Real-time Detection System for Portable Transient Electromagnetic Unexploded Ordnance

Portable transient electromagnetic systems are not limited by terrain and can detect unexploded ordnance very flexibly. However, existing data processing methods are slow and cannot achieve real-time positioning of targets. In this paper, based on a laboratory-made portable transient electromagnetic detection system, the magnetic dipole model and tensor positioning algorithm are used to achieve fast and accurate target positioning. Using the magnetic gradient tensor algorithm for positioning reduces the calculation load, allowing it to run on embedded systems, and improving target positioning speed while ensuring the accuracy of measurements. Experimental results show that the vertical and horizontal positioning errors of the UXO are within 10 cm, and single-point positioning can be completed within 10 ms.


Introduction
Unexploded ordnance (UXO) refers to explosive munitions, such as landmines, ordnances, grenades, shells, bullets, and even missiles, that remain unexploded after warfare or other military activities [1] .Currently, the main methods for UXO detection include magnetic, electromagnetic, and groundpenetrating radar methods.Compared with the magnetic and ground-penetrating radar methods, the transient electromagnetic (TEM) method has a large magnetic moment and detection depth, making it widely used for UXO detection [2,3] .
In terms of data processing, traditional detection methods usually store measurement data on hardware [4][5][6] .This system employs an ARM+FPGA dual-core system for real-time data acquisition and processing.In this paper, the magnetic gradient tensor localization algorithm is chosen.The main advantage of the tensor localization algorithm compared to other algorithms is its ability to overcome interference from the geomagnetic field using differentiation, without the need for iteration [7] .This improves the accuracy and speed of target detection [8] .

System composition
The entire system consists of a control and computation system and sensors, as shown in Figure 1.In Figure 1, the control and computation system used in this system consists of an ARM (STM32F767IGT6) and an FPGA (EP4CE15F23C8N) dual-core system.It is responsible for performing all data computations and controlling the coils while also collecting voltage signals from the coils.The sensor part consists of control circuits, transmitting coils, and receiving coils.The transmitting and receiving coils are responsible for receiving magnetic field information.
Figure 2 represents the model of the transmitting and receiving coils.The outermost transmitting coil generates the excitation magnetic field, while the inner five coils are used to receive the secondary field signals generated by the target being measured.The outer coil of the sensor is a single-component transmitting coil, and inside it, five three-component receiving coils are arranged in a cross shape.

Positioning method
In the dipole model, where the distance between the two points of the dipole is much smaller than the distance to any point in space when the object's dimensions can be abstracted as a point compared to the distance relationship, the magnetic field produced by a magnetic dipole at any point in space satisfies the equation [9]  : where n represents the unit vector pointing from the magnetic dipole to the point in space, R represents the vector pointing from the magnetic dipole to the point in space, m represents the magnetic moment of the magnetic dipole, and μ is the absolute permeability [10] .Because the magnetic field is a vector field, it has three components: B x , B y , and B z , representing the magnetic field in the x, y, and z directions, respectively [11]  .The rates of change of these three components in the x, y, and z directions are collectively referred to as the magnetic gradient tensor [12]  , G.
The relationship between the magnetic gradient tensor and the magnetic field itself is combined from Equations ( 1) and ( 2 Furthermore, since the magnetic field is a source-free field, the curl and divergence of the magnetic flux density B are both zero.Therefore, out of the 9 components in the matrix G, only 5 components need to be determined by combining Equation ( 4) with specific sensor parameters in order to draw conclusions.

System algorithm
The system algorithm mainly consists of two parts: data acquisition and position calculation.The data acquisition part describes the process of collecting the target's secondary field voltage signal from the ADC module to the final target localization.The position calculation part explains how to use the secondary field signal for target localization.
The data acquisition part is first discussed.In the entire data acquisition process of the system, the FPGA is responsible for driving the ADC to collect coil voltage signals, while the ARM is responsible for collecting coil current signals.By combining the voltage and current signals, all the information required for localization can be obtained.

Experimental design
The primary goal of this system is to achieve real-time positioning.To accomplish this goal, the accuracy and real-time performance of the system were tested in the experiment.The experiment was conducted in the field, with the sensors placed inverted on the ground.The measurement grid and objects to be measured were positioned directly above the sensors, as shown in Figure 4.The measurement area consists of a square region composed of a 5*5 grid of points.The center point of the grid is aligned with the center of the sensor.Each point is numbered as shown in Figure 5.
For the selection of measurement objects, a projectile with an outer diameter of 82 mm and a length of 27 cm was chosen as the measured object and named U1.The basic information of U1 is presented in Table 1, and the picture of unexploded ordnance is shown in Figure 6.After obtaining the environmental background data, the positioning results of 25 points were measured at three different depths: 30 cm, 50 cm, and 60 cm.The positioning time was also recorded for each measurement.In total, there are 75 sets of positioning data.

Experimental results and analysis
The positioning results of U1, when placed in an upright position, are shown in Figure 7, Figure 8, and Figure 9. (The Z-axis positioning results have been adjusted with a 10 cm compensation.)Based on Figure 7, Figure 8, and Figure 9, the positioning points with the numbers (7, 8, 9, 12, 13,  14, 17, 18, 19), which are located in the central 3*3 square area, have relatively small positioning errors at depths of 30 cm, 50 cm, and 60 cm.The average absolute values of the specific positioning errors are shown in Table 2.It means that when the object is detected within a 40 cm * 40 cm square area centered around the sensor, the system is able to achieve relatively accurate positioning with a depth error within 10 cm.The time required for target positioning, following the data collection method described in Figure 5, is shown in Figure 10.  10 is the computation time, and the system takes approximately 7 ms to 10 ms to complete the positioning calculations.The calculation time is relatively stable, indicating that the system is capable of meeting the real-time positioning requirements.

Conclusion
The real-time detection system for portable transient electromagnetic unexploded ordnance, constructed in this paper, adopts the magnetic dipole model and employs the magnetic gradient tensor-based positioning algorithm.By optimizing the positioning algorithm based on the actual sensor structure, a positioning system program was developed.The system can control the data acquisition circuit on an ARM+FPGA collaborative system, collect data from the target, and ultimately accomplish real-time target positioning tasks within a short period of time.
When the 82 mm diameter projectile is in a 40 cm * 40 cm square area centered around the sensor, the positioning errors in both vertical and horizontal directions are within 10 cm.The time required for a single positioning fluctuates between 7 ms to 10 ms, with a small variation.
Overall, this system achieves real-time positioning with an average time of milliseconds from data acquisition to positioning results.Based on the experimental results, the positioning accuracy meets the requirements, and the positioning time is short.Therefore, real-time positioning of unexploded ordnance targets can be achieved, facilitating practical applications in real-world scenarios.

Figure 1 .Figure 2
Figure 1.Composition of the control and computation system

Figure 3 .
Figure 3. Position calculation Figure 4. Measurement mode Figure 5. Measurement area and methods

Figure 7 .Figure 8 .Figure 9 .
Figure 7.The positioning result of the target at a depth of 30 cm

Table 2 .
The Average Positioning Error of the Positioning Points in the Central 3*3 Square Area