Detailed Investigation on Ambiguity Validation of Long-Distance RTK

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors,

The study is correctly designed and scientifically sound in general. However, the results should be presented more clearly, while the introductory section also needs some corrections. Below, you can find some suggestions that in my opinion will help improve the manuscript.

 

In line 10 the word "two" is repeated

Line 46-53, is it possible to find some e more recent works?

Line 55 Please, briefly describe the methods (2-5 sentences)

Line 106 please explain how the values of 1 cm and 3 cm were chosen 

In all subsections of 4.1 some discussion of the results is missing, it is rather only a statement, but if possible, try to formulate the conclusions

Fig. 4, 6,7, 15,1618,19, 23 - a legend in the fig is missing, it is needed, because there are differently colored dots

Fig. 6 and 7 why is the scale of the Y axis not linear?

Section 5 needs a slightly more detailed description of your "novel" approach. The whole section is on one page.  

 

 

 

Author Response

Comments 1: In line 10 the word "two" is repeated

Responses 1:  Corrected and thanks.

Comments 2: Line 46-53, is it possible to find some e more recent works?

Responses 2: More recent works are added. Thank you.

Comments 3: Line 55 Please, briefly describe the methods (2-5 sentences)

Responses 3: Modified and thanks.

Comments 4: Line 106 please explain how the values of 1 cm and 3 cm were chosen. 

Responses 4: The two values are chosen based on the static testing results.

Comments 5: In all subsections of 4.1 some discussion of the results is missing, it is rather only a statement, but if possible, try to formulate the conclusions

Responses 5: A summary is added as Section 4.1.5 for some discussion of the results. Thank you for your suggestion.

Comments 6: Fig. 4, 6,7, 15,1618,19, 23 - a legend in the fig is missing, it is needed, because there are differently colored dots. Fig. 6 and 7 why is the scale of the Y axis not linear?

Responses 6:  Modified as suggested

Comments 7: Section 5 needs a slightly more detailed description of your "novel" approach. The whole section is on one page.

Responses 7: Modified as suggested and thanks.

 

Reviewer 2 Report

Comments and Suggestions for Authors

Detailed investigation on ambiguity validation of long-distance RTK. This work first introduces the challenges of fixed ambiguity in long-distance RTK and focuses on validating two long baseline ambiguity testing methods: the theoretical success rate and the R-ratio test. Subsequently, a substantial amount of long baseline RTK data was analyzed to evaluate the performance of these two ambiguity testing methods. The study concludes by proposing an extended period for ambiguity testing, ranging from thirty minutes to an hour, thereby enhancing the credibility of the ambiguity testing process.

This article requires a significant amount of work, but lack of innovation. The results may be publishing, however, some aspects of the manuscript should be improved, as listed below.

 

Comments on the manuscript:

Major points:

1.   Is it reasonable to increase the observation time to improve the reliability of the ambiguity testing method for RTK. Please provide reasonable application scenario.

2.   Under kinematic conditions, the fixed reliability of ambiguity testing does not consistently increase over time. What is the effect of your proposed method in kinematic positioning for long baseline RTK? Please add the kinematic experimental results.

 Minor points:

1.   In line 109 figure reference error, it should be Figure 1.moreover， There is an issue with the drawing of Figure 1 and it needs to be modified.

2.   The analysis is inconsistent with the in Figure 9 in page 7. Please confirm and correct it.

3.   In the analysis of Figure 22, there are two methods: float and best integer, but only one method has a positioning error sequence. Why is this.

4.   Why is the ambiguity fixed incorrectly between 25 and 30 minutes in Figure 1? Can we try to analyze it? How to use your new ambiguity testing methods proposed in 5.

Author Response

Comments 1: Is it reasonable to increase the observation time to improve the reliability of the ambiguity testing method for RTK. Please provide reasonable application scenario. 

Responses 1:  Theoretically, it is reasonable to increase the obervation time to improve the reliability of ambiguity resolution, no matter which ambiguity validation method is used. But in practical applications, in order to validate ambiguity resolution, it is required to meet a threshold, which generally fail in case of bad data quality or existing outliers etc. So we can say that increasing the obervation time can improve the reliability of ambiguity resolution, but may not increase the success rate of ambiguity validation methods.

Comments 2: Under kinematic conditions, the fixed reliability of ambiguity testing does not consistently increase over time. What is the effect of your proposed method in kinematic positioning for long baseline RTK? Please add the kinematic experimental results.

 Responses 2: 

Comments 3: In line 109 figure reference error, it should be Figure 1.moreover， There is an issue with the drawing of Figure 1 and it needs to be modified. 

Responses 3: Modified and thanks.

Comments 4: The analysis is inconsistent with the in Figure 9 in page 7. Please confirm and correct it. 

Responses 4: Corrected and thanks.

Comments 5: In the analysis of Figure 22, there are two methods: float and best integer, but only one method has a positioning error sequence. Why is this. 

Responses 5: The description is not correct and it is modified to delete the description related to float ambiguit solution. There is no need to include results of float one in Figure 22. Because Figure 22 is an example with the best ambiguity resolution is correct from the first epoch to the last one in one hour. During the period, the ratio value is low and cannot reach the threshold. 

Comments 6: Why is the ambiguity fixed incorrectly between 25 and 30 minutes in Figure 1? Can we try to analyze it? How to use your new ambiguity testing methods proposed in 5.

Responses 6: As there is so many cases like that of Figure 1 and they are not analyzed one by one in this research. We will do the analysis in our future work. If we want to use the new proposed method in practical applications for the case of Figure 1, we can fix the best ambiguity resolution at the time of about 40 minutes, as till that time, the ambiguity resolution has been best for more than half an hour if the 30 minutes is the threshold set by user.  

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

(1) A brief summary (one short paragraph) outlining the aim of the paper
and its main contributions;

Paper deals with long-distance Real-Time Kinematic (RTK) positioning for applications in remote areas, such as offshore areas,
which are not covered by Continuously Operating Reference Stations (CORS) networks.
Study is dedicated to examination of ambiguity validation for long-distance RTK, focusing on two prevalent methods:
the theoretical success rate and the R-ratio test.
Author's goal is to achieve the 2-3 cm accuracy of points coordinates with RTK, applying the new approach, based the duration for which
an integer ambiguity resolution candidate maintaining the best status.
It should be noted that authors did a lot of experimental calculations using data of IGS network stations.


(2) Broad comments highlighting areas of strength and weakness. These
comments should be specific enough for authors to be able to respond;

Despite big amount of experimental processing, the description of mathematical model is weak.
Is the presented formulas (1, 2 and 3) are developed by authors? No any information on "new approach" (mentioned in line 24).
The chapter "New ambiguity resolution validation method" gives the Fig 22, presenting the
positioning error with the best integer ambiguity resolution for case No 31, however no any scientific innovations could be found.
Even no any references in the chapter "Mathematical model of long-distance RTK".
Slightly better situation is in introduction part, however list of references is weak, more modern papers should be cited.
In chapter "Experimental design", it is not clear, what software was used for calculations. Also it is a question,
should all 320 cases be presented in the paper (Annex A). It takes half of volume of a paper. Probably it could be enough to mention,
that for processing the stations enable to track BeiDou-3 satellites were included.
Presentation of the results is started from the case No 125. Why not from case No 1? Is case No 125 most important?
However the positioning errors are given for case No 38 (Fig 3), and success rate for case No. 88 (Fig 14),
positioning error with the best integer ambiguity resolution - for case No 31 (Fig 22).
In Fig 1 blue arrow goes outside the graph. How the duration could be 0 minutes?
The baselines in Fig 2 are not visible.
Minimum required time to fix ambiguity (Fig 4) should be presented according to baselines lenght, not cases.
The same for Fig 7 and 8, 11, 12, 13, 15, 16, 18, 19, 23.



 
(3) Specific comments referring to line numbers, tables, or figures.

Tables are fine. Just suggestion to omit the Appendix A.
A lot of figures should be re-done.


(4) Are the references appropriate?

Presented references are appropriate, however list of references should be extended.


(5) Overall conclusion

Scientific soundness is low, practical findings are not promising.
Paper should be corrected and re-written to be printed in "Remote sensing".

Author Response

Comments 1: Is the presented formulas (1, 2 and 3) are developed by authors? No any information on "new approach" (mentioned in line 24).

Responses 1: Thank you for your suggestions. References for formula 1, 2 and 3 are added. The information about “new approach” is in Section 5 and it is modified with more detailed information.

Comments 2: The chapter "New ambiguity resolution validation method" gives the Fig 22, presenting the positioning error with the best integer ambiguity resolution for case No 31, however no any scientific innovations could be found.

Responses 2: Thank you for your comments. The contents about “New ambiguity resolution validation method” is modified with more detailed information. But please note that the method is proposed as a last resort for cases when current used methods (mainly ratio test) become invalid and is designed for applications with long observation time.

Comments 3: Even no any references in the chapter "Mathematical model of long-distance RTK".
Slightly better situation is in introduction part, however list of references is weak, more modern papers should be cited.

Responses 3: Modified as suggested and thank you.

Comments 4: In chapter "Experimental design", it is not clear, what software was used for calculations. Also it is a question, should all 320 cases be presented in the paper (Annex A). It takes half of volume of a paper. Probably it could be enough to mention, that for processing the stations enable to track BeiDou-3 satellites were included.
Responses 4: Thank you for your comments and suggestion. The information about the used software is added in Section 3 (the first paragraph). We are also not sure about all 320 cases be presented in Annex A. If for traditional paper version, the contents should be reduced. But for current electronic version, it may be better with more detailed information as the cases are different in various ways, including observed frequency bands, GNSS system, receiver and antenna type etc. All these factors may have effect on the performance and not all them are analyzed in detail in this manuscript. It may be beneficial to reader with as much as possible information.

 

Comments 5: Presentation of the results is started from the case No 125. Why not from case No 1? Is case No 125 most important? However the positioning errors are given for case No 38 (Fig 3), and success rate for case No. 88 (Fig 14), positioning error with the best integer ambiguity resolution - for case No 31 (Fig 22).

Responses 5: Thank you for your comments and suggestions. In the manuscript, the selection of example case does not take into the order of case number into consideration. To clarify our points as much as possible, the most assumed suitable example cases are just chosen.

Comments 6: In Fig 1 blue arrow goes outside the graph. How the duration could be 0 minutes?
The baselines in Fig 2 are not visible.

Responses 6: Thank you for your comments and suggestions. Blue arrow is slightly shifted as suggested. 0 minutes mean the first epoch. In Fig 2, it is difficult to make the map not very big and keep the baselines visible at the same time. So, we decide to show the positions of the stations instead of baselines.

Comments 7: Minimum required time to fix ambiguity (Fig 4) should be presented according to baselines lenght, not cases. The same for Fig 7 and 8, 11, 12, 13, 15, 16, 18, 19, 23.

Responses 5: Thank you for your comments and suggestions. Please note that the sorting of case number is based on the ascending order of baseline length as well as the observation time. So the ascending of the case number represents the ascending of baseline length. If presented according to baseline length, there will be two problems. First, it is difficult to present multiple cases with same baseline length, second, as the distribution of baseline lengths is not even, some cases with similar baseline length will crowd together if presented according to baseline length.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Please, check the typos. 

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for the answers to all the comments. The authors addressed all issues from the original review report in a comprehensive way. In my opinion, the paper can be accepted for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank  you for your response.