Three-Dimensional ANP Evaluation Method Based on Spatial Position Uncertainty under RNP Operation

Round 1

Reviewer 1 Report

In the manuscript entitled “Three-dimensional ANP evaluation method based on spatial position uncertainty under RNP operation”, the authors attempt to construct a three-dimensional ellipsoid error probability evaluation model for the spatial position uncertainty of the navigation output of the flight management system.

As a general comment this paper seems to be interesting and rather original and the submission has the appropriated length to be understood. Furthermore, the manuscript is well constructed, the title and abstract are appropriate for the content of the text and the methodology that the authors developed is well discussed but there are several small issues that need to be revised before considering it for publication. 

In the Introduction and Related Work sections (pages 1 to 6) the authors clearly describing previous work but I recommend using the differential “dS” or “dxdy” in Equation (9). Similar suggestion in equation (29) with “dOmega” or “dxdydz”. In these sections, I recommend that the authors revise the following issues: (i) In Figure 1 caption the standard symbol “nm” is used but it conflicts with the International System of Units (SI) abbreviation for nanometre. Because of that I suggest using “NM” as used by the International Civil Aviation Organization (ICAO). It can be seen, for example, the reference: International Standards and Recommended Practices, Annex 5 to the Convention on International Civil Aviation, “Units of measurement to be Used in Air and Ground Operations”, ICAO, Fifth Edition, July 2010; (ii) The equation citation numbers on the text, e.g. in Line 119 where is cited “equation (7)” it should be “equation (9)” and in Line 121 where is cited “equation (9)” it should be “equation (11)”; (iii) There is a repetition error in Line 109 (from line 110): “The covariance matrix becomes”.

In the Method section (pages 6 to 11) the methodology is well presented, the deductions of expressions are correct and suitable, as the graphics obtained are adequate to show the paper´s results but it's need further identification of matrix A in equation (25). What does this matrix A represent?

For the Experimental Setup and Results sections (pages 7 to 16), the figures and tables presented are adequate to show the paper´s results but consider the following comments: (i) In Figure 5 – I suggest to improve its comprehension adding the values discussed in Lines L186 to L188 to the figure itself; (ii) Figures 7 to 9 – There is an issue/repetition between the figures caption and the text on the same figure. For example, the caption of figure 7: “Comparison between EEP model and SEP model in XOY plane” and the text on the same figure “a) XOY plane”, why is there the “a)” in Figure 7, the “b)” in Figure 8 and the “c)” in Figure 9? (iii) Figures 13 to 15 show the comparison results of the position estimated error of the FMS in the longitude, latitude and vertical direction with the ANP evaluation values, but in the Figure 15 the ANP curve is missing. Due to all the above issues I advise that it´s needed to be made a global revision in the figures. The selected references are prevailingly well related to the theme.

It is also necessary to correct these minor issues:

- In Line 106, where you can read “axes”, you must see “axis”;

- In Line 118 where appear only “Let”, I suggest: “Let’s consider”;

- There is missing a “s” in Line 119 conducting to: “Then equation (7) becomes”;

- In Equation (9), I recommend using the differential “dS” or “dxdy” (similar suggestion in equation (29) with “dOmega” or “dxdydz”);

- In Equation (31), the integration region after using the spherical coordinates transformation is not Omega. The authors need to integrate over an appropriate region in r_alpha_beta-space.

Abbreviations are used today in aeronautics for terms, definitions, standards, etc. As a recommendation to improve the paper´s legibility (in particular the readers that are not very familiar with some of the abbreviations) the authors could consider doing a “Abbreviations” section at the ending of the manuscript just before the “References” section (e.g., see page 19 of a paper recently published in Aerospace: https://www.mdpi.com/2226-4310/8/12/360), with the abbreviations already in the paper.

The methodology research discussed in this manuscript shows that the evaluation method proposed by the authors can accurately evaluate the actual navigation performance of airborne navigation system and has higher evaluation accuracy and precision than the traditional ANP evaluation method. The results obtained demonstrate the novelty and originality of the research study presented. Hopefully the authors find useful these suggestions and comments listed above.

Author Response

We sincerely thank the reviewers for their constructive comments, which have helped the authors to improve the manuscript. We have followed the Editors’ comments and revised our manuscript. We think we have addressed all the issues raised by the reviewers. The detailed responses to all the comments are in the attachment.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presented a three-dimensional ellipsoid error probability evaluation model for the spatial position uncertainty of the navigation output of the flight management system. The paper is well-written and the study is interesting. The authors did a good job. I think the paper is ready to be published.

 

Author Response

We sincerely thank the reviewers for their constructive comments, which have helped the authors to improve the manuscript.