Relative Kinematic Orbit Determination for GRACE-FO Satellite by Jointing GPS and LRI

Round 1

Reviewer 1 Report

Dear authors

The article is very well structured. It is highly technical in the sense of complementing the data records obtained by a set of satellites by jointly using GPS and LRI.

sincerely

 

Author Response

please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors present a method to process kinematic orbits

of the GRACE-FO satellites by jointly introduce GPS observations as well as

LRI data; finally the orbits are checked against a GFZ Reduced dynamic orbit

and the intersatellite distance is also reviewed against KBR data.

In general the idea of the paper is quite interesting. Unfortunately

the English grammar is quite problematic and there are some technical flaws

and also missing explanations. See below a quite long list of grammar hints

(please note that my commenst are by far not complete and a further check by an English native speaker would be really helpful) and also some technical questions flagged with a 'T'. The commenst refer to the line numbering scheme of the manuscript

1) Abstract, l12

'.. formation satellites equipped with

2) l14

'  the effective ability of the new...'

3) l16

'.. and GPS/LRI is proposed.'

4) l19

'.. can limit the influence of GPS observation errors and improve the stability of orbit determination of the GRACE-FO satellite formation.'

5) next sentence

'The linearization of the GPS/LRI observation model and ... are provided.'

6) l25

'The results of the reference orbit check indicates...'

7) 'T'

in the next line you refer for the first time to the X,Y.Z coordinate frame- as you do also later on in the text. Unfortunately this frame is not explained in detail, Do X,Y,Z refer to along-track, radial, cross.track or to any other definition; At least later in the text in chapter 5 this frame has to be explained /maybe also shown with a small graph

8) l27

'... precision of the relative kinematic..'

one additional technical remark. You use over the whole manuscript the term 'precision'. But precision usually denotes 'formal error' . Do you like to refer

really to 'precision' or more to 'accuracy'? mayby also the word 'quality' is sometimes better suited  in your text than 'precision'

9) l30

'The result of the KBR check.... intersatellite baseline determination is about +/-6.3mm.'

whats the meaning of the remaining sentence 'with a stable result of ...'?

re-phrase

10) Introduction, l 42

'GRACE-FO satellites carry the same equipment...'

11) l50

'.. contributes to the estimation of gravity field models with a monthly resolution [6,7]. '

12) l52

'In order to ensure a stable relative distance in formation flight, GRACE satellites are equipped with a KBR system. In addition, GRACE satellites have on-board a Laser Ranging Interferometer (LRI) [8-11].'

13) l56

'.. and provide distance data of high precision [12].'

14) l59

'Generally the relative kinematic orbit determination of LEO satellites is based on carrier-phase differential observations (CDGPS) [13].'

15) l64

'A comparison with satellite laser ranging indicates...'

16) l67

'.. long baselines (>100km)...'*

17) l69

'.. satellites are equipped with an LRI system...'

18) l70

' LRI observations...'

19) l71

'Currently, the intersatellite distances are generally used to verify...'

What do you mean here with 'resolution'? ; temporal, spatial, anything else??

20) l74 ff

'Concerning the LRI ranging system, this manuscript describes the following activities: Firstly , the inter-satellite distance observed by LRI is combined with the GPS observation data of the GRACE-FO satellites to form the GPS/LRI observations. Secondly, the estimated orbits are compared to a reference orbit and KBR measurements. '

21) l79

'.. results of GPS/LRI and GPS-only.'

22) chapter 2, l 86

'.. is the observed code pseudo range ... is the geometric distance between..'

23) 'T' , l86

here - and also later on- you mention from the 'receiver' to the 'satellite'.

But in your case the 'Receiver' are the GRACE-FO satellites and not any receiver on Earth ground. So you should clearly indicate in your text that you

measure ranges between GRACE-FO and GPS satellites. The term receiver is here somehow misleading.

24) l89

'.. is the ambiguity;'

25) l94 'T'

here you note the wavelength of the IF carrier phase LC. to which wavelength in [m] do you refer here ? to a millimeter wavelength or to a narrow lane wavelength? Is N in your case an integer?

26) , l95 'T'

concerning the observation noise I wonder that you do not distinguish here between code and phase noise

27) l99

'.. can eliminate most of the ionospheric delay .. and looses integer cahracteristics.'

28) l101

'In order to build double-difference...'

29) l111

' .. with a LRI ranging system.'

30) 'T' , l112

What do you mean with 'JPL has provided technical manual???

is this just a reference document from which you took the equation (8) or is this more/anything else; If its just a document than refer to the references list and remove this short sentence

31) l114ff

'.. is the LRI measurement (unit:m) ... is the observed phase value of LRI at t.'

'.. is the time delay correction..

.. is the time of signal transmission

.. is the LRI-frequency of the observed phase. '

32) l119

'.. of LRI mainly occurs..'

33) l122/123

'.. by a phase filter..'

'.. by residuals of...'

34) l127

'..LRI observations deliver a biased distance ...'

35) l129

'.. process for the biased LRI distance.'

36) l137 ff

'The difference between the initial value...

... and epochs with a difference greater than a threshold are marked as outliers. This threshold is defined as follows:'

37) l145

'Taking into account the LRI bias, ranging values of each epoch are corrected to obtain...'

38) l 152

'.. carrier phase observations:'

39) chapter 3, l153 'T'

equation (10) list the components of the state vector, but you have definitely to explain the coordinate parameters x,y,z- are x,y,z, the coordinates of

one or both of the GRACE -FO satellites ? or more likely the components of the baseline vector between the GRACE-FO satellites. state explicitly in the text

Furthermore do these coordinates refer to an inertial or earth-fixed reference frame?

40) l156/157

'LRI can establish the observation.... observation equation in matrix form reads as follows:'

41) 'T'

The l vector is noted in equations (11) and (13) and its components in (14)

To my understanding l contains the range differences observed minus computed; you distinguish between phase observations and code observations but I definitely miss the applied weighting between phase/code and also LRI observations. You might add a note here or in the case study chapter 5

42) l167

as noted in the begin - receivers are in your case the GRACE sats

43) l167

'.. satellites, The absolute vector l is given by...'

44) l164-165

check once more if the a coefficients are correct for double difference observations

45) l170

'.. is linearized, a Kalman filter process can be... '

46) chapter 4, l173

 '.. GPS/LRI is to regard LRI...'

47) l175

'.. GPS double-difference observations for resolving...'

48) 'T', Figure 1

• please explain in the text what the text in the green box 'Add LRI' means; I would expect to correct at this stage for the phase bias of the LRI measurement ?
•  In the middle column of the graph you have a second box with text 'Get LRI biased distance' ; but what happens at this point; all arrows point to this box; no way out ?? process stops here?

49) l179

 'The specific process...'

50) 'T' , l184

In equation (15) you show the MW LC which usually calculates the WL.Ambiguity as output ; explain if the quantity Nw really refers to the WL-Ambiguity and give a guess of the wavelength (in m). This of course is dependent on the observed frequencies.

51) 'T' equation (17) , first line

do you really set the threshold here to 5 meters?

or do you mean Nw,i+1-Nw,i <5 in cycles which still would refer to 5*0.86m = 4,3m ?

I wonder because in the second line a cycle slip is detected at the 5cm level in the GF LC?

52) l195

explain 'astral fixed coordinates' to the readers?

53) chapter 5, l221

'.. collected from doy 125 to 131 in 2019,...'

54) l224

'Then synchronous GPS,LRI and KBR data ...'

55) l225

'.. clock offsets and Earth rotation parameter files are provided by the Center...'

56) l 226

'.. provided by the International...'

57) 'T', table 3

In table 3 you note that your reference orbit from GFZ is a 'Reduced dynamic orbit solution'. Does this impact your difference plots in Figures 2 and 3. I wonder - is the GFZ orbit 'perfect' ? or do you expect also periodical error effects in this reference orbit which might show up in Figure2; have a look at the subfigures 2X and 2Y; how do you eplain the periodical behaviour of your GPS+LRI orange residuals ?

58) l232

'.. with the reference orbit.'

59) l 233

 '.. comparison to 125-131 day reference..'

60) l233

'As shown, there are no systematic..'

61) l l236

'.. belongs to a geometric...'

62) l238

'.. are obviously smaller than those...'

63) 'T'

as noted very early in the begin explain the axis directions of the X,Y,Z frame

(ECEF, Inertial, or satellite referred, or...?)

64) l 244

'Usually, a satellite can be observed  for only...'

65) l247

'Therefore, combined GPS/LRI observations can better elimintae GPS observations of poor quality...'

66) l249

'.. show that introducing GPS/LRI observations is obviously...'

67) 'T' legend Figure 2

state excatly that the time series display baseline components and not as mentioned 'orbit differences for one of the GRACE -FO satellites'

68) l255/256

'.. results of the relative kinematic orbit determination, statistics over 7 days are carried out...'

69) 'T' l267-269

 this stated 'improvement in precision' can only be judged if you also give numbers for the weighting of your GPS observations with respect to the LRI observations (already noted above)

70) l270

'.. that the joint GPS/LRI data processing can effectively...'

71) legend tables 4 and 5

for a better clarity the top line of both tables should read

  'GPS only'                        'GPS/LRI'

and not 'NO LRI'   'LRI'

72) l277

  'The KBR system...'

73) l282

'.. values and the intersatellite baseline, and then evaluate the quality of

 the orbit difference between LEO satellites.'

74) l284

'.. from doy 125 to 131...' in 2019. IT shows...'

75) l287

'.. distribution with some residual spikes.'

76) l292

'.. joint GPS/LRI reduces the orbital...'

77) l297

'In order to obtain more detailed statistical information we have conducted

for all seven days a comparison between KBR ranges and the relative kinematic orbit determination results. RMS and MEAN...'

78) l300

'.. orbit determination based on GPS only approximates 36mm while that calculated from joint GPS/LRI data approximates 6.3mm. It indicates that joint GPS/LRI improves the ...'

79) l303

'.. and confirms the results of reference...'

80) chapter 6, l310

'.. orbit determination based on joint GPS/LRI data and EKF processing.

Aditionally, this paper introduces the LRI ranging systems..'

81) l314

'.. by comparing to a referemce orbit...'

82) l316

'.. by GPS/LRI achieves more robust... '

83) l321

'Check results of KBR data.' ??

 re-phrase as a clear sentence

84) l 322

'The consistency between the relative kinematic orbit determination and the

KBR measurements is at the +/- 6.3mm level.'

 

best regards

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The presented paper deals with a relative kinematic orbit determination scheme for formation satellites integrating Kalman filters and GPS/LRI.
A major English check might be mandatory. 
The introduction is not clear. 

Chapters 2-->3 are wel presented for the math point of view.
Figure 1 is not clear. It can be updated with a sequence diagram or a flowchart.

Figure 2 and 3 are too small. 

Author Response

please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

Overall

-        The idea of integration of GPS and LRI measurement has unique originality.

-        However, the benefit of the integration (other than improved orbit precision) in this kinematic method should be clearly suggested.

-        In case of data, data span of 7 days is too short to represent the kinematic relative orbit. Expanding the data including abnormal orbital conditions (solar eclipse or orbit maneuver) will provide more persuasive results and emphasize the benefit of this kinematic method.

-        Recommend additional representation of orbit difference projected toward relative orbit frame to properly analyze the residuals.

-        Recommend to analyze the residual from orbit comparison and K-Band Ranging with more representative statistical characteristics such as median, probability distribution, or quantile.

-        As outliers of LRI measurements rely on the precision of relative kinematic orbit determination (GPS only), I recommend to add figure or table to show the precision of processed LRI measurement and how much of the LRI outliers are detected as outlier.

•        Reference 36 is not publicly available.

 

Details

 

Line 97: Ionosphere-free combination on Equation 5 is wrong. Please check typo. In addition, symbol \omega is not necessary.

Line 104: Equation 6 does not match Single Difference of Equation 3(or 4). P_{r,IF}^{s}, P_{r,IF}^{s_0}, L_{r,IF}^{s}, L_{r,IF}^{s_0} should be replaced with \rho_{r,IF}^{s} and \rho_{r,IF}^{s_0}.

Line 108: Equation 7 needs similar correction as Equation 6.

Line 118: 2.8165684e14 -> 2.81615684e14 Hz

Line 135: inverted -> introduced?

Line 141: To avoid misconception of readers, more details about threshold \sigma_{rel}could be added. The word “precision” can be understood as the Kalman filter covariance based on GPS measurements, but also it can be understood as the difference between reference orbit (here, GFZ-processed orbit) and the estimated relative orbit based on GPS measurement in this paper.

Line 154: GRACE-FO satellite (receiver) clock offset cdt_{r} is not included as parameter in equation 10 when forming double-difference observation. Description about cdt_{r} should be removed.

Line 170: Additional equations for Kalman filter implementation will help readers to understand the methodology in detail.

Line 182: Cycle slip detection process is not included in Figure 1. Addition of the pre-processing process might help readers to follow overall orbit determination process.

Line 202: Please check the terminology ‘astral fixed coordinate system’. Usually, ‘body-fixed’ frame is used to describe the phase center offset of satellite.

Line 228: Table 3 needs a few modifications on DATA TYPE. Abbreviations on first column can be expanded as original meaning except the words which previously represented in the paragraphs. For example, GPS can be replaced with GPS measurements, LRI can be replaced with LRI measurement, CLK/SP3 can be replaced with GPS precise ephemeris and clock, ERP can be replaced with Earth rotation parameters, PSO can be replaced with post-processed science orbit. Furthermore, the product name (Final or MGEX final) of precise orbit and clock might be added.

Line 231: Add reference paper or report for the orbit published by GFZ

Line 233-235: To ensure that there is no systematic error, representation of mean or median value of the figure 2 is needed.

Line 242: Recommend authors to show an extra figure to show the correlation between the number of observed GPS satellites or dilution of precision and the residuals on figure 2.

Line 296: Legend ‘NO IRL’, ‘YES IRL’ seems to be typo of LRI.

Line 311: Until this conclusion, there was no explanation of using Extended Kalman Filter (EKF).

 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear Authors

you have definitely improved your manuscript, both in style as well as clarity and scientific soundness. Congratulation

please find below a very short list of still remaining problems which can be easily corrected

The comments refer to the line number scheme of the revised manuscript

1) Abstract, l14

'.. ability of the new LRI...'

2) chapter 2 , l101

'To build double-difference observation equations, inter-satellite...'

3) l147

'.. are shown in table 1 confirming a good quality of LRI distances. More than..'

4) the revision and upgrade of chapter 4 is very helpful

5) just below table 3  , l257

I wonder about the chapter numbering scheme

'6.' Case study and analysis

here is something wrong - I think this should read chapter 5.x ??

a similar problem shows up at line 359 - '6.2 KBR validation'

currently chapter 6 are the conclusions

5) l352

'.. kinematic orbit determination is not significantly improved. The RMS of the 3D vector is decreased by 17mm which correspondes to an improvement of 25,9%.'

6) l375

'..reduces the orbital spikes of..'

7) l408, table 6

just reconsider entering the columns MEAN and MEDIAN to the table.

First of all consider if the MEAN in your comparison has to be about zero and moreover Mean and Median values of a few 0.1mm are really not significant

8) l414

'.. introduced the LRI ranging system as well as the LRI observation equation, and described the process...'

best regards

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Dear Authors, 

 

I appreciate that many of my reviews have been fulfilled.

However, I believe that, in order to agree with the publication of this draft, an additional major supplement to the main points below should be preceded.

 

• GPS/LRI integration is technically very similar to GNSS/INS, and because it is already widely known, it lacks academic contributions. Therefore, in order to reveal the originality of this draft, it is essential to include a part about how this algorithm performs better in situations such as solar eclipse or orbit maneuver.
• The bias expressed in the figure 6 are should be explained
• The relationship between the number of sats and the residuals, represented in the RSW frame, and the effect of the residuals and DOP will help the reader understand what the author represents.

Author Response

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