Robust Helmert Variance Component Estimation for Positioning with Dual-Constellation LEO Satellites’ Signals of Opportunity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Interesting paper dealing with a topic that is object of current research. Text is fluent, and graphics are ok. Also the references are fine, even if a couple of additions (see below) could be useful. The approach and content are scientifically sound.

Some suggestions to improve the paper, and especially to make it more useful to the readers:

Line 38-43: This reviewer fully agrees that LEO communication constellations are a growing area of interest with respect to possible, innovative navigation services, exploiting some key advantage as stronger power. Specifically, this reviewer was happy in finding, among citations, some papers by Kassas (references 8 and 12), who is one of most active researchers in this area. 
It would be useful to remark that also the issue of coverage has been investigated, including navigation specific parameters as GDOP for Doppler observables (see as an example Palmerini & Kapilavai, "Orbital Configurations for Large LEO Constellations Providing Navigation Services", IEEE Aerospace Conference Proceedings 2023). With respect to GDOP for Doppler, it would be also useful to tefer to "The First Step of AI in LEO SOPs: DRL-Driven Epoch Credibility Evaluation to Enhance Opportunistic Positioning Accuracy" by Yin et alii, just published this August in Remote Sensing. Finally, please remark - for clarity - that GDOP for Doppler observables clearly differ from standard GDOP for pseudorange observables.

Line 103, please better specify that both the satellites' oscillator and the receiver's one are included in the δ terms, both for Iridium and Starlink. By the way, why do not divide the source (satellite) and the receiver clocks contributions, given that they are almost certainly very different in magnitude?

Line 106 (important) the steady observer will be actually steady only in a Earth-Centered Earth-Fixed (ECEF) frame, and this fact should be specified. It would be fine to use this reference system as far as also the kinematic state of the satellites (poistion, velocity) are projected into it. Otherwise, it can be considered that velocity due to the Earth rotation is quite small with respect to orbital one, and indeed it can be assumed (even if not accurate) to consider a steady observer at theEarth as having also inertial speed close to zero and negligible. In the opinion of this reviewer, these considerations should be added and the choice made by authors stressed,
to the advantage of the readers. 

A comment about the approach: authors look for an iterative improvement of the weights, that is certainly a feasible - and above all fruitful, as proofed by results - approach. Another possibility would be to include an iterative improvement of one of the ingredients most prone to errors, which is the ephemeris data. It is well known in literature that two line elements (TLE) provided by celestrack (citd at line 154) can be only a first approximation, as they are not necessarily updated at fixed, short intervals. The inclusion of orbital parameters in the iterative process can provide also an independent check during simulations, because they can be compared with their a posteriori, far better estimation based on later updates of TLE. Notice that I am not saying this is a better approach, but only an alternative one, with its pros' and cons'. Maybe it could be recalled in the text or in the conclusion to provide a wider view to readers.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper introduces a robust weighting pipeline for dual-LEO SOP Doppler positioning, combining slope-based observation and Helmert variance component estimation to improve accuracy. The method was validated using a real experiment dataset. In general, this paper is well written and technically sound.

Here are some comments:

1. What would be the values of parameters (threshold), such as in the IGG-III, and the principles of selecting them? Is the performance sensitive to the choice of parameters?
2. It is reasonable to assume the existence of outliers in the real experimental data. But the key contribution of this manuscript is around robustness. Some controlled way of adding outliers should be included to investigate the performance. For example, some simulated outliers can be added to show the performance comparison between the proposed method and conventional methods.
3. The data is available upon request. How about the code? Is it possible to share the code to accelerate the development of this field?
4. Is it a typo for "Ring Alter signals" -> "Ring Alert signals"?
5. It would be nicer to have a consistent precision in Table 2, such as 12.0, 75.000, 23.340 (or their actual value at that precision)

Author Response

Please see the attachment.

Author Response File: Author Response.pdf