Investigating the Global Performance of the BDS-2 and BDS-3 Joint Real-Time Undifferenced and Uncombined Precise Point Positioning Using RTS Products from Different Analysis Centers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Reviewer comments: minor revision

This paper investigates the performance of BDS-2 and BDS-3 joint real-time UU-PPP on a global scale, and five RTS products are utilized in this assessment. The workload is sufficient and can provide BDS users with important guidance on the selection of RTS products. What’s more, the high calculation accuracy of BDS-2+3 UU-PPP has the ability to provide possibilities for extracting ionospheric information. However, some confusion and details need to be explained further.

 

1. The RTS orbit refers to the satellite phase center. Specifically, does it pertain to the satellite phase center of the L1 frequency or the ionospheric combination?

2. Why does the author utilize the median value instead of the average value of the RTS-minus-GBM satellite clocks to derive the clock datum for real-time clocks?

3. Has the author considered the correlation between the radial direction of the orbit and the clock? It is advisable to incorporate the radial error into the clock when evaluating the clock error.

4. Does the number of satellites in Table 1 contain GEO satellites? The number of BDS satellites here is significantly less than that of the final precise ephemeris.

5. Table 2. The “BRDM” should be replaced by “broadcast ephemeris”. The “igs14_2233” should be corrected as “igs14_2233.atx”.

6. Some references related to tropospheric delay and ISB processing need to be added.

 

7. Figure 3. In the statistical process of orbit and clock accuracy, how to deal with gross errors?

Author Response

1. The RTS orbit refers to the satellite phase center. Specifically, does it pertain to the satellite phase center of the L1 frequency or the ionospheric combination?

Reply: thank you for your comments. In our study, the satellite phase center of RTS orbits for selected five analysis centers is based on the L1 frequency. This detail of data processing has been added to the revised manuscript as follows: “It should be noted that the satellite phase center of RTS orbits for selected five ACs is based on the L1 frequency rather than the DF ionospheric combination”.

 

2. Why does the author utilize the median value instead of the average value of the RTS-minus-GBM satellite clocks to derive the clock datum for real-time clocks?

Reply: thank you for your comments. Compared with the average value of the RTS-minus-GBM satellite clocks, the median value method can avoid the negative impact of gross errors on clock datum calculation. This key point has been mentioned in the reference [9] of the original manuscript.

 

3. Has the author considered the correlation between the radial direction of the orbit and the clock? It is advisable to incorporate the radial error into the clock when evaluating the clock error.

Reply: thank you for your comments. The correlation between the radial orbit error and clock error has not been considered in our study, the radial orbit and clock are treated as independent error component.

 

4. Does the number of satellites in Table 1 contain GEO satellites? The number of BDS satellites here is significantly less than that of the final precise ephemeris.

Reply: thank you for your comments. The number of satellites in Table 1 does not include GEO satellites. Since the RTS orbit accuracy of GEO satellites can reach up to 2 m, five GEO satellites (CO1-05) are generally excluded from the real-time PPP domain. Undoubtedly, the number of available RTS BDS satellites is much less than that of the final precise products like GBM, WUM.

 

5. Table 2. The “BRDM” should be replaced by “broadcast ephemeris”. The “igs14_2233” should be corrected as “igs14_2233.atx”.

Reply: thank you for your comments. The “Broadcast ephemeris” and “igs14_2233.atx” have been added in Table 2 of the revised manuscript.

 

6. Some references related to tropospheric delay and ISB processing need to be added.

Reply: thank you for your suggestions. The new reference [33] has been added in Table 2 of the revised manuscript.

“33. Zhou, F.; Dong, D.; Li, P.; Li, X.; Schuh, H. Influence of stochastic modeling for inter-system biases on multi-GNSS undifferenced and uncombined precise point positioning. GPS Solut. 2019, 23, 59.”

 

7. Figure 3. In the statistical process of orbit and clock accuracy, how to deal with gross errors?

Reply: thank you for your comment. In our study, the orbit errors exceeding 1.5 m are considered as gross errors and need to be removed in RMS calculation. As for clock evaluation, the gross error is defined as 3 ns. Some descriptions have been added to the revised manuscript as follow: “The orbit errors exceeding 1.5 m in any direction are considered as gross errors and need to be removed in assessment, while for clock evaluation, the gross error is defined as 3.0 ns”.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript focuses on evaluation of the BDS-2+3 real-time UU-PPP using different RTS products. The comparison of UU-PPP and IF-PPP is discussed in both static and kinematic mode. Overall, workload is reasonable, and the paper is tightly written. However, my biggest concern is that there has been some research working on the performance evaluation on the BDS PPP, what is the main difference of this paper from previous work?

 

Line 12-29. The specific values of RTS orbit accuracy are not described. Although the convergence performance of kinematic PPP is not ideal for BDS, its specific time should be presented in Abstract.

 

Line 33-37. I suggest putting the first and second paragraphs together.

 

Line 248. Please add more information on the estimated parameters in Table 2, e.g. tropospheric delay, and random-walk noise, etc.

 

Line 256-257. There are some unforeseeable gross errors in the SSR data steam, how to handle this problem? Did the RMS and STD statistical values in Figure 3 exclude gross errors?

 

Line 338, Figure 4. Both GBM and GFZ RTS are provided by GFZ analysis center. If GBM files are used as reference values, will the accuracy of GFZ RTS products be artificially high?

Author Response

1. This manuscript focuses on evaluation of the BDS-2+3 real-time UU-PPP using different RTS products. The comparison of UU-PPP and IF-PPP is discussed in both static and kinematic mode. Overall, workload is reasonable, and the paper is tightly written. However, my biggest concern is that there has been some research working on the performance evaluation on the BDS PPP, what is the main difference of this paper from previous work?

Reply: thank you for your comment. Compared with previous papers and work, there are two main contributions in our study. (1) Most research on the assessment of BDS RTS products is mainly focused on the early stages (i.e., 2020-2021) of BDS-3 full completion. In this manuscript, a comprehensive evaluation was conducted on the BDS-2+3 RTS products accuracy at the end of 2022. We need to explore whether the quality of BDS RTS products has been improved. (2) Up to now, most of the research on BDS PPP has focused on multi-GNSS combined positioning, post-processing positioning, and RT positioning using PPP-B2b corrections. There is limited study related to BDS-only RT PPP driven by RTS products, and only the IF model has been adopted for positioning. In our study, the global performance of BDS-2 and BDS-3 joint RT UU-PPP using RTS products from five ACs was investigated for the first time.

 

2. Line 12-29. The specific values of RTS orbit accuracy are not described. Although the convergence performance of kinematic PPP is not ideal for BDS, its specific time should be presented in Abstract.

Reply: thank you for your suggestions. The related descriptions have been added to the revised manuscript as follows: (1) “There is not much difference in the RTS orbit accuracy of medium earth orbit (MEO) satellites among all analysis centers (ACs), and the optimal orbit accuracy is better than 5, 9, and 7 cm in the radial, along-track, and cross-track directions, respectively. The orbit accuracy of inclined geosynchronous orbit (IGSO) satellites is worse than that of MEO satellites”. (2) “As for the kinematic mode with poor convergence performance, with the introduction of RT-VTEC constraints, the convergence time of RT UU-PPP can be slightly shorted and reaches about 55 and 60 min in the horizontal and vertical components, respectively”.

 

3. Line 33-37. I suggest putting the first and second paragraphs together.

Reply: thank you for your suggestions. The first and second paragraphs have been merged into one paragraph in the revised manuscript.

 

4. Line 248. Please add more information on the estimated parameters in Table 2, e.g. tropospheric delay, and random-walk noise, etc.

Reply: thank you for your comments. To explain the strategy of the parameter estimation, two new references [33] and [34] has been added in Table 2 of the revised manuscript.

“33. Zhou, F.; Dong, D.; Li, P.; Li, X.; Schuh, H. Influence of stochastic modeling for inter-system biases on multi-GNSS undifferenced and uncombined precise point positioning. GPS Solut. 2019, 23, 59.”

“34. Chen, H.; Niu, F.; Su, X.; Geng, T.; Liu, Z.; Li, Q. Initial Results of Modeling and Improvement of BDS-2/GPS Broadcast Ephemeris Satellite Orbit Based on BP and PSO-BP Neural Networks. Remote Sens. 2021, 13, 4801.”

 

5. Line 256-257. There are some unforeseeable gross errors in the SSR data steam, how to handle this problem? Did the RMS and STD statistical values in Figure 3 exclude gross errors?

Reply: thank you for your comments. Due to the uncertainty of RTS corrections, the gross error is inevitable in recovering real-time precise orbits and clocks. In Figure 3, the orbit errors exceeding 1.5 m are considered as gross errors and need to be removed in RMS calculation. As for clock evaluation, the gross error is defined as 3 ns and should also be eliminated in STD calculation. Some descriptions have been added to the revised manuscript as follow: “The orbit errors exceeding 1.5 m in any direction are considered as gross errors and need to be removed in assessment, while for clock evaluation, the gross error is defined as 3.0 ns”.

 

6. Line 338, Figure 4. Both GBM and GFZ RTS are provided by GFZ analysis center. If GBM files are used as reference values, will the accuracy of GFZ RTS products be artificially high?

Reply: thank you for your comments. Your viewpoint is correct, but this situation cannot be avoided. At present, the analysis centers that can provide high-precision and sufficient BDS satellites are mainly GFZ and WHU. If we choose WUM precise products as reference instead of GBM, the accuracy of WHU RTS products may also be artificially high, but it is very limited. On the other hand, the accuracy difference of GBM and WUM products can be maintained within a few mm , which is negligible for BDS RTS products assessment.

Reviewer 3 Report

Comments and Suggestions for Authors

- The paper is comprehensive and well structured. The performance comparison between RT IF-PPP and UU-PPP is very much appreciated. The reviewer has few comments below.

- In Introduction, the contributions of the paper needs to be further clarified. 

- Minor. The definition of acronyms such as GBM and BRDM is missing.

Author Response

The paper is comprehensive and well structured. The performance comparison between RT IF-PPP and UU-PPP is very much appreciated. The reviewer has few comments below.

1. In Introduction, the contributions of the paper need to be further clarified.

Reply: thank you for your comments. Some related descriptions have been added to the revised manuscript as follows:

(1) “Currently, most research on the assessment of BDS RTS products is mainly focused on the early stages (i.e., 2020-2021) of BDS-3 full completion. With the hardware and software upgrades of the GNSS receivers, more and more IGS monitoring stations can be used to track BDS-3 satellites, it is worth exploring whether the accuracy of BDS RTS products has been improved. In this contribution, a comprehensive assessment was conducted on both BDS-2 and BDS-3 RTS products for five analysis centers (ACs) at the end of 2022. This work is important for current BDS real-time users and has the potential to provide critical guide for numerous engineering applications”.

(2) “Up to now, most of the research on BDS PPP has focused on multi-GNSS combined positioning, post-processing positioning, and RT positioning using PPP-B2b corrections [19-23]. Compared with the PPP-B2B-enhanced RT PPP that only serves China and surrounding areas, the RTS-enhanced RT PPP has global service capabilities and is more conducive to the global application and promotion of BDS. However, there is limited study related to BDS-only RT PPP driven by RTS products. More importantly, almost all BDS-related RT PPP users only adopt DF IF model, and the research on performance of DF UU model using BDS-only observations is in a missing state. Thus, the global performance of BDS-2 and BDS-3 joint RT UU-PPP using RTS products from five ACs was investigated for the first time”.

 

2. Minor. The definition of acronyms such as GBM and BRDM is missing.

Reply: thank you for your comments. The “GBM” represents “GBM (Geodetic Benchmark Multi-GNSS)” and has been added to the revised manuscript. The “BRDM” has been replaced by “Broadcast ephemeris” in Table 2 of the revised manuscript.

Reviewer 4 Report

Comments and Suggestions for Authors

Summary:

The authors investigated the global performance of BDS-2 and BDS-3 joint RT UU-PPP using different RTS products and obtained some valuable conclusions. Although the writing of this article is good, the innovation is not particularly significant.

 

Main points:

1.        In section 2.2, why did the authors choose GBM final products as references instead of other analysis center products? Please explain clearly.

2.        The representation of equation 14 may not be very standardized, and semi-brackets are best written after the equal sign to distinguish between the two types. In addition, the basis for the selection of the variance of the ionospheric delay and variation should be explained.

3.        In kinematic experiments, why does the convergence time of RT UU-PPP shorten so obviously? Please analyze the reasons.

Comments on the Quality of English Language

None.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have made a good improvement on the manuscript.