A Comparative Study on the Solar Radiation Pressure Modeling in GPS Precise Orbit Determination
, Huizhong Zhu 1, Maorong Ge 2,3, Aigong Xu 1 and Harald Schuh 2,3Round 1
Reviewer 1 Report
This paper presented Solar Radiation Pressure Modeling in GPS precise orbit determination. Especially, the shadow factor was dealt with for the POD solution. The suggested adjustable box-wing model combined with ECOM1 could be useful for further GNSS data analysis. Here are some comments.
- p.2, you may add a reference for eclipsing beta angle (13.25 degrees).
- p.3, you may describe the meaning of D, Y, and B directions.
- p.4, you may add a reference for function (7) for Penumbra.
- p.5, The first paragraph may be written more intensively for readers.
- p.6, the arc length was defined 24-hour. You may describe the reason for selecting the arc length. (because the orbital period of GPS satellite is about 12-hour.)
- p.19, the last paragraph was well written.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
The reviewed article contains interesting considerations. The extensive practical analysis of issues related to the a comparative study on the solar radiation pressure modeling in GPS precise orbit determination, but the current version need improved, for details se below:
- line 26-27, left column: give them the name of the author and the title of the article,
- line 221,222: complete the sentence “More details are given in …”,
- line 280: change “prameterizaiton” to “parameterization”,
- line 465: format the table as required by the journal,
- line 504: format the table as required by the journal,
- References: is required Abbreviated Journal Name
- References: add DOI,
- References: please format according to the journal guidelines
https://www.mdpi.com/files/word-templates/remotesensing-template.dot
In future publications, authors should devote more time to editing the article according to the requirements of the journal. This will then avoid quite a number of insights into editing.
The reviewed article is a valuable publication. It can serve readers as a set of knowledge that can be used as a basis for further innovative and implementation studies.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Review of the paper ‘ A Comparative Study on the Solar Radiation Pressure Modeling in GPS Precise Orbit Determination’ by L. Tang et al.
Submitted to Remote Sensing
The paper focuses on the comparison of a number of models of the Solar Radiation Pressure acting on different types of GPS satellites. In particular it concentrates on the combination of box wings models with the CODE’s empirical models. The argument is very interesting because, as it is correctly pointed out by the authors, the SRP is the most important non gravitational force acting on the satellites. It is also pointed out that different Analysis Centers of the IGS use different approaches for the SRP modelling. This is at least in part responsible for the mean discrepancy among the orbit products of the various Analysis Centers, which is roughly of the order of 1 cm.
After an excellent review of the state of the art on this particular subject of the SRP, the Authors set (line 120) the criteria for assessing the quality of the orbit: the authors choose that the day to day discontinuity and the difference of the recovered ERPs to the IERS reference value should rank a SRP model, if I understand correctly.
Sect. 2 clearly details the a priori and parametrized contributions to the SRP acceleration. The shadow factor is introduced and its action onto the various components is discussed, according to the various schools of thought. The differences between the ECOMs models in terms of multiples of cycle per rev terms is discussed in detail. Here I have missed an analysis of the accuracy with which we know the various angles (beta, epsilon, mu), in other words how do we know the attitude data and with which accuracy. It should be emphasized that we measure the position of the centre of phase of the GPS antenna in some reference frame IGb14 and with some antenna model (this is important!!).
The 12 tested SRP models are presented in Table 1. The criteria for quality assessment are presented on lines 235 and ff. Besides the DTD discontinuity and the agreement of the recovered ERPs with a reference IERS solution (of unspecified uncertainty), the correlation between the recovered pairs of parameters is introduced.
The analysis strategy is summarized in Table 2. If I understand correctly, double difference phase data with integer ambiguity resolution is used to estimate a number of parameters, from station coordinates (minimally constrained, I assume) to ERPs and also the 6D vector of state of each satellite (one set per day, I assume), plus the SRP model parameters. For the 12 considered models I would have expected that the rms of the post fit residuals is given, as an indication of the goodness of the fit. Also the percentage of the ambiguities solved as integers would have been interesting, for each of the 12 models.
The results of the analysis are presented in Sect. 4. Figg. 3 and 4 give the correlation coefficients between the various parameters of the ECOMs models, the satellite vector of state and ERPs, for an eclipsing and noneclipsing scenario. The results should clearly rule out some models, as one cannot meaningfully assign values to variables which are highly correlated. I have the impression that, because of the high correlations, some models are overparametrized and perhaps a smaller number of parameters would be sufficient for a decent fit to the data.
Figure 7 highlights the DPD discontinuity, which has a 4-5 cm rms spread regardless of the SRP model. Figure 8, 9 and 10 describe the differences in the radial direction as a function of the angles beta and delta_mu. These differences are of the order of few mm, depending on the model, and are largest at eclipse (beta near to zero)
The DPD discontinuities are considerably larger, from 4 to 9 cm, regardless of the beta angle. The rms’s in Table 3 suggest that the various models are difficult to rank, according to this criterion, as the values are all very similar.
Same reasoning applies to the ERP/LOD values: the ranking seems hardly doable on this criterion, as the values are very similar: do the authors believe that the differences in table 4 are statistically significant?
Likewise, in Figure 12: are the plots significantly different? Without error bars it is very hard to tell!
The conclusions are presented in sect. 5: I am not sure I can agree with the statements there, because the various SRP models which have been presented have shown no particular difference among each other, at least in my view.
I have the impression that the paper dwells on the values of a number of model parameters, without first asking a) if the available data are able to estimate unambiguously them (i.e. with small correlations coefficients) and b) if the ranking criteria are sufficiently effective in establishing which is the ‘best’ SRP model. In my view, I would have examined timeseries of position residuals in the Tangential, Radial and Cross track directions, and identified signatures which clearly correlate with the beta, delta_mu and epsilon angles. Then I would have generated synthetic time series based on the SRP models, and tried to optimize the parameters based on the criterion that the synthetic signal best fits the position residuals. The uncertainty of the data and of the estimated variables should be tracked very accurately. I am for example not sure that the satellite positions (center of mass) are known with mm uncertainty. Do we have a control of the ARP to CoM vector at this level of accuracy for all satellites and under any condition of thermal distortion, e.g. during an eclipse? Maybe yes, but a reference should be given.
In conclusion the paper is interesting but the analysis method and the ranking criteria for the various models of SRP are to me not convincing. For this reason I would recommend a major revision, and that in the end one of the models would clearly emerge as the ‘best’, according to some convincing rule.
Author Response
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Round 2
Reviewer 3 Report
If the paper addresses a comparison among different models of SRP effect on the GPS orbits, in the end there should be a ranking based on criteria which are able to discriminate among the various models. The overall improvement caused by the use of a model relative to others should be measurable with an decrease of the rms of the fit to the data (I now understand that it is a PPP kind of solution). I do not find this information in the revised text. So I have the impression that several models have been tested but, based on the adopted ranking criteria, none is above the others. The conclusion of the paper the should be than no matter what model is used the overall quality of the fit to the data will be the same.
