Elsevier

Signal Processing

Volume 80, Issue 8, August 2000, Pages 1669-1686
Signal Processing

A two-dimensional generalized likelihood ratio test for land mine and small unexploded ordnance detection

https://doi.org/10.1016/S0165-1684(00)00100-6Get rights and content

Abstract

The fundamental goals of land-mine and small unexploded ordnance (UXO) detection are to achieve a high probability of detection (Pd) and a low probability of false alarm (Pfa). Conventional methods usually fulfill the first goal at the cost of a high Pfa. In our previous work (Collins et al., IEEE Trans. Geosci. Remote Sensing 37 (2) (March 1998) 811–819; Gao and Collins, Proceedings of SPIE, Orlando, FL, April 1998; Gao, Master's Thesis, Duke University, December, 1997), we have shown that a Bayesian decision theoretic approach can be applied to improve the detectibility of land mines and small UXO targets using a single spatial sample of the electromagnetic induction (EMI) sensor data. In this paper, we present an alternative approach which significantly improves Pd at a fixed Pfa by utilizing features that capture the physical nature of EMI data within a statistical signal processing framework. The method we develop is a two-dimensional generalized likelihood ratio test (2-D GLRT) which utilizes spatial information from the sensor output. To illustrate the performance improvement, results obtained with the 2-D GLRT detector are compared to those for the standard threshold test for single-channel time-domain sensor data, as well as the energy detector, the integral detector, and the single location generalized likelihood ratio test (1-D GLRT) detector for multi-channel time-domain EMI sensor data.

Zusammenfassung

Die wesentlichen Ziele bei der Detektion von Landminen und kleiner nicht explodierter Munition (UXO) sind die Erzielung einer hohen Detektionswahrscheinlichkeit (Pd) und die Erzielung einer kleinen Fehlalarmwahrscheinlichkeit (Pfa). Herkömmliche Methoden erreichen üblicherweise das erste Ziel auf Kosten einer hohen Fehlalarmwahrscheinlichkeit. In unserer früheren Arbeit (Collins et al., IEEE Trans. Geosci. Remote Sensing 37 (2) (March 1998) 811–819; Gao und Collins, Proceedings of SPIE, Orlando, FL, April 1998; Gao, Master's Thesis, Duke University, December, 1997) haben wir gezeigt, daß ein auf der Bayesschen Entscheidungstheorie beruhender Ansatz benützt werden kann, um die Detektierbarkeit von Landminen und kleinen UXO-Zielen zu verbessern, wobei eine einzige räumliche Stichprobe der von elektromagnetischen Induktionssensoren (EMI-Sensoren) gewonnenen Daten verwendet wird. In diesem Artikel stellen wir einen alternativen Ansatz vor, der die Detektionswahrscheinlichkeit bei festgehaltener Fehlalarmwahrscheinlichkeit signifikant verbessert. Dabei werden Merkmale ausgenützt, welche die physikalischen Eigenschaften der EMI-Daten im Rahmen der statistischen Signalverarbeitung erfassen. Die von uns entwickelte Methode ist ein zweidimensionaler verallgemeinerter Likelihood-Quotiententest (2-D GLRT), der die im Sensorausgangssignal enthaltene räumliche Information benützt. Um die Verbesserung der Leistungsfähigkeit zu veranschaulichen, vergleichen wir Ergebnisse des 2-D GLRT mit Ergebnissen des Standard-Schwellentests für Zeitbereichs-Sensordaten eines einzigen Kanals sowie mit Ergebnissen für Zeitbereichs-Sensordaten eines einzigen Kanals sowie mit Ergebnissen des Energiedetektors, des Integraldetektors und des auf einem einzigen Standort beruhenden verallgemeinerten Likelihood-Quotiententests (1-D GLRT) für Mehrkanal-Zeitbereichsdaten von EMI-Sensoren.

Résumé

Les buts fondamentaux de la détection des mines terrestres et des petits matériels non explosés (UXO) sont d'attendre une haute probabilité de détection (Pd) et une petite probabilité de fausse alarme (Pfa). Les méthodes conventionnelles remplissent généralement le premier objectif au prix d'une Pfa élevée. Dans nos travaux précédents (Collins et al., IEEE Trans. Geosci. Remote Sensing 37 (2) (March 1998) 811–819; Gao et Collins, Proceedings of SPIE, Orlando, FL, April 1998; Gao, Master's Thesis, Duke University, December, 1997), nous avons montré que l'approche théorique par décision Bayésienne peut être appliquée pour améliorer la détectabilité de mines terrestres et de petites cibles UXO en utilisant un seul échantillon spatial des données d'un senseur à induction électromagnétique (EMI). Dans cet article, nous présentons une méthode alternative qui améliore significativement Pd à Pfa fixe en utilisant des attributs qui capturent la nature physique des données EMI dans un cadre de traitement statistique de signaux. La méthode que nous développons est un test de rapport de probabilités généralisé à deux dimensions (2-D GLRT) qui utilise l'information spatiale de la sortie des senseurs. Pour illustrer l'amélioration de performances, des résultats obtenus avec le détecteur 2-D GLRT sont comparés à ceux d'un test de seuillage standard pour des données de senseurs à canal unique dans le domaine temporel, de même que de détecteurs à énergie, de détecteurs intégraux et de détecteurs à test de rapport de probabilités généralisé à localisation unique (1-D GLRT) pour des données de senseurs EMI multi-canaux dans le domaine temporel.

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 (<1MHz), 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, r, at each location surveyed with the sensor can be modeled as a superposition of weighted resonant responsesr=n=1NAnejωnt,where 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 asr=Ae−αt,where 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 320μs to 30ms following the incident pulse [13]. Thus, the received signal from the Geonics EM61-3D sensor can be expressed asr=Ae−αt,where {ti}, an element of t, 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 asr=i=0NAe−α(t0+t),where 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]. r|H1N(S1(A11),σ2I) and r|H0N(S0(A00),σ2I) where r 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, X. 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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