Research on Blunder Detection Methods of Pseudorange Observation in GNSS Observation Domain
Round 1
Reviewer 1 Report
Data quality is one key factor in GNSS positioning and navigation. Systematic error, random error and gross error may be present in GNSS observations. Gross errors should be detected and repaired for further GNSS applications. Three methods are proposed in the manuscript for GNSS data gross errors. The case studies show the methods are effective. The English writing should be polished.
[1] Lines 18-19: The pseudorange gross error may not cause the observational anomaly of GNSS, which may be caused by the GNSS signal, receiver, and environment.
[2] Line 22: What is the different type?
[3] Line 28: C2 and P2 may not be frequency.
[4] Line 39: Here, GPS and BDS should have different thresholds.
[5] Line 103: The sentence may not be right.
[6] Line 106: If you focus on real time, you must consider the efficiency and time consuming for these three methods.
[7] Line 128: In eq. (1), why no antenna receiving center variation?
[8] Line 140: What is the combined noise? Colorful noise or white noise?
[9] Line 146: How to reasonably determine these two thresholds?
[10] Section 3.2: What are the statistical parameters used?
[11] Line 248: Please show much information of GNSS observations?
[12] Table 1: How to determine the threshold? More statistics should be listed, like max, min, mean, std, rms, etc. How to identify and judge gross errors?
[13] Table 2: Here the threshold is the same as that in table 1. How to determine the threshold? More statistics should be listed, like max, min, mean, std, rms, etc. How to identify and judge gross errors?
[14] Table 3: Here the threshold is the same as that in tables 1 and 2. How to determine the threshold? More statistics should be listed, like max, min, mean, std, rms, etc. How to identify and judge gross errors?
[15] Line 344: How to select the thresholds? What about the effect of threshold on the gross error detection?
[16] Section 4.5: How to verify these results calculated with these methods? What about the effect of these gross errors on positioning? How to repair these corresponding observations?
[17] Section References: Here more literatures should be cited. And more latest literatures should be listed.
Author Response
Response to Comments for Reviewer 1
Dear reviewer,
Thank you very much for your favourable consideration of our manuscript entitled “A Research on Gross Error Detection Methods of Pseudo-Range Observation in GNSS Observation Domain” (Manuscript ID: remotesensing-1933286). 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. For example, Blunder, outliers, faults are commonly used for gross errors. For this reason, gross error is changed to blunder.
[1] Lines 18-19: The pseudorange gross error may not cause the observational anomaly of GNSS, which may be caused by the GNSS signal, receiver, and environment.
Reply: The statement here is not strict enough. This sentence is revised as: GNSS signal quality, type of receiver equipment, and external environment can cause GNSS observations to be anomalous, and these anomalies are sometimes reflected in GNSS pseudorange observations rather than phase observations.
[2] Line 22: What is the different type?
Reply: Thanks for your pointing out! The experimental data used in this paper are all pseudorange observations of GPS or BDS, but the pseudo-range observations in each system correspond to different frequencies and code types. For example, C/A code and P code in GPS are different code types, one is coarse code, the other is precision code. while B1I and B3I in BDS belong to two different frequency signals of I branch. To make it clearer, we changed the ‘different type’ in the text to the ‘different code types’. And change the ‘same type’ in the text to the ‘same code type’.
[3] Line 28: C2 and P2 may not be frequency.
Reply: Sorry! The spelling here is wrong, it should be C2 and P2 code pseudorange observation, The whole paper has been revised uniformly. Corrected.
[4] Line 39: Here, GPS and BDS should have different thresholds.
Reply: It's really not clear here. At the beginning of the period, our idea was to use the MGEX station data of one system to investigate the experiment, but we found that the MGEX GPS observation data under case2 and the BDS observation data of the MGEX station under case1 were seriously insufficient. To this end, the experimental data were used for the data of the two systems. Therefore, this sentence is revised as: According to the RMSE of 3 times as the limit, it is recommended that the threshold be set to 5 m under case1 for GPS and 15 m under case2 for BDS, which is half of the existing reference value.
[5] Line 103: The sentence may not be right.
Reply: After our thinking, the first half of this sentence has already expressed the same meaning, for this reason, we delete this sentence and merge it with the next paragraph.
[6] Line 106: If you focus on real time, you must consider the efficiency and time consuming for these three methods.
Reply: We calculated the computation time for the three methods in both cases based on your comment. Since the configuration of each computer is different, we only calculate the ratio (relative time) between the calculation time of each method in each case and the total time, expressed as a percentage, as shown in the following table, and the table 6 is shown in line 365 on page 11.
|
type |
Time(%) |
Time(%) |
|
CODM |
32.4 |
24.4 |
|
ICODM |
32.5 |
37.2 |
|
IICODM |
34.9 |
38.4 |
[7] Line 128: In eq. (1), why no antenna receiving center variation?
Reply: Equation (1) is based on the difference between two code observation equations at one station, and the receiver phase center variation is eliminated during the difference process. We revised the above sentence of Equation (1) to be: For any station, the following test statistic can be constructed.
[8] Line 140: What is the combined noise? Colorful noise or white noise?
Reply: Equation (1) is the difference of two code pseudorange observation equations. This equation eliminates geometric distances, weaken common errors possessed by differential observations, so the combined noise here is the remaining residual term and the observation difference in noise. Generally we assume white noise. Since this paper only uses these two difference observation equations, and does not discuss their noise types, it does not belong to the research scope of the paper. We revised this paragraph as: The two differences are mainly manifested in the remaining hardware delay bias at the satellite and receiver sides, the remaining residual term and the difference of observation noise.
[9] Line 146: How to reasonably determine these two thresholds?
Reply: The existing threshold value is mainly based on the error propagation law to calculate the RMSE of the test statistic, and the size of the threshold value is given according to the relationship between the threshold value and the RMSE, but this is only limited to the use of the posterior method for blunder detection. This paper emphasizes again that blunders are detected in the observation value domain based on the test statistic constructed from the original observations, and subsequent positioning calculations are not required, so the propagation law cannot be used to calculate them. At present, it is not possible to find a reasonable and best method for calculating the threshold value, so we use Bessel's formula to calculate, see formula (11), this method is a safe method, and it is simple and very practical. In addition, I also consulted with the author Professor Guofei in the reference. He also used the empirical method to obtain the threshold. We will further study the problem of accurate calculation of the threshold in future work, which has been explained in the conclusion section, see page 12.
[10] Section 3.2: What are the statistical parameters used?
Reply: I am feel sorry! I am not clear here, the statistical parameters here are mainly the test statistics , , , , , under the case1 and case2, see equations (5)~(10) respectively. In order to express it more clearly, we revised formula (11).
[11] Line 248: Please show much information of GNSS observations?
Reply: Thanks a lot for your opinion! The sampling interval of each station in the MGEX network is 30 seconds, and each day contains 2880 epochs. The number of GPS and BDS visible satellites in each epoch is about 6-16. there are more visible satellites in individual areas or stations, In particular, BDS has more visible satellites in China than in other regions. Each epoch basically has GNSS pseudorange observation information. This passage This paragraph is reorganized, see line 260 in page 6 for details.
[12] Table 1: How to determine the threshold? More statistics should be listed, like max, min, mean, std, rms, etc. How to identify and judge gross errors?
[13] Table 2: Here the threshold is the same as that in table 1. How to determine the threshold? More statistics should be listed, like max, min, mean, std, rms, etc. How to identify and judge gross errors?
[14] Table 3: Here the threshold is the same as that in tables 1 and 2. How to determine the threshold? More statistics should be listed, like max, min, mean, std, rms, etc. How to identify and judge gross errors?
Reply: Thank you so much for pointing it out! Questions 12-14 are a question that I will answer together here. Threshold calculation is indeed a concern in this paper. I have already answered part of it in question 9.
For the calculation of the threshold value, I wanted to use a machine algorithm or an artificial intelligence algorithm at the beginning, but found that the content is beyond the scope of this article, mainly because this article is based on a simple and practical principle, which is to detect blunders in the observation domain, and finally, the threshold value is determined according to the triple relationship between the limit error and RMSE (see Formula (11)). Although this method is not the best, it is also a conservative method. For the calculation of the threshold, we will conduct further research in the future, and we have already made an outlook in the conclusion section. To this end, we revised the paper as follows:
(1) Line 259 on page 6 describes how the threshold value is calculated and how to use this value for blunder identification.
(2) Table 1, Table 2, Table 3 added the maximum value, minimum value, Std of the threshold value.
[15] Line 344: How to select the thresholds? What about the effect of threshold on the gross error detection?
Reply: In this paper, the threshold value calculation is to use formula (11) to calculate the RMSE of the test statistic, and then take three times the average value of the RMSE as the threshold value. It has been explicitly stated below Equation (11). For the blunder detection effect, we have already analyzed it in Section 4.5. In the case of the same code type and different frequencies, the absolute value of the test statistics of almost all MGEX stations of the three methods does not exceed 10 m, the absolute value of the test statistic calculated by the three methods does not exceed 30 m under the same frequency and different code types. We have also analyzed the cases where the test statistic exceeds the threshold. For example, we found that the test statistics exceeding the threshold in Figure 9 are related to the BDS C58 and C59 satellites, which are not only test satellites but also GEO satellites, and the data quality is relatively poor. It shows that the blunder detection method proposed in this paper has a certain effect on blunders larger than the threshold. We discussed it on page 10, line 370.
[16] Section 4.5: How to verify these results calculated with these methods? What about the effect of these gross errors on positioning? How to repair these corresponding observations?
Reply: The pseudorange blunder detection method proposed in this paper is carried out in the observation domain, that is to say, a preprocessing before the positioning solution can only detect blunders greater than the threshold. Of course, only blunder greater than the threshold can be detected, this method is applicable to the large gross errors in the pseudorange observations before GNSS data processing, so as to eliminate the blunders contained in the original GNSS code pseudorange observations. Otherwise, when the GNSS contains blunders, it may be considered to be caused by the cycle slip of the GNSS carrier phase observations, and the original normal carrier phase observations are mistakenly deleted. For the verification of these methods, we discussed in Section 4.5. For example, the blunders detected based on BDS observation of the BRMG station are related to C58 and C59 satellites, which are GEO satellites and the quality of the observation data is relatively poor. It shows that the method proposed in this paper has a certain effect on the detection of pseudorange blunders. Since this paper mainly proposes three pseudorange blunder detection methods, and gives a specific mathematical model, and suggests the threshold size, and finally verifies the detection performance. As for the impact on positioning, how to repair the gross error and how to deal with the blunder observation (generally delete it in the corresponding epoch or lower the weight to deal with it) will be the content of future research. We added them in conclusion (4), see page 13 for details.
[17] Section References: Here more literatures should be cited. And more latest literatures should be listed.
Reply: We have added references in the last two years. Please refer to the references, please see pages 13-14.
Author Response File: 
Author Response.docx
Reviewer 2 Report
How to more accurately detect gross errors in pseudorange observations is important, the research is attractive. The article uses an interesting research methodology. Nevertheless, there are some details need to be clarified as follows.
Line 31 (0.327, 0.421, 0.526) and (7.066, 31 5.489, 5.310), lack unit.
Line 134 , are time variables should be expressed in pseudorange. In the following formulas, the same problem exists.
Author Response
Response to Comments for Reviewer 2
Dear reviewer,
Thank you very much for your favourable consideration of our manuscript entitled “A Research on Gross Error Detection Methods of Pseudo-Range Observation in GNSS Observation Domain” (Manuscript ID: remotesensing-1933286). 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. For example, Blunder, outliers, faults are commonly used for gross errors. For this reason, gross error is changed to blunder.
[1] Line 31 (0.327, 0.421, 0.526) and (7.066, 31 5.489, 5.310), lack unit.
Reply: Corrected, please see abstract, thanks.
[2] Line 134, are time variables should be expressed in pseudorange. In the following formulas, the same problem exists.
Reply: Sorry! The unit of equation (1) is meter. For this reason, we have revised this part uniformly. We uniformly revise the hardware delay into hardware delay bias. Other changes have also been made.
Author Response File: Author Response.docx
Reviewer 3 Report
1. The authors refer to the approach described in [24], at the same time, this source is unavailable for viewing.
2. The authors write (p.2), «Therefore, Guo (2013) proposed a gross error detection method in the observation value domain [19]. What is the reference to [19]? Not clear.
3. The pseudorange real-time gross error detection method can only detect a fault that is instantly large enough to trig the alarm, which cannot meet more stringent applications, for example, in aviation. What is the ultimate goal of this method? It is known that RAIM/ARAIM is embedded in most GNSS receivers that can detect and identify faults from satellite observations in real time. The main procedure of RAIM algorithm (snapshot and filtering) is designed to detect and exclude fault measurements through consistency checking. What is the essential advantage of this approach?
4. If we find gross errors in pseudorange observations in real time, further go into mode data preprocessing and finally to SPP/PPP, then where is the effect?
5. Conclusion of the authors regarding calculated threshold is are somewhat strange and premature and it is not clear what the Bessel formula is for here?
Author Response
Response to Comments for Reviewer 3
Dear reviewer,
Thank you very much for your favourable consideration of our manuscript entitled “A Research on Gross Error Detection Methods of Pseudo-Range Observation in GNSS Observation Domain” (Manuscript ID: remotesensing-1933286). 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. For example, Blunder, outliers, faults are commonly used for gross errors. For this reason, gross error is changed to blunder in this paper.
[1] The authors refer to the approach described in [24], at the same time, this source is unavailable for viewing.
Reply: This reference is a doctoral dissertation of a Chinese scholar. We have corrected it. Thank you!
[2] The authors write (p.2), «Therefore, Guo (2013) proposed a gross error detection method in the observation value domain [19]. What is the reference to [19]? Not clear.
Reply: I'm sorry, now the reference number corresponding to this paragraph is 29, corrected.
[3] The pseudorange real-time gross error detection method can only detect a fault that is instantly large enough to trig the alarm, which cannot meet more stringent applications, for example, in aviation. What is the ultimate goal of this method? It is known that RAIM/ARAIM is embedded in most GNSS receivers that can detect and identify faults from satellite observations in real time. The main procedure of RAIM algorithm (snapshot and filtering) is designed to detect and exclude fault measurements through consistency checking. What is the essential advantage of this approach?
Reply: In the past, the blunder detection was mainly carried out in the position domain after the solution. The pseudorange blunder detection method proposed in this paper is based on the principle of simplicity, practicality and efficiency, and is carried out in the observed range. Of course, only blunder larger than the threshold can be detected. The ultimate goal of the method is to detect the large blunders in the pseudorange observations before GNSS data processing, so as to eliminate the blunders contained in the original GNSS pseudorange observations. Otherwise, when the GNSS contains blunders, it may be considered to be caused by the cycle slip of the GNSS carrier phase observations, and the original normal carrier phase observations are mistakenly deleted.
To verify the performance of these methods, we discussed them in Section 4.5. For example, the blunders detection observation of BDS based on BRMG station are related to C58 and C59 satellites, which are GEO satellites, and the quality of observation data is relatively poor. The results show that the method proposed in this paper has a certain effect on the detection of pseudorange bluders.
Because this paper mainly proposes three methods of pseudorange blunder detection, gives a specific mathematical model, proposes the threshold size, and finally verifies the blunder detection performance. As for the impact of this method on positioning, how to repair gross errors, and how to deal with blunder observation (generally in the corresponding epoch deletion or weight reduction processing), we plan to continue our research in the positioning domain. The advantages and disadvantages of this method have been described in conclusion (4), see page 12 for details.
[4] If we find gross errors in pseudorange observations in real time, further go into mode data preprocessing and finally to SPP/PPP, then where is the effect?
Reply: We have repeatedly emphasized that the pseudorange blunder detection method proposed in this paper is carried out in the observation range, and the observation data of each satellite included in an epoch and between epochs in an observation station are independent of each other. These methods can be used together in the epoch by epoch solution. Because the model is simple, it will not have much impact on the SPP/PPP solution efficiency.
For the detected blunders, we reduce the weight of the corresponding observation to 0 or eliminate the observation. We have given the gross error detection of individual points in Section 4.5. As shown in Figure 9, observation data of C58 and C59 contain blunders after gross error detection of BRGM, The weight of the corresponding observation is reduced to 0 or the corresponding observation is deleted in the later SPP/PPP.
[5] Conclusion of the authors regarding calculated threshold is are somewhat strange and premature and it is not clear what the Bessel formula is for here?
Reply: In this paper, the threshold value calculation is to use Bessel formula (11) to calculate the RMSE of the test statistic, and then take three times the average value of the RMSE as the threshold value. It has been explicitly stated below Equation (11). For the blunder detection effect, we have already analyzed it in Section 4.5. In the case of the same code type and different frequencies, the absolute value of the test statistics of almost all MGEX stations of the three methods does not exceed 10 m, the absolute value of the test statistic calculated by the three methods does not exceed 30 m under the same frequency and different code types. We have also analyzed the cases where the test statistic exceeds the threshold. For example, we found that the test statistics exceeding the threshold are related to the C58 and C59 satellites in Figure 9, which are not only test satellites but also GEO satellites, and the data quality is relatively poor. It shows that the blunder detection method proposed in this paper has a certain effect on gross errors larger than the threshold. We've discussed it on page 10, line 370. For the conclusion section, we revise it again. Please refer to the conclusion on page 11.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
1) What is the test statistics in Fig. 2? 2) The legends in Figs. 3, 5 and 7 may be bad. 3) Waht is the test statistics in Figs. 8 and 9? 4) Positioning cases should be studied using the new method to detect gross errors, which can verify the method. 5) More literatures should be cited.
Author Response
Response to Comments for Reviewer 1
Manuscript Number: remotesensing-1933286
Section: GNSS Precise Positioning and Geoscience Application
Article Title: Research on Blunder Detection Methods of Pseudorange Observation in GNSS Observation Domain
Journal: Remote Sensing
We would like to thank the anonymous reviewers for providing an opportunity to revise the manuscript again. The comments and suggestions of reviewers are all valuable and very helpful. We have studied them carefully and have revised them to improve the manuscript. Revised portions are marked in red in the manuscript and the main corrections and additions are given below with a comment followed by a reply.
(1) What is the test statistics in Fig. 2?
Reply: Sorry! This is caused by my mistake. Fig.2 shows two test statistics corresponding to the two cases, corrected.
(2) The legends in Figs. 3, 5 and 7 may be bad.
Reply: Sorry! Mistakes occurred in the drawing of these three figures, which have now been corrected. To express it more clearly, we change the colors in the three figures.
(3) What are the test statistics in Figs. 8 and 9?
Reply: This error is the same as the first one, corrected.
(4) Positioning cases should be studied using the new method to detect gross errors, which can verify the method.
Reply: Thank you again for reminding me that the blunder detection method proposed in this paper is very necessary for positioning analysis. Due to time constraints, I did not analyze the content of this aspect when revising the manuscript for the first time. I do this work this time. Specifically, Section 4.6 is added. we mainly use the CODM to detect blunders of GPS observation data of SC04 station and BDS observation data of BRMG station, analyze the effect of blunders detection, and compare the positioning results before and after blunders elimination. Please see pages 12-13 for details.
(5) More literatures should be cited.
Reply: We have added five literatures in recent three years.
Author Response File: Author Response.docx
Reviewer 3 Report
The article has undergone cosmetic changes, its perception has improved somewhat, but almost all previous comments on it have remained.
Author Response
Response to Comments for Reviewer 3
Manuscript Number: remotesensing-1933286
Section: GNSS Precise Positioning and Geoscience Application
Article Title: Research on Blunder Detection Methods of Pseudorange Observation in GNSS Observation Domain
Journal: Remote Sensing
We would like to thank the anonymous reviewers for providing an opportunity to revise the manuscript again. The comments and suggestions of reviewers are all valuable and very helpful. We have studied them carefully and have revised them to improve the manuscript. Revised portions are marked in red in the manuscript and the main corrections and additions are given below with a comment followed by a reply.
(1) The article has undergone cosmetic changes, its perception has improved somewhat, but almost all previous comments on it have remained.
Reply: Thank you for your criticism. Based on our first revision, we revised your previous comments again. The most important problem is that we did not use the gross error detection method proposed in this paper to analyze the impact on the positioning. Due to time constraints, I did not analyze the content of this aspect when revising the manuscript for the first time. I did this work this time. Specifically, Section 4.6 is added. we mainly use the CODM to detect blunders of GPS observation data of SC04 station and BDS observation data of BRMG station, analyzes the effect of blunders detection, and compare the positioning results before and after blunders elimination. See pages 12-13 for details. See pages 12-13 for details.
Author Response File: Author Response.docx
