Assessment of Swarm Kinematic Orbit Determination Using Two Different Double-Difference Methods
Round 1
Reviewer 1 Report
The paper proposes a new double-difference orbit determination strategy, which is validated using Swarm's three satellites. The paper provides a clear description of the entire orbit determination process, including pre-processing, ambiguity fixing, and accuracy comparison. However, there are some issues that need to be addressed.
1. The innovation of this paper lies in the double-difference orbit determination strategy. However, the description of the differences between Equation (8) and Equation (9) in the theoretical part is insufficient. Equation (9) requires real-time determination of the reference star's position through single-point positioning, and the accuracy of single-point positioning needs to be provided as it may be a key factor in orbit accuracy.
2. Although there are existing differential methods for orbit determination, including some differences in the strategy proposed in this paper, a brief overview of the differences in your method should be provided. In addition, although the introduction part extensively describes the research status of non-differential orbit determination, the advantages of double-difference orbit determination are not introduced in the following sections, and there is no comparison with the non-differential part in the experimental section.
3. Why is the elevation cutoff angle set to 0 in Table 2? Will setting it to 0 have an impact, as the usual practice is to set the elevation cutoff angle to 15° in positioning? Please provide an explanation.
4. There are also some issues in the analysis in the experimental section. You used different double-difference orbit determination strategies for SwarmA, SwarmB, and SwarmC, but in the subsequent analysis of the differences in RMS, you only considered the effects of orbit and data quality, without considering issues with your strategy. However, is it possible that the poor quality of the results is not due to data quality, but rather due to the solution of a priori information (ambiguity fixing or single-point positioning coordinates), as indicated by the ambiguity fixing rate? Perhaps improving your results can start with pre-processing. Because you compared SwarmA and SwarmC with other products and found that SwarmA and SwarmC were relatively poor, rather than comparing SwarmA and SwarmC of ESA and SLR, which showed better quality, an explanation was not provided.
5. Since the influence of solar activity is mentioned later, appropriate explanations should be provided in the theoretical part using equations, or this part can be moved to the discussion section. Relevant references on how the ionosphere affects satellite altitude should be cited appropriately.
6. The provided figures do not have sufficient comparison. In the analysis section, two images should be placed in one figure for comparison, such as using a dual y-axis in Figure 11 to show the influence of solar radiation index on daily average RMS more convincingly.
Comments for author File: 
Comments.doc
Certainly! Based on my overall assessment, the English in the article could benefit from some moderate revisions to enhance its quality. While the content is generally understandable, there are areas where improvements could be made to ensure clearer and more natural language usage. Some sentences may require rephrasing for better coherence and flow, and there may be opportunities to use more precise and concise language. Additionally, attention to grammar, punctuation, and word choice could further enhance the overall readability and professionalism of the article. With some moderate revisions, the English in the article can be polished to a higher standard.
Author Response
Point 1: The innovation of this paper lies in the double-difference orbit determination strategy. However, the description of the differences between Equation (8) and Equation (9) in the theoretical part is insufficient. Equation (9) requires real-time determination of the reference star's position through single-point positioning, and the accuracy of single-point positioning needs to be provided as it may be a key factor in orbit accuracy.
Response 1: We have added explanations for equations (8) and (9). In fact, we first performed single point localization based on zero-difference model and eliminated the non-difference orbit results with significant errors. Improving the accuracy of single point positioning is our further research direction. We hope to improve the accuracy of orbit determination by implementing single point positioning as a priori information and jointly solving with double difference method.
Point 2: Although there are existing differential methods for orbit determination, including some differences in the strategy proposed in this paper, a brief overview of the differences in your method should be provided. In addition, although the introduction part extensively describes the research status of non-differential orbit determination, the advantages of double-difference orbit determination are not introduced in the following sections, and there is no comparison with the non-differential part in the experimental section.
Response 2: Due to the fact that most scholars have focused on zero-difference methods in recent years, we introduced a lot of related research. After the introduction of non-difference, we have added the research status of using double difference methods in recent years. In the Results, we have added a comparison with the zero-difference kinematic orbit. We have discussed the advantages and disadvantages of zero-difference and double-difference methods in Discussion section.
Point 3: Why is the elevation cutoff angle set to 0 in Table 2? Will setting it to 0 have an impact, as the usual practice is to set the elevation cutoff angle to 15° in positioning? Please provide an explanation.
Response 3: In precise positioning measurement, the smaller the elevation cutoff angle is, the more significant the tropospheric delay and multipath effect, and the measurement error will also increase accordingly. Therefore, the elevation cutoff angle is usually set to 15°. However, the larger the cutoff angle is, the fewer available observations are. In Swarm orbit determination, three satellites flying on orbits of around 500km. The impact of the troposphere can be ignored. Due to the good performance of the receiver, the impact of multipath error is also minimal. Setting the cutoff angle to 0 can obtain more available observations.
Point 4: There are also some issues in the analysis in the experimental section. You used different double-difference orbit determination strategies for SwarmA, SwarmB, and SwarmC, but in the subsequent analysis of the differences in RMS, you only considered the effects of orbit and data quality, without considering issues with your strategy. However, is it possible that the poor quality of the results is not due to data quality, but rather due to the solution of a priori information (ambiguity fixing or single-point positioning coordinates), as indicated by the ambiguity fixing rate? Perhaps improving the results of your positioning can start with pre-processing. Because you compared SwarmA and SwarmC with other products and found that SwarmA and SwarmC were relatively poor, rather than comparing SwarmA and SwarmC of ESA and SLR, which showed better quality, an explanation was not provided.
Response 4: Undoubtedly, the performance of the orbit is definitely related to our orbit determination strategy. In fact, we are very careful with our orbit determination strategy, optimizing data preprocessing methods as much as possible, making full use of all observations., improving the accuracy of a priori non-difference orbit, and focusing on the fixed efficiency and accuracy of double-difference ambiguity (the key to constraining the accuracy of double-difference baseline solution). We have made corresponding supplements in the theoretical section. We also added an analysis of the fixing rates and the impact of fixed ambiguity on orbit accuracy in the Results section. And ESA has released a daily orbit quality report, including the results of comparing ESA orbits with SLR data (as mentioned in the manuscript: with an accuracy of 2cm), proving that the quality of ESA orbits is relatively high. So we did not provide a detailed comparison between ESA and SLR in the manuscript.
Point 5: Since the influence of solar activity is mentioned later, appropriate explanations should be provided in the theoretical part using equations, or this part can be moved to the discussion section. Relevant references on how the ionosphere affects satellite altitude should be cited appropriately.
Response 5: Firstly, we have added relevant references on how the ionospheric activity affects GPS positioning in the last paragraph of the Introduction. In 2021, solar activity began to be frequent, so it is necessary to consider the impact of solar activity. We have moved this part to the Discussion section. In addition, for the reviewer's suggestion to use equations for appropriate explanation in the theoretical part, we carefully consider that it cannot be adopted temporarily. The reasons are as follows: 1) We did not use corresponding formulas to calculate ionospheric activity related data (such as STEC), but directly used F10.7 to demonstrate the strong solar activity. 2) The formula and principle for calculating Spearman correlation coefficients are relatively simple and can be obtained from cited references. If specifically introduced, the content is relatively small and clearly not the focus of the article.
Point 6: The provided figures do not have sufficient comparison. In the analysis section, two images should be placed in one figure for comparison, such as using a dual y-axis in Figure 11 to show the influence of solar radiation index on daily average RMS more convincingly.
Response 6: We have displayed the solar radiation index F10.7 (black) and the change in 3D orbit difference RMS in one figure (Figure 14). In the other analysis part of the manuscript, we have tried to increase the comparability of the figures as much as possible.
Point 7: Based on my overall assessment, the English in the article could benefit from some moderate revisions to enhance its quality. While the content is generally understandable, there are areas where improvements could be made to ensure clearer and more natural language usage. Some sentences may require rephrasing for better coherence and flow, and there may be opportunities to use more precise and concise language. Additionally, attention to grammar, punctuation, and word choice could further enhance the overall readability and professionalism of the article. With some moderate revisions, the English in the article can be polished to a higher standard.
Response 7: We have revised the English expression to the best of our ability. Detailed revisions are presented in the revised manuscript.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
1. the double-differenced LEO POD approach was presented here first? Has there ever been a study on it? If there has, you should introduce them in the manuscript, and state the difference of your work in more detail.
2. The main work of this manuscript is to implement two different double-differenced methods in LEO POD. So, experiments should focus on the performance of double-differenced methods compared with undifferenced approaches. Comparative analysis experiments should be supplemented.
Otherwise, owing to the quick movement of LEO satellites, the fixing time of ambiguity could be largely shortened. Analysis on the fixing time of ambiguity by the double-differenced and undifferenced methods should also be added.
The manuscript is not well written in the language. Oral vocabulary often occurs. I suggest the authors check the manuscript carefully for grammar and typos.
Author Response
Point 1: The double-differenced LEO POD approach was presented here first? Has there ever been a study on it? If there has, you should introduce them in the manuscript, and state the difference of your work in more detail.
Response 1: We have added the research status of the double-difference method in the Introduction. The advantages and disadvantages of the double-difference method were discussed. The configuration of two double-difference models was supplemented in the method section.
Point 2: The main work of this manuscript is to implement two different double-differenced methods in LEO POD. So, experiments should focus on the performance of double-differenced methods compared with undifferenced approaches. Comparative analysis experiments should be supplemented.
Response 2: In the Results, we have added a comparison with the zero-difference kinematic orbit, and corresponding accuracy improvement. We have discussed the advantages and disadvantages of zero-difference and double-difference methods in Discussion section.
Point 3: Otherwise, owing to the quick movement of LEO satellites, the fixing time of ambiguity could be largely shortened. Analysis on the fixing time of ambiguity by the double-differenced and undifferenced methods should also be added.
Response 3: We have added an explanation of the LAMBDA algorithm in the method section. The fixing rate of wide-lane and narrow-lane ambiguity is given in the Results, and the influence of fixed ambiguity solutions on phase residual and orbit accuracy is discussed.
Point 4: The manuscript is not well written in the language. Oral vocabulary often occurs. I suggest the authors check the manuscript carefully for grammar and typos.
Response 4: We have revised the English expression to the best of our ability. Detailed revisions are presented in the revised manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
In this research assessment of Swarm kinematic orbit determination using two different double-difference methods investigated. My comments are as follows:
-Abbreviation of SWARM, GPS, RMSE,… need expand in abstract.
-Add a flowchart to implement the entire research
- Possible future studies to be added.
-The advantages and disadvantages of the proposed method should be added to the discussions.
-How much accuracy is improved by the proposed method? to be clearly highlighted.
The quality of the language is good.
Author Response
Point 1: Abbreviation of SWARM, GPS, RMSE,… need expand in abstract.
Response 1: We have expanded the abbreviations of GPS, ESA, RMS,… in Abstract. For Swarm, we have carefully studied the official documents of ESA, and reconfirmed that Swarm is not an abbreviation. In addition, we continued to check the abbreviations in the manuscript, and expanded them.
Point 2: Add a flowchart to implement the entire research.
Response 2: The flow chart of the research has been added in Section 2.3.
Point 3: Possible future studies to be added.
Response 3: At the end of the Conclusions, we have presented some shortcomings that need further research and improvement. Such as, in phase residual analysis, it is also necessary to study the inherent effects of phase residual change, multipath error, and observation noise. For zero-difference kinematics orbit determination, the performance of error processing model needs to be improved. Consider adding dynamic models to achieve reduced dynamic orbit determination.
Point 4: The advantages and disadvantages of the proposed method should be added to the discussions.
Response 4: We have discussed the advantages and disadvantages of the zero-difference method and the proposed method in Discussion section. (The zero-difference model is efficient in solving the problem, but requires an accurate error correction model. On the contrary, the double-difference model can effectively weaken or eliminate the same kind of error sources, such as the GPS satellite clock offset and receiver clock offset. As expected, the accuracy of the final double-difference model with ambiguity resolution is higher than zero-difference model and float resolution. However, it is inevitable that solving double difference observations requires a significant amount of computational time and storage space. )
Point 5: How much accuracy is improved by the proposed method? to be clearly highlighted.
Response 5: In the Results and Conclusions section, we have particularly emphasized the improvement of the accuracy of the double-difference model with ambiguity resolution (compare to the zero-difference model and float resolution).
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The current manuscript addresses previously unarticulated issues and makes significant improvements. However, further research is still needed, especially in tasks that have a significant impact on trajectory determination accuracy, such as determining prior values ​​of PPP Compared to the original manuscript, the current manuscript has been significantly improved in English, addressing the spoken language as much as possible. However, further revision is required to correct some inaccurate English expressions.Reviewer 2 Report
this manuscript can be accepted.
