A Hybrid ECOM Model for Solar Radiation Pressure Effect on GPS Reference Orbit Derived by Orbit Fitting Technique

Round 1

Reviewer 1 Report

A very thorough analysis of the problem with logical presentation of why the proposed solution should be adopted. There are only a few minor grammatic errors such as

p2 "change it sign"

p.12 "this not"

p.15 "may compensates the deficiencies"

Author Response

We would like to thank the reviewer for commenting on this work. We have prepared the responses as attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

This is an interesting study in general. The author assesses the ECOM1 and ECOM2 SRP models and proposes the hybrid ECOMC model for the GPS orbit determination and demonstrates the performance using the dynamic orbit fitting and PPP. However, I have several major concerns that should be clarified.

1. The most critical issue is that by fitting the IGS final orbit, the only goal is to be as close as possible to the reference orbit, i.e., the IGS product. In this case, the modeling strategy adopted by IGS plays the dominant role. To put it in a simple way, if there is only one Analysis Center contributing to the IGS and this AC uses the ECOM1 model, then you should be able to perfectly fit this orbit with ECOM1 with all the residuals very close to zero. Of course, it is not the case, as the more than 10 ACs usually adopt different SRP modeling methods, and IGS adopts an over-simplified method to combine them by only taking the mathematical average (or median) values, without using any dynamic orbit model. Nevertheless, fitting the reference IGS orbit only demonstrates how close your model is to this reference, but does not present how good your model is. Of course, it can help to analyze the orbit characteristic, but I would strongly recommend applying this model in the precise orbit determination using real observations. Otherwise, the argument is not strong enough.
2. Another problem with this orbit modeling is that with more coefficients to be fit, just like the proposed ECOMC model that combines ECOM1 and ECOM2 together, the orbit fitting residual can be very small, but there is a huge risk of over-parameterization.
3. In line 124-126, the author stated that using the nine-parameter ECOM1 is for feasible than using the five-parameter ECOM1 in the orbit fitting. Again, it is more related to how the reference is modeled, and once again, there is the risk of over-parameterization. In the case of a reference orbit modeled with the five-parameter ECOM1, the nine-parameter ECOM1 can for sure perfectly fit it, but this does not mean that it is better, as the nine-parameter ECOM1 contains the five-parameter ECOM1, and the rest coefficients are very likely to be zero.
4. In line 176, what is the problem of PRN04? For PRN18, changing the SVN number does not matter in this case, as the author does not investigate satellite by satellite, so please explain more.
5. Figure 4, 5, 6. The color bar is very hard to read. Please consider using another color set that people can easily distinguish.
6. Instead of the day boundary discontinuity statistic in Table 4, I am more interested in the orbit prediction overlap. For instance, you fit two 24-hour orbits, predict 6 hours, and compare the overlapped 6 hours. This is much more useful than the day boundary discontinuity, especially for real-time users.
7. The IGS final clock is used in the PPP evaluation. It is quite tricky because the IGS clock is a mathematical combination without considering the orbit. As the fitted orbit is used, the PPP performance does not present which model is better, but rather which model is closer to the IGS.
8. In Table 5, why not give the results of using IGS orbit and clock combination? I would assume that will provide the best PPP solution. In other words, what potential application of using the fitted orbit and IGS clock instead of the IGS orbit and clock?
9. Using one station for PPP is too far from convincing. At least select 10-20 globally distributed stations. If you want to same some time, you can calculate one week per month.
10. From Figure 14 I can clearly see the semi-seasonal signal of the time series in the up component, which is weird as you are comparing it to the IGS weekly solution. Also, in this case, the weekly repeatability would be a better indicator.
11. Nevertheless, I would strongly suggest that the author clarify the purpose of this study and the potential application of the proposed model and correct it accordingly.

Author Response

We would like to thank the reviewer for commenting on this work. We have prepared the responses as attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The IGS as well as other organizations provide high quality orbits in positions with a given sampling (15 or in same cases even 5 minutes). This means for applying these orbits for GNSS measurements in a higher sampling the satellite positions need an interpolation. In particular for PPP applications this interpolation is an essential step asking for the best possible reproduction of the satellite poitions.

In this context the authors propose a combination of the welle stablished ECOM1 and ECOM2 models that are primary designed to orbit determination. The authors can show the benefit of their combined proposed orbit model with respect to the original ECOM1 and ECOM2 models.

Because these empirical SRP-related parameters are only one element of a complex orbit model it is difficult to assess whether the additionally estimated terms just compensate a deficiency of their orbit model with respect to the refernce orbit to be fitted or to which extent it is a general feature when using the ECOM1/ECOM2 orbit models. This can be assessed by fitting selected IGS AC orbits and compare the behave in relation to differences in the orbit modelling strategies applied by the ACs according to the AC processing log sheet.

The other question is whether an advanced orbit model as presenteed by the authors is needed just for interpolation of satellite positions at all since also direct interpolation methods in the Earth-fixed frame do exist. In this context an advanced orbit model is only needed either for orbit determination or orbit extrapolation. Both application scenarios the authors do not include. Some additional motivation why they believe that such an advanced orbit model is needed for their applciations should be added to the manuscript.

Some more minor and partially also major points I made directly in PDF.

Comments for author File: Comments.pdf

Author Response

We would like to thank the reviewer for commenting on this work. We have prepared the responses as attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Thanks for your efforts and for considering the precious comments.

However, I am still not very convinced by the PPP validation part. 

1. For the GNSS users the Lagrange interpolation is commonly used instead of the polynomial function, so using the polynomial function for orbit interpolation is rather rare. The Lagrange function works perfectly. For real-time users, the satellite orbit is predicted using the dynamic orbit modeling, so the interpolation method does not matter. Therefore, I still do not see the potential of using this orbit fit method for real-time users.
2. Yes, the PPP solution is affected by the station geography. However, this has nothing to do with your PPP investigation. Using one station is simply not persuasive enough.
3. Again, I would suggest that you clarify your objective more clear. Simply fitting the IGS orbit and investigating which model fits the IGS product better is fine. But if you want to indicate which model is better for PPP users, I do not say any potential applications at all.
4. I do not like the way that the different SRP parameters are presented. You can always use "hsv(n)" in Matlab to specify the different paraemters, instead of the misleading figures of the current manuscript. I would strongly suggest that you correct the corresponding figures.

Author Response

Please see the attachment.

Author Response File: Author Response.docx