Dear Dr. Wu,

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Sher Muhammad, PhD

Academic Editor

PLOS ONE

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 “This paper was supported by major projects of the Changsha Science and Technology Bureau in 2020 (kq2011001), key research and

development projects of the Hunan Provincial Department of Science

and Technology in 2022 (2022GK2026), the Hunan Natural Science

Foundation Project (2022JJ30636), and the Excellent Youth Program

of the Scientific Research Program of the Department of Education

of Hunan Province (22B0838), and the science and technology plan

project of Hunan Provincial Department of Natural Resources (2023-78),

the Aid Program for Science and Technology Innovative Research Team

in Higher Educational Institutions of Hunan Province, and the Open

Fund of the Xi’an Key Laboratory of Integrated Transport Big Data and

Intelligent Control (Chang’an University) (Project No.: 300102343515).”

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Additional Editor Comments:

Reviewer #1:

General Comments

The study is new and presents a positioning algorithm. The experiment is also original and no indication of another manuscript with this title or method.

Here are a few limitations.

This study presents a design that is sound but statistical validation is quite weak. Authors are advised to show more provide more statistical data for robustness of results.

Raw experimental data and processing software are not made available. While the figures illustrate output, reproducibility cannot be independently verified

The manuscript is generally standard in language but has some minor grammatical issues and awkward phrasing, however, argument flow is coherent.

Language issues:

Line-by-Line Error Review

Lines 12–13"During relatively low-speed rotation of the rotating carrier, the receiver can rely on capturing the finite time signal only when the antenna is turned in the direction of the

satellite..."

Edit:

"During relatively low-speed rotation, the receiver captures the signal only when the antenna faces the satellite..."

Reason: Redundant wording ("rotating carrier"), awkward phrasing (“finite time signal”).

Line 15

"...as wild values, but for non-continuous reception environments, if it is simply rejected, however, this will..."

Edit:"...as outliers. However, in non-continuous reception environments, simple rejection reduces..."

Reason: Run-on sentence and excessive conjunctions (“but… however…”). Replace “wild values” with “outliers” for standard terminology.

Line 27

"Nowadays, the positioning of rotating carriers remains a focus of research..."

Edit:

"Positioning of rotating carriers remains a focus of research..."

Reason: "Nowadays" is informal and redundant with "remains."

Line 44

"PDOP is the value of the open root sign of the sum of the squares..."

Edit:

"PDOP is the square root of the sum of squared errors..."

Reason: "Open root sign" is not standard English.

Line 66–68

"1) Errors related to carrier speed include carrier speed measurement errors and errors caused by speed magnitude. 2) Errors related to the antenna include antenna placement bias and receiver antenna phase center bias. 3) Errors caused by the carrier motion environment are primarily multipath errors and errors caused by carrier motion road conditions."

Edit:

"1) Errors in speed measurement and magnitude; 2) Antenna placement and phase center bias; 3) Environmental motion effects such as multipath and terrain-induced disturbances."

Reason: Condense and clarify repetitive structure.

Line 103–105

"The signal may be lost again after capture when it is too late for the convergence of the observation data."

Edit:

"The signal may be lost again before observation data can converge."

Reason: Passive and awkward phrasing.

Line 152

"The Chebyshev polynomials are used to achieve the solution of the extrapolated pseudorange value..."

Edit:

"Chebyshev polynomials are used to extrapolate the pseudorange value..."

Reason: "Achieve the solution of" is wordy and unidiomatic.

Line 217

"...the mean square error array of the a priori estimation, the residual of the observation and the measurement variance are calculated."

Edit:

"...the mean square error of the a priori estimate, observation residual, and measurement variance are calculated."

Reason: Clean grammar; simplify list structure.

Line 370

"the effect of the algorithm at 1/18 s/r is slightly inferior to that of lower rotational speeds."

Edit:

"...the algorithm performs slightly worse at 1/18 r/s than at lower speeds."

Reason: More direct and clearer comparison.

Line 406–407

"...the law of satellite navigation received signal during low-speed rotation..."

Edit:

"...the behavior of satellite signal reception during low-speed rotation..."

Reason: “Law” is vague and misused in this context.

Reviewer #2:

Major Revisions:

(a) Methodology clarity and internal consistency:

Problem: The state vector includes velocity and acceleration, but the measurement model described is pseudorange only; Doppler or carrier-phase models (if used) aren’t specified. This mismatch leaves R (measurement noise) definition and observability unclear.

Required revision: Explicitly list all observation types used (code, Doppler, carrier-phase), their equations, units, update rates, and the exact R and Q you used (numerical values, not just symbols). Provide the full, readable A matrix and define Δt and any inputs u/B (the current matrix printout is unreadable)

(b) Ad-hoc weighting function without principled tuning

Problem: The equivalence weight function hinges on thresholds a and b “obtained after iterative validation,” with only range hints and no objective selection method, sensitivity analysis, or cross-validation.

Required revision: Provide a principled parameter-selection procedure (e.g., grid search with cross-validation on held-out sequences) and a sensitivity analysis showing performance vs a and b. Add an ablation: (i) no weighting, (ii) Chebyshev prediction but fixed weights, (iii) your full method.

(c) Insufficient baselines

Problem: The “traditional filtering algorithm” baseline is not fully defined, and there’s no comparison against robust estimation alternatives (e.g., common robust loss/weighting schemes or integrity monitoring used in GNSS). The current comparison (scatter vs. scatter) leaves effect size uncertain.

Required revision: Describe the baseline precisely (state/process models, Q/R, gating, outlier rules) and add at least two robust baselines. Report RMSE/MAE/P50/P68/P95 with 95% CIs across multiple runs.

(d) Ground-truthing and experiment design:

Problem: "Horizontal error" and "elevation vs time" are shown, but how error is computed (ground truth source, alignment, reference frame) is not described. Also, claims about improved PDOP are made but numerical PDOP results aren't shown.

Required revision: Specify the ground truth system (e.g., RTK/INS/total station), synchronization, datum, and error computation pipeline. Provide PDOP time series and statistics pre/post weighting and include repeat trials at each speed.

(e) Hardware/testbed details are incomplete:

Problem: The rig and “self-developed receiver board” are mentioned, but antenna models, placement/spacing, RF chain, sampling rate, loop bandwidths, firmware versions are missing, these all affect discontinuity behavior.

Required revision: Provide a reproducible description: antenna model & gain patterns, separation and mounting geometry, cable lengths/delays, receiver chip/firmware, sampling and navigation rates, loop bandwidths, and rotation rate accuracy.

(f) Statistics are minimal/informal:

Problem: Results rely mainly on P95 tables and qualitative plots; no uncertainty quantification or significance testing across runs.

Required revision: For each speed, report N (number of seconds/epochs and runs), distribution summaries (median, IQR, P68/P95), RMSE ± 95% CI, and paired tests vs baseline (or bootstrapped differences). Include effect sizes.

(g) Units, notation, and terminology:

Problem: Table 1 mixes “revolutions per minute (r/s)”- rpm vs r/s is inconsistent. The manuscript frequently uses “calendar element” for “time step,” and the PDOP definition uses nonstandard phrasing (“open root sign”).

Required revision: Standardize units (e.g., rps or rpm, not both), replace “calendar element” with “time step/epoch,” and correct PDOP definition to a clear, standard form.

Minor Revisions:

(a) Clarify what “intraweek seconds” means in Fig. 6 axes/captions and how it’s mapped to UTC.

(b) Ensure rotation speed labels are consistent across text, tables, and captions (e.g., “1/18 r/s” vs. “18 s/r” anywhere it appears).

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Yes

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

Reviewer #2: No

**********

3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

**********

Reviewer #1: General Comments

The study is new and presents a positioning algorithm. The experiment is also original and no indication of another manuscript with this title or method.

Here are a few limitations.

This study presents a design that is sound but statistical validation is quite weak. Authors are advised to show more provide more statistical data for robustness of results.

Raw experimental data and processing software are not made available. While the figures illustrate output, reproducibility cannot be independently verified

The manuscript is generally standard in language but has some minor grammatical issues and awkward phrasing, however, argument flow is coherent.

Language issues:

Line-by-Line Error Review

Lines 12–13"During relatively low-speed rotation of the rotating carrier, the receiver can rely on capturing the finite time signal only when the antenna is turned in the direction of the

satellite..."

Edit:

"During relatively low-speed rotation, the receiver captures the signal only when the antenna faces the satellite..."

Reason: Redundant wording ("rotating carrier"), awkward phrasing (“finite time signal”).

Line 15

"...as wild values, but for non-continuous reception environments, if it is simply rejected, however, this will..."

Edit:"...as outliers. However, in non-continuous reception environments, simple rejection reduces..."

Reason: Run-on sentence and excessive conjunctions (“but… however…”). Replace “wild values” with “outliers” for standard terminology.

Line 27

"Nowadays, the positioning of rotating carriers remains a focus of research..."

Edit:

"Positioning of rotating carriers remains a focus of research..."

Reason: "Nowadays" is informal and redundant with "remains."

Line 44

"PDOP is the value of the open root sign of the sum of the squares..."

Edit:

"PDOP is the square root of the sum of squared errors..."

Reason: "Open root sign" is not standard English.

Line 66–68

"1) Errors related to carrier speed include carrier speed measurement errors and errors caused by speed magnitude. 2) Errors related to the antenna include antenna placement bias and receiver antenna phase center bias. 3) Errors caused by the carrier motion environment are primarily multipath errors and errors caused by carrier motion road conditions."

Edit:

"1) Errors in speed measurement and magnitude; 2) Antenna placement and phase center bias; 3) Environmental motion effects such as multipath and terrain-induced disturbances."

Reason: Condense and clarify repetitive structure.

Line 103–105

"The signal may be lost again after capture when it is too late for the convergence of the observation data."

Edit:

"The signal may be lost again before observation data can converge."

Reason: Passive and awkward phrasing.

Line 152

"The Chebyshev polynomials are used to achieve the solution of the extrapolated pseudorange value..."

Edit:

"Chebyshev polynomials are used to extrapolate the pseudorange value..."

Reason: "Achieve the solution of" is wordy and unidiomatic.

Line 217

"...the mean square error array of the a priori estimation, the residual of the observation and the measurement variance are calculated."

Edit:

"...the mean square error of the a priori estimate, observation residual, and measurement variance are calculated."

Reason: Clean grammar; simplify list structure.

Line 370

"the effect of the algorithm at 1/18 s/r is slightly inferior to that of lower rotational speeds."

Edit:

"...the algorithm performs slightly worse at 1/18 r/s than at lower speeds."

Reason: More direct and clearer comparison.

Line 406–407

"...the law of satellite navigation received signal during low-speed rotation..."

Edit:

"...the behavior of satellite signal reception during low-speed rotation..."

Reason: “Law” is vague and misused in this context.

Reviewer #2: Major Revisions:

(a) Methodology clarity and internal consistency:

Problem: The state vector includes velocity and acceleration, but the measurement model described is pseudorange only; Doppler or carrier-phase models (if used) aren’t specified. This mismatch leaves R (measurement noise) definition and observability unclear.

Required revision: Explicitly list all observation types used (code, Doppler, carrier-phase), their equations, units, update rates, and the exact R and Q you used (numerical values, not just symbols). Provide the full, readable A matrix and define Δt and any inputs u/B (the current matrix printout is unreadable)

(b) Ad-hoc weighting function without principled tuning

Problem: The equivalence weight function hinges on thresholds a and b “obtained after iterative validation,” with only range hints and no objective selection method, sensitivity analysis, or cross-validation.

Required revision: Provide a principled parameter-selection procedure (e.g., grid search with cross-validation on held-out sequences) and a sensitivity analysis showing performance vs a and b. Add an ablation: (i) no weighting, (ii) Chebyshev prediction but fixed weights, (iii) your full method.

(c) Insufficient baselines

Problem: The “traditional filtering algorithm” baseline is not fully defined, and there’s no comparison against robust estimation alternatives (e.g., common robust loss/weighting schemes or integrity monitoring used in GNSS). The current comparison (scatter vs. scatter) leaves effect size uncertain.

Required revision: Describe the baseline precisely (state/process models, Q/R, gating, outlier rules) and add at least two robust baselines. Report RMSE/MAE/P50/P68/P95 with 95% CIs across multiple runs.

(d) Ground-truthing and experiment design:

Problem: "Horizontal error" and "elevation vs time" are shown, but how error is computed (ground truth source, alignment, reference frame) is not described. Also, claims about improved PDOP are made but numerical PDOP results aren't shown.

Required revision: Specify the ground truth system (e.g., RTK/INS/total station), synchronization, datum, and error computation pipeline. Provide PDOP time series and statistics pre/post weighting and include repeat trials at each speed.

(e) Hardware/testbed details are incomplete:

Problem: The rig and “self-developed receiver board” are mentioned, but antenna models, placement/spacing, RF chain, sampling rate, loop bandwidths, firmware versions are missing, these all affect discontinuity behavior.

Required revision: Provide a reproducible description: antenna model & gain patterns, separation and mounting geometry, cable lengths/delays, receiver chip/firmware, sampling and navigation rates, loop bandwidths, and rotation rate accuracy.

(f) Statistics are minimal/informal:

Problem: Results rely mainly on P95 tables and qualitative plots; no uncertainty quantification or significance testing across runs.

Required revision: For each speed, report N (number of seconds/epochs and runs), distribution summaries (median, IQR, P68/P95), RMSE ± 95% CI, and paired tests vs baseline (or bootstrapped differences). Include effect sizes.

(g) Units, notation, and terminology:

Problem: Table 1 mixes “revolutions per minute (r/s)”- rpm vs r/s is inconsistent. The manuscript frequently uses “calendar element” for “time step,” and the PDOP definition uses nonstandard phrasing (“open root sign”).

Required revision: Standardize units (e.g., rps or rpm, not both), replace “calendar element” with “time step/epoch,” and correct PDOP definition to a clear, standard form.

Minor Revisions:

(a) Clarify what “intraweek seconds” means in Fig. 6 axes/captions and how it’s mapped to UTC.

(b) Ensure rotation speed labels are consistent across text, tables, and captions (e.g., “1/18 r/s” vs. “18 s/r” anywhere it appears).

**********

what does this mean? ). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy

Reviewer #1: Yes:  John Adjah

Reviewer #2: Yes:  Shake Ibna Abir

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/ . PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org . Please note that Supporting Information files do not need this step.

A GNSS Receiver Positioning Algorithm Based on Weighting the Statistical Properties of Discontinuous Signals at Lower Rotation Speeds

PONE-D-25-24422R1

Dear Dr. Wu,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager®  and clicking the ‘Update My Information' link at the top of the page. For questions related to billing, please contact billing support .

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Sher Muhammad, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Thank you for addressing the review comments from both the anonymous reviewers. Both the reviewers are now satisfied with the revision and recommended acceptance, I likewise recommend acceptance.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: (No Response)

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

**********

Reviewer #1: (No Response)

Reviewer #2: 1. Units and Symbols

(a) Double-check unit spacing and consistency (e.g., “m”, “r/s”, “°”). In several tables, units appear concatenated (e.g., “0.1476m”)—insert a thin space before “m”.

(b) In equations, ensure all Greek symbols are italicized, and vectors/matrices are bold.

2. Figure Quality

(a) Check that all plots (especially Fig. 6 and 9) are high resolution (≥300 dpi) and font sizes readable when scaled for journal layout.

3. Reference Formatting

(a) Double-check that all references have complete metadata (journal name, volume, page, DOI if available). PLOS ONE has strict XML parsing rules.

(b) Please Check bracket style consistency [1]–[33].

4. Data and Code Link

If possible, provide a permanent link (DOI or GitHub repository) in the Data Availability section instead of just “Supporting Information files.” That increases transparency and citation potential.

**********

what does this mean? ). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy

Reviewer #1: Yes:  John Adjah

Reviewer #2: Yes:  Shake Ibna Abir

**********