm Based on NSWOA for Multi-Constellation LEO Satellite Dynamic Opportunistic Navigation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for the opportunity to review this manuscript. The paper addresses an interesting and timely topic with clear potential to contribute to the field of satellite constellations and applications. While the study is well-structured overall, I recommend minor revisions. Below are my detailed suggestions:

 

Literature Context & Novelty：The introduction would benefit from a more thorough review of recent advancements in satellite applications to better position the novelty of this work. Specifically, I suggest incorporating the following key references to contextualize the study:

 

• X. Sun, Y. Wang, J. Su, J. Li, M. Xu, and S. Bai, "Relative orbit transfer using constant-vector thrust acceleration," Acta Astronaut., vol. 229, pp. 715–735, 2025, doi: 10.1016/j.actaastro.2025.01.023
• Cinelli, M., Ortore, E., Laneve, G. et al. Geometrical approach for an optimal inter-satellite visibility. Astrodyn 5, 237–248 (2021). https://doi.org/10.1007/s42064-020-0099-0
• Guo, S., Zhou, W., Zhang, J. et al. Integrated constellation design and deployment method for a regional augmented navigation satellite system using piggyback launches. Astrodyn 5, 49–60 (2021). https://doi.org/10.1007/s42064-020-0091-8.

 

Computational Time Comparison: The manuscript does not include a comparison of computational time for the proposed methods. Adding such results (e.g., in tabular form) would strengthen the practical applicability of the study.

 

Equation and Figure Issues: Equations 6–7: There appears to be symbolic inconsistency/confusion in these equations. Please carefully revise the notation for clarity.

 

Figure 1: The resolution/quality of this figure is suboptimal. Consider regenerating it to ensure readability.

 

Optional Suggestion for Improvement: The current experiments simulate only a single trajectory (coastal "8"-shaped flight). To demonstrate robustness, I recommend testing additional scenarios (e.g., varying trajectories or operational conditions).

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors,

Here are my observations.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper titled “A Fast Satellite Selection Algorithm Based on NSWOA for Multi-Constellation LEO Satellite Dynamic Opportunistic Navigation” needs  revision:

1. The abstract introduces the problem and the proposed NSWOA-based solution clearly, but it would benefit from including quantitative results. Mentioning the percentage improvements in DGDOP or computational efficiency compared to baseline algorithms would better highlight the contributions.
2. The current keywords are too broad. Consider refining them to: LEO-PNT, Doppler-based positioning, NSWOA, multi-objective optimization, satellite selection, UAV navigation.
3. The introduction is rich in detail but could be more concise. Presenting the research gap and ojectives earlier in the section would improve readability.
4. The key innovations, such as the archive set and guidance selection mechanism in NSWOA, should be explicitly stated in a numbered or bulleted list to clearly differentiate the work from previous research.
5. Replace dense numeric citation blocks (e.g., [10–14]) with narrative citations for key foundational works (e.g., “Deb et al. [34] proposed…”). This would improve flow and contextual understanding.
6. Section 2.1 is mathematically sound, but the gradient matrix and linearization steps would benefit from a visual aid or brief example to enhance understanding.
7. Clearly state any assumptions made in the system model, including noise characteristics, satellite motion simplifications, or Doppler estimation models, and their implications for real-world applications.
8. Important parameter tables (Tables 3 and 4) should be introduced earlier within their respective sections to support the methodological explanations and simulation setups.
9. While NSGA-II, PSO, and GWO are valid baselines, justify why these were selected for comparison, especially considering real-time optimization constraints in UAV applications.
10. Beyond DGDOP and IGD, consider including other performance metrics such as execution time, convergence speed, or UAV positioning accuracy to provide a more complete evaluation.
11. Figures 3–7 are informative but crowded. Improve clarity by adjusting legends, color contrast, and adding consistent subfigure labels (a, b, c...).
12. The paper could better explain how the IGD metric reflects solution diversity and convergence, particularly for readers unfamiliar with multi-objective performance indicators.
13. The fixed-satellite experiment (n = 5) should include a justification for why this number was chosen. Link it to UAV performance constraints or environmental assumptions.
14. The computation results are promising, especially in Figure 7b. Explicitly quantify the reduction in run time or number of satellites selected, and relate this to onboard UAV processing limitations.
15. The archiving and guiding mechanisms are key contributions but are buried in the methodology. Highlight them in a distinct subsection and consider a flowchart to clarify their integration.
16. Table 2 contains long pseudocode. Consider dividing it into separate steps or converting it into a block diagram or flowchart to make it easier to follow.
17. Discuss how NSWOA scales with increasing numbers of LEO satellites (e.g., 10,000+ in future constellations). Address potential computational bottlenecks or algorithmic adaptations.
18. Include a brief discussion of how the proposed algorithm might be implemented on real-time embedded systems (e.g., UAVs). Mention hardware constraints or efficiency considerations.
19. Please cite this related recent work, which is relevant to deep Q- learning algorithms that it can be used in Doppler-based navigation using LEO satellite signals:

https://link.springer.com/article/10.1007/s42452-024-05690-y

20. The conclusion restates results well but would benefit from a structured recap of contributions and a brief future work plan (e.g., flight testing, 3D path integration).
21. The manuscript is generally clear but could benefit from minor grammatical polishing and simplification of long sentences to improve clarity.
22. Figures should be reviewed for formatting consistency, label clarity, and resolution quality suitable for publication.

Comments on the Quality of English Language

Can be rechecked. 

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

• In lines 140-155, 159-165, 204-212, 228-232, 276, 300, etc.. and more are some problem with the elements from equations. Some conversion errors. Must be fixed in the final document. Please revise this.
• Figure 4, 5, 6 and 7 are not clear. please use a better image with a higher resolution for the 4 figures

Author Response

Comments 1: [In lines 140-155, 159-165, 204-212, 228-232, 276, 300, etc.. and more are some problem with the elements from equations. Some conversion errors. Must be fixed in the final document. Please revise this.]

Response 1: Thank you for pointing this out. We have thoroughly reviewed the entire manuscript and corrected all equation formatting problems. These issues were not present in the original Word file or in PDFs generated locally using Word’s built-in export functions. However, they appear to have been introduced by the journal’s online PDF conversion system. We have contacted the editorial office regarding this matter. To avoid such conversion-related errors, we have uploaded a properly formatted PDF version along with the revised Word file. Comments 2: [Figure 4, 5, 6 and 7 are not clear. please use a better image with a higher resolution for the 4 figures.] Response 2: Agree. We appreciate the reviewer’s suggestion. All four figures have been updated with vector graphics to ensure improved clarity.

Reviewer 3 Report

Comments and Suggestions for Authors

After a thorough review of the revised manuscript, I confirm that the authors have successfully addressed all concerns and incorporated the necessary improvements. The paper now meets the journal's standards. 

Author Response

Comments 1: [After a thorough review of the revised manuscript, I confirm that the authors have successfully addressed all concerns and incorporated the necessary improvements. The paper now meets the journal's standards.]

Response 1: Thank you for your positive feedback. We have thoroughly reviewed the entire manuscript and resolved the remaining formatting issues, including those related to figures and equations, to ensure that the final version meets the journal’s standards.