Toward a Geodesy and Time Reference in Space (GETRIS): A Study of Apparent Satellite Clocks of a Future GNSS Satellite Constellation

Round 1

Reviewer 1 Report

Review of the paper „Towards a Geodesy and Time Reference In Space (GETRIS): A Study of Apparent Satellite Clocks of a Future GNSS Satellite Constellation”.

 

The paper discusses the High-precision links and clocks for the advancement of satellite precise orbit determination (POD) and navigation. This is dependent on future ranging and time transfer capabilities. The GEodesy and Time Reference In Space (GETRIS) concept proposes using high-precision clocks on geosynchronous orbit (GSO) satellites, along with high-precision optical links, to establish connections with Medium Earth Orbit (MEO) and Low Earth Orbit (LEO) satellites, as well as for Earth satellites. The authors conducted a simulation study to analyze the capabilities of clock synchronization using a combination of L-band observations, high-precision dual one-way Optical Inter-Satellite Links (OISL), and ground-space-based dual one-way links, called Optical Two-Way Links (OTWL). By comparing the apparent clocks of MEO-only constellations to MEO+GSO constellations, the authors evaluated the accuracy of clock estimation and prediction using both Passive Hydrogen Masers (PHM) and the Atomic Clock Ensemble in Space (ACES) clock as a high-precision clock example. In general, the paper is well prepared with a properly designed simulation study and description of the results.

 

One remark: There will be the ESA-funded mission GENESIS for the co-location of space geodetic techniques. The GENESIS white paper could be mentioned in the manuscript as it will be possibly equipped with a high-accuracy clock and will provide a substantial contribution to the realization of ITRF and deriving geodetic parameters. 

Minor English polishing would be welcome. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The content of this work is worth publishing. However, a number of major and minor issues need first to be resolved, to improve clarity and structure. My suggestion is to re-shape the text to follow a more structured flow, with the aim of aiding the reader to follow the different scenarios addressed and the processing logic used.
In the following, I am going to list a number of general remarks, following by a list of comments in the paper.

General remarks:  

[GR1] perhaps the authors should consider a second through read by someone fluent in English, to point out grammar and syntax mistakes that make the paper hard to read at times. Some examples are given below.  

[GR2] In the abstract, it is not immediately clear the scope of this work. The authors mention connecting satellites in different orbits and ground station with optical links for a generic “synchronization”, aiming at reaching “the future POD and clock determination goals”. It is not clear what these goals are and why one would need optical links.  

[GR3] What is the reason to consider a complementary constellation of IGSO satellites? An introduction of the core idea behind the GETRIS concept is missing.

[GR4] Reading through the manuscript proved hard, at places. I became often confused about what is what, in particular for terms like “apparent clock”, “clock bias”, “clock error”, “clock offset”. In particular, it was not clear what “apparent clock” means, exactly. Is it the estimated clock? Why call it apparent?

[GR5] It is very difficult to understand what is being estimated. Other than clock and satellite orbits, what else goes in the estimation process? Are optical and/or L-band biases estimated too? Table 5 does not clarify this: does the bias model match the bias injected in the measurements? The paper, especially in Section 3, lacks overall clarity and requires some guessing to understand the estimation chains.

[GR6] Normally, the offsets and hardware biases in a typical GNSS all refer to a single chain that links the satellite center of mass to the transmit antenna reference point. With OISLs, a third offset is introduced, the optical phase center. Thus, one additional potential bias per optical link is present, the offset between the optical and L-band measurement reference points. Is this assumed to be fully calibrated? These considerations need to be made clear in the formulation of the scenario addressed.

[GR7] In the application addressed in the paper, the authors refer to [14] for the scheduling details, but I would suggest to add this information somewhere: are the authors using close measurement topologies at each epoch? Or are satellites linking to each other with just one single terminal per satellite, and keep switching over time?

Throughout the paper:

15: „dual one-way“, how to interpret this? Simultaneous two-way? Or time-division?

15: more than “synergy”, I seem to understand a “complementary” role for the two type of observables (L-band and Optical)

17: “observation technique combination”: this is an odd formulation

29: “dual one-way high-low satellite-to-satellite … links”: I suppose high-low refers to the different orbits? If so, it would be less confusing if these words were to be removed, and these links made explicit: between MEOs? MEO to GSO? MEO/GSO to ground?

30-31: “These links are European Data Relay System (EDRS; [3], [4]) like optical links used for data communication with GSO satellites” - unclear syntax. Also, EDRS are GEO-to-LEO (these could be GSO, of course) optical links, for the time being.  

32: these links (EDRS) are technically also (capable of) providing time-transfer and thus ranging, although with low accuracy, via network time protocols for synchronization. I would rephrase this to address high-accuracy time-transfer.

33 (and all occurrences thereafter): high-stability, more than high-precision

37-39: check syntax

40: 3E-15 is oddly specific, talking about a diverse group of clocks. Perhaps “E-15 region”?

51: this statement is questionable. One may argue that stable clocks would allow to perform less frequent synchronization with respect to a given reference time scale. However, one may also argue that having a way to continuously and precisely synchronize distant clocks may remove the need for stable clocks. So, the pre-requisite of optical links to harvest the better clock accuracy could be a logical fallacy.

75: “reduced”? I think the authors meant increased (accuracy)?

76: It is not clear what the statement here means. What results were achieved in [15]? Do the authors mean that they are expanding on the results presented therein, or are they comparing with those? The paragraph that follows compares this work with that one, summarizes that one, or summarizes this one?

112: “with each one clock” à one clock each?

113: “we simulated PHM carried by each participating entity” check syntax. A simply “we emulated a PHM clock on each satellite.”

113: it is not clear what model was used to simulate the clock. Two state? Three state?

116: “nearer” à near

Table 3: a) It is not clear what the “constant bias” refers to. Hardware delays? Code or phase? In case of hardware delays, these seem rather small. B) carrier phase ambiguities are not accounted for? c) “Variation with once per revolution: .. temperature dependent inter-technique bias”: what does inter-technique refer to? Inter-frequency biases?

171-177: the mathematical notation should be improved: the “-“ superscript looks like a typesetting error. Also, I would suggest to find a way to distinguish the different models for B, in eq. (1),(2), and (3)

183: this is not clear. What is it for? It is easy to confuse the clock bias - which is here probably a clock difference measurement biases - with station clock offsets.

187: “we performed all results” check syntax

Table 6: a) remove/move the term “weighting”, it is confusing over the first column b) probably this table is not needed c) it is not explained the reason for the vastly different weighting coefficient when using GEO compared to the other cases.

200-201: “Then we analyze the resulting clock errors by the apparent clock offset”: check syntax

209: “or the ground clock biases were introduced but not estimated”, what is the reason behind this approach?

211-212: it is unclear to me why the clock errors are not dependent on the clock bias constraints. It is just an observation on the results obtained, or you identified an exact reason for this?

241: what is the reason for the large offset? Are modelling errors responsible? What are the results if no modelling errors were introduced (sanity check)?

445: the clock model should be specified in the data simulation part.

448: “ACES clock, on the other hand, does not have a quadratic drift” by specification, this may be true. Its behavior in space has not been verified. Also, I suggest the authors insert “quadratic phase drift”, which translates to a frequency linear drift, to avoid ambiguities.

Grammar and syntax to improve. Readibility is impacted.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I have still a number of general comments, and a few minor ones.

+ First of all, I thank the authors to act on my previous comments about the general work description. The structure of Section 2 is now very clear, it was a good job to reshape it.

+ Every now and then I still needed to second-guess the authors’ intentions. Examples are given below.

+ Equations, figures and tables are misplaced (off margins), but I guess it will be taken care of during final editing.

+ I do not think the abstract does a good job in introducing the rationale behind the GETRIS concept, and it is equally hard to read as it was in the first version. I here list the reasons, in my view:

8-12: The phrase in 10-11 is a repetition of 8-9, basically.

11: „Clocks with a higher stability enhance the prediction of the clocks.“ This statement comes out-of-the-blue, there is no context.

12-14: „which aims to build up a geodetic reference frame for ranging and time transfer with the potential to connect the near Earth environment and deep space.“ This phrase reads as if a reference frame is built FOR range and time-transfer, which I am not sure what it means, or whether it is correct at all. A clearer explanation is the one given in the Introduction, 44-52.

14-15: unclear why this is needed from the premises.. why is ps time-transfer necessary for building a geodetic reference frame?

19: not clear why GSO orbits help links to deep space. MEO/GEO/GSO are all more or less the same, talking about deep space distances (say, beyond lunar range)

All over the abstract: „low mm level“ means 1-3mm? In case, please attach a quantitative term (e.g. „between 1 and 5mm“), . „mm-level“ would work too, if the intention is to qualitatively express the range 1-9mm.

I understand the authors analyze the impact of combining inter-satellite and satellite-to-ground time-transfer and ranging observables with L-band measurements in a classical GNSS orbit determination and clock synchronization processing scheme. Why a GSO satellite is considered is still unclear. The abstract must be made on point and without unnecessary de-tours (optical versus L-band consideration can be moved to the introduction, for example).

 

+ line 203: this definition of “clock bias” generates quite some confusion, and took me a long time to understand what the “clock bias constraining” (Section3.1) means. Is it correct, that the clock bias introduced here is not a clock bias per-se, but a measurement bias on the time-transfer function of the OISL or OTWL measurements? How can this be interpreted in practice? Is it a bias in the link between the satellite clock and the link terminals, so that the pseudorange observations add a (daily constant) bias in the functional models? If so, I suggest to reconsider this wording, since it mixes up with the overall satellite clock estimation bias, which I could not understand how it could be constrained without introducing a clock model into the estimation process, which is not mentioned so I excluded this possibility. Figure 2, later on, highlights the confusion: if I understood correctly, these plots do not show any bias, but the quality of the clock estimation when the error can map to a (non-generic) bias in the residuals of the OISL or OTWL measurements. This mapping is mitigated with the hard-constraint approach. Explicitly giving the functional model of the OISL and OTWL measurements could help the reader following the analyses. Also, how is the loose/hard constraining discussed in Section 3.1 realized in practice? Is it simply a different weighting of OISL and OTWL observations?

 

Minor comments across the paper:

41-43: I cannot follow the reasoning: are the authors saying that the links in EDRS can support high precision, but not high accuracy? I cannot decipher these two sentences.

44: “..as THE ONE we follow..”

55: iodine “cells” perhaps is better understood

71-72: the clocks do not have prediction capabilities. I’d rather say “.. to have stable clocks, since their drift can be predicted with good accuracy for longer time intervals.”

72-73: I understand that the statement “However, a more stable clock does not allow improvements for an epoch-wise processing.” comes from the author’s previous analyses. However, the logical chain is arguable. A stable clock is a clock that can be better modeled with, for example, two- or three-state dynamic models, or a polynomial function (see for example Galileo: the advantage it has over other GNSSs is that the clocks are really stable, and can be predicted with good accuracy with a simple linear model). If this is true, then it is the epoch-wise processing the problem, not the clock, since the stability of the clock does not play a role in this case, indeed. Instead of using a floating clock parameter, one may use a clock model and vastly reduce the number of unknown in the processing chain.

77: I do not know about “most common”, no such scheduling is applied in practice, yet

96: the authors should clarify this aspect better, since so formulated it raises a few questions. What does it mean to “achieve ps level clock accuracy”? I suppose the authors mean that the target is to estimate the satellite clocks offsets with respect to a ground reference time scale (e.g. GNSS system time, or UTC) with an accuracy at ps-level?

97: “carry PHMs” or “carry a PHM each”.

99: now the term “apparent” clock appears only here, and in the title. Since I am not sure this is common terminology, why not eliminating it completely? The title can easily be adjusted as “.. ..a study of satellite clock estimation accuracy of a ..”

130 (Table 1): what is the meaning of “longitude” in an IGSO satellite? Do the authors mean the phasing of the satellites (i.e. their distribution over the inclined orbital plane)?

134: “period of 10 days”

137-138: “The clocks were simulated from the noise taken from an Allan Deviation.” Does not yet clarify how the clocks are emulated. Pragmatically, how is the clock varying offset (drift from an initial arbitrary value) simulated? Two-state model with proves noise from the ADEV? Random walk with noise from ADEV? Since the clock estimation is at the core of this analyses, the authors should make this crystal clear.

146: “The simulated link(?) types” Do the authors mean observation types?

147: “optical ranging and time transfer concept OISL” I cannot understand (due to syntax, I think)

174 (Table 2): the measurement rate is very low, at 60s for all observable types. Is there a reason for this?

207-208: do the authors mean that the biases are “absorbed” by the float ambiguities? The meaning of “compensated” is not immediately clear, at least to me

227: double parentheses

262-263 (and 317 and 329): why defining the estimation error as true-adjusted? True-estimated gives it right away, without adding again an ambiguous term: “adjusted” is not defined anywhere.  

264: “Using only PHM satellite clocks in [17], ..“ please rephrase, it reads as only PHMs are used in this analysis too, although the next phrase corrects it

283-284: “The results for the clock errors are mostly given in centimeters to relate to the positioning error which is analyzed in this work.” I do not know what this statement tries to convey.

286-288: strongLY / weakLY ? Is it not more commonly accepted to use the terms hard/loose constraints?

301-302: the caption is very involuted: what is the bias of the estimated clock? This contradicts the text above the figure. The caption should be as clear and as self-contained as possible. These plots show the mean clock estimation error as function of the type of observables used (each plot), and hard/loose constraining (left and right) plots. The minimum, mean, and maximum values are reported, as well as the value bounding the 5% or 95% of the results. Is this correct? If so, could the authors attempt at writing it clearly? This comment applies also to the text discussing the results.

 

Please have the paper internally reviewed by someone who is not familiar with this work.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf