Uncertainty of Aircraft Localization with Multilateration and Known Altitude

Round 1

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

The paper, “Uncertainty of aircraft localization with multilateration and
known altitude " describe the methods TOA, TDOA and a Raccon approach for multilateration. It provides a DOP estimation and mentions the extension of altitude to the estimation.

For me, the paper has server problems, and restructuring is needed, as the mix of very different problems is in the current status quite confusing to me. Moreover, the script still had  annotations of the authors included that were not included in the text. 

First, the authors highlight their major contribution as adding altitude estimation to Foy's approach. This approach is not introduced; either the extension is shown, just very briefly described verbally.  Please describe this in more depth! Whereas the Kalman filter and UFIR algorithm are introduced in depth but used only as showcases. This could be erased, IMHO, as there is no contribution from the authors.

Her some more detialed comments to the sections:

Introduction: The introduction provides a good overview of the contribution the authors planned to make. This contribution is lost in the further curse of the paper.

 

Related Work:  This section provides an overview in quite depth on MLAT and tracking; However, the in the abstract and introduction mentioned methods are not covered.

 

Proposed method 
 Problem formulation 

For the reader, the text would be of high benefit if the formulas were included in the text rather than separated somewhere in the text. I also would stress the point if the approaches TOA and TOAq need to be separated. As the TOAq approach is just a realization of the TOA approach. For the extension of Foy's approach, the formulas that were extended should be described here in more detail.

For the MSE I would expect a theoretical discussion of benefit to find global and local maxi and minim, as this is later an important rule.

Calculating measurement error

The name of the section does not fit the DOP computation, as DOP does not describe a measurement error; it describes the delusion of our result due to the geometry. Therefore, I doubt that equation (7) results in a DOP. The definition is also not described in reference. [3]. For the DOP, the covariance Q should not have an effect. Maybe the authors meant to describe accuracy or error? Please also identify which DOP you want to use.

Tracking: This section does not fit the scoop described in the introduction and abstract.

Software: I liked the description of the software and I am looking forward to test it!

 

 Experimental results and discussion

 It is unclear to me why only one set with altitude is used; what was described as the main contribution of the paper? Also, it is not covered if the altitude of the transmitter has an influence, which would be highly interesting. The conclusion: However, the height of 
The stations are not so important. “  Is not true in all cases, as shown in Ref. . [3]. Please provide a description of why this is the case for your scenario. Especially as this was your main motivation according to your abstract.

 

Testing algorithms

I have doubts about the results in Fig. 2.  So, especially the DOP for the TOAq seems not plausible to me. When the transmitter moves out of the triangle, the DOP should raise. Due to the limited time for the review, I am not able to investigate and understand the problem here further. If I was misled here, please give a more detailed interpretation.

For the reader, the differences of the results would be simpler to understand if a bar chart were used for each set or similar graphics. Also, the description of the results is rather short. I would also like to see some example plots where the local and global maxima are located.

Tracking:

Please motivate the added value for the reader more; this part seems only loosely connected to the rest of the paper. Maybe discuss tracking in a follow-up paper?

 

 Conclusions

 In general, I can agree on the conclusion, beside the DOP computation. However, for me, it is difficult to find the claims mentioned here in the paper. Also, the altitude aspect does not play any role here anymore. 

 

Overall, it seems to me that the paper has undergone a lot of iteration, which makes it now hard to follow the overall text. Please restructure the text and clearly focus on your contributions.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The paper presents valuable contributions but requires major revisions to clarify methodological novelty, strengthen experiments, and improve readability. After addressing these points, the manuscript would be suitable for reconsideration.

1.Explicitly contrast the proposed method with existing approaches (e.g., Chan’s or Schau’s algorithms) in the "Related Work" or "Introduction."

2.Add a figure or pseudocode to illustrate coordinate conversions, and annotate key equations with practical interpretations.

3. (1) Include statistical tests for error comparisons; (2) Add tests with variable altitude/velocity to assess robustness.

4. Provide a case study showing how the software optimizes station placement, with metrics (e.g., DOP reduction).

5. Expand the "Conclusions" section to address these points systematically.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

In this paper, the authors propose Uncertainty of aircraft localization with multilateration and Known altitude. At the same time, the positioning accuracy is improved by introducing known altitude data. A corresponding software tool is developed to analyze the impact of the layout of MLAT receiving stations on measurement uncertainty. Generally speaking, the content is informative, and the test analysis is complete. The work is interesting however some details are still to be discussed and the manuscript should be revise.

1.The innovation of this article needs to be further clarified. It is obvious that the author has accumulated many methods, but no specific innovations have been proposed. Suggestions are given to enhance the significance of the paper's work and the description of the new methods.

2.The paper describes in detail the nonlinear optimization problem and its solution, including three different measurement methods: TOA, TDOA and TOAq. However, the paper does not discuss the local minimum problem that may exist in nonlinear optimization problems, and it is recommended to further analyze and discuss how to avoid or reduce this effect.

3.The "MLAT Analyzer" software tool developed in the paper provides strong support for engineers in designing and optimizing MLAT systems. However, the paper does not describe the specific functions and usage of the software in detail. It is recommended to add more screenshots and usage examples of the software interface so that readers can better understand and apply the software.

4.References in the paper should be expressed in a unified format, such as Ref.5, etc.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

Dear Authors,

I still think that we have a different understanding of the undergoing problem.

 

For the covariance Q, indeed, it shows the correlation between measurements; however, as you also quoted, they do not influence the GDOP. It is purely a figure of merit for the correlation, so for me there is no need to include it in the GDOP calculation. This becomes important when you discuss the estimation variance of the results. I still have the feeling that estimation variance and GDOP are mixed up in the paper.

 

Regarding figure 2, I still believe that a different color map would be highly beneficial; however, the plot for the fourth case is now in a different style, so I suggest streamlining this.

 

I also strongly believe that a weak point of this paper is that it is discussed that altitude is a significant influence. However, the shown scenarios never show different altitudes for the same station constellation.

 

Therefore, it is hard to conclude that the shown results are held in all scenarios from the tests.

 

For the simulation, I could not find the meaning of TDOq+noise, as all simulations have added noise according to the text.

 

Also, the simulation scenario is just seeming to repeat the results from the GDOP calculation; this is not necessarily true. I believe that noise plays here also an important rule, which is indeed out of scope for this paper. (Here Q would be crucial as it describes how each variance influences the results, depending on the noise.). My major concern is that the claims are made general in the conclusion, while only GDOP is discussed in the paper and are only presented for one altitude per scenario.

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

Dear Authors, thank you for considering my feedback.

We are on the same page for the Q matrix now; thank you for the explanation. My question was pointing towards why you used it in the paper.

However, I suggest some minor improvements:

Line 38: TDoA should be changed to TDOA

Line 298-301 could be streamlined with respect to the description of the sets.

Line 333-334: Could you add a reference to the requirement of the second message? This is not obvious. The noise floor of the receiver should be the same for all cases. Also, the reception power should depend on the activation response.

Line 333: massage should be  message.

Table 6. : Please check the values of the table; for me, it is not clear why the 1st set at the 4th point for TDOAq the values are not comparable to the 4th and fifth set. If this is the influence of the altitude, this should be discussed.

Author Response

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Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

 

The paper focuses on the error characteristics of multilateral positioning under the premise of known altitude information. This revised paper did not carefully follow the reviewer’s comments and did not provide specific optimization methods for nonlinear equation systems. It only emphasized three contributions of this paper in the introduction, but none of them provided core novelty points. The paper does not have innovative algorithms, and the data results are not significant. It is recommended to reject or resubmit after supplementing the algorithm. The reasons are as follows:

1) The algorithms known altitude information have no practical significance. The authors believes that using a barometric altimeter is high-precision and can be considered as a known altitude. This premise may be unreasonable, as barometric altimeters still have measurement errors and drift deviations, and are more affected by environmental factors in low altitude spaces. There are many articles that combine the barometric altimeter with other ranging and positioning information. It is reasonable to do information fusion according to different sensor accuracy.

2) The multilateral positioning known altitude, formulas (4), (5), and (6) only provide a goal to the minimum possible mean square error. The key is how to solve this problem. The paper does not disclose the solution process, but emphasizes that others solve three unknown variables. This paper assumes that the two unknown variables are to be solved with one variable known. Can this be considered novel? If there is innovation, specific optimization processes should be supplemented for readers to evaluate.

3) Secondly, in the introduction, the third contributions means that the algorithms can be used for locating non cooperative targets such as drones. However, assuming that the altitude is known is even more unrealistic, and non cooperative drones cannot actively disclose their altitude information.

4) As can be seen from Figure 3. The positioning results in the paper can only be significantly improved by using Kalman or UFIR algorithms, but Kalman or UFIR algorithms are ready-made technologies and cannot reflect the advantages of the algorithm in this paper.

Reviewer 2 Report

Comments and Suggestions for Authors

The comments are in the uploaded file.

Comments for author File: Comments.pdf