Bayesian FDOA Positioning with Correlated Measurement Noise

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The author presents a comprehensive introduction to the GDM method to achieve the localization problem that using only FDOA. However, there are some formatting errors and unclear expressions. The following is a summary of the suggested revisions:

Comment 1: Figure 4 on page 14 shows a lot of curves, and the diamond marker (representing the GN algorithm) is hard to be seen because it is hidden by others. The author should try to improve the figure.

Comment 2: The GDM algorithm requires multiple iterations. Compared to other algorithms , may this lead to longer algorithm time? It is suggested that the author supplement the analysis of the computational complexity of the algorithm.

Comment 3: What is the special physical significance of using virtual TDOA to divide areas on page 11 in Section 4? For example, is there any difference between this and dividing the area enclosed by the FDOA curve equally?

Comment 4: On line 148 of page 5, it is mentioned that "replacing $p \ (\ bf {x}) $with $\ bar p (\ bf {x} | {z1}) $". Will this substitution affect the calculation of the final expectation about the target position?

Comment 5: Pay attention to formatting and writing error . For example the first letter of "correlated measurement noise" in the keywords is not capitalized.

Comments on the Quality of English Language

It is ok.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes a novel source localization technique based on FDOA measurements, called Gaussian Division Method (GDM), for narrowband signal source localization. The method converts FDOA measurements into a Gaussian mixture model and uses nonlinear filtering techniques to optimize the localization results. Simulation results show that GDM achieves Cramér-Rao Lower Bound (CRLB) accuracy under moderate noise levels, outperforming existing methods.
Here are some questions as follows:
1. In formulation (5) of Section 2 with the FDOA positioning model, why the non-diagonal elements of the noise covariance matrix are the same? Will the value affect the performance of the GDM?
2. In equation (23), the proof of the ratio relationship between two Gaussian distributions is not provided in detail. Please add some more proof details. 
3. The paper does not explicitly discuss the computational complexity of the GDM algorithm, especially the high-dimensional matrix operations involved in the KF-2 stage. Please add some discussion of the algorithm complexity.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors The issue presented in the article seems to be important in the current state of technology.
In my opinion, it is to find an application in the face of the increasingly common use of jammers
generating a noise signal that disrupts the operation of GNSS systems.
Therefore, the authors' idea deserves support.
I believe that the structure of the article and the review of sources presented at the beginning
are correct. It is also correct to state the problem.
Finally, authors proposed new method of noise transmitting object. Proposed method gives clear
results with accuracy comparable to other known methods. The core contribution of the work is
proposed Gausian Division Method based on Bayesian approach.
I do not see any wspect which should be corrected in the text.
However i have comment according the title. I am guided by the principle that before an abbreviation appears in the text, the full version
of the version of the expression should appear. Especially in the title, abbreviations should
not be used if it is not a commonly known abbreviation.
I believe that the title should be corrected.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf