Algorithm for Taming Rubidium Atomic Clocks Based on Longwave (Loran-C) Timing Signals

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper reports the results of a campaign of measurement using Loran-C groundwave broadcasts to discipline a rubidium clock to UTC. They compare the performance to that obtained from GNSS signals. Loran-C is an old technology but is relevant due to renewed concerns about the resilience of satellite navigations systems. The authors use simple regression analysis to model the periodic noise on the timing signals in order to improve the stability and extract clock parameters for steering the timescale.

This report would be useful to anyone looking to replicate this setup and to discipline a local clock with remote long wave timing signals. I was not able to find recent reports on the same topic and so I find the paper to be novel enough to deserve publication.

My main concern with the methodology of the paper is that there is only data from a very limited time frame supporting the conclusions. The FFT analysis should be conducted over a longer window, as should the steering of the Rubidium clock shown in Fig. 11 and 12.  My concern is that the short term stability is compromised by the steering action and that something approaching equilibrium conditions should be presented instead.

I attach an annotated copy of the manuscript with further minor comments.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

What the authors refer to as "taming" throughout the paper is properly called "disciplining" (an oscillator).

I recommend getting an expert in professional English communication to help with the language of the paper, however I was able to understand the content without too much trouble.

Author Response

Dear editors and reviewers,

 

Thank you very much for your careful reading and for giving me positive evaluations, valuable opinions and practical suggestions. All of these have greatly improved the overall quality and clarity of my manuscript. In the past few days, I have carefully considered each comment from the reviewers and made corresponding revisions to the manuscript.

 

The following are the detailed comments of the reviewers and my responses:

Comments 1: Title spelling error: Roran-C.

Response 1: Thank you for reading my paper carefully and giving me the above valuable suggestions.

I have revised the title to: Algorithm for taming rubidium atomic clocks based on longwave (Loran-C) timing signals. And it has been marked in red.

 

Comments 2: The reviewer pointed out in the annotation of the first paragraph of the Introduction: Be specific about the kinds of clocks referred to, Cs and Rb clocks are often interchangeable and encompass many different technologies.

 Response 2: Thank you for pointing this out. I agree with this comment.

This part of the content has been revised in the first paragraph of the introduction in Chapter 1 of this article, and the revised part is marked in red.

 

Comments 3: The reviewer pointed out in the annotation on page 4 of the paper: It's not unparalleled. Phase tracking techniques such as PPP can give significant improvements over standard GNSS signals.

Response 3: Thank you for reading my paper carefully and giving me the above valuable suggestions.

The previous statement was not rigorous enough. I have already made the modification in the text (in the conclusion part of Section 2.1) and marked it in red.

 

Comments 4: The reviewer pointed out in the annotation of the first paragraph of Section 2.2 in the paper: You must justify the choice of looking only at a single day. Given that your largest fluctuations are of similar period the frequency resolution of the FFT will be terrible.

Response 4: Thank you for reading carefully and giving reasonable suggestions.

On the basis of the original spectral analysis of one day in Figure 4, I have added an additional spectral analysis chart for the original long-wave time difference data of all 10 days in Figure 2. Through comparison, it can be clearly seen that whether it is the data of multiple days or the data of any single day, the characteristics of the 24-hour daily cycle are extremely prominent and clearly distinguishable. I have replaced the original Figure 4 with the updated spectral analysis chart and marked it in red.

 

Comments 5: The reviewer pointed out in the annotation of the first paragraph of Section 2.2 in the paper: Eq. 2 presumably.

 Response 5: Thank you for reading my paper carefully. I agree with this comment.

There was an error in the formula numbering in the paper. I have made the corrections in the text and marked them in red.

                 

Comments 6: The reviewer pointed out in the annotation of Formula 4 on Page 7 of the paper: These three terms appear to be equivalent to the pseudo-inverse of A.

 Response 6: Thank you for pointing this out. I agree with this comment.

The first three terms of Formula 4 are indeed equivalent to the pseudoinverse of matrix A. During the derivation process, I employed the conventional matrix solution method to expand it, and thus obtained such a result.

 

Comments 7: The reviewer made a comment on the text below Figure 5 on page 7 of the paper, pointing out that: stability, if you want to claim accuracy then explain how you are traceable to UTC.

Response 7: Thank you for pointing this out. I agree with this opinion.

The 1PPS referenced by all the time difference data in this paper is derived from the output of China's Coordinated Universal Time UTC (NTSC) maintained by the National Time Service Center of the Chinese Academy of Sciences. The 1PPS output of UTC (NTSC) has extremely excellent stability, with a stability of up to 8.3×10⁻¹⁶ over 5 days and a stability of up to 4.7×10⁻¹⁶ over 30 days. With such a high level of stability, this 1PPS can completely serve as a benchmark for measuring the quality of the 1PPS signals output by systems such as long-wave or BeiDou. The relevant description of this content has been added to the section of "Construction Scheme of Long-wave Ground Wave Propagation Time Delay Measurement System" in the first paragraph of Chapter 2 of the paper and presented in red.

 

Comments 8: The reviewer pointed out in the annotation of the first paragraph of Section 3.1 on page 9 of the paper: This is not a law but merely a useful model.

 Response 8: Thank you for reading my paper carefully. I agree with this comment.

I have carefully corrected each incorrect expression in the text and marked them in red.

 

Comments 9: The reviewer pointed out in the annotation of the first paragraph below Figure 8 in the paper: Recommend stating that it is much more stable than the clock being tested.

Response 9: Thank you for your careful review. I concur with this opinion.

In line with the approach taken for Question 7, regarding the key point you mentioned, I have added the corresponding explanatory content to the section titled "Construction Scheme of Long-wave Ground Wave Propagation Time Delay Measurement System" in the first paragraph of Chapter 2 of the paper, and have marked the newly added part in red. 

 

Comments 10: The reviewer pointed out in the annotation of the first paragraph of Chapter 4 in the paper: Cite other techniques for comparison.

Response 10: Thank you for reading carefully and giving reasonable suggestions.

Here, I would like to explain to you that this paper mainly focuses on a long - wave correction algorithm. It elaborates on the content of this algorithm and validates the feasibility of using the corrected long - wave to tame a rubidium atomic clock. Therefore, various algorithms for taming rubidium clocks are not the core research subject of this paper, considering the large number of atomic clock taming algorithms. However, your suggestion is extremely valuable. In the subsequent research process of this project, I plan to conduct in - depth exploration and attempt various different taming algorithms, striving to find the optimal algorithm for taming rubidium clocks using long - waves. At that time, relevant technical comparisons will be included in the presentation of research results. 

 

Comments 11: The reviewer pointed out in the text annotation above Figure 11:Reduce to two or three significant figures. This goes for the data presented in tables as well.

Response 11: Thank you for your careful review. I concur with this opinion.

In accordance with your suggestion, I have adjusted the data throughout the entire text. All the data have been uniformly retained with two significant figures, and the adjusted data have all been marked in red. 

 

Comments 12: The reviewer pointed out the error in Figure 12:The legend is incorrectly labeled. The red line is GNSS and the black line should be Rubidium free.

Response 12: Thank you for your careful review. I concur with this opinion.

I have replaced the incorrect picture with the revised one and marked it in red. 

Dear editor and reviewers,

 

We tried our best to improve the manuscript and made some revisions in the manuscript. And here we did not list the changes all but marked in red in revised paper.

We appreciate for editor and reviewers’ warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

 

Yours sincerely

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The authors present results of  frequency comparison between the rubidium atomic clock, GNSS signal and Loran-C longwave timing system using UTC timing signal as a reference. The experiment is of certain interest to the community, because taming of local oscillators with LORAN-C system remain important in certain cases.

 

The  authors numerically analyze the dataset obtained during 10 days of comparison and suggest a method providing improvement of calibrations by taking into account long-correlated processes in rubidium clock and Loran-C signal (including periodic day-to-day variations). As  mentioned, the article and argumentation is of interest to the community and well fits topically the journal, I have several comments which must be answered before publication.

1) The dataset on Fig 1 (blue) possess a periodic structure of 1 day (1.15E-5 Hz). This should manifest itself in the Allan deviation plot presented in Fig 3 as a visible bump at approx. 1E5 s in Logwave Origin (blue) data. How authors explain its absence?

2) There are several questions concerning Fig3. A) What reference is used for calculation of the ALlna deviation, UTC? If yes, please indicate the (expected) plot for UTC itself, how much the frequency fluctuations of UTC contribute for different time intervals? B) The Allan deviation is plotted for 1, 10, 100,…. 1E5 s. I recommend authors to give more data points (e,g, 1, 5, 10, 50… ) s, add vertical error bars for Allan deviation and (important!) add at leas one point for 3E5 seconds which is relatively straightforward having the dataset of fig 2 at hand.

3) In the abstract, text, tables, etc the authors give excessively many signs which is meaningless, taking into account data uncertainties. I recommend to check it over the text, rewrite and give corresponding uncertainties.

4) The most crucial comment. The main message if the manuscript is that the authors suggest some mathematical model which allows to improve the calibration of rubidium clock by excluding periodic and long-term fluctuations. They take a 10-day dataset and basically do a multi-parametrical fit to the data which is then use for the post-correction. It is self-obvious that the data statistics will be improved on this dataset (as demonstrated). Still, this result is useless in the “accidental switching off of UTC and GPS” scenario described in the Introduction. The question is, for how long time the model based on the existing dataset (e.g. day 1-10) will be valid for the next dataset (e.g. day 11-20) and how the statistics will be changed. I expect certain improvements, taking into account long-term correlations.

I recommend authors to take a ~100-day dataset and to plot the Allan deviation up to 1E6 seconds. Then implement their model using a 10-day data analysis and re-plot the corrected Allan deviation. It will obviously show the productivity of the model and its characteristics. Otherwise the manuscript makes trivial conclusions and possesses no productivity for Rb clock taming.

Author Response

Dear editor and reviewers,

I'm extremely grateful for your careful reading and for giving me positive evaluations, valuable opinions and practical suggestions. All of these have significantly improved the overall quality and clarity of my manuscript. In the past few days, I've carefully considered every comment from the reviewers and made corresponding revisions to the manuscript. The following are the detailed comments of the reviewers and my responses:

Comments 1: The dataset on Fig 1 (blue) possess a periodic structure of 1 day (1.15E-5 Hz). This should manifest itself in the Allan deviation plot presented in Fig 3 as a visible bump at approx. 1E5 s in Logwave Origin (blue) data. How authors explain its absence?

Response 1: Thank you very much for carefully reading my paper and giving me valuable suggestions. 1、In order to present the details of the Allan variance of all the data in the article more meticulously, I will use the TimeLab analysis software that comes with the Microchip 53100A phase noise analyzer to comprehensively replace all the stability analysis diagrams and data tables involved in the article, and mark all of them in red. 2、Allan deviation is the standard time domain measure of frequency stability. It is defined as , where is the -th of fractional frequency values averaged over the measurement (sampling) interval, . Note that these y symbols are sometimes shown with a bar over them to denote the averaging. Therefore, its definition determines that as the measurement duration increases, the value of the denominator M will continue to increase. Based on this characteristic, at the time point of approximately 1E5 seconds, a significant bulging feature may not necessarily occur. For details, please refer to Figure 3.  

Comments 2: There are several questions concerning Fig3. A) What reference is used for calculation of the ALlna deviation, UTC? If yes, please indicate the (expected) plot for UTC itself, how much the frequency fluctuations of UTC contribute for different time intervals? B) The Allan deviation is plotted for 1, 10, 100,…. 1E5 s. I recommend authors to give more data points (e,g, 1, 5, 10, 50… ) s, add vertical error bars for Allan deviation and (important!) add at leas one point for 3E5 seconds which is relatively straightforward having the dataset of fig 2 at hand.

Response 2: Thank you for pointing this out. I agree with your suggestion. A.Yes, The 1PPS referenced by all the time difference data in this paper is derived from the output of China's Coordinated Universal Time UTC (NTSC) maintained by the National Time Service Center of the Chinese Academy of Sciences. The 1PPS output of UTC (NTSC) has extremely excellent stability, with a stability of up to 8.3×10⁻¹⁶ over 5 days and a stability of up to 4.7×10⁻¹⁶ over 30 days. With such a high level of stability, this 1PPS can completely serve as a benchmark for measuring the quality of the 1PPS signals output by systems such as long-wave or BeiDou. The relevant description of this content has been added to the section of "Construction Scheme of Long-wave Ground Wave Propagation Time Delay Measurement System" in the first paragraph of Chapter 2 of the paper and presented in red. According to the existing data, the published quality of Coordinated Universal Time (UTC) only includes the results of long-term stability. Therefore, unfortunately, I am unable to provide the data on the contributions of UTC frequency fluctuations within different time intervals. B.Similar to the handling of Question 1, I have comprehensively redrawn all the stability diagrams and data tables in the full text, and have marked the revised content in red.

Comments 3: In the abstract, text, tables, etc the authors give excessively many signs which is meaningless, taking into account data uncertainties. I recommend to check it over the text, rewrite and give corresponding uncertainties.

Response 3: Thank you for reading my paper carefully, I agree with your suggestion. In accordance with your suggestion, I have adjusted the data throughout the entire text. All the data have been uniformly retained with two significant figures, and the adjusted data have all been marked in red.  

Comments 4: The most crucial comment. The main message if the manuscript is that the authors suggest some mathematical model which allows to improve the calibration of rubidium clock by excluding periodic and long-term fluctuations. They take a 10-day dataset and basically do a multi-parametrical fit to the data which is then use for the post-correction. It is self-obvious that the data statistics will be improved on this dataset (as demonstrated). Still, this result is useless in the “accidental switching off of UTC and GPS” scenario described in the Introduction. The question is, for how long time the model based on the existing dataset (e.g. day 1-10) will be valid for the next dataset (e.g. day 11-20) and how the statistics will be changed. I expect certain improvements, taking into account long-term correlations.

Response 4: Thank you for pointing this out. My analysis is as follows: 1.In this paper, the roles played by the UTC and GPS signals mainly serve as reference benchmarks for comparison, rather than being components necessary for the operation of the system. The core purpose of introducing the UTC and GPS signals in this paper is to clearly illustrate that after the long-wave is corrected, its quality can approach the level of the GPS signal. Given that the technology of using GPS to discipline rubidium atomic clocks has been widely applied at present, during the research process, I selected the GPS signal quality as the reference standard. Through a series of experiments and analyses, it has been confirmed that the quality of the long-wave signal can be improved to a level comparable to that of the GPS signal. This means that the corrected long-wave signal also has the feasibility to be used for disciplining rubidium atomic clocks. 2.Currently, there are certain limitations in data collection, and we have only obtained data for 10 days. Nevertheless, we have made full use of the existing 10-day data to conduct rigorous analysis and verification of the model, and presented the corresponding research results in the paper. In the follow-up, we plan to continuously promote data collection as a key task and strive to obtain the dataset with the duration you suggested. Once we have obtained sufficient data, we will immediately carry out in-depth research and analysis according to your suggestions, further verify the performance of the model, and promptly supplement the new research results into the relevant research to more effectively demonstrate the effectiveness and characteristics of the model. Thank you again for your attention and suggestions, which are of great guiding significance to our research work.

 

Dear editor and reviewers, We tried our best to improve the manuscript and made some revisions in the manuscript. And here we did not list the changes all but marked in red in revised paper. We appreciate for editor and reviewers’ warm work earnestly, and hope that the correction will meet with approval. Once again, thank you very much for your comments and suggestions. Yours sincerely

Author Response File: Author Response.docx