Underground Target Localization based on Improved Magnetic Gradient Tensor with Towed Transient Electromagnetic Sensor Array

Errors of target localization with the traditional magnetic gradient tensor mainly comes from three aspects, namely, the large equivalent error of the magnetic gradient tensor for shallow targets, the low signal-to-noise ratio (SNR) of the target response for deep targets, and the overlapping responses of multi-targets. In this study, a towed transient electromagnetic sensor with a 3 × 3 receiving coils array is constructed. On the basis of the sensor array, an improved magnetic gradient tensor is proposed to accurately locate targets. For shallow targets, the magnetic gradient tensor is constructed using the responses of four adjacent receiving coils to reduce the equivalent error of the magnetic gradient tensor. For deep targets, all the responses of nine receiving coils are used to improve the SNR. Both the early and late time responses are used to roughly estimate the positions of multi-targets to improve the localization accuracy of the overlapping responses of multi-targets. Experimental results show that for underground targets within 2 m, the depth errors of the targets do not exceed 10 cm, and the horizontal errors of the targets are mostly within 10 cm, even if the responses of two adjacent targets overlap each other, indicating that the proposed method can effectively improve the localization accuracy of underground targets.


I. INTRODUCTION
Unexploded ordnances (UXO) seriously threaten human security and hinder economic construction and land reuse [1]. Many harmless targets, such as metal fragments and shrapnel, are usually scattered around UXOs, resulting in a high false alarm rate of detection [2]. Therefore, the quick and accurate detection and identification of UXOs from these harmless targets have become a concern of researchers at home and abroad [3].
In recent years, different kinds of UXO detection methods, such as ground-penetrating radar (GPR) [4,5], magnetic detection [6,7], and electromagnetic induction (EMI) [8,9], have been widely developed and applied with the development of detection technology. GPR can locate underground targets by transmitting high-frequency electromagnetic waves, which are easily affected by geological conditions. Magnetic detection has high efficiency and low cost but can only detect magnetic targets. The working frequency of EMI ranges from tens to hundreds of kHz, including frequency and time domain detections. EMI can detect magnetic and non-magnetic targets with a strong anti-interference ability. Time-domain transient electromagnetic (TEM) detection has been effectively used for underground target detection.
The clearance of UXO is mainly achieved in three steps: detection, inversion, and identification. In the detection step, various TEM systems are designed and developed based on different detection platforms to locate underground targets. Portable and vehicle systems are two typical detection systems. These TEM systems usually include two working modes: the survey and cued modes. The position of underground targets can be roughly determined according to the maximum response in the survey mode. The target position can be accurately calculated by different algorithms according to the measured response in the cued mode.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.   Portable systems, like the MPV-I, MPV-II systems designed by G & G Sciences [10,11], and the portable metal detector designed by Jilin University [12], have effectively detected underground targets. Vehicle systems, like Metal-Mapper [13], Berkeley UXO Discriminator [14], and the Timedomain Electromagnetic Multi-sensor Tower Array Detection System, were developed to detect underground targets [15]. Compared with portable systems, these vehicle systems usually adopt large transmitting magnetic moments, multiple transmitters, and multiple receivers to detect deep and large area targets. A magnetic gradient tensor can locate a single target without iteration and has been effectively used in magnetic detection [16]. The localization accuracy of a magnetic gradient tensor is related to the sensor signal-to-noise ratio (SNR) and the target depth. In TEM detection, the target localization error of the magnetic gradient tensor is large due to the influence of the overlapping response of adjacent targets. In this paper, the combination of the magnetic gradient tensor with the early and late responses of the target is proposed to improve the localization accuracy of overlapping signals. First, the target position is roughly estimated based on the towed TEM system. And, the number of underground targets is preliminarily determined with the maxima of the early and late responses. Then, the target position can be further estimated accurately with the constructed magnetic gradient tensors.
The rest of this paper is organized as follows. Section II mainly introduces the towed TEM system and the single dipole model. Section III provides a detailed introduction to magnetic gradient tensor localization. Section IV presents the experimental results and discussion. Section V presents the conclusions.

II. BASIC METHOD
Target responses are obtained by the towed TEM array system, and data processing is based on the single dipole model.

A. TOWED TEM SYSTEM
The towed TEM system consists of three transmitting coils (i.e., the x, y, and z components) and nine three-component receiving coils, which operate in two modes. In the survey mode, the z component transmitting coil transmits the current in the frequency of 125 Hz to roughly estimate the location of underground targets. In the cued mode, three transmitting coils sequentially emit currents with a frequency of 12.5 Hz to excite the underground target. The 3 × 3 array receiving coils synchronously collect responses. The structure and picture of the system are shown in Figure 1.
As shown in Figure 1(a), the green, yellow, and red squares are the respective x, y, and z component transmitting coils wound by overlapping loops with a copper line with a cross-area of 6 mm 2 . The x and y component transmitting coils are constructed with two inverted series rectangular coils. The 9 three-component receiving coils are designed in a 3 × 3 array with a 20-cm interval. The side length, the resonance frequency, and the distance between the sections of each receiving coil are 8 cm, 230 kHz, and 7 mm, respectively. The nine receiving coils adopt the combination of double-layer shielding and center tapped grounding to improve the SNR of the receiving response. Figure 1(b) is physical picture of the system. Table I presents the parameters.
On the basis of the sensor design above, this study completed the target localization according to the single dipole model.

B. SINGLE DIPOLE MODEL
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.

FIGURE 3. (a) Target localization with 4 coils, (b) target localization with 9 coils.
When the distance between the sensor and an underground target is more than 2.5 times the target size, the target can usually be treated as a dipole model for data processing [17].
As shown in Figure 2, the secondary field (BS) of the underground target at the position (r) of the receiving coil can be denoted as where eR = R/|R|, |R| is the modulus of position R = rrd.
rd represents the target position. The size of identity matrix is Green's function, which only depends on target position R. Dipole moment m is expressed as where M is the magnetic polarizability tensor, which is a symmetric matrix and is determined by the shape, size, orientation, permeability, and conductivity of the target. Bp represents the primary field of the target.

A. MAGNETIC GRADIENT TENSOR
The target position can be effectively estimated by the magnetic gradient tensor in magnetic detection. According to Equation (1), the difference between the secondary field (BS′) at position R + n dR and the BS at position R is expressed as [18]   which can be rewritten as where G is the magnetic gradient tensor, which is a symmetric matrix and expressed as According to Equation (4), target position R is denoted as The sum of the diagonal elements for G is zero. Five independent elements of matrix G must be calculated.
For shallow targets, that is, the target depth is near the distance between the two receiving coils, a large equivalent error of the magnetic gradient is obtained. The equivalent error will decrease as the target depth increases. For different target depths, two magnetic gradient tensor algorithms are proposed to improve the localization accuracy.
The magnetic gradient tensor constructed in Figure 3(a) is used to locate shallow targets, and that in Figure 3(b) is used to locate deep targets. In Figure 3(a), BS1 is the equivalent central response of the four coils (R1, R4, R2, and R5), which is expressed as where B1, B2, B4, and B5 are the target responses acquired by receiving coils R1, R2, R4, and R5, respectively. According   to the four receiving coils in Figure 3(a), the five independent elements of matrix G are expressed as follows: where Bij is the target response. i = 1, 2, 4, 5 is the coils number. j = x, y, z corresponds to the three components of each sensor. In Figure 3(b), receiving coil R5 collects response data BS. The five independent elements of matrix G are expressed as follows: where Bij is the target response. i = 1, 2, 3, 4, 6, 7, 8, 9 is the number of the eight sensors. j = x, y, z corresponds to the three components of each sensor. All receiving coils are utilized to improve the localization accuracy.
According to the magnetic gradient tensor constructed in Figure 3(a), the shallow target can be located using Equation (5) to Equation (8). In Figure 3(b), the deep target can be located by Equations (5, 6, and 9).

B. TARGET LOCALIZATION PROCESS
Figure 4is the target response collection and localization. The target localization process is based on the towed TEM sensor array. First, the target response is obtained by nine receiving coils. The early and late responses are drawn. Second, according to the maximum responses, the number and horizontal position of underground targets are roughly determined, and the magnetic gradient is constructed to further locate underground targets.
On the basis of the above-mentioned sensor array and magnetic gradient tensor localization theory, the effectiveness of the proposed method is verified by field experiments. The experiments and the analysis are discussed in the next section.

IV. EXPERIMENT DESIGN AND DISCUSSION
On the basis of the towed TEM system, the field experiment was carried out in the southern suburb of Changchun City, Jilin Province. The experiments are described in detail below.

A. EXPERIMENT DESIGN
In the field experiment, 12 UXOs and 9 harmless targets were buried. The diagram and detailed parameters of the targets are shown in Figure 5 and Table II, respectively. As shown in Figure 5, the UXOs are numbered from U1 to U12, and the harmless targets are numbered from O1 to O9. In Table II  cm, and the diameter ranges from 37 mm to 130 mm. A total of 19 UXOs were buried. The lengths of the two cartridge cases (O1, O2) are 16 and 25 cm, with diameters of 30 and 37 mm, respectively. O3 to O6 are iron pipes, with a diameter of 75 mm and lengths ranging from 5 cm to 30 cm. O7 is a discus with a length and a diameter of 2 cm and 150 mm, respectively. O8 is an iron ball with a diameter of 64 mm. O9 is a three-way tube with a height of 12.5 cm. A total of 10 harmless targets were buried.
The experimental site has an area of 13 m × 8 m. Twentynine targets were buried, and the specific target distribution is shown in Figure 6. A total of 19 UXOs and 10 harmless targets were buried in the area. At survey line y = 1 m, five groups of multiple targets and four single harmless targets were buried at the approximate depth of 0.5 m. At y = 3 m, three groups of multiple targets and four single UXOs were buried at the approximate depth of 1.0 m. At y = 6 m, five UXOs were buried separately at different depths from 1.2 m to approximately 2.0 m. Two targets in each group are 40 cm apart. Figure 6(b) is the physical diagram of the towed TEM system.

B. RESULTS AND DISCUSSION
In the experiment, the towed system transmitted a 12.5-Hz bipolar rectangular current with the z-component transmitting coil. Three survey lines (y = 6, 3, 1 m) were collected in the area. Sixty-six measuring points were collected in each line, and the interval between the measuring points on the survey line is 0.2 m.
The early response was calculated by averaging the responses from 0.15 ms to 0.63 ms. The late response was calculated by obtaining the average value of the responses from 2.5 ms to 15.8 ms. The results are as shown in Figure 7.   .0 m are weak, and the peak is relatively flat. When the system moved in the x direction from above the peak, at x = 10.2, 12.4 m, the responses slowly decayed due to the influence of the adjacent target responses. When the system moved in the x direction from above the peak x = 0.8 m, the response fluctuated and quickly decayed due to the low SNR. From these positions, five targets at y = 6 m can be preliminarily judged. Figure 7(b) shows five groups of target localization results. The magnetic gradient tensor constructed in Figure 3 Table III. In Table III, the depth and horizontal errors of UXO at approximately 2 m do not exceed 10 and 16 cm, respectively. The depth and horizontal errors of the target at different depths from 1.2 m to 1.6 m do not exceed 5 cm and 7 cm, respectively. The result shows that the depth errors of the target do not exceed 10 cm, and the magnetic gradient tensor constructed in Figure 3(b) can accurately locate single underground targets within 2 m.
According to the obtained responses with y = 3.0 m and the magnetic gradient tensor constructed in Figure 3(b), the results are shown in Figure 8.   four groups of targets. Thus, the maximum response and adjacent measuring points are used to estimate the target position, and the localization of the maxima responses are near the true positions. Figure 8(b) shows that the target position can be accurately estimated by the magnetic gradient.
According to the magnetic gradient tensor constructed in Figure 3(b), the target localization at y = 3.0 m is shown in Table IV. In Table IV, the horizontal and depth errors of the buried single target do not exceed 7 cm. The horizontal and depth errors of the multi-target do not exceed 8 and 10 cm, respectively. The localization results show that the magnetic gradient tensor constructed in Figure 3(b) can effectively reduce the localization errors caused by the overlapping responses of adjacent targets and accurately locate the target within 1 m.
According to the obtained responses at y = 1.0 m and the magnetic gradient tensor constructed in Figure 3(a), the results are shown in Figure 9. According to the magnetic gradient constructed in Figure  3(a), the target localization is shown in Table V.
According to the maxima responses, the target positions estimated by the magnetic gradient tensor constructed in Figure 3(a) are shown in Table V. The true depths of the targets are approximately 40 cm to 50 cm. The horizontal and depth errors of a single target do not exceed 8 and 6 cm, respectively. The horizontal and depth errors of multi-targets do not exceed 10 and 5 cm, respectively. The response of target O3 at x = 9.6 m is extremely weak, and the localization failed due to the response of the adjacent targets. The results show that the magnetic gradient tensor constructed in Figure  3(a) can accurately locate the target at the depth of approximately 0.5 m.
In general, according to the maxima of the early and late responses, the magnetic gradient tensor constructed in this study can effectively and accurately locate underground targets within a 2-m depth.

V. CONCLUSION
On the basis of the responses collected by a towed TEM system with a 3 × 3 sensor array, the two kinds of magnetic gradient tensors constructed in this study can accurately locate targets within 2 m.
The towed system consists of three transmitting coils and nine receiving coils. The z-component transmitting coil transmits a rectangular current of 12.5 Hz, and the 3 × 3 sensor array obtains the target response to estimate the target position.
The combination of the magnetic gradient tensor with the early and late responses can effectively distinguish the number of targets and considerably reduce the localization error caused by the overlapping responses of adjacent targets. According to the maxima of the early and late responses, the two forms of magnetic gradient tensors constructed using four sensors can effectively reduce the magnetic gradient equivalent error for shallow targets. The magnetic gradient tensor constructed using nine sensors can accurately detect deep targets and improve the SNR. The experimental results show that the proposed method can locate underground targets within 2 m, and the depth error does not exceed 10 cm.
In summary, the proposed method can effectively locate underground targets within 2 m and provide a research method for transient electromagnetic fast detection and the identification of targets.