Contribution of PPP with Ambiguity Resolution to the Maintenance of Terrestrial Reference Frame
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Authors,
I have carefully reviewed your manuscript titled "Contribution of PPP with Ambiguity Resolution to the Maintenance of Terrestrial Reference Frame." The paper provides a detailed analysis of the feasibility of using PPP-AR for long-term coordinate time series analysis, demonstrating results consistent with IGSR3, which is significant for enhancing regional geodetic reference frames. Overall, the study is valuable and contributes to the field.
However, I would like to offer a small suggestion for improvement. In the introduction, you state: "However, these studies were limited to regional velocity field, and none have explored the role of globally distributed station coordinates, obtained through PPP-AR, in global velocity field analysis." It is important to note that Chen's paper ("Comparison between GPS network analysis with undifferenced and double differenced integer ambiguity resolution: A practical perspective") has already compared and analyzed the differences between global and regional station PPP-AR solutions and network solutions. I recommend that you add this point in the introduction to provide a more comprehensive context. Additionally, in the results analysis section, it would be beneficial to compare your findings with those in Chen's study to highlight any differences.
I believe addressing this point will strengthen the manuscript and provide a more robust comparison with existing literature.
Author Response
Please see the attachment.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsThe topic presented in this manuscript is of interest to the scientific community. The use of PPP-AR is increasingly widespread to address various aspects of geodetic research and the possible contribution to the reference frame maintenance is important to exploit. Many analyses have been done to try to address different aspects of the issue, from the accuracy of coordinates, velocities and seasonal signals and the coordinate prediction from velocities.
General comments:
There is a formatting problem of the citations in the pdf file, it should be fixed in the final version of the paper.
There are references that are not attainable (PhD theses or in Chinese). Is it possible to replace them with online papers in English?
Some software, even if well-known to the scientific community, are present in the text, without the relative reference.
Furthermore, the first time ITRF2020 and the IGS Repro3 solution are cited, the references are not made explicit.
In section 3.2 and also in other places it is emphasized that the uncertainty on the vertical component is three times higher than the horizontal one and is attributable to geophysical phenomena, but It should not be overlooked the geometry and distribution of the satellites, as an additional cause.
Regarding the statement that the formal error in the ITRF horizontal velocity field is 1 mm/yr, have the authors considered the ITRF plate motion model (https://doi.org/10.1029/2023GL106373) which states that the accuracy of the horizonal ITRF2020 velocity field is 0.25 mm/yr WRMS?
For me, a greater difference between PPP and PPP-AR, apart from the E component, was expected. Could it be due to the limited length of the time series? Probably if tens of years of data were analyzed, greater benefits of a more expensive but more precise technique could be appreciated.
In addition:
Line 166: ambiguity should be added before … fixed rate at….
Figures 4 and 6: It is not clear to me why the time series of geocentric coordinates X, Y and Z are presented, even though all calculations and considerations are made on the E, N and U components, including the values ​​presented in Tables A1-A3 in the Appendix. They add anything, but rather create confusion.
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsThe manuscript presents an investigation into the contribution of PPP-AR to the long-term position time series. The study is novel and meaningful, with results that are highly satisfactory (e.g., improvements in series statistics such as RMS and velocity uncertainty) and draws effective conclusions. The manuscript is well-organized and recommended for publication, pending the resolution of the following concerns before the manuscript may be accepted:
Specific Comments:
- In Section 3, the reasons for the low fixed rate of MAKE and the unreliable results of KIRU are not adequately explained. Please provide a more detailed discussion on these issues.
- Line 96, the term "main methodologies" might be better replaced by "steps" for clarity.
- In the author's statement, the relationship between time series, velocity, and other relevant terms to the reference frame is not addressed. Could you please provide a detailed explanation of these connections?
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Reviewer 4 Report
Comments and Suggestions for AuthorsThe paper is well-written and reads fluently. The methodology and the results are clearly presented and discussed. I only have editorial remarks.
The references to the bibliography should be enclosed between brackets, eg. on line 61, "678" should be [6][7][8].
line 126: the sentence starting with "Since the" does not seem grammatically correct.
In eq (1), the \omega, t_k^1 and t_k^2 parameters should be described.
Fig 6: put the red trace in the back and the blue trace in front for easier visibility (the red trace is more noisy, so it should preferably be behind the blue trace).
line 264: give short explanation about the "colored noise model"
line 321: grammar: the verb is missing.
line 407: "the precision can reach sub-mm level improvements": I find this statement difficult to interpret. Does it mean that the improvement is only at the sub-mm level (i.e. mostly negligible)? I'd suggest to rephrase or delete this clause.
Tab 8: am I correct that this table provides the RMS values of the results shown earlier in Fig 8? Then I'd suggest already referring to Table 8 in the discussion about Fig 8.
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Reviewer 5 Report
Comments and Suggestions for AuthorsIt is an interesting paper, which represents a considerable effort. However, I’m at a loss and have some problems with it, namely that it may potentially create a confusion, Precise Point Positioning (PPP) is here presented as an efficient alternative to global network GNSS solutions of positions, orbits and clocks. In reality PPP critically depends and is a part of such solutions and represents an efficient, but approximate densification (back substitution) of stations positions, were the global solution orbits/clocks are fixed. So PPP is only as good as, or its precision only approaches the precision of the underlying global solution. So, when using PPP, the corresponding global solutions (for orbits/clocks/positions) should be clearly identified as it is the primary factor effecting the PPP precision (assuming that the PPP software is consistent with the global one, using the same conventional modeling and constants). This is why the global solution should be here clearly identified both in the abstract, introduction or even in the title.
The position precision of PPP (float/AR) based on IGSR3 orbits/clocks/OSBs, should be significantly better than the typical AC network precision 1, 1 and 3 mm in E, N and U, with respect to IGSR3 (see https://presentations.copernicus.org/EGU21/EGU21-2144_presentation.pdf). These AC position precision’s are significantly better (by almost a factor of 2) than the PPPAR precision’s obtained here, indicating a possible deficiency (inconsistency) of the PPPAR with respect to the IGSR3 combined global solutions.
The IGS R3 combined orbit/clock and OSB files are readily available at the IGS Data Centers and include GPS, GLONASS and Galileo. The IGS R3 combinations are truly remarkable and are indeed highly accurate and complete, more so than any of the 11 AC solutions combined in IGS R3 orbits/clocks/OSBs and position solutions. The IGS R3 orbits/clocks/OSBs represent an incredible achievement and milestone, thanks to WUH combination Center!
-There are additional problems, namely that IGS R3 includes GPS, GLONASS and Galileo, while PPPAR and PPP here used only GPS and Galileo, but not GLONASS. GLONASS contribution is significant and should have also been included here.
-The relatively large standard deviations or RMS of position differences PPPAR-IGSR3 and of the East (E) component in particular, as well as statistically significant biases may indicate possible inconsistency of the used PPP software with respect to the IGS R3 combination solutions, which should also be addressed and investigated. In fact when GPS, GLONASS and Galileo (or even GPS, Galileo only) are used in PPPAR offer only marginal improvement in the E component only (unlike in case of single GNSS PPPs).
- Considering that AR, in rare occasions may fail and may cause problems (which may be the case of the deleted stations with low AR rates), float PPP may be more appropriate for such ITRF studies, using static PPP. PPPAR are most beneficial only for kinematic PPPs, in particular so for single GNSS kinematic PPPs.
In my opinion the main contribution of this paper is the use and verification of consistency of the new IGS R3 orbit/clock combinations with the IGS R3 position combinations by means of PPP. Float PPP, rather than PPPAR may be more appropriate and acceptable as it is more robust, in particular when GPS, GLONASS and Galileo are used. For these reasons the paper is worth publishing.
Since some possible inconsistency were shown, it would very useful to investigate them, i.e., if it is due to the PPP software (which is likely the case), or due to an inconsistency between separate IGSR3 combinations of orbits/clocks and positions. This can be possibly verified by using a different and independent PPP software. In any case, GLONASS should be included in all such PPP analysis, including the one presented here.
In order the paper to be acceptable the text should be modified to clearly show which global orbit/clock solutions was used for PPP (In the title/abstract/introduction) as well as highlighting its critical role for PPP.
-------More detail comments/suggestions/corrections are listed below--------
l.15 & 19: Precise Point Positioning
l. 23: Should mention that the IGS R3 orbits/clocks/OSBs global network combined solutions was used for the PPPAR.
l. 25: 2/5mm horizontal/vertical standard deviations (STD) are not roughly equivalent to IGS R3, the obtained 2/5 mm STDs are much worse, by about a factor of about 2 than IGS R3, or even then individual AC contributions (see above [39], or
https://presentations.copernicus.org/EGU21/EGU21-2144_presentation.pdf , Typical AC position standard deviations ( SDs) are 1, 1 and 3 mm), the IGS R3 precision (SD) are still better than that since it is a combination of the 11 ACs!
l. 27: within 1 mm/yr, which are lower than the formal error of ITRF??? The current ITRF formal errors are much better, nevertheless ITRF formal errors are not relevant here, the IGS R3 ones are!
l. 28-31: Really, most of the 11 AC network solutions contributed into IGS R3 combination solution are significantly better than the PPPAR shown here
l. 45: .. which is obtained through the combination 11 network solutions [39]
l, 79: .. However, these studies were limited to regional velocity field …??? This is not true, since JPL has been using PPPAR for global (ITRF) stations since late 1990’s! Today they use PPPAR in near real time (see https://sideshow.jpl.epnasa.gov/post/series.html). This should be properly acknowledged here
l. 86: we use PPP-AR with IGS R3 orbit/clock/OSB solutions ..(reference below)
Geng, J., Yan, Z., Wen, Q. et al. Integrated satellite clock and code/phase bias combination in the third IGS reprocessing campaign. GPS Solut 28, 150 (2024). https://doi.org/10.1007/s10291-024-01693-9
https://link.springer.com/article/10.1007/s10291-024-01693-9
l. 90: is [15] the correct reference for Net_Diff software?
l. 91: using precision, rather than accuracy here and after would be more appropriate (accuracy is quite elusive and difficult to asses)
l. 99: what is QOCA platform? An explanation and/or reference would be appropriate here (in addition, or instead of l. 157)
l. 102-111: IGS core stations are the best performing, globally distributed stations to be used by IGS ACs to align unconstrained AC global (orbit/clock/position solutions to ITRF (to the current IGS realization of ITRF, to be exact). Consequently, they represent the best (the most optimistic) scenario for any ITRF comparisons.
l. 115-118: To avoid confusion: The IGSR3 orbit/clock/OSB combination solutions were produced by WHU AC and are readily available at the IGS Data Centers.
l. 127: why not also GLONASS (IGSR3 contains GPS, GLOASS and Galileo!) , GLONASS contribution is more significant and more consistent than Galileo, which was still evolving from 3 satellites in 2015 to 23 in 2020! Whereas GLONASS was complete and had 23-24 satellites during 2015-2020! GLONASS not only improves significantly E RMS (so that PPPAR improvements becomes almost insignificant!), but also reduces annual and semi-annual signals due to GLONASS orbital periods which are different from the GPS ½ sidereal day ones. It makes no sense to omit GLONASS here!
l. 163: What % was eliminated for PPP and PPPAR ? Was it the same, or they were additional PPPAR rejections (due to AR failures)?
l. 166: fix rate of what? Epochs, observations, or ambiguities? Needs to be specified
l. 169: What about float PPPs at these rejected stations, were they OK and likely acceptable? Note a low AR does not necessarily mean a bad data, or to be a sufficient reason for a station rejection, unless the float PPPs also failed. (it may only be an AR failure). Were the deleted stations also analysed by float PPP?
l. 201-205: There RMS values are rather high, significantly higher, by a factor of about 2, than the AC RMS in the IGS R3 combination, which are typically at 1, 1 and 3 mm in E, North (N) and height (U) (see [39]). Furthermore, E RMS for PPPAR should be the same or lower than N RMS! Also, it is a miss-norm and inappropriate to quote IGS figures, which were selected to be rather conservative (to be on a safe side) , and refer to GPS accuracy rather than internal precision/comparisons. In fact PPP and PPPAR RMS should be lower than individual AC RMS, since it is an internal precision of IGSR3 densification (an approximation of; a rigorous back substitution; after all a rigorous back substitution would yield RMS=0 in such comparisons). If they are higher than the AC one and in particular so for the E component, this may indicate a PPP software inconsistency with respect to IGS standard/conventions
Fig. 5 and Fig. 8: In most cases PPPAR E RMS should be equal or smaller than N RMS, this may be an indication of a possible PPP AR problems/inconsistencies?
l. 220-223: Indeed, there seems to be some inconsistencies, since the PPPAR-IGSR3 RMS should be smaller, (below 1,1 and 3 mm seen for ACs) and in particular the E RMS should be smaller, or equal to N RMS!
Fig. 7: indicates biases, in particular for E and U. Since IGS R3 combined orbits/clocks were used, there should not be any biases, assuming consistency of IGS R3 orbits/clocks and IGS R3 position combined solutions (this should perhaps could be investigated by here or by IGS)
l. 237-240, 251: the STD and RMS are too large, in particular for E, by a factor of 2, or more
l. 252: this is not true! The PPPAR are much larger than the formal error of the IGSR3 position combination! Please change or remove
Tab. 2: only Tx and D are statistically significant. Also needs to list STD for the trends.
What about float PPP transformation parameters, are they smaller/better or also statistically significant? The Tab. 2 and Fig. 7 may indicate inconsistency between the separate IGSR3 orbit/clock/OSB combinations and IGSR3 position combinations, or a PPP software problems (inconsistency with IGS R3), which is more likely.
Note IGS orbit/clock and position combinations are done separately but with an extreme care to maintain the orbit/clock and position solution consistency. Namely, each contributing AC is required to submit unconstrained solutions with variance-covariance matrix, which are then transformed into IGS realization of ITRF by using the set of the 55 core stations. Nevertheless, it would be beneficial if the consistency of IGSR3 combination of orbits/clocks with IGSR3 position combination is independently verified, e.g. by using another (PPP) software
Fig. 8: Again, RMS are too large, in particular the E ones, they should be equal or smaller than N ones for PPPAR or even for PPP!
l. 275: 1 mm/y ITRF formal error? This cannot be correct, please check/correct with reference
l. 277: please note the IGS values of 2mm/0.2mm/y are rather conservative and are meant to represent accuracy, but here we are dealing with precision/consistency between two IGSR3 combinations and so uncertainties of the internal comparisons should be much smaller
Fig. 9: Again the E component should be equal or less than the N one for PPPAR
l. 308, 309: see l. 275 and l. 277, 1 mm/y ITRF formal error cannot be correct, 0.2 mm/y is accuracy, not internal precision seen here
l. 340-343: Lower annual amplitudes for PPPAR and IGSR3 than for the GPS-only series is due to including Galileo and GLONASS, which , unlike GPS, do not have orbital period aliasing with sidereal day, causing draconian year periodical position signals
Figs 12,13: The larger E differences may be caused by AR problems, may not be in float PPP
l. 356: interpolation and prediction
l. 364: all 30 s epochs?
l. 366-368: there are no IGSR3 position solutions after 2020, but then to what the PPPAR and IGSR3 predictions were compared in Tab. 7 ?
l. 391 and after: Did PPP used identical data as PPP AR? Was the solution rejection the same as for PPPAR. Were the 2 rejected station due to low AR rate also processed/checked by PPP?
l. 399: only slightly in E, the N and U are virtually the same
l. 401: How the PPP Helmert transformation parameters compared to the PPPAR ones in
Tab. 2: were Tx and D for PPP also statistical significant as in Tab. 2?
l. 422: not true, ITRF formal error are much smaller than 1 mm/y (see l. 308)
l. 424: particularly in the N direction , not E!
l. 434: we innovatively propose to retrieve?
PPP and PPPAR has been used for global (ITRF) for more than 2 decades (e.g. by JPL)!
Note: In my opinion the main contribution of this paper is the use and verification of consistency of the new IGS R3 orbit/clock combinations with the IGS R3 position combinations by means of PPP.
l. 448: are roughly equivalent to the formal error of the IGS solutions ? Not so this internal comparison precision/consistency is larger than the (conservative) IGS accuracy
l. 450-451: That is lower than the formal error of ITRF 1mm/y
please remove, this is not correct!
l. 455: the same as l. 450-451, please correct/omit
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Round 2
Reviewer 5 Report
Comments and Suggestions for AuthorsThe paper made some modifications indicated in my previous review, however, some were not addressed, such as PPP-AR and PPP rejection comparisons, the PPP and PPP-AR Helmert transformation parameter comparisons. Also, as pointed out in my previous review, I’m still concern that this paper may create a potential confusion, as it is claiming that an internal precision of PPP (-AR) solutions wrt the IGSR3 position combination is comparable to the official ITRF/IGS accuracy estimates. As stated before, the precision of PPP (-AR) with respect to IGS R3, obtained here, should be significantly better, about the same or less than the individual AC precision wrt the IGSR3. I.e., with STDs of about 1, 1 and 3 mm in E, N and U [4], assuming that the separate IGSR3 position and orbits/clock combinations are consistent, which is likely the case. Any significantly larger STDs, such as the one obtained here, may be an indication of a PPP software inconsistency wrt to IGS solutions/conventions. (In my opinion, omitting GLONASS cannot explain the large STDs obtain here) …
Below listed are some detail suggestions/corrections, which should considered by the authors.
------detail comments/suggestions ----------------
l. 21: the combined orbit, …
l. 156: , even though GLONASS contributions to ITRF solutions are significant, the analysis here focuses on these two systems, which allow AR and to demonstrate PPP-AR improvements..
Tab. 1: Initial value: GPT2w+SAAS+VMF1? Why GPT2w? VMF1 file contains all the necessary information, for each of the selected station , no need for GPT2w+SAAS!
l. 201: low quality observation … [36] ? this reference is to the station logs, which list only the equipment and the measured antenna offsets, but no data quality. Most likely reason for MKEA is not the data quality, but the extreme height (3700 m?) and/or possible PPP software problems with such extreme station height?
l. 260: blue dots represent IGS R3 solutions, red dots represent PPP-AR solutions ? See the Fig legend, it is the opposite, is the legend wrong?
l. 281-282: These residuals are roughly equivalent … Strongly disagree, they are significantly larger by about a factor of 2! Please remove Tab 2: D is statistical significant, also the trends need STDs
(part of the reason may be the missing GLONASS)
l. 299-304: The main reason is the height solution uncertainty (PPP or network) typically larger than the horizontal one, by a factor of about 3. This is due to the fact that unlike for largely balanced horizontal observations, height observations are unbalanced, only in the upper half of the observation hemisphere
l. 330: also GLONASS is missing, including GLONASS, due to its different orbital period, further suppresses the annual (draconian year period caused by GPS)
l. 399: you mean the IGS R3 and PPP-AR solutions of the last day of 2019 (otherwise the 2020 values for PPP-AR and IGS R3 would have been the same)
Tab. 7 Legend should read RMS
Author Response
Please see the attachment.
Author Response File: Author Response.docx
