Center of Mass Auto-Location in Space^†

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Attached file.

Comments for author File: Comments.pdf

Author Response

•  The conclusions presented in Section 4 (Discussion) are too superficial and lack depth.

- Great point, thanks. Section 4 has been augmented to reduce superficiality and increase depth, particularly using verbiage that includes the originally stated research objectives and purpose of the research. Specific results achieved are also elaborated in direct comparison to the declared comparative contemporary benchmark.  

Should be clarified/changed:

• The Abstract (lines 11–26) should not include detailed research results. It is recommended to either remove this section or generalize it appropriately.

- The MDPI publication guidance repeated in the manuscript template stipulates itemized parts of the abstract as: “(1)…..; (2)…..; (3) Results: summarize the article’s main findings in broadest, widely understandable, quantitative terms; (4)……..”. Compliance with this Reviewer request will violate the journal guidance and likely generate objections from other Reviewers, Academic Editors, and possibly (while unlikely) typesetters. Please consider permitting this instance of compliance with the published guidance.

• It is not advisable to start the article with figures (Figure 1). A figure should supplement the text, and its placement should be clearly indicated and referenced within the main body.

- Wiley Publishers recently completed an analysis to compare key article usage metrics of articles with Front Cover Images against the average metric values of articles that published in the same issue. Since May 2021, and compared to articles from the same issue without, articles with a Cover Image average: 55% higher full text views on Wiley Online Library; and 31% higher Altmetric Attention scores. [https://authorservices.wiley.com/author-resources/Journal-Authors/Promotion/journal-cover-image.html] Please consider allowing the use of front cover images in hopes of increasing views and Altmetric attention scores.

• I recommend revising Box 1 (lines 44–57) in terms of format. A graphical form such as a table or box is not recommended. The content related to research methodology—Problem Statement and Research Objectives—is appropriate in this section. However, the Key Contributions, if they present results, should be moved to the Discussion or Conclusion sections.

- The recommendation is ceded completely and the graphical display has been eliminated and the key contributions have been generalized in accordance with the Reviewer’s recommendations.

• I disagree with the statement: “The study results confirmed hunches of satellite operators who believed the roll axis was probably well aligned, while the other two axes have erroneous mass and inertia distribution assumptions”, as it is not scientific. It is advised to refer to assumptions rather than “hunches,” which implies subjectivity and undermines the objectivity of the research process (Section 4: Discussion, line 360).

- The point is ceded completely, and the offending phrase is completely eliminated in the revision.

• In Section 4.1 (Future Research Directions), it is recommended to justify the proposed directions—why the authors want to explore these areas, what purpose it serves, and what outcomes they expect (lines 370–375).

- Thanks for the great recommendations. They are accepted completely and accommodated in section 4.1 of the revision.

• The final conclusions should be expanded.

- Especially to tie the final conclusions to the original statement of research goals, text was contextually pegged to the initial declaration in Box 1.

Reviewer 2 Report

Comments and Suggestions for Authors

 

In this paper, authors present a method for autonomously determining the center of mass (CoM) of spacecraft in orbit based on time-varying estimates of inertia properties derived from attitude maneuvers. The paper seems to be well organized. Major concerns:

 

1. The paper presents multiple estimation techniques and experimental validations, but the main innovation and contribution could be stated more clearly in the abstract and introduction. Consider succinctly highlighting what sets this method apart from previous ones.

 

2. The proposed two-norm optimal projection learning method is a novel advancement, particularly its rapid convergence demonstrated in Figures 11 and 17. However, the manuscript should clarify how this approach fundamentally differs from prior inertia identification techniques (e.g., [15,19]) beyond computational efficiency. A direct comparison with the "Huber extended Kálmán filter" [19] in terms of robustness to sensor noise would strengthen claims of superiority.

 

3. The 0.1% error claim in validating experiments (Section 3.4) lacks statistical backing. Provide uncertainty intervals (e.g., Monte Carlo simulations) for inertia estimates under varying noise levels.

 

4. Table 6’s performance metrics are unclear due to undefined percentage values (e.g., "36%" for x-coordinate). Reformat this table using absolute errors (meters) relative to ground-truth CoM positions, and compare with state-of-the-art benchmarks like [7,15] to contextualize improvements.

 

 

Author Response

• The paper presents multiple estimation techniques and experimental validations, but the main innovation and contribution could be stated more clearly in the abstract and introduction. Consider succinctly highlighting what sets this method apart from previous ones.

- The suggestion is ceded completely and the abstract and introduction are both revised. “…proposing a novel two–norm optimal projection learning method….” Has been added to the abstract, while “…Additional novelty stems from seminal introduction of a two–norm optimal projection learning method…” has been added to the introduction.

• The proposed two-norm optimal projection learning method is a novel advancement, particularly its rapid convergence demonstrated in Figures 11 and 17. However, the manuscript should clarify how this approach fundamentally differs from prior inertia identification techniques (e.g., [15,19]) beyond computational efficiency. A direct comparison with the "Huber extended Kálmán filter" [19] in terms of robustness to sensor noise would strengthen claims of superiority.

- Great point. A more detailed (pre) elaboration of the proposed methods is place amidst the discussion of the (not completely dissimilar) methods proposed in [15] and [19]. The relatively short space between the two augmentations might aid the reader keep the comments in mind throughout the introduction.

• The 0.1% error claim in validating experiments (Section 3.4) lacks statistical backing. Provide uncertainty intervals (e.g., Monte Carlo simulations) for inertia estimates under varying noise levels.

- The Reviewer’s comments illustrate the author has not well explained this aspect. Verbiage has been revised at the end of section 3.4.

• Table 6’s performance metrics are unclear due to undefined percentage values (e.g., "36%" for x-coordinate). Reformat this table using absolute errors (meters) relative to ground-truth CoM positions, and compare with state-of-the-art benchmarks like [7,15] to contextualize improvements.

- Thanks for catching this. The confusion is now obvious. Section 3.1 (including Table 6) is a very brief excerpt from a prequel (analytic and numerical) work, where Table 6 can be eliminated in hopes of avoiding exactly this confusion, especially since it has slight impact on the current presentation of the experimental validation of the prequel numerical study. Thanks again.

Reviewer 3 Report

Comments and Suggestions for Authors

 Using the parallel axis theorem, in this paper, the location of the mass center is parameterized using the cross products of inertia, and that information is extracted from spaceflight maneuver data validating modeling and simulation. In general, the results of this paper are interesting. I have the following concerns.

1. The PAT derivation assumes rigid bodies with fixed mass distribution. What if the mass distribution is time-varying as the study metions time-varying estimates.
2. It seems that there is a lack of sensitivity analysis on how angular velocity cross terms affect the conditioning of the regression matrix in eq. (20).
3. It is better to give a discussion on the selection of the gain of the observer.
4. What if there are white noise for the sensor data?
5. What if the spacecraft is flexible other than rigid?

Author Response

1. The PAT derivation assumes rigid bodies with fixed mass distribution. What if the mass distribution is time-varying as the study metions time-varying estimates.

• Thanks for the revision request. The critiques are accepted completely and revised verbiage is now in section 2.1 to ameliorate the confusion. Thanks again.

1. It seems that there is a lack of sensitivity analysis on how angular velocity cross terms affect the conditioning of the regression matrix in eq. (20).

• Good point, thanks. Discussion of such has been added and the task has been added to the list of recommended future research in section 4.1.

1. It is better to give a discussion on the selection of the gain of the observer.

• Great point. Thanks. Discussion has been added to the observer figure caption describing the selection methods used (in figure A18).

1. What if there are white noise for the sensor data?

• Great point, thanks. Particularly since noise enhances persistent excitation improving estimation, elaboration of white noise in both the sensor and command is in the caption of figure 9 and the caption of table 6.

1. What if the spacecraft is flexible other than rigid?

• Great point, thanks. Discussion of flexible extensions from rigid body treatment has been added section 4.1 Future research directions.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

No

Reviewer 2 Report

Comments and Suggestions for Authors

The revised manuscript is satisfactory and can be accepted.