Precise Relative Orbit Determination for Chinese TH-2 Satellite Formation Using Onboard GPS and BDS2 Observations

Round 1

Reviewer 1 Report

Corrections are given in the PDF document.

Comments for author File: Comments.pdf

Author Response

Author’s response

Dear Reviewer,

Thank you for the patient corrections for our manuscript. We have studied these comments and suggestions carefully. Some corrections have been made in the paper. Revised portions are marked in red in the revised manuscript.

The following pages are our point-by-point responses to the comments. Once again, thanks to all reviewers for valuable suggestions!

Best regards,

Bin Yi

Responses to the comments of Reviewer #1:

Reviewer #1:

(1) Lines 2-3: correct: title. Precise Relative Orbit Determination for Chinese TH-2 Satellite Formation Using Onboard GPS and BDS2 Observations

Response:

Thank you for your comments. The corresponding statement has been corrected.

(2) Lines 29-30: correct: 7.08 mm. Assigning different weights to GEO satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD can be improved to 7.08 mm with the GEO weighting strategy.

Response:

Thank you for your comments. The corresponding statement has been corrected.

(3) Lines 64-66: add: (Precise Point Positioning). Liu et al. studied PPP (Precise Point Positioning) based on GPS and BDS, results showed that the ambiguity fixing rate within 10 min for GPS is only 17.6%, when adding IGSOs and MEOs, the percentage improved significantly to 42.8% [11].

Response:

Thank you for your comments. The corresponding statement has been corrected.

(4) Lines 74-75: correct: and Teunissen. Verhagen and Teunissen showed that GPS+BDS was more conductive to real-time relative orbit determination than GPS-only or BDS-only [14].

Response:

Thank you for your comments. The corresponding statement has been corrected.

(5) Lines 84-86: correct: Montenbruck et al. [17] and Moon et al. [18]. Montenbruck et al. [17] and Moon et al. [18] discussed the TanDEM-X mission by using the GRACE as a reference case to illustrate the processing concept and expected accuracy.

Response:

Thank you for your comments. The corresponding statement has been corrected.

(6) Lines 86-89: correct: Montenbruck et al. [19] and Allende-Alba and Montenbruck [20]. Montenbruck et al. [19] and Allende-Alba and Montenbruck [20] adopted an internal consistency check, which comparing the baseline solutions resulting from the differential carrier phase processing against the relative positions derived from differential POD (dPOD) solutions.

Response:

Thank you for your comments. The corresponding statement has been corrected.

(7) Line 101: correct (bold): 2. Data collection and quality evaluation

Response:

Thank you for your comments. The corresponding statement has been corrected.

(8) Lines 109-111: correct: ≈. It works in a solar-synchronous orbit at ≈ 518 km altitude and the incidence angle range from 35° to 46°, separated from each other only a few hundred meters in space [26].

Response:

Thank you for your comments. The corresponding statement has been corrected.

(9) Line 201 versus line 345: correct: 4. Results and discussion or 5. Discussion ???

Response:

Thank you for your comments. The corresponding statement has been corrected. 4. Results, 5. Discussion.

(10) Lines 263-265: correct: 7.08 mm; add: (global). The average value of the daily RMS is 7.08 mm, 8.00 mm and 11.40 mm in 3D (global) when the weight of GEOs is 1, 0.5 and 0.2, respectively.

Response:

Thank you for your comments. The corresponding statement has been corrected.

(11) Pages 10-11: correct in Table 3: 2nd row: The non-Asia-Pacific region/mm; 3rd row: The Asia-Pacific region/mm

Response:

Thank you for your comments. The corresponding statement has been corrected.

(12) Lines 316-317: add: (full name). The RMS of DD ionospheric‐free OC (full name) phase residual of GPS and BDS2 are 4.2 mm and 8.5 mm, respectively.

Response:

Thank you for your comments. The corresponding statement has been corrected.

(13) Lines 375-378: correct: 7.08 mm. When assigning the same weight to MEO, IGSO and GEO satellites, the RMS of difference between the GPS‐based and BDS2‐based PROD in 3D components is 7.08 mm, 2.89 mm and 7.96 mm in global, Asia‐Pacific region and non‐Asia‐Pacific region, respectively.

Response:

Thank you for your comments. The corresponding statement has been corrected.

(14) Pages 16-17: In References: [1], [2], [4], [6], [8], [9], [10], [11], [12], [13], [15], [16], [17], [18], [21],[22], [26], [28], [29], [30], [32], [33], [34]: write names of all authors (instead of et al.)

Response:

Thank you for your comments. The corresponding statement has been corrected.

(15) For the development and modernization of GNSS see articles:

https://satellite-navigation.springeropen.com/articles/10.1186/s43020-020-00023-x https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=319453&lang=en

Barnes, D. (2019). GPS status and modernization. Presentation at Munich Satellite Navigation Summit 2019.

China Satellite Navigation Office. (2019). Development of the BeiDou Navigation Satellite System (Version 4.0). Published by CSNO, Dec. 2019.

Response:

Thank you for your comments. New references were added.

8.China Satellite Navigation Office. Development of the BeiDou Navigation Satellite System (Version 4.0). December. 2019.

11.Guenter W.H. Status, perspectives and trends of satellite navigation. Satellite Navigation, 2020, 1, 22.

(16) Figures must be of better quality

Response:

Thank you for your comments. The pictures have been redrawn.

(17) For figure and table size see: Instructions for Authors

Response:

Thank you for your comments. All the figures and tables have been modified.

(18) New references add in References

Response:

Thank you for your comments. New references were added.

(19) For References list see: Instructions for Authors

Response:

Thank you for your comments. All the references have been modified.

(20) English must be proofread

Response:

Thank you for your comments. We have used one of the editing services listed at  https://www.mdpi.com/authors/english.

Thanks again for your all valuable suggestions!

Author Response File: Author Response.docx

Reviewer 2 Report

TH-2 is China’s first short-range satellite formation system and second, after TanDEM,-X in the world used to realize interferometric synthetic aperture radar (InSAR) technology. In the article "Precise relative orbit determination for Chinese TH-2 satellite formation using onboard GPS and BDS2 observations" the Authors performed the precise relative orbit determination (PROD) for TH-2 based on GPS, BDS2 and GPS+BDS2 observations.

The structure of the article is considered and clear. The background and comprehensive review of the problem's literature were presented. 
In the main part of the manuscript, data collection and quality evaluation have been presented. TH-2 satellite formation system, performance of onboard GNSS receiver and data quality of multi-GNSS observations have been described. Precise relative orbit determination have been analysed using NDT and CHS approach. Results of the research have been presented in graphic form. Conclusions, on the basis of the research, are clear. 

The article is very interesting and has high scientific advantages.
Main questions for Authors and observations are following:
1. How the number of visible navigation satellites can be 7.5 or 9.5? (line 32-33).
2. What does it mean: the RMS ... is better than 1.5mm? In my opinion the value/error/accuracy can be smaller or greater. 
3. Section 2 (line 101) should have the format for section, not for subsection (bold).

Author Response

Author’s response

Dear Reviewer,

Thank you for the patient corrections for our manuscript. We have studied these comments and suggestions carefully. Some corrections have been made in the paper. Revised portions are marked in red in the revised manuscript.

The following pages are our point-by-point responses to the comments. Once again, thanks to all reviewers for valuable suggestions!

Best regards,

Bin Yi

Responses to the comments of Reviewer #2:

Reviewer #2:

TH-2 is China’s first short-range satellite formation system and second, after TanDEM-X in the world used to realize interferometric synthetic aperture radar (InSAR) technology. In the article "Precise relative orbit determination for Chinese TH-2 satellite formation using onboard GPS and BDS2 observations" the Authors performed the precise relative orbit determination (PROD) for TH-2 based on GPS, BDS2 and GPS+BDS2 observations.

The structure of the article is considered and clear. The background and comprehensive review of the problem's literature were presented.

In the main part of the manuscript, data collection and quality evaluation have been presented. TH-2 satellite formation system, performance of onboard GNSS receiver and data quality of multi-GNSS observations have been described. Precise relative orbit determination have been analysed using NDT and CHS approach. Results of the research have been presented in graphic form. Conclusions, on the basis of the research, are clear.

The article is very interesting and has high scientific advantages.

Main questions for Authors and observations are following:

(1) How the number of visible navigation satellites can be 7.5 or 9.5? (line 32-33).

Response:

Thank you for your comments. The average number of visible GPS and GPS+BDS2 satellites from TH-2A and TH-2B at each time of day is 7.5 and 9.5, respectively. The corresponding statement has been corrected.

Lines 31-33: correct: When BDS2 is added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improves from 7.5 to 9.5.

(2) What does it mean: the RMS ... is better than 1.5mm? In my opinion the value/error/accuracy can be smaller or greater.

Response:

Thank you for your comments. The corresponding statement has been corrected.

Lines 372-373: correct: The RMS of difference between NDT and CHS solutions in 3D is smaller than 1.5 mm outside the maneuver periods.

(3) Section 2 (line 101) should have the format for section, not for subsection (bold).

Response:

Thank you for your comments. The corresponding statement has been corrected.

Thanks again for your all valuable suggestions!

Author Response File: Author Response.docx

Reviewer 3 Report

Review of “Precise relative orbit determination for Chinese TH-2 satellite formation using onboard GPS and BDS2 observations” by Yi et al

This is an interesting contribution on the important topic of precise relative orbit determination of multiple satellites using on-board GNSS data. The paper is generally well written with interesting results and important comparisons. However, as successful carrier-phase integer ambiguity resolution is crucial for this high-precision relative orbit determination, the treatment and documentation of integer ambiguity resolution in this contribution needs improvements. These are listed below:

1. At various places in this contribution the authors state that they used the least-squares ambiguity decorrelation method (LAMBDA). This is indeed important as the LAMBDA guarantees that one can achieve the highest possible ambiguity success-rate (i.e. probability of correct integer resolution). However, the authors have neglected to include the proper and original reference of the LAMBDA method. It is important to do so, also for our readers sake.
2. The authors have not shown the ambiguity success-rates that were achieved in their analyses. This would be important information to assess the reliabilities of their ambiguity resolution. Nowadays, the success-rates can be computed easily by using open domain softwares, like for instance the Ps-LAMBDA s/w [Verhagen et al (2013): Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications. Computers & Geosciences. 54: 361-376].
3. It is not quite clear why the authors used the ‘integer rounding’ for the CHS, since it is well known that such would not produce the best success-rates. Already the easy-to-compute method of ‘integer bootstrapping’ would give much better success-rates and it moreover has an analytical expression for its success-rate. The authors are asked to elaborate on this.
4. The authors state that they use ‘the often used ambiguity dilution of precision (ADOP) method to evaluate the accuracy of the float ambiguities’. Also here no proper reference is made to where the ADOP and its properties were introduced first. The ADOP was introduced in [Teunissen (1997): A canonical theory for short GPS baselines. Part IV: precision versus reliability. Journal of Geodesy, 71: 513-525]. Next to introducing a proper reference, it is also suggested that the authors give a brief description of the ADOP, such that our readers understand why the authors have used it in their analyses.

Author Response

Author’s response

Dear Reviewer,

Thank you for the patient corrections for our manuscript. We have studied these comments and suggestions carefully. Some corrections have been made in the paper. Revised portions are marked in red in the revised manuscript.

The following pages are our point-by-point responses to the comments. Once again, thanks to all reviewers for valuable suggestions!

Best regards,

Bin Yi

Responses to the comments of Reviewer #3:

Reviewer #3:

This is an interesting contribution on the important topic of precise relative orbit determination of multiple satellites using on-board GNSS data. The paper is generally well written with interesting results and important comparisons. However, as successful carrier-phase integer ambiguity resolution is crucial for this high-precision relative orbit determination, the treatment and documentation of integer ambiguity resolution in this contribution needs improvements. These are listed below:

(1) At various places in this contribution the authors state that they used the least-squares ambiguity decorrelation method (LAMBDA). This is indeed important as the LAMBDA guarantees that one can achieve the highest possible ambiguity success-rate (i.e. probability of correct integer resolution). However, the authors have neglected to include the proper and original reference of the LAMBDA method. It is important to do so, also for our readers sake.

Response:

Thank you for your comments. New references were added in References:

32. Teunissen P.J.G. The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J. Geod, 1995, 70(1-2), 65-82.
33. de Jonge P.J, Tiberius C.C.J.M. The LAMBDA method for integer ambiguity estimation: implementation aspects. Delft Geodetic Computing Centre LGR Series, No.12, Delft University of Technology, 1996.
34. Teunissen P.J.G.; de Jonge P.J.; Tiberius C.C.J.M. Performance of the LAMBDA method for fast GPS ambiguity resolution. Navigation, 1997, 44(3), 373-383.

(2) The authors have not shown the ambiguity success-rates that were achieved in their analyses. This would be important information to assess the reliabilities of their ambiguity resolution. Nowadays, the success-rates can be computed easily by using open domain softwares, like for instance the Ps-LAMBDA s/w [Verhagen et al (2013): Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications. Computers & Geosciences. 54: 361-376].

Response:

Thank you for your comments. In the NUDTTK software, the DD wide-lane ambiguities are solved by analyzed the Melbourne-Wubbena linear combination. Then, the wide-lane ambiguities are introduce as known to resolve the narrow-lane ambiguities. Both the wide-lane and narrow-lane ambiguities use the LAMBDA method to search for integer values. For the integer ambiguity validation, the ratio of the squared norms of the ambiguity residuals in the metric of the covariance for the best and second best integer solution obtained from the LAMBDA method, k_S/B [5], is examined. The critical value, k_S/B, is taken as 3.0. The absolute values of the individual ambiguity residuals of the wide-lane float solution and integer solution, k_w [5] is also examined. k_w is taken as 0.3. The ambiguity fixed rate is the fixed ambiguity divided by the total ambiguity. The DD ambiguity fixed rate is 100% based on GPS-only. The ambiguity fixed rate is only 92.6% based on BDS2-only. When BDS2 co-worked with GPS, the ambiguity fixed rate of GPS and BDS2 are both 100.0%.

(3) It is not quite clear why the authors used the ‘integer rounding’ for the CHS, since it is well known that such would not produce the best success-rates. Already the easy-to-compute method of ‘integer bootstrapping’ would give much better success-rates and it moreover has an analytical expression for its success-rate. The authors are asked to elaborate on this.

Response:

Thank you for your comments. Within the CHS software, the ambiguities are resolved to their integer values by the search strategy, which is related to the so-called fast ambiguity resolution approach algorithm [37].

The following information from the initial least-square adjustment is used:, the part of the solution vector consisting of all real-valued double-difference ambiguities, where u is the number of double-difference ambiguities, Q the corresponding cofactor matrix, andthe a posteriori variance factor. From the a posterior variance factor and the corresponding cofactor matrix the standard deviation m_i for the ambiguity parameter p_i or the standard deviation m_i,j for the difference p_i,j between two ambiguity parameters may be computed:

,.

Choosing a confidence level  and using Student’s distribution to compute the upper and lower range-widthfor the integer valued alternative parameter between two such parameters, here, is taken as 3.0. There is no significant difference between any value in the confidence interval and. If there is only one integer in the confidence interval, the integer is the integer solution of. If the confidence interval does not contain any integers, or contains multiple integers,  continues to be real-valued; then, the fixed ambiguities are introduce as known to resolve the other ambiguities. This process is repeated until there are no new integer ambiguity parameters.

It is more correct to state as ‘search strategy’, not ‘integer rounding’. Within the CHS software, the DD ambiguity fixed rate is about 94% based on GPS-only. The corresponding statement has been corrected

(4) The authors state that they use ‘the often used ambiguity dilution of precision (ADOP) method to evaluate the accuracy of the float ambiguities’. Also here no proper reference is made to where the ADOP and its properties were introduced first. The ADOP was introduced in [Teunissen (1997): A canonical theory for short GPS baselines. Part IV: precision versus reliability. Journal of Geodesy, 71: 513-525]. Next to introducing a proper reference, it is also suggested that the authors give a brief description of the ADOP, such that our readers understand why the authors have used it in their analyses.

Response:

Thank you for your comments. The ambiguity dilution of precision (ADOP) measures the average precision of the ambiguities and is invariant for the class of admissible ambiguity transformations. It is based on the determinant of the ambiguity variance matrix. Here, ADOP can be used to evaluate the accuracy of the float ambiguity, which depends on the number of visible satellites and the quality of their phase and code observations. And new references were added in References:

41.Teunissen, P. J. G.; Odijk, D. Ambiguity Dilution of Precision: definition, properties and application. Proceedings of The Institute of Navigation’s ION GPS-1997, Kansas City, MO, 1997; pp. 891–899.

42.Teunissen P.J.G. A canonical theory for short GPS baselines. Part IV: precision versus reliability. J. Geod. 1997, 71, 513-525.

Thanks again for your all valuable suggestions!

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Corrections are given in the PDF document.

Comments for author File: Comments.pdf

Author Response

Author’s response

Dear Reviewer,

Thank you for the patient corrections for our manuscript. We have studied these comments and suggestions carefully. Some corrections have been made in the paper. Revised portions are marked in red in the revised manuscript.

The following pages are our point-by-point responses to the comments. Once again, thanks to all reviewers for valuable suggestions!

Best regards,

Bin Yi

Responses to the comments of Reviewer #1:

Reviewer #1:

(1) All figures should be displayed in full (they should not be cropped). Figure 15 is fine.

Response:

Thank you for your comments. All figures were displayed in full.

Thanks again for your all valuable suggestions!

Author Response File: Author Response.docx

Reviewer 3 Report

The revised manuscript has properly taken the points of the reviews into account and can therefore be accepted for publication.

Author Response

Thanks to the expert for your evaluation and affirmation of the work.

Author Response File: Author Response.docx

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.