An Improved Carrier-Smoothing Code Algorithm for BDS Satellites with SICB

Round 1

Reviewer 1 Report

The authors have proposed an improved CSC method by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. and the performances of improved method were examined to investigate their capabilities in positioning. It was observed that the new method achieved better positioning results. Authors have introduced the method before presenting the experiment results to support their conclusions. The results may be worth publishing, however, some aspects of the manuscript should be improved, as listed below.

(1)   The language should be polished and re-edited to avoid the minor flaws, such as the absence of equation (4)

(2)   “carrier-to-code leveling (CCL)” or “carrier smoothing code”, which one is better?

(3)   In the title, “BDS-2/BDS-2 3 IGSO/MEO/GEO” can be shortened as BDS to make it more concise

(4)   Table 5 can be removed safely and test stations can be marked in Figure 2

(5)   Authors only marked the signal frequency (i.e., B1/B2/B3), and more detailed signal types are suggested to be specified

(6)   Is the correction model satellite-dependent or station-dependent? More information about the using method of the model are required.

(7)   The CCL/CSC is also widely used in GNSS ion modeling, and the authors can further evaluate their method in ion modeling (in future work)

A professional editing of English language is required

Author Response

Response to comments for Reviewer 1

Dear reviewer,

Thank you very much for your favourable consideration of our manuscript entitled “An improved carrier smoothing code algorithm for BDS satellites with SICB” (remotesensing-2635609). Also, we would like to thank the reviewer for their valuable comments. Those comments are very valuable and helpful for revising and improving our paper, as well as the important guiding significance to our further research. We have studied the comments carefully and tried our best to revise our manuscript with additional experiments and edits in response to the comments by the reviewers. Revised portion are marked in red in the manuscript and the main corrections and additions are given below with a comment followed by a reply.

According to the comments of the three reviewers, the whole paper has also been revised in terms of grammar and wording.

[1] The language should be polished and re-edited to avoid the minor flaws, such as the absence of equation (4)

Reply: Sorry. Formula number and reference number have been corrected and the full paper has been checked.

[2] “carrier-to-code leveling (CCL)” or “carrier smoothing code”, which one is better?

Reply: We refer to relevant references and understand them as follows: CCL and CSC are similar in nature. They both use pseudorange and carrier to calculate the float ambiguity solution without cycle slip. The float solution does not solve the specific value but is passed between epochs. CCL is primarily used in ionospheric calculation, while CSC is mainly used to calculate real-time positioning results. CSC can also be used for ionospheric extraction. Compared with CCL, CSC is a real-time filter that can be used in different environments with different smoothing factors. CCL is suitable for ionospheric extraction, while CSC is affected by the ionospheric change rate, resulting in diverging positioning results.

The references are as: Zha, J., Zhang, B., Yuan, Y. et al. Use of modified carrier-to-code leveling to analyze temperature dependence of multi-GNSS receiver DCB and to retrieve ionospheric TEC. GPS Solut 23, 103 (2019).

[3] In the title, “BDS-2/BDS-2 3 IGSO/MEO/GEO” can be shortened as BDS to make it more concise

Reply: You are quite right. BDS already includes BDS-1, BDS-2, and BDS-3 and heterogeneous satellites, so the title is changed to “An improved carrier smoothing code algorithm for BDS satellites with SICB”.

[4] Table 5 can be removed safely and test stations can be marked in Figure 2

Reply: Thanks. Table 5 has been deleted and test stations have been added to Figure 2, please see page 7.

[5] Authors only marked the signal frequency (i.e., B1/B2/B3), and more detailed signal types are suggested to be specified.

Reply: Thank you for your reminder! B1/B2/B3 is replaced by B1I/( B2I /B2a)/B3I In this paper. Since BDS-3 satellite does not broadcast B2I, B2a is used instead, and B2 uses two frequency points (B2I and B2a).

The reference is this. Beidou satellite Navigation System space signal interface control file open service signal B1I (version 3.0).

[6] Is the correction model satellite-dependent or station-dependent? More information about the using method of the model are required.

Reply: We have done a correlation analysis between SICB and stations, satellites, and seasons. The results are shown in Figure 3(different satellites), Figure 4(different stations), and Figure 5(different seasons). SICB is not strongly related to satellites, stations, and seasons but is related to satellite frequencies. Please see pages 7 to 8. Thanks.

[7]The CCL/CSC is also widely used in GNSS ion modeling, and the authors can further evaluate their method in ion modeling (in future work)

Reply: That's an excellent question that we will focus on in the future. We added this sentence to the conclusion of page 18. “Since CCL/CSC is also widely used in GNSS ionospheric modeling, we will focus on evaluating the application performance of these two methods in the future”.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper should be revised according to the following statements:

Do not use the abbreviation of satellite induce code deviation in the abstract. I believe satellite-induced code bias is more convenient to use.  

How logical to apply IF combination to SPP? Since sub-m to m level horizontal and vertical accuracy can be obtained from SPP, I believe the usage of IF combination is redundant for this study. 

Moreover, most off-the-shelf low-cost GNSS devices are based on SPP using single frequency.  

Why the authors didn't investigate the effect of satellite-induced code deviation on PPP-IF? I believe this will bring more scientific value to the GNSS community.  

Why the authors didn't cite or compare their results to "Wanninger, L., and Beer, S., 2015. Beidou satellite-induced code pseudorange variations: diagnosis and therapy. GPS solutions, 19 (4), 639–648."

In Table 4, "Carry slip detection" should be changed to Cyle-slip detection.

The authors stated that "it is found that the BDS-2 satel-350 lite IGSO/MEO satellite has a systematic deviation that changes with elevation angle", this has already been revealed from previous studies related to the satellite code induce bias.

The authors stated that "After adding SICB correction to the original MP time series, the MP system bias (SICB) was significantly alleviated" This was also already revealed in "An Improved BDS Satellite-Induced Code Bias Correction Model Considering the Consistency of Multipath Combinations"

Author Response

Response to Comments for Reviewer 2

Dear reviewer,

Thank you very much for your favourable consideration of our manuscript entitled “An improved carrier smoothing code algorithm for BDS satellites with SICB” (remotesensing-2635609). Also, we would like to thank the reviewer for their valuable comments. Those comments are very valuable and helpful for revising and improving our paper, as well as the important guiding significance to our further research. We have studied the comments carefully and tried our best to revise our manuscript with additional experiments and edits in response to the comments by the reviewers. Revised portion are marked in red in the manuscript and the main corrections and additions are given below with a comment followed by a reply.

According to the comments of the three reviewers, the whole paper has also been revised in terms of grammar and wording.

[1] Do not use the abbreviation of satellite induce code deviation in the abstract. I believe satellite-induced code bias is more convenient to use. 

Reply: Sorry! The satellite induce code deviation was corrected as satellite-induced code bias, and the relevant expressions in the paper have been changed to satellite-induced code bias.

[2] How logical to apply IF combination to SPP? Since sub-m to m level horizontal and vertical accuracy can be obtained from SPP, I believe the usage of IF combination is redundant for this study. 

Reply: Thanks for your pointing out! Under normal circumstances, the positioning accuracy of SPP and SPP-IF is not much different, but the research in this paper involves dual-frequency data, our logic for using IF-SPP is as follows：

(1) The carrier smoothing pseudorange is affected by twice the ionospheric delay variation. In order to reduce the ionospheric effect on SICB correction, IF SPP is adopted.

(2) GEO satellite multipath requires dual-frequency data, so we adopt a dual-frequency ionosphere-free combination model.

(3) In the case of large ionospheric disturbance or extreme environment, the positioning accuracy of SPP cannot reach the sub-meter level, so it is necessary to study the dual-frequency positioning.

[3]Moreover, most off-the-shelf low-cost GNSS devices are based on SPP using single frequency.

Reply: As you said, low cost GNSS receivers use single frequency data. However, as mentioned above, we needed to use dual-frequency data in our study, so we used it conveniently. In theory, the positioning accuracy of dual-frequency data is more reliable than that of single-frequency data. At present, smart phone position has the trend of dual-frequency development, so dual-frequency research is still significant.

[4]Why the authors didn't investigate the effect of satellite-induced code deviation on PPP-IF? I believe this will bring more scientific value to the GNSS community.  

Reply: Thank you for pointing it out and it is a valuable suggestion. First, there are many researches on the effect of satellite-induced code bias on IF-PPP in the existing literature, but there are few researches on the SICB in carrier smooth pseudorange.

Next, according to your opinion, we have also implemented SICB impact study on IF-PPP in these days, and the results show that The SICB correction has no significant effect on the B1/B3 IF-PPP ( Part of the positioning results at the end of this response letter, but this paper mainly focuses on the influence of SICB on carrier smooth pseudo-range positioning, so no detailed analysis process is given. Only a conclusion on the effect of SICB on PPP-IF is given, specifically on page 18, line 398). It will even affect the convergence time in direction E to a certain extent. The speculated reasons may be: although the SICB of B1 is large, the SICB of B3 is small, resulting in the effect of SICB on IF PPP is not obvious. The reference (Chen J , Yue D , Zhu S ,et al.Correction model of BDS satellite-induced code bias and its impact on precise point positioning[J].Advances in Space Research, 2019, 63(7):2155-2163.DOI:10.1016/j.asr.2018.12.010) shows that SICB accelerates the convergence time of B1/B2 IF-PPP by 2-4 minutes, and the positioning accuracy is improved at the millimeter level. However, in this paper, the noise level of B1/B3 is lower than that of B1/B2. Do not add paper because the effect is not significant.

[5] Why the authors didn't cite or compare their results to "Wanninger, L., and Beer, S., 2015. Beidou satellite-induced code pseudorange variations: diagnosis and therapy. GPS solutions, 19 (4), 639–648."

Reply: Thank you for your advice. References have been added, and comparative experiments and results of the two methods are added, the results are shown in Figure 8-9 on page 11. Since GEO SICB modeling is also considered and VMD-WT method is proposed in this paper, there is no further comparison of positioning performance.

In Table 4, "Carry slip detection" should be changed to Cyle-slip detection.

Reply: Sorry, the error has been corrected.

[6]The authors stated that "it is found that the BDS-2 satel-350 lite IGSO/MEO satellite has a systematic deviation that changes with elevation angle", this has already been revealed from previous studies related to the satellite code induce bias.

Reply: Thank you for your reminder. This sentence is revised as: the MP of BDS-2 IGSO/MEO has a weak negative correlation with the elevation angle of the satellite, which indirectly indicates that there is a systematic bias between the pseudorange observation and the carrier observation of the BDS 2 IGSO/MEO satellite, that is, SICB.  See page 18, lines 403-406 for details.

[7]The authors stated that "After adding SICB correction to the original MP time series, the MP system bias (SICB) was significantly alleviated" This was also already revealed in "An Improved BDS Satellite-Induced Code Bias Correction Model Considering the Consistency of Multipath Combinations"

Reply: Thanks to your suggestion, the original discussion has been removed and replaced with a comparison of the existing reference (Wanninger, L., Beer, S. BeiDou satellite-induced code pseudorange variations: diagnosis and therapy. GPS Solut 19, 639–648 (2015). https://doi.org/10.1007/s10291-014-0423-3), The results are shown in Figure 8-9 on page 11.

Non-correct                  IGSO/MEO SICB-corr ect

Author Response File: Author Response.docx

Reviewer 3 Report

This paper presents an improved CSC algorithm, which takes into account 16 SICBs of GEO, IGSO and MEO satellites in the BDS constellation. The modified model of IGSO/MEO satellite SICB-17 is established by piecewise weighted least squares third-order 18 curve fitting method (TOCFM). The correction model of GEO satellite SICB is established by using variational mode decomposition and wavelet denoising model (VMD-WT). From June 7 to 13, 2023, MAL2, KRGG, ULAB and 22 ALIC stations were selected to collect 30 MGEX (Multiple GNSS Experiment, MGEX) BDS stations mod-21 eling SICB for 7 consecutive days. The effectiveness of the algorithm is verified.

However, in my opinion, the current state of the manuscript is obviously not optimistic if it wants to be included by remote sensing.

In my opinion, this is a research article rather than a review article. Therefore, is it necessary to elaborate such basic concepts as "Carrier smoothing code (CSC)" in the abstract? At the same time, the abstract should fully explain the innovation and specific work results of the manuscript, without highlighting the process. This prevents the reader from grasping the highlights of the manuscript quickly.The section should be rewritten.

After reading the full text, it is not difficult to find that the manuscript is a research article based on pure simulation. From a methodological point of view, this is not a problem, but without a large number of data comparison validation, it seems impossible to directly define the proposed method can play a so-called "correction" role. This is particularly important for a new method or "algorithm".It is recommended to add a large number of data sets for validation.

In addition, more details should be shown to show whether the adaptability of the proposed method is really suitable for "correcting" or "calibrating" satellite data.

There are problems with the language style and grammar, and it is recommended to revise the whole text (preferably with the participation of native English speakers).

Author Response

Response to Comments for Reviewer 3

Dear reviewer,

Thank you very much for your favourable consideration of our manuscript entitled “An improved carrier smoothing code algorithm for BDS satellites with SICB” (remotesensing-2635609). Also, we would like to thank the reviewer for their valuable comments. Those comments are very valuable and helpful for revising and improving our paper, as well as the important guiding significance to our further research. We have studied the comments carefully and tried our best to revise our manuscript with additional experiments and edits in response to the comments by the reviewers. Revised portion are marked in red in the manuscript and the main corrections and additions are given below with a comment followed by a reply.

According to the comments of the three reviewers, the whole paper has also been revised in terms of grammar and wording.

This paper presents an improved CSC algorithm, which takes into account 16 SICBs of GEO, IGSO and MEO satellites in the BDS constellation. The modified model of IGSO/MEO satellite SICB-17 is established by piecewise weighted least squares third-order 18 curve fitting method (TOCFM). The correction model of GEO satellite SICB is established by using variational mode decomposition and wavelet denoising model (VMD-WT). From June 7 to 13, 2023, MAL2, KRGG, ULAB and 22 ALIC stations were selected to collect 30 MGEX (Multiple GNSS Experiment, MGEX) BDS stations modeling SICB for 7 consecutive days. The effectiveness of the algorithm is verified.

However, in my opinion, the current state of the manuscript is obviously not optimistic if it wants to be included by remote sensing.

[1]In my opinion, this is a research article rather than a review article. Therefore, is it necessary to elaborate such basic concepts as "Carrier smoothing code (CSC)" in the abstract? At the same time, the abstract should fully explain the innovation and specific work results of the manuscript, without highlighting the process. This prevents the reader from grasping the highlights of the manuscript quickly. The section should be rewritten.

Reply: Thank you for pointing it out. This paper proposes a carrier smoothing pseudorange algorithm that considers SICB, a piecewise third-order polynomial with 0.1-degree interval is proposed to fit IGSO/MEO SICB, and a VMD-WT that takes into account SICB for GEO satellite noise reduction is proposed. Continuous data in the second half of 2022 and the first half of 2023(details are shown in Table 1 on pages 6-7) in different seasons are uniformly selected for SICB modeling. The results show that SICB is not related to station, satellite, and season, but only to satellite frequency. After adding IGSO/MEO/GEO SICB correction, the positioning accuracy is improved by about 10% compared with IF CSC SPP. The positioning accuracy is improved by about 20% compared to IF SPP.

Therefore, the abstract was rewritten, the basic concept explanation was deleted, the innovation and specific work results of this paper were emphasized. For details, see the entire abstract on page 1.

[2]After reading the full text, it is not difficult to find that the manuscript is a research article based on pure simulation. From a methodological point of view, this is not a problem, but without a large number of data comparison validation, it seems impossible to directly define the proposed method can play a so-called "correction" role. This is particularly important for a new method or "algorithm". It is recommended to add a large number of data sets for validation.

Reply: According to your opinions, we re-selected BDS data of 30 stations in different seasons to remodel SICB, and compared it with experimental results in existing reference (Wanninger, L., and Beer, S., 2015. Beidou satellite-induced code pseudorange variations: diagnosis and therapy. GPS solutions, 19 (4), 639–648). The results are shown in Figure 9 and on page 11.

Next, we selected 6 out of 30 stations with different global locations to verify the algorithm's effectiveness The verification results show that: The accuracy of IF-SPP after SICB correction is improved by 24.42%, 27.94%, and 24.98%, respectively in E, N, and U directions compared with that of IF-CSC-SPP without correction. The accuracy of IF-CSC-SPP after SICB correction is improved by 7.03%, 6.50%, and 10.48% in the E, N and U directions, respectively, and 9.86% in 3D, compared with the uncorrected IF-CSC-SPP. The results are shown in Table 6 on page 17.

In addition, we have also implemented SICB impact study on IF-PPP in these days, and the results show that The SICB correction has no significant effect on the B1/B3 IF-PPP (Part of the positioning results at the end of this response letter, but this paper mainly focuses on the influence of SICB on carrier smooth pseudo-range positioning, so no detailed analysis process is given. Only a conclusion on the effect of SICB on PPP-IF is given, specifically on page 18, line 398). It will even affect the convergence time in direction E to a certain extent. The speculated reasons may be: although the SICB of B1 is large, the SICB of B3 is small, resulting in the effect of SICB on IF PPP is not obvious. The reference (Chen J , Yue D , Zhu S ,et al.Correction model of BDS satellite-induced code bias and its impact on precise point positioning[J].Advances in Space Research, 2019, 63(7):2155-2163.DOI:10.1016/j.asr.2018.12.010) shows that SICB accelerates the convergence time of B1/B2 IF-PPP by 2-4 minutes, and the positioning accuracy is improved at the millimeter level. However, in this paper, the noise level of B1/B3 is lower than that of B1/B2. Do not add paper because the effect is not significant.

[3]In addition, more details should be shown to show whether the adaptability of the proposed method is really suitable for "correcting" or "calibrating" satellite data.

Reply: Thanks for your reminder, we have done the following work.

(1) The comparison between single-station modeling results and multi-station modeling results is increased, the results are shown in Figure 7 on page 10.

(2) The comparison of the correction effect between the experimental results and existing literature is added, the results are shown in Figure 9 on page 11.

(3) GEO satellite VMD-WT noise reduction results were added, and the average improved accuracy table of each GEO satellite at multiple stations has been added, the results are shown in Figure 9 and Table 4 on pages 13-14.

(4) The calculation method was validated with data from 6 sites for 11 consecutive days, and comparison of the number of visible satellites and HDOP and VDOP for the E, N, and U directions with different methods were added, the results are shown in Figure 13 on page 16. Satellite elevation angle and pseudorange residual of different methods are added, the results are shown in Figure 14 on page 16.

Non-correct                  IGSO/MEO SICB-correct

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Authors have answered my questions, and improved their manuscript greatly. I have no  concerns anymore.

English language has been improved and fine

Author Response

Response to comments for Reviewer 1

Dear reviewer,

We appreciate the editor and reviewers very much for their positive and constructive comments and suggestions on our manuscript entitled “An improved carrier smoothing code algorithm for BDS satellites with SICB” (remotesensing-2635609). We have fully revised our manuscript and have addressed all of the reviewers’ comments. Changes in the text are indicated in red. The main corrections in the paper and the responses to the reviewer’s comments are given below.

According to the comments of the third reviewers, the English language, grammar, punctuation, spelling and overall style of the whole paper have been revised through the English polishing of MDPI institution for better publication.

Author Response File: Author Response.docx

Reviewer 2 Report

I suggest that the revised version of the paper is suitable for publication.

Author Response

Response to Comments for Reviewer 2

Dear reviewer,

We appreciate the editor and reviewers very much for their positive and constructive comments and suggestions on our manuscript entitled “An improved carrier smoothing code algorithm for BDS satellites with SICB” (remotesensing-2635609). We have fully revised our manuscript and have addressed all of the reviewers’ comments. Changes in the text are indicated in red. The main corrections in the paper and the responses to the reviewer’s comments are given below.

According to the comments of the third reviewers, the English language, grammar, punctuation, spelling and overall style of the whole paper have been revised through the English polishing of MDPI institution for better publication.

Author Response File: Author Response.docx

Reviewer 3 Report

The author has made modifications to my question and may consider accepting it after minor grammar revisions.

minor revision

Author Response

Response to Comments for Reviewer 3

Dear reviewer,

We appreciate the editor and reviewers very much for their positive and constructive comments and suggestions on our manuscript entitled “An improved carrier smoothing code algorithm for BDS satellites with SICB” (remotesensing-2635609). We have fully revised our manuscript and have addressed all of the reviewers’ comments. Changes in the text are indicated in red. The main corrections in the paper and the responses to the reviewer’s comments are given below.

According to the comments of the three reviewers, the whole paper has been edited for correct English language, grammar, punctuation, spelling, and overall style.

[1] The author has made modifications to my question and may consider accepting it after minor grammar revisions.

Reply: Thank you for your suggestion. The English language, grammar, punctuation, spelling and overall style of the whole paper have been revised through the English polishing of the MDPI institution. We have made the following changes:

(1) We have corrected the tenses of the sentences throughout the paper to make them clearer.

(2) We corrected inappropriate and ambiguous sentences throughout the paper.

(3) The unsuitable short sentences in the paper are converted into long sentences to make the paper smoother.

(4)The reference [8], [12], [17], [28], [29] was modified to MDPI format, see page 19-20 for details.

Author Response File: Author Response.docx