An AI Approach in Radioactive Source Localization by a
Network of Small Form Factor CZT Sensors
Aristotelis Kyriakisβ Konstantinos Karafasoulisβ
Institute of Nuclear and Particle Physics, NCSR Hellenic Army Academy
"DEMOKRITOS" 16673, Vari, Attica, Greece
15341, Agia Paraskevi, Attica, Greece ckaraf@gmail.com
kyriakis@inp.demokritos.gr
ABSTRACT developed localization algorithms. The capabilities of the above
We present a small form factor (0.5ππ 3 ) static CZT sensor net- NDD network to localize radioactive sources were investigated
work consisted of a number of Non- Directional Detectors (NDD) using simulated data produced by GEANT4 [4] software via the
capable to localize a stationary radiation source in 3D. The localiza- SWORD (SoftWare for Optimization of Radiation Detectors) pack-
tion is performed with a fusion algorithm based on AI techniques. age [23]. Then a series of verification tests were performed using
The algorithms are based on Multilayer Perseptron Neural Net- experimental data collected by a locally developed data acquisition
work (MLP) and Gradient Boosted Decision Trees (BDTG). They system from the CZT sensor network realized in our lab. The lo-
have been trained using simulated data produced by the SWORD calization algorithms were based on machine learning techniques,
simulation software based on Geant4 framework. The localization such as Neural Networks (MLP) and Boosted Decision Trees (BDT).
efficiency of the algorithms was verified with experimental data
taken in our laboratory using a 137πΆπ source of 180ππΆπ. The local-
ization resolution of the order of 10cm to 15cm has been archived 2 RELATED WORK
in Vertical and Horizontal directions respectively and of the order
The radiation localization problem has been studied extensively in
of less than 20cm in the depth direction within a monitored volume
the last years in the framework of homeland security. Localization
of 5m x 2.8m x 2m .
algorithms evolved from single detector ones to sensor networks
and to mobile sensor networks. The complexity of the problem also
CCS CONCEPTS
evolved from the localization of single radiation source to many
β’ Computer systems organization β Embedded systems; Re- radiation sources and to mobile radiation sources.
dundancy; Robotics; β’ Networks β Network reliability. The single detector algorithms are based on the determination
of a threshold on the count rate of the detector [14]. The threshold
KEYWORDS is unusually defined as a multiple of the estimated background
Neural networks, Boosted Decision Trees, CZT sensors, Radiation, count rate. Although such an algorithm can detect the presence of
Source Localization a radiation source, it lacks the ability to efficiently localize it. This
limitation has been surpassed with the use of radiation sensor net-
1 INTRODUCTION works that have the ability to record the radiation information (e.g.
In the new era of homeland security there is a growing concern counts or spectra) for the same time window. Radiation information
regarding the possession and the potential use of radiological ma- is then fused in order to localize the radiation source. Several fusion
terials by terrorist groups usually in the form of a radiological algorithms have been proposed by various researchers.
dispersion device (RDD), also known as "dirty bomb". Since the de- The Ratio of Square-Distance (RoSD) algorithm [12] uses infor-
fended areas from such a threat may not have specific entrance and mation provided by 3 sensors to estimate the location of the source.
exit points, the problem of how to localize and identify a radioactive The algorithm suffers from the estimation of a second position of the
source in an open area should be investigated. The detection has to radiation source together with the real position, often mentioned
overcome a variety of uncontrollable factors, such as the presence as phantom estimate. The origin of the problem lies in the inability
of benign sources, time and space varying background noise, and of the algorithm to distinguish a strong source far away from the
obstacles that may occlude signal from sources. An overview of sensors from a weaker source located in a shorter distance. A more
the related work in this subject can be seen in section 2. In this elaborate approach that resolves the above ambiguity involves the
work we focus on the localization of stationary radioactive sources deployment of more than 3 sensors. However, the method is still
using a network of small form factor static spectroscopic detectors prone to noisy data in the real world scenario, where it could not
(Non-Directional Detectors - NDD) realized using CZT crystals. localize the source at all.
This network was used as a verification platform for the set of the The Maximum Likelihood Estimation (MLE) algorithm has been
β Both authors contributed equally to this research.
proposed by [5], [3], [10] for the localization of the source and the
estimation of its activity in 2D. The method handles the assessment
of the source parameters as a multidimensional minimization prob-
AINST2020, September 02β04, 2020, Athens, Greece lem, where the function to be minimazed is the error between the
Copyright Β© 2020 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0). recorded and estimated sensor readings. The method can converge
on local minima, which leads to the detection of phantom sources.
A faster algorithm with respect to the MLE has been proposed sensors was recorded for a grid of 3000 different source position
by S. Nageswara et al [20], the Mean-of-Estimator (MoE). The algo- points per layer.For simplicity we simulated source positions in
rithm evaluates the mean of all candidate source estimates. How- planes parallel to the detectors plain, however during the training
ever,it is prone to large source localization errors when phantom phase the events (source position) were randomly picked up from
sources are included in the sample. the above sample.
The complexity of the localization problem increases at the pres-
ence of multiple radiation sources. In such a scenario the number
of the radiation sources is not known and it must be estimated from
the data. This can be done by applying a statistical test which eval-
uates the most probable number of sources prior to the localization
algorithm.
Bayesian algorithms have been proposed in [22], [7], [13], [8]
for the source localization problem. The source parameters i.e. the
activity of the source and its location are estimated using a set of
observables, the sensor readings. To do so the algorithm computes
the posterior probability distribution based on an estimated prior
distribution. However, the prior estimates can not be easily deter-
mined in real world scenarios where the background can not be
modeled as a Poisson distribution due to the presence of obstacles.
Also source localization has been proposed by a Delayed Rejection
Adaptive Metropolis (DRAM) algorithm [19] .
In addition a particle filter approach has been used in [18],
[11],[17] in order to estimate the source location. In this algorithm
a large number of random samples of source activity and location
( called particles ) have been used to estimate the probability dis-
tribution function (ππ·πΉ ). For each particle the expected radiation Figure 1: Simulation setup of the " 5 Sensor Cross topology "
readings of the sensors are estimated and the probability to record a ( S2, S5, S7, S8, S9) in blue. The energy response of the sensors
specific set of measurement is calculated. The accumulation of more has been recorded when a radioactive source i.e.137πΆπ (in
measurements causes the expectation of particles to converge to red) has been placed in various position (in green) at planes
the real source location and activity. Although, this approach works parallel to the sensor plane.
well for single radiation source the complexity of the algorithm
increases exponentially with the number of sources [9].
The approach of using static radiation sensors is good when the
3.2 MVA techniques description
target is the protection of a restricted monitoring area. In contrast, Although the energy spectra, of each sensor is recorded, for the
when the target is the protection of a big city this approach is not same time window Ξπ‘ this work uses only the total recorded counts
sufficient. Thus, mobile sensor networks have been proposed in in each sensor (π ). This is done to increase the sensitivity of the
[16] for detecting people carrying radioactive material and in [24] sensors by taking into account not only the photo-peak informa-
for detecting radioactive sources in urban areas 2019. tion but the scattered radiation as well. The localization of the
However, in this work we focus on an AI approach for the ra- radiation source algorithms have been designed to handle sources
dioactive source localization based on MVA techniques. independent of their activity, by using the sensor with the maxi-
mum response (maximum number of counts) as a normalization
3 NON DIRECTIONAL DETECTORS factor for all the sensors. In general: π β π΄π βππ /π 2 , where A is
related to the source activity and the sensor efficiency, π is the at-
SIMULATION
tenuation coefficient and π is the distance between radiation source
3.1 Geometrical Setup of the Simulation and sensor. It is obvious that without normalization the algorithms
Detailed simulation has been used to study the ability of the NDD could be biased by the source activity. Thus the normalization we
network to localize a radioactive source within a volume of 28π 3 . performed to the maximum recorded counts is mandatory to get rid
A model of 5 CZT spectroscopic sensors in cruciform topology off the dependence of the source activity. The set of the recorded
(" 5 Sensor Cross topology ") having an active volume of 0.5ππ 3 normalized counts by all sensors, is the set of the input variables to
each, has been irradiated by a 137πΆπ source having an activity of the Multivariate Analysis algorithms (MVA) and it defines a single
1ππΆπ for Ξπ‘ = 45π ππ in the absence of NORM background. The event. The TMVA [6] toolkit has been used for the MVA methods
inter-sensor distance in the horizontal axis was set to 2.5π whilst through the ROOT [2] framework.
the vertical inter-sensor distance was set to 1.4π. This setup was The basic steps of our approach are the following:
selected to match with our experimental hall specification. The β’ Normalize Sensor Readings to the sensor with the maximum
source has been placed at various positions (figure 1) i.e. within recording during the same time window.
parallel planes at distances between 40ππ to 200ππ away from the β’ Use MVA techniques to estimate independently the Horizon-
sensor plain in steps of 40ππ. The energy response of the 5 CZT tal (π ), Vertical (π ) and Depth (π ) position of the source by
taking into account the normalized sensor counts.We have Table 1: Neural Network Parameters
chosen three independent models one for each space coordi-
nate and not one model with two or three position outputs Neural Network Parameter Value
since the number of simulated events is not sufficient large
Number of Training Samples 12000
to support this exercise.
Number of Testing Samples 3000
For the second step above the following regression techniques Number of Cycles(Epochs) 1000
have been evaluated: Hidden Nodes 26
β’ Multi Layer Persepton Artificial Neural Network (MLP), Training Method BFGS
β’ Gradient Boosted Decision Trees (BDTG) Activation Function tanh
Convergence 1πΈ β6
Both of the above regression techniques are supported by the TMVA
[6] toolkit.
3.3 MLP method
Neural Networks are used in a variety of tasks such as pattern
recognition, computer vision, speech recognition and regression
problems. They consist of interconnected nodes, called neurons,
which are organized in layers. Signals travel from the first layer
(input), to the last layer ( output ). Their internal layers are known
as hidden layers. In this article the Multi-Layer Percepton Artificial
Neural Network (MLP) realized in the TMVA package has been used
(figure 2). During the learning phase the network was supplied with
ππ‘πππππππ = 12000 training and ππ‘ππ π‘ = 3000 test samples from the
simulated data ( the normalized sensor counts ) where the output
of the network (the radiation source coordinate) is known. The
neuron weights are adjusted by the BFGS [21] algorithm and π‘ππβ
as activation function. The parameters used in MLP can be seen in
Table 1.
Figure 3: The linear correlation matrix of the input vari-
ables for the MLP method.
3.4 Gradient Boosted Decision Trees (BDTG)
method
Decision Trees started to play an important role in discriminating
data in two classes when a set of input variables provides enough
information to separate the data after a series of cuts in the input
Figure 2: Schematic of the neural network with 5 input variables. Usually data provided by simulation are used to train the
nodes(the normalized sensor counts), 1 hidden layer with 26 Decision Tree, where class identification is known a priori. How-
nodes and one output node for the Source Coordinate esti- ever, decision trees suffer from instabilities depending on the data
mation. training set. This problem has already been solved [15] by creat-
ing a forest of trees, where each misclassified event is reweighted
(boosted) in order to be used in the next tree in the forest. A scoring
The linear correlation matrix of the input variables is shown in algorithm that spans through all trees in the forest defines the final
figure 3 where a clear lack of correlation is observed. In figure 4 class decision for the event. A similar approach is used if instead of
the successful convergence test is shown where no overtraining is a classification, we have to deal with a regression problem, where
observed since the test line ( blue dot line ) lies above the training the end leaf defines the achieved value (figure 5). The parameters
line ( red line ). of the Gradient BDT used in our case can be seen in Table 2.
Table 2: Gradient BDT Parameters
BDT Parameter Value
Number of Training Samples 12000
Number of Testing Samples 3000
Number of Trees 2000
Granularity 20
Maximum Depth 4
Boost Type Gradient
Separation Type Regression Variance
Prune Method Cost Complexity
method and BDTG method respectively as a function of the corre-
sponding true horizontal coordinate, (b),(d) the horizontal source po-
sition accuracy from the MLP method and from the BDTG method
respectively. As can be seen the horizontal accuracy is almost flat
with respect to the true source horizontal coordinate except some
small deviation towards the edges of the monitoring volume. It
Figure 4: The MLP convergent test. No overtraining is ob-
is well centered to zero with resolution (the RMS of the accuracy
served since the test line (blue dot line) lies above the train-
distribution) of the order of 10ππ in accordance to our grid segmen-
ing line(red line)..
tation (10ππ) of the source locations used in the training. Figure 7
refers to the "5 Sensor Cross topology" and shows: (a),(c) the vertical
source position accuracy (estimated vertical coordinate minus its
true value) by the MLP method and BDTG method respectively as
a function of the corresponding true vertical coordinate, (b),(d) the
vertical source position accuracy from the MLP method and from
the BDTG method respectively. It can be seen the vertical accuracy
is almost flat with respect to the true source vertical coordinate
except some small deviation towards the edges, it is well centered
around zero with resolution of the order of 9ππ close to our grid
segmentation (5ππ) of the source locations used in the training.
100 dX_Data_MLP
- XTrue ) [cm]
Events
Entries 3000
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600 Mean β 0.1331
(a) 5 Sensors Cross Topology (b) 5 Sensors Std Dev 8.873
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Simulated Data 20 500
Cross Simulated
Calculated
40
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15 Topology Data
(X
0
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β20
10
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β60
Cs-137 MLP 5
100 Cs-137 MLP
Figure 5: Schematic of the Gradient BDT Boost Type for the β80
β100
β250 β200 β150 β100 β50 0 50 100 150 200 250
0 0
β100 β80 β60 β40 β20 0 20 40 60 80 100
Source Coordinate estimation. True Horizontal (X
True
) Source Coordinate [cm] (X
Calculated
- XTrue ) [cm]
100 dX_Data_BDTG
- XTrue ) [cm]
Events
Entries 3000
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30 Mean β 0.48
(c) 5 Sensors Cross Topology 600 Std Dev 9.731
(d) 5 Sensors
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Simulated Data 25
500
4 EVALUATION OF MVA ALGORITHMS Cross Simulated
Calculated
40
20
20
400
Topology Data
(X
After the training of both the MLP and BDTG methods, the produced
0
15
300
β20
weights were evaluated with simulated samples from 137πΆπ source,
β40 10
200
β60
Cs-137 BDTG Cs-137 BDTG
not previously seen in the training phase.
5 100
β80
β100 0 0
β250 β200 β150 β100 β50 0 50 100 150 200 250 β100 β80 β60 β40 β20 0 20 40 60 80 100
True Horizontal (X ) Source Coordinate [cm] (X - XTrue ) [cm]
True Calculated
4.1 Evaluation with 137πΆπ source
Figure 6: Simulated "5 Sensors Cross topology" with a 137πΆπ
An evaluation sample was produced with a 137πΆπ source at a dis-
Source (1ππΆπ) at 1m from sensor plain that radiated for 45π ππ.
tance of 1m away from the sensor plain of the same activity (1ππΆπ)
Horizontal source position accuracy by the MLP method (a)
and for the same radiation exposure time (Ξπ‘ = 45π ππ) as the train-
and by the BDTG method (c) vs the true horizontal source
ing sample, using the SWORD package. This sample was not used
coordinate. Horizontal source position accuracy by the MLP
during the training phase. Figure 6 refers to the "5 Sensor Cross
method (b) and by the BDTG method (d).
topology" and shows: (a),(c) the horizontal source position accuracy
(estimated horizontal coordinate minus its true value) by the MLP
100 20 dY_Data_MLP 5 EXPERIMENTAL SETUP
- YTrue ) [cm]
Events
Entries 3000
80 18 600 Mean β0.3095
(a) 5 Sensors Cross Topology (b) 5 Sensors Std Dev 9.06
60
Simulated Data 16
500
Cross Simulated
5.1 Source Position Platform
Calculated
40 14
20 12 400
Topology Data For the verification of the data fusion algorithms a test- bed was
(Y
0 10
setup using CZT detectors purchased by RITEC[25]. A 3-D step-
300
β20 8
β40 200
motor rail system that positions a radioactive source in predefined
6
β60
Cs-137 MLP 4
100 Cs-137 MLP
position has been developed and installed in the testbed area.(the
β80 2
β100 0 0
β150 β100 β50 0 50 100 150 β100 β80 β60 β40 β20 0 20 40 60 80 100
RMS of the accuracy distribution) The 3-D step motor system is con-
True Vertical (Y ) Source Coordinate [cm] (Y - YTrue ) [cm]
True Calculated
100 20 dY_Data_BDTG
trolled by an Arduino microcontroller [1]. A software GUI written
- YTrue ) [cm]
Events
700 Entries 3000
Mean 0.1316
in java controls and sends the appropriate commands to Arduino
80 18
(c) 5 Sensors Cross Topology 600
Std Dev 9.663
60
Simulated Data 16 (d) 5 Sensors
microcontroller in order to position the radiation source in the
Calculated
40 14 500
Cross Simulated
20 12
400
desired position.
(Y
0 10 Topology Data
300
β20 8
β40 6 200
β60
Cs-137 BDTG
5.2 DAQ System
4
100 Cs-137 BDTG
β80 2
β100 0 0
A locally developed Data Acquisition System (DAQ) has been used
β150 β100 β50 0 50 100 150 β100 β80 β60 β40 β20 0 20 40 60 80 100
True Vertical (Y ) Source Coordinate [cm] (Y - YTrue ) [cm]
True Calculated
to collect the spectra for the various radioactive source positions.
Figure 7: Simulated "5 Sensors Cross topology" with a 137πΆπ The DAQ system consists of two software components.
Source (1ππΆπ) at 1m from sensor plain that radiated for 45π ππ. The main tasks of the client are :
Vertical source position accuracy by the MLP method (a) and β’ to connect to the sensor and control it. To send commands
by the BDTG method (c) vs the true vertical source coordi- to the sensor and receive the responses.
nate. Vertical source position accuracy by the MLP method β’ to accept control connections from the server. Through these
(b) and by the BDTG method (d). connections, it receives commands and sends back the re-
sponses.
β’ to send measurement data to the server.
Figure 8 refers to the "5 Sensor Cross topology" and shows: (a) the The main tasks of the server are:
depth source position accuracy by the MLP method at the source β’ to send commands to the clients.
distance of 1m from the sensor plain and (b) the corresponding β’ to provide feedback during the execution of the commands.
depth source position accuracy by the BDTG method. A small β’ to receive and store measurements from the clients in a
bias at the central value with a resolution of the order of 12ππ database.
was observed less to our grid segmentation (40ππ) of the source β’ to allow retrieval of past measurements for analysis.
locations used in the training
The client follows a layered structure. Each layer communicates
only with the layer above or below it. This layered architecture
achieves low coupling between the client logic and the sensor type.
dZ_Data_MLP dZ_Data_BDTG Adding support for a new type of sensor requires only creating
Entries
Entries
a new sensor manager implementation for the specific sensor. In
Entries 3000 400 Entries 3000
400 (a) 5 Sensors Mean β 3.428
(b) 5 Sensors Mean β 1.975
Cross Std Dev 12.97
350 Cross
Std Dev 13.86
addition the server communicates through the command controller
layer while the sensor communicates through the sensor manager
350 Topology
Topology
300
300 implementation corresponding to its type. The software for the
250
250
Simulated
fusion node utilizes web technologies [26] which make it possible
Simulated
200 Data for the sensors, the fusion node, and the operator to be at different
Data
locations. A session is a series of measurements performed by a
200
150
150
number of sensors over a specific period of time. For each session
100
100 we can define the type of the radiation source (or background), the
Cs-137 BDTG
date and time that the measurement started and the configuration.
Cs-137 MLP
By the term configuration we mean the number of measurements
50 50
0
β100 β80 β60 β40 β20 0 20 40 60 80 100
0
β100 β80 β60 β40 β20 0 20 40 60 80 100
that every sensor will perform and the duration of each one of these
(ZCalculated - ZTrue ) [cm] (ZCalculated - ZTrue ) [cm] measurements. A small paragraph of text can also by recorded for
each session containing further details.
Figure 8: Simulated "5 Sensors Cross topology" with a 137πΆπ
Source (1ππΆπ) at 1m from sensor plain that radiated for 45π ππ 5.3 Sensor Energy Response
(a) the depth source position accuracy from the MLP method In figure 9 an indicative response of the five sensors π2(π‘ππ),
at the source distance of 1m from the sensor plain and (b) π8(ππππ‘πππ), π5(πππ‘π‘ππ), π7(πππβπ‘) and π9(ππ π π‘) is shown after
the corresponding depth source position accuracy from the 3πππ of irradiation with a 180ππΆπ 137πΆπ source and after back-
BDTG method. ground subtraction for a central source position. For each source
position the sensors spectrum was saved every 10π ππ of acquisi-
tion time, resulting in 18 spectrum stamps during the 3πππ of total
acquisition time. The source is located at a distance 120ππ away this information. An easy solution to this problem was to calculate
from the sensor plain inside our test volume. Clear evidence of the above correction (shown in figure 13) and subtract it from the
the presence of the 137πΆπ source is the photo-peak around 662πππ estimated depth coordinated. Another solution is to fine tune the
seen more pronounced by sensors, π9, π8, π7 and π5. model by including real data in the training phase giving in this
way the missing information concerning the signal attenuation due
Events/1.639keV
to scattering in the surrounding material.
60
Source Location: (16, -14, 120) [cm]
50
137
Cs Bare Source
40
dX_Data_MLP
Horizontal Accuracy [cm]
100 5
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18 Entries 112
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80 (a) 5 Sensors Cross Topology 4.5
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Mean
Std Dev 14.51
20
60
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14 Cross
10
40 3.5 Experimental
0
0 200 400 600 800 1000 1200 1400
12 Topology
20 3
Energy [keV]
10 Data
0 2.5
8
β20
Events/1.639keV
Events/1.631keV
Events/1.622keV
20 2
140
14 18
β40 1.5 6
120
12
100
16
β60 4 Cs-137 MLP
10 14
12
Cs-137 MLP 1
8 80 β80 0.5 2
10
6 60 8 β100 0 0
β250 β200 β150 β100 β50 0 50 100 150 200 250 β100 β80 β60 β40 β20 0 20 40 60 80 100
4 40 6
4 TRUE Horizontal Source Coordinate [cm] Horizontal Accuracy [cm]
2 20
2
0 0 0
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(d) 5 Sensors Mean
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Events/1.711keV
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40 40
2.5 14
Topology Experimental
20
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00 200 400 600 800 1000 1200 1400
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Cs-137 BDTG 0.5
4
Cs-137 BDTG
β80 2
β100 0 0
β250 β200 β150 β100 β50 0 50 100 150 200 250 β100 β80 β60 β40 β20 0 20 40 60 80 100
TRUE Horizontal Source Coordinate [cm] Horizontal Accuracy [cm]
Figure 9: The response after 3πππ of exposure at a
180ππΆπ 137πΆπ source of the five sensors π2(π‘ππ), π8(ππππ‘πππ),
Figure 10: Experimental "5 Sensors Cross topology" with a
π5(πππ‘π‘ππ), π7(πππβπ‘) and π9(ππ π π‘) after background subtrac- 137πΆπ Source (180ππΆπ) at 1.2π from sensor plain that radiated
tion. Clear evidence of the presence of the 137πΆπ source is the
for 3πππ. Horizontal source position accuracy by the MLP
photo-peak around 662πππ and the π β πππ¦ peak of 32πππ .
method (a) and by the BDTG method (c) vs the true horizon-
tal source coordinate. Horizontal source position accuracy
The energy spectra received are consisted of two parts: (a) the by the MLP method (b) and by the BDTG method (d).
photo-peak and (b) the continuum part of the spectrum. In the case
of the unshielded sources studied in our case (this can be verified by
the presence of the π β πππ¦ peak around 32πππ seen in the spectra 7 CONCLUSIONS
plot and more pronounced by sensor π8), the continuum part of the The ability of a sensor network consisting of five small form factor
spectrum is mainly due to Compton scattering in the surrounding CZT sensors having a co-planar topology to estimate a radioac-
the detector material. tive source position in 3D has been evaluated using supervised
machine learning techniques on fully simulated data samples. The
6 ALGORITHM VERIFICATION WITH algorithms have been verified by a series of experiments, where
EXPERIMENTAL DATA the CZT sensor network has been irradiated by a 137πΆπ Source of
The weights produced from the simulated data were used to evalu- 180ππΆπ. A localization accuracy within a volume of 5m x 2.8m x 2m
ate the algoritms with experimental data. The source spatial accu- of 10ππ to 15ππ in vertical and horizontal source coordinates re-
racy estimated by the "5 Sensor Cross Topology" system is presented spectively has been achieved after an exposure time of 3πππ while
in figures 10 (Horizontal accuracy), 11 (Vertical accuracy) and 12 the depth is estimated with a resolution of less than 20ππ but with
(Depth accuracy) respectively. The Horizontal and Vertical resolu- a bias in the accuracy mean value that can be easily corrected.
tion (the RMS of the accuracy distribution) is of the order of 10ππ
to 15ππ in accordance to the simulation results but the Depth reso- 8 ACKNOWLEDGMENTS
lution is worse with a pronounced bias in the mean value as can This research has been funded by NATO (SfP-984705) SENERA
be seen in figure 13, where the mean depth accuracy is plotted as a project.
function of the true depth source coordinate. A clear bias of almost
the almost the same level is observed and this is subtracted from REFERENCES
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dY_Data_MLP
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Mean (Z
β60
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5
Cs-137 MLP 50 50
β80
β100 0 0
β150 β100 β50 0 50 100 150 β100 β80 β60 β40 β20 0 20 40 60 80 100
TRUE Vertical Source Coordinate [cm] Vertical Accuracy [cm]
40 40
dY_Data_BDTG
Vertical Accuracy [cm]
100 7
Events
Entries 112
β 4.518
80 (c) 5 Sensors Cross Topology 25
Mean
Std Dev 13.05
6
(d) 5 Sensors 30 30
60
Experimental Data Cross
40 5 20
20
4
Topology Experimental
15
Data p0 53.89 Β± 1.161 p0 52.79 Β± 1.202
0
20 20
3
β20
10
β40 2
β60
Cs-137 BDTG 5 Cs-137 BDTG
β80
1
10 10
40 50 60 70 80 90 100110120 40 50 60 70 80 90 100 110 120
β100 0 0
β150 β100 β50 0 50 100 150 β100 β80 β60 β40 β20 0 20 40 60 80 100
TRUE Vertical Source Coordinate [cm] Vertical Accuracy [cm] ZTrue [cm] ZTrue [cm]
Figure 11: Experimental "5 Sensors Cross topology" with Figure 13: A clear bias of almost the same level is observed in
a 137πΆπ Source (180ππΆπ) at 1.2π from sensor plain that radi- the estimated source depth as a function of the true source
ated for 3πππ. Vertical source position accuracy by the MLP depth for both methods i.e MLP (left) and BDTG (right). This
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source coordinate. Vertical source position accuracy by the depth.
MLP method (b) and by the BDTG method (d).
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Entries
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