Some Key Issues on Pseudorange-Based Point Positioning with GPS, BDS-3, and Galileo Observations

Round 1

Reviewer 1 Report

This manuscript presents a comprehensive analysis on pseudorange-based/single point positioning (SPP)  among GPS, BDS-3, and Galileo at a global scale. It is a good work. A few minor issues still need to be modified before possible acceptance.

1. Line 201, DOY32-> DOY 32

2. In the manuscript, BDS indicates BDS-3? Or BDS-2/3, see line 200

3. Many places need to add whitespace, such as line 241, 40–180E

4. In figure 6, the font size needs to be amplified, the same as figure 8, figure 9

5. Figure 19, Obviously, it has a different font than the other figures.

Author Response

Reply to comments on manuscript entitled “Some key issues on pseudorange-based point positioning with GPS, BDS-3, and Galileo observations”

Thank you very much for your comments. We have revised the manuscript carefully and responded point by point to the comments as below. (C and R indicate comment and response, respectively). Our revisions are highlighted in the revised manuscript with the “Track Changes” function.

C: Line 201, DOY32-> DOY 32

R: Accepted and modified.

C: In the manuscript, BDS indicates BDS-3? Or BDS-2/3, see line 200

R: In the manuscript, BDS indicates BDS-3. We have modified to make it more clearly in the revision.

C: Many places need to add whitespace, such as line 241, 40–180E

R: Accepted and modified.

C: In figure 6, the font size needs to be amplified, the same as figure 8, figure 9

R: Accepted and modified.

C: Figure 19, Obviously, it has a different font than the other figures.

R: Accepted and modified.

Reviewer 2 Report

This study aims at assessing SPP performance with the current GPS, BDS-3, and Galileo systems at a global scale. Some conclusions are interesting and meaningful. The manuscript needs some further improvements to be published on Remote Sensing.

1. The manuscript needs to be polished to make it more readable, and some grammar errors should be corrected.

2. Why is GLONASS ignored in the analysis of this study?

3. For the BDS-3 SPP, which types of satellites were used, only MEO, or MEO + IGSO, or MEO + IGSO + GEO? Please explain the reason.

4. For SPP, ionospheric delay and observation noise are two main error sources. Single-frequency SPP will not amplify observation noise, but cannot effectively deal with ionospheric delay. Dual-frequency SPP can completely eliminate the influence of the first-order ionospheric delay, but it will inevitably amplify the observation noise. Hereto, how to balance them?

Author Response

Reply to comments on manuscript entitled “Some key issues on pseudorange-based point positioning with GPS, BDS-3, and Galileo observations”

Thank you very much for your comments. We have revised the manuscript carefully and responded point by point to the comments as below. (C and R indicate comment and response, respectively). Our revisions are highlighted in the revised manuscript with the “Track Changes” function.

C: The manuscript needs to be polished to make it more readable, and some grammar errors should be corrected.

R: Thank you for your suggestions. We have already found a native English speaker to help us polish the manuscript.

C: Why is GLONASS ignored in the analysis of this study?

R: There have been many studies about SPP performance analysis considering GLONASS. The main purpose of this study is to comprehensively evaluate the global positioning performance of the new emerging BDS-3 and Galileo systems and the overall comparative analysis of SPP with GPS.

C: For the BDS-3 SPP, which types of satellites were used, only MEO, or MEO + IGSO, or MEO + IGSO + GEO? Please explain the reason.

R: SPP tests with BDS-3 MEO, MEO + IGSO, and MEO + IGSO + GEO have been performed. The results showed that the influence of adding IGSO and/or GEO was mainly concentrated in the Asia-Pacific region. Compared with MEO, the positioning accuracy is improved obviously by adding IGSO satellites. While, compared with MEO + IGSO, the improvement of positioning accuracy is not obvious by adding IGSO satellites. Considering the low accuracy of GEO satellite orbit and clock errors, this study only uses MEO and IGSO for BDS-3 SPP.

C: For SPP, ionospheric delay and observation noise are two main error sources. Single-frequency SPP will not amplify observation noise, but cannot effectively deal with ionospheric delay. Dual-frequency SPP can completely eliminate the influence of the first-order ionospheric delay, but it will inevitably amplify the observation noise. Hereto, how to balance them?

R: We first performed single- and dual-frequency SPP for BRMG and ABPO, and plotted their positioning error sequences. It can be found that when the dual-frequency observations are added to the three systems, the accuracy of both tracking stations becomes worse in the E direction and better in the N and U directions, because the systematic difference in the E direction is smaller and the error caused by the increased noise after the introduction of dual-frequency is larger than the ionospheric error corrected by dual-frequency. Therefore, when the system difference is small, single-frequency SPP can be chosen, and when the system difference is large, dual-frequency SPP can be used.

Reviewer 3 Report

Manuscript:

Some key issues on pseudorange-based point positioning with GPS, BDS-3, and Galileo observations

submitted by:

Feng Zhou and Xiaoyang Wang

Pseudorange-based/single point positioning (SPP), as one of the most basic modes of GNSS, is used by users in various fields. The first one that can be used for SPP is the GPS. At present, the positioning accuracy of GPS SPP in horizontal and vertical components is limited to 1-2 m in horizontal, and 2-3 m in vertical components. Positioning accuracies of Galileo are 2-3 m in horizontal and 2-7 m in vertical components and single-frequency BDS SPP is better than 2 m and 5 m in horizontal and vertical components, respectively.

The structure of the manuscript is considered and clear. In the introduction, the background and comprehensive review of the problem's literature were presented. The Authors present methodology of SPP: pseudorange observation equations, single-frequency SPP, dual-frequency SPP. 

In Data sets and processing strategies and Result validation and discussion sections, the Authors present availability analysis of GNSS constellations, Single-system and single-frequency SPP (G, C, E), Single-system and dual-frequency SPP (G, C, E) and Dual-system and single-frequency SPP (GE, GC, CE). Results of the research have been presented in graphic form. Conclusions, on the basis of the research.

Following suggestions should be taken into consideration: 

Line 50: Abbreviationsshould be defined the first time they appear in each of three sections: the abstract; the main text; the first figure or table (Instruction for Authors). It concerns MEO, IGSO, GEO and many other abbreviarions/acronyms.

Line 66:  There are five accuracies for four systems: 1/3/1/1.5/1.5 m, nent there ary onlu four: 1.5/3/1.5/1.5 m. Please check, if it is OK

Line 86: degrees should be just after the values with no spaces

Line 88: 30 degrees, but in line 86 are 10°, 20°, 30° and 40°

Line 95: IOV should be defined, as line 50

Table 2: where is table 1? 

Table 2: symbols in rows 3 and 4 are unclear; are they commas?

Line 189: the star should be replaced by x to define a dimension (or resolution)

Additionally, refenences should be adjusted to instruction for Authors.

Figures can be enlarged, especially 2, 3, 5, 6, 8, 9, 10, and 12.

Descriptions of axes in figures could be adjusted; plese compare e.g. figures 18 and 19 - in figure 19 are too large.

Author Response

Reply to comments on manuscript entitled “Some key issues on pseudorange-based point positioning with GPS, BDS-3, and Galileo observations”

Thank you very much for your comments. We have revised the manuscript carefully and responded point by point to the comments as below. (C and R indicate comment and response, respectively). Our revisions are highlighted in the revised manuscript with the “Track Changes” function.

C: Line 50: Abbreviations should be defined the first time they appear in each of three sections: the abstract; the main text; the first figure or table (Instruction for Authors). It concerns MEO, IGSO, GEO and many other abbreviations/acronyms.

R: Accepted and modified.

C: There are five accuracies for four systems: 1/3/1/1.5/1.5 m, while there are only four: 1.5/3/1.5/1.5 m. Please check, if it is OK

R: We are very sorry for the mistake. We have modified it in the revision.

C: Line 86: degrees should be just after the values with no spaces

R: Accepted and modified.

C: Line 88: 30 degrees, but in line 86 are 10°, 20°, 30° and 40°

R:  The paper we cite here to analyze the SPP for cutoff angles of 10°, 20°, 30° and 40°. The values we described below are all for a cutoff angle of 30°, and we used ''more than''. Also when 40° is reached, it is worse than the currently described value, so we describe the number of satellites, PDOP and positioning accuracy for 30°.

C: Line 95: IOV should be defined, as line 50

R:  Accepted and modified.

C: Table 2: where is table 1?

R:  We are very sorry that the table is marked from 2. We have modified it.

C: Table 2: symbols in rows 3 and 4 are unclear; are they commas?

R:  Yes. We used the wrong punctuation here and have changed it to a comma.

C: Additionally, references should be adjusted to instruction for Authors.

R:  Accepted and modified.

C: Figures can be enlarged, especially 2, 3, 5, 6, 8, 9, 10, and 12.

R:  Accepted and modified.

C: Descriptions of axes in figures could be adjusted; please compare e.g. figures 18 and 19 - in figure 19 are too large.

R:  Accepted and modified.

Reviewer 4 Report

Comments for author File: Comments.pdf

Author Response

Reply to comments on manuscript entitled “Some key issues on pseudorange-based point positioning with GPS, BDS-3, and Galileo observations”

Thank you very much for your comments. We have revised the manuscript carefully and responded point by point to the comments as below. (C and R indicate comment and response, respectively). Our revisions are highlighted in the revised manuscript with the “Track Changes” function.

C: Authors analyze SPP performance. However there are many different signal. Noise is different for each of them. For example E5 AltBOC signal noise is close to the phase measurements noise (see reference Padokhin, A. M., Mylnikova, A. A., Yasyukevich, Y. V., Morozov, Y. V., Kurbatov, G. A., & Vesnin, A. M. (2021). Galileo E5 AltBOC Signals: Application for Single-Frequency Total Electron Content Estimations. Remote Sensing, 13(19), 3973.). Which could give better performance in terms of positioning accuracy. Please add the discussion on how different signal are performed in SPP.

R: Thank you for your suggestion. Nowadays, GPS, BDS-3, and Galileo broadcast three, six, and five civilian signals, respectively. The impact of different signals on positioning performance is a very meaningful topic. This study is mainly to investigate the overall SPP positioning performance analysis of GPS, BDS-3 and Galileo at the global scale. We will continue to conduct in-depth research on your suggestions in future work. We have added the study of Padokhin et al. as a reference and described the corresponding text in the Introduction.

C: It seems that different plots in Figure 2 are given in different colorscale or data are wrong. BDS MEO performs as good as Galileo. However BDS satellites number should be better according to simulation provided in [Yasyukevich, Y. V., Vesnin, A. M., Kiselev, A. V., Mylnikova, A. A., Oinats, A. V., Ivanova, V. A., & Demyanov, V. V. (2022). MITIGATOR: GNSS-Based System for Remote Sensing of Ionospheric Absolute Total Electron Content. Universe, 8(2), 98.]

R: We used precise ephemeris from GFZ for analysis of number of satellites and PDOP at the global scale. In practice, it is possible that one or several satellites have adverse effects such as health conditions, resulting in a decline in the number of satellites. This may differ slightly from the simulated results.

C: Figure 4 is not informative since PDOP and number of satellites strongly depends on the geographical position. Global statistics of those parameters can be incorrect for a particular position. Some kind of sectors (by latitude and longitude) can be introduced based on Figure 2 and 3 as well as 8 and 9 and statistics for each sector might have much more sense.

R: Thank you for your comments. We have delete Figure 4 and its corresponding description in the revision.

C: Please provide bigger versions of Figure 8 and 9. They can be at least page-wide. Fix Figure 9 caption. Provide the description of how relative performance is calculated is it (C_error-G_error) /(C_error+G_error) for C vs G plot or something different.

R:  Accepted and modified. It is (C_error-G_error) /(G_error) for C vs G

C: From Figure 13 it seems like there is systematic error.

R:  The ionospheric error exists because single-frequency SPP is performed here.

C: Figure 15 doesn’t allow to estimate all the GIM data products used in research COD curve is almost buried below others.

R:  Accepted and modified.

C: Line 25: global ionospher map → global ionospheric maps

R:  Accepted and modified.

C: Fix caption for the Figure 3.

R:  Accepted and modified.

C: Please check the text for the typos.

R:  Thanks for your comment. We have checked and modified them in the revision.

Reviewer 5 Report

The article presents a comparison of the GPS, Galileo and BDS-3 systems. The authors mainly focus on the number of satellites, its consequences in the form of PDOP and the accuracy of the systems under different ionosphere models. As an addition, a summary of ISB for the different variants is presented.

I don't see anything new in the work that I would expect from a scientific article. The authors in the Introduction motivate their work by the lack of such a study in the literature that discusses the above issues but this is not entirely true. There are already a number of publications showing specifically the issues of the number of satellites and PDOPs for different GNSS systems and their combinations. Such comparisons are now often presented when working on the development of PPP methods, where this is also relevant. The authors focus on SPP in their analyses, but in this case it is the same issue and there is nothing to duplicate. The same is the case with the ISB analyses.

Another comparison concerns ionosphere models. In fact, the comparison is about the products provided only by CODE. The conclusion that the final models give better results than the rapid and predicted ones is obvious. It adds nothing to common knowledge. I also don't know what the purpose of this comparison is.

The paper also contains a few imperfections, such as captions of tables and figures. E.g. Fig. 2 and 3 are signed the same way. There is a lack of consistency in placing error values on the same type of figures (Fig. 13). Sometimes the results are described too casually, e.g. "system error in the E component is small...". in line 361 - what does "small" mean?

In conclusion, I think the paper does not add much to the subject of GNSS and should not be accepted for publication. The authors need to rethink what exactly they want to prove and present in the paper. They also need a better overview of already published works. If the paper was only supposed to be a comparison, it should be considered as a different form than a scientific article (some kind of report?).

Author Response

Reply to comments on manuscript entitled “Some key issues on pseudorange-based point positioning with GPS, BDS-3, and Galileo observations”

Thank you very much for your comments. We have revised the manuscript carefully and responded point by point to the comments as below. (C and R indicate comment and response, respectively). Our revisions are highlighted in the revised manuscript with the “Track Changes” function.

C: I don't see anything new in the work that I would expect from a scientific article. The authors in the Introduction motivate their work by the lack of such a study in the literature that discusses the above issues but this is not entirely true. There are already a number of publications showing specifically the issues of the number of satellites and PDOPs for different GNSS systems and their combinations. Such comparisons are now often presented when working on the development of PPP methods, where this is also relevant. The authors focus on SPP in their analyses, but in this case it is the same issue and there is nothing to duplicate. The same is the case with the ISB analyses.

R: Thank you for your comments. The main focus of this study is on the comprehensive comparative analysis of the new emerging systems such as BDS-3 and Galileo SPP positioning performance on a global scale and also demonstrating the differences and comparisons with GPS, and the number of stations selected is large enough and evenly distributed. The impact of adding MEO, IGSO, and GEO satellites for BDS-3 SPP is investigated, which has been added in the revision. For ISB analysis, the stability and variability of ISBs derived from single-frequency and dual-frequency SPP were demonstrated, and some interesting conclusions were found, i.e., the differences of ISBs among different receivers with single-frequency SPP is smaller than that of dual-frequency SPP. We have added the corresponding description in the revision.

C: Another comparison concerns ionosphere models. In fact, the comparison is about the products provided only by CODE. The conclusion that the final models give better results than the rapid and predicted ones is obvious. It adds nothing to common knowledge. I also don't know what the purpose of this comparison is.

R: Single-frequency SPP performance with CODE final, rapid, 1-day predicted, and 2-day predicted GIM was tested, and the comparison with those of single-frequency and dual-frequency ionospheric-free SPP was given. From the result, we can see that the positioning performance of dual-frequency is significantly improved compared with single-frequency SPP, but the error sequence is relatively noisier. While, SPP with CODE final, rapid, 1-day predicted, and 2-day predicted GIM outperformed dual-frequency SPP, and the error sequence is flatter. 1-day predicted, and 2-day predicted GIM products can be used for real-time SPP, and how to distribute these products to users is a topic worthy of in-depth study

C: The paper also contains a few imperfections, such as captions of tables and figures. E.g. Fig. 2 and 3 are signed the same way. There is a lack of consistency in placing error values on the same type of figures (Fig. 13). Sometimes the results are described too casually, e.g. "system error in the E component is small...". in line 361 - what does "small" mean?

R: Thanks for your comments. We have modified them in the revision to make the manuscript more readable.

Round 2

Reviewer 4 Report

Thank you for providing revised version and your responses to the comments/

Reviewer 5 Report

In my opinion, the work is more of a review than an original article. It summarizes the current quality of SPP positioning. For this reason, more research in the global literature should be done. Take this as a guideline for the future.