Quickest Detection of Nuclear Radiation using aSensor Network

Lijun Qian†, John Fuller†, Ing Chang‡† Department of Electrical and Computer Engineering

‡ Department of Mechanical EngineeringPrairie View A&M University, Texas A&M University System

Prairie View, Texas 77446, USA{liqian, jhfuller, inchang}@pvamu.edu

Abstract—In the future, the nuclear threat is less likely froma massive nuclear attack, but more likely from crude devices,such as dirty bombs perpetrated by an individual or group ofterrorists. Detection and prevention of these nuclear devices arecritical to the safety and security of the general population. Ingeneral, the research of detecting various radioactive sourcesusing individual sensors has been well established in terms ofboth detection devices and detection methods, most of whichare dedicated to single or co-located sensor systems. Largemonitoring systems at choke points (e.g. commercial airportsand harbors) can prevent the entry or exit of nuclear sources.However, it cannot protect a perimeter that spans a large area,such as land and sea borders. Furthermore, in many practicalscenarios, it is desirable to detect low-level radiation and identifylow-level radioactive sources. Recent advances in sensor networktechnologies have opened up the potential for improved detection,as well as the estimation of source parameters, by utilizingmeasurements from multiple, geographically dispersed sensors.Different from the existing works on radiation detection usingsensor networks, in this paper, we focus on the quickest detectionmethod that would identify nuclear radiation as soon as possibleafter it occurs, while keep the false alarm rate low. Specifically,we propose that each sensor performs a nonparametric versionof the Page’s Cumulative Sum (CUSUM) test based on its localmeasurements, since the occurrence of the nuclear radiationis unpredictable and we assume that we do not have priorknowledge of the adversary (e.g., who carries a dirty bomb).Then the local decisions from multiple sensors are sent to afusion center for combining and a final decision is made. Wepresent numerical results to demonstrate the effectiveness of theproposed scheme using the experimental measurements from aCOTS detectors in our lab.

I. INTRODUCTION

The September 11, 2001 terrorist attack imposed upon theUnited States the fundamental importance to our safety of thereduction in the global threat from terrorism and weaponsof mass destruction. High on the list of threats are nuclearweapons and nuclear devices. In the future, the threat isless likely from a massive nuclear attack, but more likelyfrom crude devices, such as dirty bombs perpetrated by anindividual or group of terrorists. Detection and prevention ofthese nuclear devices are critical to the safety and security ofthe general population [1].

In general, the area of detecting various radioactive sourcesusing individual sensors has been well established in termsof both detection devices and detection methods [2], most of

which are dedicated to single or co-located sensor systems.Large monitoring systems at choke points (e.g. commercialairports and harbors) can prevent the entry or exit of nuclearsources. However, it cannot protect a perimeter that spans alarge area, such as land and sea borders [3]. Furthermore, inmany practical scenarios, it is desirable to detect low-levelradiation and identify low-level radioactive sources as a part ofthe defense strategy against, for instance, dirty bomb scenarios.The ability to identify the signatures of such sources willenable their detection before they are set off, in particular,while the sources are being transported or stored [4].

Recent advances in sensor network technologies haveopened up the potential for improved detection, as well as theestimation of source parameters, by utilizing measurementsfrom multiple, geographically dispersed sensors; e.g., theworks in [3], [5], [6], [7], [8], [9], [10], [11], [12], and recently,using both directional and non-directional detectors [13]. Inaddition to the complexity of a large sensor system, the abilityof efficient detection, identification and localization dependson a variety of uncontrollable factors such as the presence ofbenign sources that may cause false alarms, time and spacevarying background noise, and obstacles that may occludesignal from sources. Under the influence of these factors, asuccessful system should be able to detect and locate nuclearradiation sources in real-time with low false alarm probability.Moreover, it is also desirable to track the suspected subject ifnecessary. These requirements are very difficult to achieve ashas been shown in the literature, and not a single algorithmthat has been proposed so far produces good results in allscenarios.

In this paper, we focus on the quickest detection methodthat would identify nuclear radiation as soon as possible after itoccurs, while keeping the false alarm rate low. Specifically, weconsider a moving radiation source that may be well shieldedand thus its radiation intensity is well below the backgroundradiation. We propose that each sensor performs a nonpara-metric version of the Page’s Cumulative Sum (CUSUM) testbased on its local measurements, since the occurrence of thenuclear radiation is unpredictable and we assume that we donot have prior knowledge of the adversary (e.g., who carriesa dirty bomb and where or when). Then the local decisionsfrom multiple sensors are sent to a fusion center for combining

978-1-4673-2709-1/12/$31.00 ©2012 IEEE 648

and a final decision is made. We present numerical results todemonstrate the effectiveness of the proposed scheme.

This paper is organized as follows. The network model,problem formulation and the proposed method are illustratedin Section II. Experimental setup and simulation results andanalysis are provided in Section III. Related works are dis-cussed in Section IV. Section V contains the concludingremarks.

II. PROBLEM FORMULATION AND THE PROPOSEDMETHOD

A distributed radiation sensor network is proposed inthis work. The network model and information flow of theproposed radiation sensor network is shown in Fig.1. It isassumed that there exists background radiation that may varyalong time. A moving radiation source may emerge at anunknown time and place, such as in a dirty bomb scenario.The newly appeared moving radiation source would changethe probability distribution of the radiation and the goal isto detect such change as soon as possible. In this study, we

Figure 1: The network model and information flow of theproposed radiation sensor network.

use a commercial-of-the-shelf (COTS) Gamma-ray detectorto measure the intensity of nuclear radiation. The proposeddistributed radiation detection includes two components: thedistributed nonparametric cumulative sum (CUSUM) test [14]at each participating radiation sensor, and a combining proce-dure after the information from the sensors are collected at acentral controller.

A. Distributed CUSUM method

It is observed that the radiation intensity follows differentdistributions when a nuclear radiation source emerges [15].Therefore, the technique of quickest detection is applied in thispaper to detect such changes as quickly as possible. We assumethat each radiation sensor will perform individual CUSUM testbased on its own measurement on radiation intensity.

Denote the radiation intensity by S, and we assumethat a radiation source emerges at time t∗. The mea-surements {S1, S2, · · · , St∗−1} are independent and identi-

cally distributed (i.i.d.) with a fixed distribution B0, and{St∗ , St∗+1, · · · } are i.i.d. with another distribution B1. Wedenote by td the time when the change is detected, and definethe detection delay as r = td− t∗. Consequently, we have twoprobable events: one is td < t∗, which is a false alarm; theother is td ≥ t∗, namely a delayed detection. Furthermore, thefalse alarm rate, Pf , is given by

Pf = P (td < t∗). (1)

Then the average detection delay is given by

r̄1 = E{r|td ≥ t∗}. (2)

We follow the definition of the quickest detection problem byLorden and Page [16], [14], which is to minimize the worstdetection delay subject to a constraint on the false alarm rate.The problem formulation is given by

min(sup ess sup r̄1)

s.t. Pf ≤ ηf , (3)

where ηf is a predefined threshold of the false alarm rate.In order to solve the above optimization problem, we apply

Page’s cumulative sum (CUSUM) test [14]. The log-likelihoodratio (LLR) of the radiation intensity S is given by

l(S[k]) = lnB1(S[k])

B0(S[k]). (4)

In order to use the CUSUM test, we need to obtain theprobability density functions (PDFs), B0 and B1, respectively.Then the Kullback-Leibler divergence between the probabilitydistributions B0 and B1 can be calculated. We assume that thedistribution of the radiation intensity before the emergenceof a radiation source is known. For instance, the mean ofthe radiation intensity can be estimated by taking averageof the measurements during a training period. However, inradiation detection context, the probability distribution of theradiation intensity after the emergence of a radiation sourceare generally not known or very hard to obtain. As a result,the log-likelihood ratio in equation (4) is not attainable. Inaddition, we assume that we do not have prior knowledge ofthe adversary (e.g., who carries a dirty bomb and where orwhen is the bomb).

In this work, we propose to use a nonparametric version ofthe CUSUM test at each sensor. Specifically, it is appropriateto use a score function, q, instead of using the log-likelihoodratio to detect changes [17]. We evaluate the mean value of theradiation intensity at the jth sensor, mj , before and after theemergence of the radiation source. The score function of thejth sensor, qj is selected so that it can indicate the changes ofmj after the emergence of a radiation source. The mean value,mj = E0[(S1,j , · · · , St,j)], can be estimated during each t-thtime interval, where St,j is the measured radiation intensity inthe t-th time interval at the jth sensor. The score function isdefined as:

qj (S1,j , · · · , St,j) = St,j −mj . (5)

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Once a new radiation source emerges, the CUSUM-typestatistic becomes

Xt′,j = max1≤t∗≤t′

t′∑t=t∗

qj (S1,j , · · · , St,j) (6)

for the jth sensor, where t∗ is the change-point. Then thedecision rule is{

Radiation source is not presented; if Xt′,j < θRadiation source is presented; if Xt′,j ≥ θ

, (7)

where θ is a pre-determined threshold. θ has to be carefully de-termined and it will have significant effect on the performanceof the proposed algorithm, as we will see in the numericalresults later. For the jth sensor, the declaration time for thedetection of a radiation source is obtained by the followingstopping rule:

td = min{t′ : Xt′,j ≥ θ}. (8)

It can be shown that the average detection delay is related tothe detection threshold in the following manner

r̄1 ≈θ

E[qj ]=

θ

E[St,j ]−mj(9)

B. Optimal combining

After each individual sensor has performed its own CUSUMtest using the score function as described above, an informa-tion fusion procedure can be carried out at a central controlwhere all the information is gathered. In general, the informa-tion could be either raw data (such as the CUSUM statistic orscore function) or quantized data (say binary decision results).There are many studies on information fusion using quantizeddata or binary decisions, such as [18], [19]. In this study, wetry to take advantage of the score function because of thesensitivities of the radiation sensors [20]:

1) Choose the largest quantity from any one sensor andcompare it to a threshold. This method is optimal wheneach individual sensor has sufficient sensitivity to covera predefined region given a desired false alarm rate.

2) Choose the sum of the quantities from geographicallycorrelated sensors, and compare it to a threshold. Thismethod is optimal when each individual sensor does nothave enough sensitivity, or equivalently, each sensor’scoverage area is small given a desired sensitivity.

In general, the above methods are special cases of weightedcombining, i.e., the criterion is a weighted sum of the quan-tities from all the sensors. The optimal combining problemcan be formulated as an optimization problem: Given a set ofparameters including the sensor’s characteristics (sensitivity,coverage, etc.) and the configuration of the sensor network(density and locations of the sensor nodes), assign a set ofweights such that the detection probability is maximized whilethe false alarm probability is under a predefined value.

arg maxw

Pd

s.t. Pf ≤ ηf (10)

where w is a weight vector and Pd is the detection probability.In this paper, we perform simulations to compare the perfor-mance of the combing rules with individual sensor detectionunder different sensitivities of the sensors. We firstly considerusing the sum of the score function, other methods will bestudied in our future research.

III. SIMULATION RESULTS AND ANALYSIS

In this section, we report simulation results of the proposedalgorithm based on experimental measurements using theCOTS detectors in our lab at PVAMU. The layout of theexperiments is shown in Fig. 2. We assume that there existnon-negligible background radiations by placing a backgroundradiation source close to the radiation sensors. Specifically, wetested three cases:

1) strong background radiation, Dbk = 2 cm, S =7.8uSv/h;

2) medium background radiation, Dbk = 6 cm, S =2.5uSv/h;

3) weak background radiation, Dbk = 40 cm, S =0.12uSv/h.

where Dbk is the distance between the background radiationsource and the radiation sensor. The goal is to test theperformance of the proposed algorithm under various practicalscenarios. For instance, it may be of interest to monitor movingof radiation material from a nuclear waste site, where thebackground radiation could be strong. The moving radiationsource is assumed to appear at the start of the experiment andmoving at a constant speed (0.2cm /sec) across the sensor arraythat composed of three COTS radiation sensors. Each radiationsensor record a reading every 10 seconds and each experimentlasts 400 seconds, i.e., each sensor obtains 40 readings.

Figure 2: The layout of the experiment. There is a backgroundradiation source that located nearby the radiation sensors. Themoving radiation source needs to be detected when it presents.

A. Distributed CUSUM test by a single sensor

We carried out 200 experiments to detect the movingradiation source when it presents, with 100 of them withthe moving radiation source and 100 without it, so that wecould obtain the miss and false alarm rate, as well as theaverage detection delay. We start by using only one sensor,and the results are shown in Fig.3,4,5 when the movingradiation source is not shielded. In other words, the radiation

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intensity from the moving source is pretty strongly received atthe sensor. Thus, for unshielded radiation source, there is nomiss in our experiments. However, false alarm rate is greatlyaffected by the choice of the detection threshold, as expected.It is observed in Fig.3 that the false alarm rate is lower whenthe background radiation is weaker. It is also shown that withproperly chosen threshold value, false alarm can be avoided nomatter of the background radiation. Of course, this is mainlydue to the strong radiation of the moving radiation source sinceit is unshielded. It is interesting to notice that the average

Figure 3: The false alarm rate vs. the detection threshold forunshielded radiation source.

detection delay is not affected by the background radiation,see Fig.4. This demonstrate the property of quickest detectionthat minimizes the detection delay when the false alarm iscontrolled. The tradeoff between the average detection delayand the false alarm rate is shown in Fig.5. By properly chosenthe detection threshold, say θ = 4.3, we can achieve zero falsealarm while limit the detection delay within 12 time units (120seconds).

It is clear that the proposed method works almost perfectlywhen the radiation source is not shielded. However, to examinethe performance of the proposed method against realisticsituations, we also test the cases where the radiation source isshielded, in our simulation, we reduce the radiation intensityby a factor of 30. The results are given in Fig.6 and Fig.7.The Receiver Operating Characteristic (ROC) curve in Fig.7shows that the accuracy of the proposed algorithm deteriorateswhen the background radiation becomes stronger. When theradiation intensity of background is comparable to that of themoving source, the algorithm has no false alarm and 100%detection when the detection threshold is set properly. Whenthe radiation intensity of background is 30 times higher thanthat of the moving source, the detection probability is only70% when keeping the false alarm below 10%. It can beconfirmed in Fig.6 that the detection will happen in 24 timeunits (double the time of the unshielded case).

Figure 4: The average detection delay vs. the detection thresh-old for unshielded radiation source.

Figure 5: The average detection delay vs. the false alarm ratefor unshielded radiation source.

Figure 6: The average detection delay vs. the false alarm ratefor shielded radiation source.

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Figure 7: The ROC curve for shielded radiation source.

B. Combining of scores from multiple sensors

Now we add the scores from three sensors and use thesum to perform detection, as described in Section II-B. TheROC curve is given in Fig.8. It is observed that the optimalcombining indeed improves the performance a lot. The biggestimprovement is under strong background radiation, wherenow the detection probability is about 98% when keepingthe false alarm below 2%. This is expected because the sumof the scores from geographically correlated sensors wouldcompensate the low sensitivity of each individual sensor, andthis helps the most when the background radiation is strong.

Figure 8: The ROC curve for shielded radiation source afterapplying optimal combining.

It worth pointing out that in our lab we can only have a veryslow moving radiation source due to the limited space in thelab. If the source moves much faster, say at vehicle speed inreality, the corresponding radiation sensor reading period canbe scaled down from 10 seconds to a much smaller interval.Thus, using time units rather than exact time (e.g., seconds)gives a more accurate evaluation of the “quickness” of the

proposed algorithm.

IV. RELATED WORKS

Time-series analysis is applied to vehicle count profilesto improve the effectiveness of pass-through radiation portalmonitors for detection of nuclear materials [15]. Stationaritymeasures and CUSUM statistics are applied for the detectionof anomalies, which yields insights into the nature of vehiclecount profiles. Nonparametric version of the CUSUM test isnot considered, neither multiple sensors are considered in [15].

The linear deployment of radiation detectors has beenconsidered in several works [5], [6], [10]. Measurementsfrom multiple sensors are used to estimate the parameters ofthe source in [7], assuming that the source exists. Quickestdetection techniques are not discussed in these works.

The detection of the radiation source and estimation ofthe parameters are jointly treated in [8], where a geometricdifference triangulation method or an N-sensor localizationmethod is used to estimate the location and strength ofthe source. A Sequential Probabilistic Ratio Test is derivedunder the assumption that the measurements correspondingto both background and source radiation satisfy the Poissondistribution. In our work, we do not assume any particulardistribution of the radiation sources.

The authors in [3], [9] evaluated the design tradeoffs ofradiation sensor systems constructed by multiple static andmobile radiation detectors. Information fusion was discussedbut quickest detection was not considered.

V. CONCLUSIONS

In this paper, we demonstrated the feasibility of using aquickest detection technique, a nonparametric version of theCUSUM test, to perform detection of a moving radiationsource using time-series data measured by COTS detectors.Through combined experimental measurements and simula-tions, it is observed that the proposed algorithm will detectan unshielded source almost perfectly when the radiationintensity of the source is on the same level of the backgroundradiation. When the moving radiation source is well shielded,the ROC curve showed that the proposed algorithm provideacceptable detection quickly while keeping the false alarmrate low. It is also observed that the detection threshold playsa vital role in the algorithm. By information fusion usingoptimal combining, it is possible to improve the performancefurther. More complicated optimal combining rules will beinvestigated in our future study.

VI. ACKNOWLEDGMENT

The authors would like to thank Joseph Kamto for perform-ing some of the experiments. This research work is supportedby DOE NNSA through the Sam Massie Chair of Excellenceprogram.

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