A two-dimensional generalized likelihood ratio test for land mine and small unexploded ordnance detection
Introduction
The goal of any detection system is to achieve a high probability of detection (Pd) while at the same time maintaining a low probability of false alarm (Pfa). This is particularly important in land mine detection where Pd is required by the United Nations to be 99.6%, and Pfa is directly proportional to the time and cost to remediate a site. At the current rate of clearance, 1100 years will be required to remove all land mines that are already emplaced (This statistic further assumes that no additional land mines are emplaced.) Thus, reducing the false alarm rate is of immediate importance. However, it is most often the case that land mine detectors which achieve high Pd do so at the cost of high Pfa. This is because conventional mine detection technologies simply seek anomalies caused either by land mines or clutter, but do not exploit the nature of the physical signature or the statistics of the sensor response due to mines and clutter. In this paper, we present an approach which significantly reduces Pfa at a fixed Pd by incorporating the underlying physics of electromagnetic induction (EMI) sensors into a statistical signal processing framework. This novel method is a two-dimensional generalized likelihood ratio test (2-D GLRT) algorithm, which utilizes the spatial measurements taken with an EMI sensor across a local area.
There are several devices which either have been used or have been proposed for use in land mine detection: magnetometer, infrared imager, electromagnetic induction (EMI) sensor, and ground penetrating radar (GPR). Among these sensors, the most well established is the EMI sensor. An EMI system is essentially a metal sensor which records the electromagnetic induction field that is the response from underground objects, clutter, etc., due to an incident electromagnetic field. An EMI system can detect mines which contain metal, as well as unexploded ordnance (UXO) or metallic anthropic clutter. In order to detect such targets, the EMI system normally operates at low frequencies (), at which the conductivity- and permeability-dependent skin depth of the materials varies significantly [2], [19]. Furthermore, at these frequencies the displacement current is weak enough to be neglected [11]. Hence, the response of the pulsed EMI system, , at each location surveyed with the sensor can be modeled as a superposition of weighted resonant responseswhere ωn is the nth natural resonant frequency of the object and An is the initial magnitude of the response corresponding to that natural resonant frequency. In practice, the real part of ωn is very small, and thus can be ignored [11]. Also, the late time field, which is the field recorded by EMI sensors, is dominated by the lowest mode, which is approximately an exponential damping. Therefore, to a first-order approximation the response can be modeled aswhere A is the initial magnitude of the response and α is the dominant natural resonant frequency. A is strongly dependent on the excitation level, the depth, and the orientation of the underground objects [2], [11]. The resonant frequency, α, can be used to identify land mines because it is a function of conductivity and permeability, which are unique to each metal type [2], [11], [19]. Generally, the response from a relatively high metal content mine has a lower natural resonant frequency than that of anthropic clutter, i.e. the decay rate of a target signature is slower.
In this paper, several detection approaches are explored for two types of EMI sensors: (1) multi-channel time-domain EMI systems and (2) single-channel integrated time-domain EMI systems. The detection approaches are validated using field data collected in conjunction with the DARPA Backgrounds Clutter Data Collection Experiment [13]. One example of a prototype multi-channel time-domain pulsed EMI sensor is the Geonics EM61-3D sensor, which was used to collect data in the DARPA experiment. This sensor samples the induced response at 20 geometrically spaced time gates from to following the incident pulse [13]. Thus, the received signal from the Geonics EM61-3D sensor can be expressed aswhere {ti}, an element of , is the sampling time, i=1,2,…,20. An example of the second type of sensors, a single-channel time-domain EMI system, is the Geonics EM61 sensor, also used in the DARPA study. This sensor integrates the time-domain-induced response within a pre-determined range of time to obtain a scalar value at each survey location. Therefore, its response can be expressed approximately aswhere t0 is the initial time for the integration, and the integration ends at time t0+NΔt.
The traditional approach to mine detection using data from a single-channel EMI sensor is to perform a threshold test on the data obtained at each individual survey location. As stated before, the phenomenon exploited to distinguish mines from clutter is that the decay rate of the target response is generally slower than that of clutter. Discrimination based on the initial magnitude A is not investigated in this paper; however, experimental data indicates that, on average, A for mines is greater than that of clutter. Thus, after integrating the response, the output from a single channel integrated time-domain EMI sensor due to a target is usually greater than that of clutter. An extension of this approach to multi-channel EMI sensor data is to perform a threshold test on either the energy present in the received signal, or on the integral (sum) of the sampled values at each survey location. These two approaches essentially convert the multi-channel responses to single-channel data in order to make a decision.
In addition to the conventional methods, there have been several studies on mine detection using statistical methods. In [1], [3], [7], [9], [16], [17], the statistical characterization and modeling of mine fields have been addressed. Ref. [10] introduced an area-based “δ-technique”, which incorporates spatial information through the energy levels of an EMI sensor response at the center point under test and its immediate neighbors. This technique utilizes the number of neighbors whose energy level is lower than that of the center location under test as the criterion of whether a mine is present or not. This technique is similar to CFAR detection [18].
In our previous work [3], [7], [9], we have applied signal detection theory to generate both the one-dimensional likelihood ratio test (LRT) and the GLRT for the Geonics EM61 and EM61-3D sensor data. The probability density functions describing the sensor response to target and clutter were used to formulate the likelihood ratio at each surveyed location. We have shown that the performance of the two detection approaches were the same experimentally and theoretically for multi-channel sensor data [7], [8]. In addition, the 1-D GLRT has been shown to improve performance dramatically over the performance achieved with the standard tests on multi-channel sensor data. We have also proven that a threshold test on the raw data is the optimal processor for single-channel EMI sensor data from a single location, even when the decay rates for target and clutter are not deterministic parameters [3].
In this paper, a statistical approach incorporating both the underlying physics of EMI sensors [2], [4], [5], [12], [19] and statistical signal processing theory [20], in which the statistics of local data surrounding the location under test are utilized, is presented. Since the minefields are sampled spatially, i.e. the sensor head is moved throughout the candidate area, we have hypothesized that the accuracy of the mine detectors would be improved when spatial information is incorporated into processor. The results demonstrate that this hypothesis is valid.
The remainder of this paper is organized as follows. In order to illustrate the improvement of the 2-D GLRT, it is compared to several other detection schemes including the threshold, energy, and integral detectors, the δ-technique, and the 1-D GLRT. Each of these detectors is described in Section 2. In Section 3 we introduce a two-dimensional GLRT detector for land mine and small UXO detection. The field data utilized to analyze performance is described in Section 4. Next, the results obtained by applying each of these detectors to the experimental data are presented in Section 5. Finally, the results are discussed in Section 6.
Section snippets
One-dimensional generalized likelihood ratio test and other detectors
First, several simple detection approaches are described. It is necessary to investigate these detection techniques in order to evaluate the significance of the performance improvement achieved by the 2-D GLRT. The distributions of the outputs of multi-channel time-domain EMI sensors can be modeled with multivariate Gaussian density functions [3]. and where is the output of the sensor as a function of time, A1 and A0 are the initial magnitude and α1
Detector design – two-dimensional likelihood ratio test
Generally, it can be assumed that data can be obtained at sample points which are laid out as a rectangular mesh as illustrated in Fig. 1. Our goal is to make a decision on whether there is a mine present at the center location, . The data that is available consists of the outputs from the sensor both at the center location and the surrounding locations. Three possible situations can occur:
(i) there is a mine buried under the center location; or (ii) there is nothing buried in this area; or (iii)
Data
The objective of the DARPA background clutter data collection experiment [13] was to collect data to aid in the understanding of the effects of clutter on system performance. During the course of the experiment, data was collected using four types of sensors: ground penetrating radar (GPR), electromagnetic induction (EMI), magnetometer, and infrared (IR). Data was collected at four sites distributed over two locations (Fort Carson, Colorado and Fort A.P. Hill, Virginia). The locations
Results
The data used to analyze the detection strategies were collected during the DARPA Backgrounds Clutter Data Collection Experiment [13] at four sites at two U.S. locations, Fort Carson, Colorado and Fort A.P. Hill, Virginia. The raw data were first divided into an appropriate raster based on the spatial separation of survey lines and the sampling rate of the sensors, and then all the responses collected in each grid were averaged.
The standard quantitative tool to evaluate performance of a
Conclusions
The above results indicate that the 2-D GLRT analysis can significantly reduce false alarm rates in land mine and small UXO detection scenarios using EMI sensor data. The performance improvement obtained for both multi-channel time-domain and single-channel integrated time-domain EMI data were evaluated at four test sites, and were consistently high across all sites, even at the most highly cluttered Fort A.P. Hill FP20 site. This improvement occurs because the processor may correctly model
Acknowledgements
This research has been supported by the Army Research Office under grant DAAH04-96-1-0448 (Demining MURI). The authors would like to acknowledge the valuable discussions with Dr. Lawrence Carin, Dr. Thomas Altshuler, Ms. Vivian George, Dr. Regina Dugan, Dr. Stacy Tantum, Dr. Erol Gelenbe, and Mr. Taskin Kocak regarding this work. Also, thanks to Dr. Yan Zhang for providing the EMI model code.
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