Effect of Ephemeris on Pulsar Timing and Navigation Accuracy Based on X-ray Pulsar Navigation-I Data
Round 1
Reviewer 1 Report
The paper analyzes the effect of using different sets of ephemeris
for the bodies of the Solar System on the accuracy of deep space navigation through the timing of X-ray pulsars. To this aim, they consider data obtained by the X-ray PulsarNavigation-I (XPNAV-I) satellite and correct them with different sets of ephemeris. They found a significant difference (~1ms) in the Roemer delay correction with DE200 ephemeris compared to newer versions (e.g. DE405). This difference translates into a phase shift of the Crab pulsar profile obtained by folding data, while the shape is almost unchanged. They also use different sets of ephemeris to check the accuracy of the orbit reconstruction of the XPNAV-I spacecraft and (quite surprisingly) found that DE200 seem to provide more accurate results than newer versions.
My general impression about the paper is that it hardly conveys what
are the original results obtained by the authors and how they compare
with the previous results. For instance, the article cites several
papers dealing with the same topic (e.g. refs 20-22), but there seems
to lack of comparison with the results obtained. This is especially
needed since some of those papers are hard to retrieve. I advise the authors to revise the article accordingly. My main points are listed below.
In Sec. 2.2 (line 243) the authors show that a time delay of 1.3 ms is obtained by correcting photon times of arrival with DE200 compared to newer (and more accurate) ephemeris. This result is not surprising and can be easily reproduced with, e.g. Tempo2, without the need of actual observation data. Since it is an effect that depends on the direction of observation compared to the SSB, it would be useful to study its dependence on the position of the source and the epoch of observation. Note, that it is not needed to have observation data to do this since computing the Roemer delay on fake photon arrival times will suffice. Also, I think it would be worth citing that multiple
papers showed the superior accuracy of DE405/421 in the timing of pulsars compared to older DE 200 (e.g. Splaver et al. 2005, ApJ, 620,
405; Hotan et al. 2006, MNRAS, 369, 1502; Verbiest et al. 2008, ApJ,
679, 675.).
Sec. 3.2/4.3 It is unclear why the method used by Huang et
al. [ref. 15] and that based on the significance chi2 should produce
significantly different results. It seems to me that the former is
based on the minimization of the RMS of phase residuals using a
certain timing model and a given ephemeris set. The solution that
minimizes the RMS of the phase residuals should also be the one that
maximizes the profile chi-squared. If this is
the case, why the two methods lead to different results?
Line 466. It seems weird that the DE200 better reproduce the orbit of
XPNAV-I compared to DE405/421. Is the difference significant? Also,
the difference between the reconstructed and the actual position is
quoted as 1-2 km. This is much smaller than the value reported in
ref. 15 (38.4 km). In Sec. 4.4 it is then quoted a ranging error of 15
km, which is confusing. What is the actual uncertainty of the
spacecraft position obtained from X-ray pulsar timing?
Additional minor points are listed below.
Line 270. I agree that mixing different ephemeris may
lead to incorrect results. However, it seems the case that the use of
ephemeris later than DE405 has become the norm. Why one would use the DE200 ephemeris (and the timing solution derived in the radio band
from Jodrell Bank) to perform navigation with X-ray pulsars?
Line 304. Is the proposed analysis of the single planetary contributions to eq. 16 performed in this paper?
Tables 4 and 6. What are the units of the reported quantities?
Figure 5. Why are residuals only positive? Aren't the timing residuals
calculated around the average pulse profile?
Line 402. It is unclear in which sense the residuals obtained with
DE200 are different from DE405 and later versions of the
ephemeris. The RMS is very similar and the MAE is just a little bit
larger.
Line 408. Could the authors better explain how they mixed different
ephemeris? If they calculate timing residuals of data corrected with
DE200 to the average profile evaluated with DE405, I
would expect an average offset of 1.3/30 to appear (see line 366). Is
it the case?
Author Response
Dear reviewer,
Thank you for your valuable suggestions on the revision of my paper, which are of great help to improve the quality of my paper. In response to your comments, I have made the following modifications to my paper (I have also explained in detail some of your doubts about my paper):
Point 1: In Sec. 2.2 (line 243) the authors show that a time delay of 1.3 ms is obtained by correcting photon times of arrival with DE200 compared to newer (and more accurate) ephemeris. This result is not surprising and can be easily reproduced with, e.g. Tempo2, without the need of actual observation data. Since it is an effect that depends on the direction of observation compared to the SSB, it would be useful to study its dependence on the position of the source and the epoch of observation. Note, that it is not needed to have observation data to do this since computing the Roemer delay on fake photon arrival times will suffice. Also, I think it would be worth citing that multiple papers showed the superior accuracy of DE405/421 in the timing of pulsars compared to older DE 200 (e.g. Splaver et al. 2005, ApJ, 620,405; Hotan et al. 2006, MNRAS, 369, 1502; Verbiest et al. 2008, ApJ,679, 675.).
Response 1: Thank you for your suggestion. When I first did this research, I also considered using the ATNF Tempo2 timing tools and some simulation methods for experiments. However, in order to be more practical, I decided to use the satellite data that I can easily obtain for analysis. As for Tempo2, the time system used is TCB, while the time system used in JPL DE ephemeris is TDB. In order to avoid some systematic errors, I gave up Tempo2 and used my own program for calculation. For the use of ephemeris, the current mainstream is to use newer ephemeris, such as DE405/421/430, or de440/441 newly released by JPL. These ephemeris usually have better timing performance than older ephemeris (such as DE200). However, an important research point of my paper is to test the performance when using the timing parameter Crab pulsar timing parameters of Jodrell Bank Observatory based on DE200 and other ephemeris, but the results show that, If the system deviation is corrected, the MAE values of the timing residuals of the newer three ephemerides DE405/421/430 is still smaller than that of DE200 (Table 4 and Table 5), and the internal coincidence accuracy of these ephemerides is still higher than that of DE200. In order to make my discussion more scientific, I decided to quote some references you mentioned for a comprehensive comparison(line 504-512).
Point 2: Sec. 3.2/4.3 It is unclear why the method used by Huang et al. [ref. 15] and that based on the significance chi2 should produce significantly different results. It seems to me that the former is based on the minimization of the RMS of phase residuals using a certain timing model and a given ephemeris set. The solution that minimizes the RMS of the phase residuals should also be the one that maximizes the profile chi-squared. If this is the case, why the two methods lead to different results?
Response 2: Thank you for reminding me. At first, I also thought about the differences in the principles of navigation or orbit determination based on single pulsar. The principles of the two methods are essentially similar to what you said. However, there are some essential differences in the implementation of the two methods. The method used by Huang et al. Can be said to be a real single pulsar navigation or orbit determination method. When only a small number of known quantities are provided, the orbit parameters of the satellite are recursively calculated by using the orbit dynamics model; At the control point, the satellite orbit is corrected by distance observation, and the satellite position is constrained to the normal plane; SEPO is usually a verification method. Based on the known pulsar observation profile, the simulation profile is used to approximate the observation profile, which can usually obtain high accuracy. In general, the former method belongs to a priori analysis, while the latter belongs to a posteriori analysis.
Point 3: Line 466. It seems weird that the DE200 better reproduce the orbit of XPNAV-I compared to DE405/421. Is the difference significant? Also, the difference between the reconstructed and the actual position is quoted as 1-2 km. This is much smaller than the value reported in ref. 15 (38.4 km). In Sec. 4.4 it is then quoted a ranging error of 15 km, which is confusing. What is the actual uncertainty of the spacecraft position obtained from X-ray pulsar timing?
Response 3: Thank you for reminding me. According to the data results of this paper, the difference between the orbit determination results of DE200 and DE405/421/430 is no more than 1km. For the current pulsar navigation orbit determination accuracy, the accuracy is improved but not particularly significant. The same as the previous suggestion, the method adopted in this paper is SEPO, which is different from Huang et al. In fact, in reference [17,18], Zheng et al. used SEPO to conduct orbit determination analysis on POLAR and Insight-HXMT data, and obtained high accuracy. He analyzed orbit six-parameter, in which the error between the orbit semi major axis and the real track is less than 50m. I didn't get such a high precision. On the one hand, I analyzed that the SNR of XPNAV-1 is lower than that of other satellites, and the profile simulation method I used may have some impact. The 15km ranging error is for the traditional pulsar navigation observation of multiple pulsars to achieve single point positioning. Numerically speaking, the timing residuals have positive and negative values, and the errors usually conform to the Gaussian distribution. However, orbit determination based on single pulsar is a long-term fitting process. In this process, the positive and negative errors will be offset to a certain extent, so as to eliminate the impact of single point ranging errors to a certain extent.
Point 4: Line 270. I agree that mixing different ephemeris may lead to incorrect results. However, it seems the case that the use of ephemeris later than DE405 has become the norm. Why one would use the DE200 ephemeris (and the timing solution derived in the radio band from Jodrell Bank) to perform navigation with X-ray pulsars?)
Response 4: Thank you for your advice. It is true that the DE405/421/430 and other ephemerides are used more in the study of pulsar navigation and timing. However, due to some historical reasons, products obtained by using older ephemeris, such as the Crab pulsar timing parameters of Jodrell Bank Observatory, are still widely used. At the same time, the Crab timing parameters of Jodrell Bank Observatory are relatively accurate data that can be easily obtained and have a fast update cycle, which has a good reference for similar studies. At the same time, according to your suggestion, I will discuss the necessity of using updated and more accurate ephemeris to compile pulsar timing parameters (pulsar ephemeris)(line 506-512).
Point 5: Line 304. Is the proposed analysis of the single planetary contributions to eq. 16 performed in this paper?
Response 5: Thank you for reminding me. reference[20] has made a detailed analysis on the influence of single planet in the solar system, but I think that the ephemeris influence is a coupling process, and the analysis of single planet may not be scientific.
Point 6: Tables 4 and 6. What are the units of the reported quantities?
Response 6: Thank you for reminding me. I am aware of my omission and have added corresponding units to the text.
Point 7: Figure 5. Why are residuals only positive? Aren't the timing residuals calculated around the average pulse profile?
Response 7: Thank you for reminding me of my problems. From the numerical point of view, timing residuals are indeed divided into positive and negative values, but the research in this paper only compares the absolute size of timing residuals, and initially did not distinguish between positive and negative values. At your suggestion and referring to relevant papers, I decided to distinguish positive and negative values of timing residuals and correct the corresponding charts.
Point 8: Line 402. It is unclear in which sense the residuals obtained with DE200 are different from DE405 and later versions of the ephemeris. The RMS is very similar and the MAE is just a little bit larger.
Response 8: As you said, the differences between RMSE values and MAE values of timing residuals are not obvious (also can feel the difference visually), but it can be found from Figure 5 that the timing residuals obtained by DE200 are still obvious at a single point. Unfortunately, I did not mention this point in the initial paper, and I will explain it in the modified version(line 432). Thank you for reminding me.
Point 9: Line 408. Could the authors better explain how they mixed different ephemeris? If they calculate timing residuals of data corrected with DE200 to the average profile evaluated with DE405, I would expect an average offset of 1.3/30 to appear (see line 366). Is it the case?
Response 9: Thank you for your advice. My initial paper may not explain clearly. The mixing here is simply understood that the standard profile obtained from DE405 ephemeris and the pulse profile of each group of data (35 groups of data) obtained from other ephemeris are used for cross-correlation operation to obtain timing residuals. Here, the main purpose is to compare the internal coincidence accuracy of the ephemeris. Therefore, the obvious system error of 1.3ms of DE200 compared with the other three ephemerides is corrected. The average offset is 1.3ms.
Thank you again for your valuable suggestions on my paper. I have made corresponding changes to the paper based on these suggestions. I have submitted the latest revised version. There are corresponding revision records in the text, as well as the revision contents proposed by other reviewers (sorry, the line number corresponding to the original suggestion may be changed, so you should pay attention to it when looking). If you have other suggestions on my paper, I will further improve my paper according to these suggestions.
Kind regards,
Mr. Deng
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper shows the results of the authors investigation in one of the aspects of the use of X-ray pulsar timing methods for the proposed idea of "pulsar navigation" in space: the effects of the application of different sets of solar system ephemeris in the pulsar timing algorithm, and its influence on the accuracy of the position estimation.
The paper is well written and clear, and while the results presented are not groundbreaking (and in fact conclusions are very close to what anyone could predict beforehand), the authors did a very thorough job of actually performing the analysis and finding out the actual values for the differences and uncertainty estimates resulting from using different ephemeris sets. In my opinion the paper is worth a publication, as it shows the complexity of the issue, and the importance of some of the relatively minor (at least at a first glance) aspects of the methods and algorithms used in pulsar timing on the entire idea of using pulsar observations for the purposes of space navigation.
There are however several minor ssues I would like to see clarified, and a few corrections before I would ,recommend this manuscript for publication. A full list of my comments and suggestions can be found below.
----------------------------------------------------------
Minor comments and suggestions:
Abstract, line 18:
"pulse profile can reflect the systematic deviation caused by different ephemerides in the timing calculation"
Not clear if the ators mean the shape of the pulse or its phase, hence the sentence may be confusing. Later in the paper the authors mention that the shape is not affected by the use of different ephemeris, and it becomes clear that they mean the pulse phase. The abstract should reflect that.
Abstract, lines 21-22:
"The orbit accuracy calculated by the ephemeris used in pulsar timing parameter calculation is the highest (DE200 in this paper), which explains the necessity of using a..."
This sentence is a bit confusing. Its is not clear at this stage what the autors mean by "orbit accuracy": agreement with the real position? the best compliance with the data obtained by different means? The lowest timing errors?
The second part of the sentence makes it somewhat clearer, nevertheless the first part needs clarification.
Introduction, line 35:
Change "relativistic effect" to "relativistic effects", as there are multiple of them. Additionally, these efefcts are not studied for their own sake, but to test various predictions of General Relativity and other post-newtonian theories of gravity, and this should be mentioned in the Introduction.
Introduction, line 44:
As far as I know timing observations were conducted since 1970's - see for example the Taylor-Hulse binary pulsar B1913+16, for which the timing analysis has proven the first indirect evidence fo gravitational waves, and for which we have data from 1975. As for the proposed use of pulsar timing for navigation the authors mention a cited reference would be appropriate.
Page 2, line 55:
"solar ephemeris" or "solar system ephemeris"?
Page 2, lines 75-79:
What the authors state here is reasonably clear, however there are some additional factors that are not mentioned, especially the effect of the phenomenon known as "timing noise" - which most likely arrises from undetectable micro-jumps (micro-glitches) in pulsar rotation. As the effects of such micro-jumps is cumulative, it renders the the older pulsar ephemeris very inaccurate, at least when it comes to the prediction of the pulse phase (crucial for TOA analysis and thus related to the proposed pulsar navigation). The authors should mention that aspect of timing analysis, especially that timing noise is strongest in the very young pulsars, such as the Crab pulsar, for which the data in this paper is analyzed. Hence i would put more emphasis on the use of the "most recent pulsar timing mode" where possible.
Obviously for the purposes of the authors main area of study, i.e. the comparison berween the use of different sets of solar system ephemeris, timing noise will not play a huge role, as it affects the pulsar itself, and its effects would be the same regardless of the solar system ephemeris used -- adding the same time offset between the observed and predicted TOAs. Nevertheless it suprizes me that the authors do not mention this phenomenon at all.
Page 3, line 104
"pulsar periodic information" - it would be better if authors used proper timing analysis terms in this case, like "pulsar timning model".
Page 3, lines 99-107:
Eight lines of text that are actually a single sentence. This should be divided into a few separate senteces, which would help with the reading flow, and the authors would not have to overuse the connecting "and then...."
Page 3, lines 116-117
The authors mention "large scale time delay such as double pulsar system delay". The time delays in binary pulsar systems are actually much smaller than the Roemer delay within the solar system, as most binary pulsar systems are much more compact than the Earth-Sun orbit. Hence this sentence may be a bit misleading. The main problem with binary pulsar timing is not the magnitude of the additional delays, but the fact that they're changing relatively fast, since the orbital periods of binary pulsars (especially for millisecond pulsars) are usually much shorter than 1 year.
Page 4, line 138, and further along in the paper:
"Earth" should be capitalized in the text, as should be "the Sun"
Page 4, lines 156-157
Authors quote some very long numerical values with large number of digits, which makes hard to actually compare them, and estimate the difference at a firs glance. I think adding something like "the difference of 1.09x10^-17" in the parentheses would make the diferrence easier to evaluate.
Page 4, Table 1
Similar problem to the above: long strings of digits make it hard to see and evaluate the magnitude of the differences. It would be better if autors quoted relative values, or maybe give the full values in the firs row, and only showed the differentiating digits in the consecutive rows.
Page 6, line 210
As far as I know in astronomy the term "proper motion" refers to the motion of an object on the sky (usually given in arc seconds per year), hence it reflects the tangential component of the object true motion, and as such it should not cause Doppler effect. Do the authors mean full 3D motion of the pulsar?
Page 6, Table 2
The same problem as in Table 1: the number of digits quoted makes it hard to evaluate the magnitude of actual differences present.
Page 8, lines 270-271
It would be usefull if authors quoted here the epochs of the pulsar ephemeris (timing models) used, and not only as MJDs but also actual calendar dates. This would allow the reader to easilly evaluate "how recent" these pulsar ephemeris were.
Page 8, line 285
"appealed" - "applied"?
Page 8, line 302
"and the importance of the celestial body,..." - what aouthors mean is probably the magnitude of the corrections caused by a given solar system object. The use of the term "importance of the celestial body" is a bit ambigous
Page 8, line 304
"to know the spatial absolute error of celestial bodies..." again, a very ambigous term, I think the authors mean "the absolute spatial error caused by the influence of celestial bodies"
Page 11, Table 3
Again, as in the previous tables: to many digits to easilly gauge differences.
Page 13, Table 6
The authors (or the editor) should ensure that this table fits a single page.
Page 14, line 459
"theresults are improved compared with some research results using the same data". What are the "some research results"? Reference to the works the authors mean?
Page 14, lines 475-478
The authors state that the influence of the use of different ephemeris is hard to model and the uncertainties caused by this may be hard to estimate, which I can only agree with. What I would like to see the authors discuss in this context is: what can be done to improve this situation? What kinds of research/experiments can be performed to improve these aspects of pulsar navigation?
Page 14, lines 503-505
This last conclusion is a bit surprising, as everyone would expect the newer solar system ephemeris to be more precise (that is the entire purpose of publishing new ephemeris in the first place), and yet the data is hard to question. Obviously, as the authors state, this is most likely because the pulsar timing model used in the analysis was obtained using the oldest DE200 ephemeris. I think the main conclusion here should be that we need better, more recent pulsar ephemeris, obtained using newest solar system ephemeris, not that we should use the oldest solar system data available. This should be clearly stated in the final conclusion.
Page 16, Appendix Table 3.
Timing parameters for the Crab pulsar: It would be easier to evaluate for a reader, if in addition to the MJD Reference epoch authors would also quote the calendar dates they correspond to - this would help to evaluate how recent are these timing models.
Author Response
Dear reviewer,
Thank you for your valuable suggestions on the revision of my paper, which are of great help to improve the quality of my paper. In response to your comments, I have made the following modifications to my paper (I have also explained in detail some of your doubts about my paper):
Point 1: Abstract, line 18: "pulse profile can reflect the systematic deviation caused by different ephemerides in the timing calculation". Not clear if the actors mean the shape of the pulse or its phase, hence the sentence may be confusing. Later in the paper the authors mention that the shape is not affected by the use of different ephemeris, and it becomes clear that they mean the pulse phase. The abstract should reflect that.
Response 1: Indeed, as you said, it is the overall phase offset between pulse profiles that reflects the systematic deviation, so I modify it as follows: "the pulse profile phase can reflect the systematic deviation caused by different ephemerides in the timing calculation"(line 18).
Point 2: Abstract, lines 21-22: "The orbit accuracy calculated by the ephemeris used in pulsar timing parameter calculation is the highest (DE200 in this paper), which explains the necessity of using a...". This sentence is a bit confusing. It is not clear at this stage what the authors mean by "orbit accuracy": agreement with the real position? the best compliance with the data obtained by different means? The lowest timing errors? The second part of the sentence makes it somewhat clearer, nevertheless the first part needs clarification.
Response 2: The "orbit accuracy" refers to the deviation from the real position, so I modify it to "orbit position accuracy"(line 24).
Point 3: Introduction, line 35: Change "relativistic effect" to "relativistic effects", as there are multiple of them. Additionally, these efefcts are not studied for their own sake, but to test various predictions of General Relativity and other post-newtonian theories of gravity, and this should be mentioned in the Introduction.
Response 3: Thank you for your reminding. I am aware of the problem and change "relativistic effect" to "relativistic effects" according to your suggestion(line 37).
Point 4: Introduction, line 44: As far as I know timing observations were conducted since 1970's - see for example the Taylor-Hulse binary pulsar B1913+16, for which the timing analysis has proven the first indirect evidence fo gravitational waves, and for which we have data from 1975. As for the proposed use of pulsar timing for navigation the authors mention a cited reference would be appropriate.
Response 4: After consulting relevant documents again, I found that the concept of "pulsar navigation" was first proposed by NASA JPL's downs in 1974, and pulsar timing was also proposed shortly after the discovery of pulsars. Thank you for reminding me to correct my mistakes(line 46).
Point 5: Page 2, line 55: "solar ephemeris" or "solar system ephemeris"?
Response 5: Its “solar system ephemeris”, and I also corrected similar errors in the full text(line 58).
Point 6: Page 2, lines 75-79: What the authors state here is reasonably clear, however there are some additional factors that are not mentioned, especially the effect of the phenomenon known as "timing noise" - which most likely arises from undetectable micro-jumps (micro-glitches) in pulsar rotation. As the effects of such micro-jumps is cumulative, it renders the older pulsar ephemeris very inaccurate, at least when it comes to the prediction of the pulse phase (crucial for TOA analysis and thus related to the proposed pulsar navigation). The authors should mention that aspect of timing analysis, especially that timing noise is strongest in the very young pulsars, such as the Crab pulsar, for which the data in this paper is analyzed. Hence I would put more emphasis on the use of the "most recent pulsar timing mode" where possible. Obviously for the purposes of the authors main area of study, i.e., the comparison between the use of different sets of solar system ephemeris, timing noise will not play a huge role, as it affects the pulsar itself, and its effects would be the same regardless of the solar system ephemeris used -- adding the same time offset between the observed and predicted TOAs. Nevertheless, it surprises me that the authors do not mention this phenomenon at all.
Response 6: Thank you for your detailed suggestion. I have paid attention to similar problems in pulsar timing before. But as you said, other errors can be regarded as equal when comparing the influence of ephemeris, so I don't pay much attention to these errors. At your suggestion, in order to make the paper more extensive, I decided to make a certain description in the paper by comparing the timing noise caused by undetectable micro-jumps in pulsar rotation, so that it can be related to my own research(line 82-84).
Point 7: Page 3, line 104: "pulsar periodic information" - it would be better if authors used proper timing analysis terms in this case, like "pulsar timing model".
Response 7: "pulsar timing model" is indeed a more professional term than "pulsar periodic information". At your suggestion, I decided to adopt "pulsar periodic information"(line 112).
Point 8: Page 3, lines 99-107: Eight lines of text that are actually a single sentence. This should be divided into a few separate sentences, which would help with the reading flow, and the authors would not have to overuse the connecting "and then...."
Response 8: In fact, I was aware of this problem when I first wrote, but I didn't make appropriate changes at that time. Under your reminder, I still divide it into four independent sentences to help with the reading flow(line 102-116).
Point 9: Page 3, lines 116-117: The authors mention "large scale time delay such as double pulsar system delay". The time delays in binary pulsar systems are actually much smaller than the Roemer delay within the solar system, as most binary pulsar systems are much more compact than the Earth-Sun orbit. Hence this sentence may be a bit misleading. The main problem with binary pulsar timing is not the magnitude of the additional delays, but the fact that they're changing relatively fast, since the orbital periods of binary pulsars (especially for millisecond pulsars) are usually much shorter than 1 year.
Response 9: With your reminder, I realized that it is not appropriate to use "large scale time delay" here. What I want to say here is "extrasolar delay", and change the original text to "the extrasolar delay such as double pulsar system delay and interstellar delay"(line 124).
Point 10: Page 4, line 138, and further along in the paper: "Earth" should be capitalized in the text, as should be "the Sun".
Response 10: Thank you for your reminding. I will modify similar contents in the paper.
Point 11: Page 4, lines 156-157: Authors quote some very long numerical values with large number of digits, which makes hard to actually compare them, and estimate the difference at a firs glance. I think adding something like "the difference of 1.09x10^-17" in the parentheses would make the difference easier to evaluate.
Response 11: This suggestion is very useful. I have modified it according to your suggestion, including the following tables to facilitate the evaluation of differences(line 166).
Point 12: Page 4, Table 1: Similar problem to the above: long strings of digits make it hard to see and evaluate the magnitude of the differences. It would be better if authors quoted relative values, or maybe give the full values in the first row, and only showed the differentiating digits in the consecutive rows.
Response 12: Similar to the previous suggestion, according to your suggestion, I give the full values in the first row, and only showed the differentiating digits in the consecutive lines for comparison.
Point 13: Page 6, line 210: As far as I know in astronomy the term "proper motion" refers to the motion of an object on the sky (usually given in arc seconds per year), hence it reflects the tangential component of the object true motion, and as such it should not cause Doppler effect. Do the authors mean full 3D motion of the pulsar?
Response 13: Under your reminding, I realized my initial problems in understanding and writing. The "proper motion" here, as you said, refers to the three-dimensional proper motion. The second term in the formula refers to the delay caused by the radial proper motion of the pulsar. However, it is usually a very slow motion, so it cannot be expressed as Doppler delay. I have made corresponding changes in the text. Thank you for your suggestion(line 215,221).
Point 14: Page 6, Table 2: The same problem as in Table 1: the number of digits quoted makes it hard to evaluate the magnitude of actual differences present.
Response 14: At your suggestion, I have made changes similar to table 1 to facilitate comparison of differences.
Point 15: Page 8, lines 270-271: It would be useful if authors quoted here the epochs of the pulsar ephemeris (timing models) used, and not only as MJDs but also actual calendar dates. This would allow the reader to easily evaluate "how recent" these pulsar ephemeris were.
Response 15: Thank you for your suggestion. I will quote the pulsar ephemeris (timing models) I used in the text (I put it in Section 4.1, lines 371-375, for better comparison, including the appendix), including MJDs and actual calendar dates.
Point 16: Page 8, line 285: "appealed" - "applied"?
Response 16: It should be "applied", thank you for reminding me(line 304).
Point 17: Page 8, line 302: "and the importance of the celestial body,..." - what authors mean is probably the magnitude of the corrections caused by a given solar system object. The use of the term "importance of the celestial body" is a bit ambiguous.
Response 17: At your suggestion, I realize that the use of "importance" is inappropriate. The meaning of BK is basically the same as what you said, and I have indicated it in the text. What I want to express here is the calculation method of , but in order not to make it ambiguous, I decided to change it to the “influence quantity” of the celestial body (or its weight in the error equation) (line 321).
Point 18: Page 8, line 304: "to know the spatial absolute error of celestial bodies..." again, a very ambiguous term, I think the authors mean "the absolute spatial error caused by the influence of celestial bodies"
Response 18: Thank you for your suggestion. What I want to say here (references) is the position error of celestial bodies in three-dimensional space coordinates (such as BCRS). Same as above. In order not to cause ambiguity, I decided to add a certain description and change it to “position error of celestial bodies in three-dimensional space coordinates” (line 323).
Point 19: Page 11, Table 3: Again, as in the previous tables: to many digits to easily gauge differences.
Response 19: Thank you for your reminder, but since there are few numbers to compare here, the differences are relatively intuitive, and some other references have similar writing methods, I decided not to make too many changes.
Point 20: Page 13, Table 6: The authors (or the editor) should ensure that this table fits a single page.
Response 20: Thank you for your reminder. In fact, in the paper I originally submitted to the editor, I put Table 6 in a single page, but the editor may have adjusted the format to make the page compact.
Point 21: Page 14, line 459: "the results are improved compared with some research results using the same data". What are the "some research results"? Reference to the works the authors mean?
Response 21: I'm sorry that I didn't indicate the reference I cited here. I will indicate the research reference using the same data in the text. Thank you for your reminding(line 498).
Point 22: The authors state that the influence of the use of different ephemeris is hard to model and the uncertainties caused by this may be hard to estimate, which I can only agree with. What I would like to see the authors discuss in this context is: what can be done to improve this situation? What kinds of research/experiments can be performed to improve these aspects of pulsar navigation?
Response 22: Thank you for your suggestions. I will add relevant contents in the discussion section, including some of my own opinions(line 526-531).
Point 23: Page 14, lines 503-505: This last conclusion is a bit surprising, as everyone would expect the newer solar system ephemeris to be more precise (that is the entire purpose of publishing new ephemeris in the first place), and yet the data is hard to question. Obviously, as the authors state, this is most likely because the pulsar timing model used in the analysis was obtained using the oldest DE200 ephemeris. I think the main conclusion here should be that we need better, more recent pulsar ephemeris, obtained using newest solar system ephemeris, not that we should use the oldest solar system data available. This should be clearly stated in the final conclusion.
Response 23: This suggestion is very good. I will resummarize my conclusion according to this suggestion to make it more scientific and complete. Thank you for your advice(line 560-563).
Point 24: The authors state that the influence of the use of different ephemeris is hard to model and the uncertainties caused by this may be hard to estimate, which I can only agree with. What I would like to see the authors discuss in this context is: what can be done to improve this situation? What kinds of research/experiments can be performed to improve these aspects of pulsar navigation?
Response 24: According to your suggestion, I have made corresponding modifications to the Table, including "Reference epoch" and "Time range" both use MJD and calendar dates for comparison.
Thank you again for your valuable suggestions on my paper. I have made corresponding changes to the paper based on these suggestions. I have submitted the latest revised version. There are corresponding revision records in the text, as well as the revision contents proposed by other reviewers (sorry, the line number corresponding to the original suggestion may be changed, so you should pay attention to it when looking). If you have other suggestions on my paper, I will further improve my paper according to these suggestions.
Kind regards,
Mr. Deng
Author Response File: Author Response.docx
Reviewer 3 Report
In this paper, the authors presented evidence of the importance of having accurate epheremis for pulsar timing and navigation. The topic of pulsar navigation is gaining more and more momentum as NASA and ESA try to find ways of incorporating them to their missions for the next decade. Thus, the paper do provide very useful results. All the conclusions reached on the paper are well supported by the results obtained during their study.
While some of the aspects discussed on section 2 are well known and discussed previously in the literature, the authors present them in a different way by comparing different ephemeris sources. I think the inclusion of these better-known sections here, benefits the potential use of this paper.
I therefore, recommend its publication on this journal once some minor corrections are applied to the original text.
1.- The abstract does not seem to flow very well. Some sentences are unconnected, others very long. It spends a bit too much describing the results and jumps in one line to the impact of the study. I would recommend the authors to try simplifying it a bit more and allow themselves to show the impact of their results a bit better.
2.- Line 11: Change Solar ephemeris to either Solar System ephemeris or possibly better, barycentric ephemeris (if this second one selected, please change it throughout the text too for consistency).
3.- Line 42: remove extraterrestrial. Just saying space exploration is enough.
4.- (Optional): I think it would be interesting to add the advantages of XPNAV over traditional space navigation. In particular the fact that the precision of the location of the spacecraft does not depend on its distance to Earth and the capability of the mission to self-locate itself without needed communication to Earth.
5.- I feel that the authors could talk a bit more about the different JPL ephemeris that they are comparing. Is the main difference just that shown in Table 1? Either a subsection on section 2 or a bit more information on the introduction, I think would benefit the paper.
6.- The text in the caption of Figure 1 should be improved. The sentence starting with Considering the small difference (line 169) is long and convoluted. The verb "calculate" seems out of place there.
7.- I am sorry if I missed this on the main text, but if I did, maybe it could mean that it is properly not highlighted. I think it is very interesting that the separations shows in Figures 1 and 2 (specially in figure 1) seem to get better as more time passes on. Intuitively, I would have expected these effects to be cumulative, not the opposite. Unless there is something I didn't understand well. I would appreciate if the authors could comment on this, thanks.
8.- Title in section 4.1 (line 358): Capital letter for Pulse
9.- In figures 3 and 4, I am not entirely sure what is the goal of the partial period figures. Could the authors comment?
10.- Caption figure 6. Capital Timing (line 412)
11.- Caption Figure 7 and table 6: use symbol for chi squre rather than words.
Author Response
Dear reviewer,
Thank you for your valuable suggestions on the revision of my paper, which are of great help to improve the quality of my paper. In response to your comments, I have made the following modifications to my paper (I have also explained in detail some of your doubts about my paper):
Point 1: The abstract does not seem to flow very well. Some sentences are unconnected, others very long. It spends a bit too much describing the results and jumps in one line to the impact of the study. I would recommend the authors to try simplifying it a bit more and allow themselves to show the impact of their results a bit better.
Response 1: Thank you for your suggestion. I will simplify my abstract as much as possible to better show the impact of the results(line 15-21).
Point 2: Line 11: Change Solar ephemeris to either Solar System ephemeris or possibly better, barycentric ephemeris (if this second one selected, please change it throughout the text too for consistency).
Response 2: Thank you for your reminding. I have changed "Solar ephemeris" to " Solar System ephemeris " in the text(line 11).
Point 3: Line 42: remove extraterrestrial. Just saying space exploration is enough.
Response 3: Thank you for reminding me of this problem(line 44).
Point 4: Line 42: (Optional): I think it would be interesting to add the advantages of XPNAV over traditional space navigation. In particular the fact that the precision of the location of the spacecraft does not depend on its distance to Earth and the capability of the mission to self-locate itself without needed communication to Earth.
Response 4: Thank you for your suggestion. In fact, I also wanted to mention this kind of content in the paper at the beginning. However, in order to avoid my introduction being too long, and there are many similar expressions in many articles on pulsar navigation, I have omitted this content.
Point 5: I feel that the authors could talk a bit more about the different JPL ephemeris that they are comparing. Is the main difference just that shown in Table 1? Either a subsection on section 2 or a bit more information on the introduction, I think would benefit the paper.
Response 5: Thank you for your suggestion. I have explained and compared the four ephemerides used in this article in the appendix. At the same time, there are many literatures comparing these ephemerides separately. My research is mainly to compare the use of ephemeris in pulsar navigation and timing,so I made some simplifications to make the paper more compact(appendix).
Point 6: The text in the caption of Figure 1 should be improved. The sentence starting with Considering the small difference (line 169) is long and convoluted. The verb "calculate" seems out of place there.
Response 6: Thank you for your suggestion. I have simplified the content and changed inappropriate words(line 182-184).
Point 7: I am sorry if I missed this on the main text, but if I did, maybe it could mean that it is properly not highlighted. I think it is very interesting that the separations show in Figures 1 and 2 (specially in figure 1) seem to get better as more time passes on. Intuitively, I would have expected these effects to be cumulative, not the opposite. Unless there is something I didn't understand well. I would appreciate if the authors could comment on this, thanks.
Response 7: Thank you for reminding me. As you can see, the difference between curves decreases with the passage of time. Since the observation data I used is only one month's observation data, it cannot reflect its change trend in a longer time range. This is also a pity of this paper or a point worth studying later. Other documents, such as reference [20] of this paper, compare the changes of TE200 and TE405 time ephemeris in this century, the difference fluctuates around 0 and shows a certain periodicity (this is a paper of the last century, and there are few studies on this in recent years). In addition, from the perspective of time conversion and light-travel delay calculation, this impact will not accumulate, because both of them are calculated for a single point in time. However, if the final timing solution needs to accumulate to get the pulse profile, this impact may accumulate. I will also do more discussion in this paper. Thank you(line 260-266).
Point 8: Title in section 4.1 (line 358): Capital letter for Pulse.
Response 8: Thank you for your reminding. I will correct this small mistake(line 378).
Point 9: In figures 3 and 4, I am not entirely sure what is the goal of the partial period figures. Could the authors comment?
Response 9: I do this mainly to highlight the differences in some phase points of the profiles, because it is difficult to see the specific differences in these points from the full profile. I will also explain this in the caption of Figure 6. Thank you for your reminding(line 388).
Point 10: Caption figure 6. Capital Timing (line 412)
Response 10: Thank you for your reminding. I will correct this small mistake(line 447).
Point 11: Caption Figure 7 and table 6: use symbol for chi-square rather than words.
Response 11: Thank you for reminding me. I will correct my chart.
Thank you again for your valuable suggestions on my paper. I have made corresponding changes to the paper based on these suggestions. I have submitted the latest revised version. There are corresponding revision records in the text, as well as the revision contents proposed by other reviewers (sorry, the line number corresponding to the original suggestion may be changed, so you should pay attention to it when looking). If you have other suggestions on my paper, I will further improve my paper according to these suggestions.
Kind regards,
Mr. Deng
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
I thank the authors for taking into accounts my comments, and I recommend the paper to be accepted in the present form.
