A Conical Model Approach for Invariant Points of Very Long Baseline Interferometry and Satellite Laser Ranging
Round 1
Reviewer 1 Report
This paper deals with an attractive topic (i.e., modelling invariant points of VLBI and SLR), which is essential to implement and maintain a global geodetic frame by space geodetic observations. This research has proposed a conical model approach as well as successfully tested it with a real-world application which demonstrated its efficiency and reliability. The organization of this paper is logical and clear. The general presentation of the paper is excellent. The discussions and conclusions are sound and clear. In addition, this paper has appropriately cited references in the research field that provides readers with the technical issues in the area of modelling IVP of space geodetic techniques. In general, the reviewer believes that this paper reaches the international standard and has a merit to be published in Remote Sensing.
Author Response
Thank you very much for reviewing this paper and for your valuable comments.
Reviewer 2 Report
Dear authors,
This manuscript evaluates a conical approach for the determination of the IVP in VLBI and SLR antennas.
The manuscript is well written and easy to read and understand. The methods applied are appropiate and the results seem consistent and properly presented.
It would be of interest to include a comparison of the results with the conventional approach and also with the GNSS-SLR-VLBI vectors derived from the ITRF2020 results.
Please find attached minor comments for your consideration.
Best regards
Comments for author File: 
Comments.pdf
Author Response
Thank you very much for reviewing this paper and for your valuable comments.
The detailed explanation is answered in the attached file.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper developed a conical model to estimate the IVPs of space geodetic sensors. The authors are expected to make more explanations and I suggest a minor revision.
1. Eq. (1a): The matrix P is called weight matrix, while its inverse is called cofactor matrix.
2. The symbols alpha, beta and gamma have already occurred in Eq. (3), while the corresponding explanation is given below Eq. (5).
3. Please reformulate the equation before Line 140 as: min \xi’S\xi s.t. N\xi = c. In addition, give a number to this equation.
4. Line 140: Is the matrix S restricted to be symmetric?
5. The authors are expected to explicitly give the solution form to the model (1).
6. The correspondence between the parameter partition in Eqs. (2)—(3) and the design matrix partition in Eq. (4) is not very clear.
7. Please explain the statement in Line 178.
8. Line 243: Please add the following references concerning TLS and the symmetric transformation:
Fang, X. (2013). Weighted total least squares: necessary and sufficient conditions, fixed and random parameters. Journal of Geodesy, 87(8), 733-749.
Fang, X. (2015). Weighted total least-squares with constraints: a universal formula for geodetic symmetrical transformations. Journal of Geodesy, 89(5), 459-469.
Author Response
Thank you very much for reviewing this paper and for your valuable comments.
The detailed explanation is answered in the attached file.
Author Response File: Author Response.pdf
Reviewer 4 Report
An article introduces a conical model approach for IVP for the VLBI and SLR, the investigated topic is quite interesting, however, I find some disadvantages within the text:
1. The references are quite out of date.
2. Figures and equations could be better explained.
3. I am missing the site and ground measurements description.
4. I am missing the comparison and verification of authors approach with so-called 'conventional' approaches and/or results from previous/other studies.
5. Conclusion section does not contain the main results with the main massage and value-added from this study (just a description of what has been done)...
6. It would be nice to provide the local tie values (distance between IVP for each technique) based on this study as it is necessary information for this community.
Please see also the pdf file attached.
Comments for author File: Comments.pdf
Author Response
Thank you very much for reviewing this paper and for your valuable comments.
The detailed explanation is answered in the attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 4 Report
One short remark considering GNSS, SLR, VLBI, DORIS references: each of these techniques has a dedicated article that should be used for citing/referencing, please go by each mentioned website [references 5-8], find dedicated paper, and use it for citation, e.g. for IGS it is (https://www.igs.org/about/#citation) ...
Johnston, G., Riddell, A., Hausler, G. (2017). The International GNSS Service. Teunissen, Peter J.G., & Montenbruck, O. (Eds.), Springer Handbook of Global Navigation Satellite Systems (1st ed., pp. 967-982). Cham, Switzerland: Springer International Publishing.
