Performance Analysis and Sensor-Target Geometry Optimization for TOA and TDOA-Based Hybrid Source Localization Method

Round 1

Reviewer 1 Report

Both paper organization and presentation (accuracy of language and clarity) is sub-standard.

1. The  sensor-target geometries optimization is an interesting area in localization. However, the treatment to this problem is superficial. 

2. The motivation of the study is vague. The TOA measurement is usually used for active localization, while TDOA measurement  is usually applied in passive localization. It is not clear how to combine the two different measurements in practical applications. 

3. In the simulation part, the hybrid TDOA/AOA localization error is lower than the CRLB which seems not right. Moreover, the TDOA localization error or the TOA localization error can reach the CRLB of hybrid TDOA/AOA localization. It seems  that the CRLB in Figure 2 is for TOA or TDOA localization, but the CRLB described in sec.2.2 is for hybrid TDOA-TOA localization. 

4. The distribution of noise vector n below (5) is not given. 

5. The physical meaning of za, zb, ya, yb, xa, xb in (30) is not described.  

Author Response

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Reviewer 2 Report

A mathematical model had been proposed for analyzing the performance of a hybrid source localization technique using both TOA and TDOA measurements. The numerical examples from the simulations in Section 4 have demonstrated the application of the proposed mathematical model and verified the better performance of the hybrid localization technique over those that employ only TOA or TDOA measurements. However, the results do not include the values for the system parameters used in the calculation of these numerical results. The lack of such details would not make it possible for any to repeat the same results given in that section.

 

The proposed solution assumes two separate groups of stations for reporting the TOA and TDOA measurements. In practice, it is not clear why two sets of stations are needed for reporting TOA and TDOA measurements. For instance, I don't see a reason why station D1 cannot be used for reporting TOA measurements along with the intended TDOA measurements. It seems that the same station (aside from D0) has been selected to report both the TOA and TDOA measurements in the simulation example shown in Figure 2(d). Thus, is there any reason/advantage of having two separate groups of stations at different locations for reporting these two different measurements? The results shown in Figure 5(d) show a different set of placements for the TOA and TDOA stations, but it is not clear why they should be different.

 

In the first paragraph Section 2.1, the parameters S1 to S3 were defined for the three observation stations in the TOA. However, they were later redefined with a different numbering scheme in the subscripts, namely S4 to S6. I suggest being consistent with these definitions to avoid any confusions to the reader.

 

The technique proposed in Section 3 for station placement optimization appears to be suitable for the case of optimizing the location measurements for a single user. Can you elaborate on how this proposed optimization technique scales for a practical network with a number of mobile users? I assume the optimal placement of stations should be for serving more than just a single user. The example shown in Figure 5 seems to indicate that this optimal placement was determined for a "population quantity of 200" (which I assume implies users), and further implies that the users are assumed to travel along a single line trajectory ("Target Track"). In such examples, I can see that the optimization technique would be applicable and the solution for one user should roughly be the same for N users. However, such an assumption yields a result with a very limited application, since it is likely not the case in practical systems that involve users with varying mobility patterns.

 

Please state the definitions for some of the less-known operators used in the manuscript, such as "blkdiag" in equation (23). This would help identify these operations to the readers that are not familiar with MATLAB.

 

In Figure 6, can you please redefine the axes labels in a form that is familiar to the general reader of this journal?

Author Response

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Reviewer 3 Report

Overall work of the paper is good

Novelty of the work also clearly mentioned

Results give the high impression about the paper

 

Author Response

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Round 2

Reviewer 1 Report

The updated version of the paper has clarified the questions of the reviewer. 

Apart from the hybrid TOA-TDOA localization case considered in this manuscript, there are many other hybrid localization case, such as hybrid TDOA-AOA localization [R1], localization using TDOA and FDOA [R2] and localization using time delay and Doppler shift [R3].  These studies are not mentioned in the Introduction. Please add them in the revised paper. 

 

[R1] T. Jia, H. Wang, X. Shen, Z. Jiang, and K. He, “Target localization based on structured total least squares with hybrid TDOA-AOA measurements,”Signal Process., vol. 143, pp. 211–221, Feb. 2018.

[R2] K. C. Ho and W. Xu, “An accurate algebraic solution for moving source location using TDOA and FDOA measurements,” IEEE Trans. Signal Process., vol. 52, no. 9, pp. 2453–2463, Sep. 2004.

[R3] T. Jia, H. Wang, G. Wang, and K. C. Ho, “Localization using time delay and Doppler shift by moving monostatic sensors,” IEEE Trans. Aerosp. Electron. Syst., vol. 58, no. 3, pp. 4745–4760, Jun. 2022.

[R1] T. Jia, H. Wang, X. Shen, Z. Jiang, and K. He, “Target localization based on structured total least squares with hybrid TDOA-AOA measurements,”Signal Process., vol. 143, pp. 211–221, Feb. 2018.

[R2] K. C. Ho and W. Xu, “An accurate algebraic solution for moving source location using TDOA and FDOA measurements,” IEEE Trans. Signal Process., vol. 52, no. 9, pp. 2453–2463, Sep. 2004.

[R3] T. Jia, H. Wang, G. Wang, and K. C. Ho, “Localization using time delay and Doppler shift by moving monostatic sensors,” IEEE Trans. Aerosp. Electron. Syst., vol. 58, no. 3, pp. 4745–4760, Jun. 2022.

Author Response

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Reviewer 2 Report

Thank you for considering the reviewers' comments in the revised manuscript.

Author Response

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Author Response File: Author Response.docx