The Analysis and Verification of Unbiased Estimator for Multilateral Positioning

Round 1

Reviewer 1 Report

Title and real content of the paper needs to adjust - finally there are comparison of two position calculation results by ranging distances, but there no generalization or at least condition of the distance measuring keypoint or map of area.

Results of the analysis begs for better presentation - fig.3 and fig.6 brings no clear answer about implemented methods.

Formulation of  the research is really missing, therefore results and conclusions are unclear.

Author Response

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Reviewer 2 Report

My comments for Authors:

1. abstract, please add obtained results from experiment.

2. main body of text, all acronyms must be explained if you used their first time, please check it.

3. line 78-80, please much better describe the novelty of paper.

4. equations (1-14), all symbols must be explained in text, e.g. x0,y0,x2,d, etc.

5. line 107, I don't know Chinese language

6. line 131,  I don't know Chinese language

7. line 185, what means "m^2"? Is this the correct unit?

8. discussion, please also compare your solution with scientific knowledge analysis (e.g. papers from References). Why your solution is better? 

9. conclusion must be correct, please add obtained results from experiment.

Author Response

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Reviewer 3 Report

Minor:

- Chinese characters in lines 107, 131.

- 5.1. simulation should be Simulation

- line140: "where e obeys a normal distribution with mean 0 and standard deviation σ m " It is not clear sentence. E.g.  σ m ? Someone could guess that m is subscript (index) or SI unit or typo, etc...

- Figure 2: legend should be elsewhere.

- Figure 3: legend should be placed elsewhere or outside the figure, because it covers a part of image and we cannot see if there is something there.

- Chinese characters in Figure 5. I don't understand what does it mean. 

- line 178: no spaces between number and units. Check the entire text.

- check style, spaces and, letter cases of reference list

Major:

- Last sentence of the conclusions: Is the basis of this conclusion presented in 5.1 or 5.2. section?  If it is based on the experiment (not simulation experiment), than this data is not presented in quantity to make such conclusion and should be added.

- You used https://0-doi-org.brum.beds.ac.uk/10.1145/3501409.3501590, but I don't see it on the reference list. It is about 2% of the total text of the proposed manuscript.

- you could update references with some novel papers from last 2-3 years.

- The article leaves a worse impression due to all these mistakes and due to not obvious explanation of the scientific contribution. It looks like diploma thesis or seminal work. However, the paper have valuable contribution, which is not emphasized enough. You should explicitly declare aims, goals and contributions of the paper in the introduction and/or conclusions.

- All mentioned disable reviewers to see a main story of the paper and to evaluate it correctly.

Author Response

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Round 2

Reviewer 1 Report

Figure 6 - text contradicts the figure content - please, react.

Please, provide nomenclature - abbreviations spread over the text, hard to read.

Figure 4 - necessary to improve legend, also, unify scale and size of output graphs with fig.3 and fig. 2, legends in all of them are unaligned, missing units or notes about dimensionless scale.

Also - there no mentioned - are here provided results are simulations or real experiments, please, clearly note that.

Author Response

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Reviewer 2 Report

I accept the paper.

Author Response

Thank you for your valuable suggestions, which have played a very important role in our article.

Reviewer 3 Report

I'm satisfied with answers to the first round questions.

However, the paper should be improved by clearly stated in the Introduction what are the contributions, aims and goals of the paper (see Point 4).

Author Response

Point : the paper should be improved by clearly stated in the Introduction what are the contributions, aims and goals of the paper (see Point 4).

Response : Thanks for your comment, We have made further supplementary modifications to the article contribution section in introduction.

First, we put forward the reasons for the formation of the method:” most of the existing localization methods are based on simple error model assumptions, while ignore the complexity of the actual error model, especially the fact that the square of the ranging value may be a biased estimator. If the squared value of ranging is involved in the solution process, it may lead to biased results.”

To solve this problem, we propose the method of unbiased estimator:” In order to illustrate the problem of this biased distance estimator, this paper analyzes and derives a type of ranging error model, whose error variance increases as distances increase and draws a conclusion: for those biased situation, localization accuracy can be improved if variance of the ranging error model can be known.”

The advantage of this method is also illustrated in introduce:” Theoretically, the method in this paper is suitable for the positioning algorithm adopting the square value of the ranging, which can make further improvements of localization accuracy.”

Finally, multilateral localization algorithm is used to illustrate the inspiration and contribution of this paper:” This paper verifies the improving feasibility of a ranging error model through simulations and practical experiments. More importantly, it shows that the improvement of unbiased estimation of complex ranging error models can improve the positioning accuracy. similar improvement of unbiased estimator for other ranging error models can also make similar improvement for localization accuracy.”

Round 3

Reviewer 1 Report

Paper improved, but final presentation picture begs form improvement and fig. 6 has no x-axis legend and units.

There are unclear items in other figures, too.

Author Response

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