Adaptive Basis Function Method for the Detection of an Undersurface Magnetic Anomaly Target

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

A new adaptive basis functions (ABFs) approach is proposed in this article, which permits the detecting platform to search a possible target at different speeds along any course.

But the manuscript is not compete. The authors should give further study on the ABFs via simulation.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a novel approach for detection of undersurface magnetic dipole targets. It uses three adaptive basis functions to build the signal model. The basis functions are constructed using the real-time data of GPS and triaxial fluxgate, which provide the position/course and attitude of the detecting platform. In the traditional methods, the signal model is built by assuming the detecting platform to move uniformly along a straight path, which does not support to search a target along any a course, such as in a circling way. Some improved data preprocessing techniques are employed to reduce the impacts of geomagnetic field, platform interferences and diurnal magnetic noise. In addition, an imaging scheme is introduced to display the possibility for a target situated at a geographical position in latitude and longitude. Moreover, the approach is validated by using on-site experimental data. As a whole, the authors have done a good work, and publication is recommendable. Some minor concerns should be clarified to improve the quality, including

(1) For noise-based detection methods, a signal model is not needed. Are signal-based methods always better than noise-based methods?

(2) How long  is taken in your examples? What are the resolutions  and  in the moving and transverse directions?

(3) In the Monte Carlo simulations (Eq. (41) and Figure 6), the magnetic noises are actually measured, while the target signals are artificially generated. Are the noises white or color? How to generate the target signals?

(4) How about the real-time performance of the proposed approach? The sliding window scheme seems time consuming.

Comments on the Quality of English Language

Minor editing of English language is required.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1.     Page 3, L. 105: “possibility for a target located..”. - Should be ” possibility for a target localization”

2.     Page 4, L. 153: “where ai, bi, ci (i = 1,2,3) are coefficients relevant to the depression angle υ_s - “First, you have called this angle as a pitch angle on page 3. Second, it is not right! These coefficients depend also on target magnetic moment orientation.

3.     Page 4, L. 164: - “detecting platform moves uniformly along a straight course”. Since a GPS on-board sensor is now present on any aerial platform, an exact platform position is known at each instance of time. Then, it is possible to resample the readings within t_d and get uniform (in space) field values within every section of survey line. It means that requirement of “uniform moving” along a straight course is unnecessary for standard Orthogonal Basic Functions (OBF) approach.

4.     Page 5, L. 188: “eddy interference due to the time-varying geomagnetic field” – eddy interference is mainly NOT due to the time-varying geomagnetic field, but due time varying platform attitude relative to the Earth’s magnetic field (EMF).

5.     Page 5, L. 203: “Once these coefficients are found, we will obtain the remaining magnetic field” – You need to calculate (estimate) 68 coefficients all in all. It’s not a trivial task. Have you implemented usual mean least square regression? What about stability of your estimation? Did you need to make use of ridge regression (Tikhonov regularization)? Have you performed “box” flight (envelope flight) with pitch, roll, and yaw maneuvers? What are the results of FOM (Figure Of Merit) test after interference compensation? In (15) you have included f₁(t)=t which is a part of diurnal variation. How can you distinguish between EMF linear temporal trend and constant field gradient which looks like a linear time function for uniform platform move along straight line?

6.     Page 6, L. 227: “The magnetic moment is found by solving df(t_d)/dM_i) = 0, i=(1,2,3) “ – It requires detailed explanations. Real values of target magnetic moments in you experiment are not given at all! Nor they are compared with estimation based on experimental data.

7.     Page 7. All these transformations from geocentric coordinates to local geographic coordinates seem to be absolutely unnecessary in the context of target detection/localization.

8.     Page 8. “Experimental validation.” – A shape of flight for target detection and further localization seems to be very strange. I guess, you need to start with a straight-line path. At this stage, your basic functions are traditional OBF. After getting detection alert, you need to turn (left or right?) in order to localize the target. Here standard OBF for a straight-line path should start to be gradually transformed to OBF for circular track (these circular track OBF’s are also known from the literature). To my mind, you need show some examples of dynamically changing ABF’s.

9.     Are these ABF’s orthonormalized? Is orthonormalization being implemented in real time on-flight?

10.  P.11, L340: “constant speed” – See note 3..

 

Comments on the Quality of English Language

N/A

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Enhancements are required to elevate the general standard of English. This include aspects like as style, grammar, and spelling. 

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

In paragraph 3.1, you introduce an extension of the Tolles-Lawson model. One would then expect that you would detail it rather than simply mention it, and illustrate the benefits of that extension. From a practical point of view a statement  on the calculation load induced by the ABFs would be of interest (by the way, was it implemented in real time or post-processed?). The description of the work is clear, although some explanations/developments beyond the equations would be appreciated. Similarly, a more detailed discussion of the results would be of interest (comments on the positioning errors for instance). At end of paragraph 4 and in the conclusion, you state that the ABF is superior to OBF and MED especially at lower SNRs. This is not particularly obvious on Figure 6

Comments on the Quality of English Language

Minor editing of english language is recommended (reduce use of passive form for verbs)

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

After corrections made, the quality of the manuscript has been somewhat improved.

Can be recommended for publication w/o further changes.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have considered all comments and have given satisfactory responses.

Comments on the Quality of English Language

English has improved and is now acceptable.