Electromagnetic passive localization and tracking of moving targets in a WSN-infrastructured environment

Abstract

In this paper, an innovative strategy for the passive localization of transceiver-free objects is presented. The localization is yielded by processing the received signal strength data measured in an infrastructured environment. The problem is reformulated in terms of an inverse source one, where the probability map of the presence of an equivalent source modeling the moving target is looked for. Toward this end, a customized classification procedure based on a support vector machine is exploited. Selected, but representative, experimental results are reported to assess the feasibility of the proposed approach and to show the potentialities and applicability of this passive and unsupervised technique.

Full text

UNIVERSITY
OF TRENTO
DIPARTIMENTO DI INGEGNERIA E SCIENZA DELL’INFORMAZIONE
38123 Povo – Trento (Italy), Via Sommarive 14
http://www.disi.unitn.it
ELECTROMAGNETIC PASSIVE LOCALIZATION AND TRACKING
OF MOVING TARGETS IN A WSN-INFRASTRUCTURED
ENVIRONMENT
F. Viani, P. Rocca, M. Benedetti, G. Oliveri, and A. Massa
January 2011
Technical Report # DISI-11-100

.

Eletromagneti Passive Loalization and Traking of
Moving Targets in a WSN-Infrastrutured Environment
F. Viani, P. Ro a, M. Benedetti, G. Oliveri, and A. Massa
Department of Information Engineering and Computer Siene,
University of Trento, Via Sommarive 14, 38123 Trento - Italy
Tel. +39 0461 882057, Fax +39 0461 882093
E-mail:
andrea.massaing.unitn.it,
{
federio.viani, paolo.roa, manuel.benedetti, giaomo.oliveri
}
disi.unitn.it
Web-site:
http://www.eledia.ing.unitn.it
1

Eletromagneti Passive Lo alization and Traking of
Moving Targets in a WSN-Infrastrutured Environment
F. Viani, P. Ro a, M. Benedetti, G. Oliveri, and A. Massa
Abstrat
In this paper, an innovative strategy for passive lo alization of transeiver-free
objets is presented. The lo alization is yielded by proessing the reeived signal
strength data measured in an infrastrutured environment. The problem is reformu-
lated in terms of an inverse soure one, where the probability map of the presene of
an equivalent soure mo deling the moving target is looked for. Towards this end, a
ustomized lassiation proedure based on a support vetor mahine is exploited.
Seleted, but representative, experimental results are reported to assess the feasibil-
ity of the proposed approah and to show the potentialities and appliability of this
passive and unsupervised tehnique.
Key words
: Ob jet traking, wireless sensor networks, transeiver-free objets, reeived
signal strength indiator, lassiation problem, support vetor mahine.
2

1Introdution
In the reent years, there has been a wide and rapid diusion of wireless sensor networks
(
W SN
s) [1℄ thanks to the availability of suh low-p ower and pervasive devies integrating
on-board sensing, pro essing, and radio frequeny (
RF
) iruitry for information trans-
mission. Usually, short-range ommuniations are at hand sine the wireless nodes are
generally densely distributed and haraterized by low p ower onsumption to ensure a
long lifetime. Therefore,
W SN
s have been also protably used for lo ation and traking
purposes. In suh a framework, the main eorts have b een devoted to develop ad-ho  sys-
tems based on dediated transponders/sensors [2℄ or assuming an ative target equipped
with a transmitting devie [3℄[4℄. Dierent properties of the reeived signal, suh as the
time of arrival (
T OA
) and the diretion of arrival (
DOA
), have been suessfully exploited
to address the lo alization problem [5℄[6℄. Other modalities to lo ate ative targets are
based on the evaluation of the reeived signal strength (
RSS
) [7℄[8℄[9℄[10℄. This is an
easily measurable quantity that has b een also used to loalize the wireless nodes of the
network through eetive triangulation strategies [8℄. Moreover, the distane between
nodes has been estimated thanks to simplied radio propagation models. Although easier
than a passive loalization tehnique, the main drawbak of these approahes is the need
of the target to be equipp ed with an ad-ho  devie. Whether suh a fat an b e onsid-
ered negligible when traking either ob jets or animals (although the osts unavoidably
inrease), other problems arise when dealing with p eople (e.g., privay) and espeially
with non-ooperative sub jets as for elderly people. Moreover, suh wearable devies an
undergo (asual or voluntary) damages thus limiting the reliability of the traking system.
Other strategies onerned with transeiver-free targets have b een also presented in the
sienti literature. State-of-the-art approahes are based on Doppler radar systems able
to estimate the distane between the target and the sensor [11℄. As a matter of fat,
moving targets an be traked through the analysis of the Doppler signature indued
by the objet motion [12℄. Unfortunately, the arising performane in real environments
an b e strongly inuened by non-negligible instabilities leading to several false alarms.
Furthermore, slow-moving targets [13℄ are not generally deteted.
3

This paper is aimed at presenting an inversion proedure, preliminary validated in [14℄, for
the loalization and traking of passive objets starting from the measurements of the
RSS
indexes available at the nodes of a
W SN
. Sine the transmission of information among
the wireless nodes is allowed by
RF
signals, the arising eletromagneti radiations an be
also protably exploited to sense the surrounding environment. Indeed, any target lying
within the environment interats with the eletromagneti waves radiated by the no des.
Therefore, the measurements of the perturbation eets on the other reeiving nodes
is dealt with a suitable inversion strategy to determine the equivalent soure modeling
the presene of the target/satterer generating the perturbation itself. By virtue of the
fat that the numb er of nodes in a
W SN
an vary and the need to have a simple and
exible traking/loalization method allowing real-time estimates, a learning-by-examples
(
LBE
) strategy based on a Support Vetor Mahine (
SV M
) is used. Although only
reently applied for the solution of eletromagneti inverse problems, eetive approahes
based on learning-by-examples tehniques have b een already proposed for the estimation
of the diretion of arrival of desired/undesired signals [15℄[16℄, the detetion of buried
objets [17℄[18℄[19℄, and the early b east aner imaging [20℄ thanks to their eieny and
versatility.
The outline of the paper is as follows. The mathematial issues onerned with the pro-
posed approah are detailed in Set. 2 where the
SV M
-based method is desribed, as well.
In Set. 3, representative results from a wide set of experiments dealing with the traking
of single as well as multiple targets in both outdo or and indoor
W SN
deployments are
shown. Eventually, some onlusions are drawn (Set. 4).
2Mathematial Formulation
Let us onsider the two-dimensional (
2D
) senario shown in Fig. 1(
a
). The investigation
domain
D
is inhomogeneous and onstituted by a set of obstales and moving targets to
be loalized/traked all lying in free-spae. The known host senario (i.e., the target-free
domain) is desrib ed by the ob jet funtion
τh(r) = εh(r)−1−jσh(r)
ωε0
where
ω
is the
working angular frequeny,
r= (x, y)
is the p osition vetor,
εh
and
σh
being the dieletri
4

permittivity and the ondutivity, resp etively. Moreover, the target/s is/are identied
by the dieletri distribution
τo(r)
,
r∈Do
. The area under test is infrastrutured with
a
W SN
and
S
nodes are deployed at
rs
,
s= 1, ..., S
spatial loations. The
s
-th wireless
node radiates an eletromagneti signal,
ξinc
s(r)(1)
, and the eld measured by the other
S−1
nodes and arising from the interations of the inident eld with the senario under
test is given by
ξtot
s(rm) = ξinc
s(rm) + ZD
J(r′)G0(r′, rm)dr′
(1)
where
G0
is the free-spae Green's funtion [21℄ and
rm
is the position of the
m
-th (
m=
1, ..., S −1
) reeiving node. As a matter of fat, the eld indued in
D
is equivalent to
that radiated in free-spae by an equivalent urrent density
J(r) = τ(r)ξtot (r)
,
r∈D
[22℄ modeling the presene of whatever disontinuity of the free-spae (i.e., b oth the
obstales and the moving targets) where
τ(r) = τo(r)
if
r∈Do
and
τ(r) = τh(r)
if
r∈Dh=D−Do
,
Do
and
Dh
being the support of the targets and its omplementary
area.
Equation (1) an be reformulated in a dierent fashion by dening a dierential equivalent
urrent density
ˆ
J(r)
radiating in the inhomogeneous host medium [21℄ [Fig. 1(
b
)℄. Sine
the host medium is
a-priori
known, the radiated eld an be then expressed as
ξtot
s(rm) = ˆ
ξinc
s(rm) + ZDo
ˆ
J(r′)G1(r′, rm)dr′
(2)
where
ˆ
ξinc
s(rm) = ξinc
s(rm) + ZD
τh(r′)ξtot
s,u (r′)G0(r′, rm)dr′
(3)
is the eld of the senario without targets and equivalent to an inident eld on the
targets,
ˆ
J(r) = ˆτ(r)ξtot
s,p (r)
and
ˆτ(r) = τ(r)−τh(r)
is the dierential objet funtion.
In (3), the seond term on the right side is the eld sattered from the host medium
without targets,
ξtot
s,u
being the eletri eld related to
ξinc
s
in orrespondene with the
(1)
The salar ase has been onsidered to simplify the notation. However, the extension to the
vetorial ase is straightforward.
5

target-free senario. Moreover,
G1
is the inhomogeneous Green's funtion for the target-
free onguration [21℄, whih satises the following integral equation
G1(r, r′) = G0(r, r′) + ZD
τh(r′)G0(r, r”) G1(r”, r′)dr”.
(4)
With the knowledge of
G1
(i.e., the knowledge of the target-free senario) the sattering
problem turns out to b e the retrieval of the dierential soure
ˆ
J
oupying the target
domain
Do
. The detetion of the target position and the denition of the target tra jetory
in
D
an be then formulated as the denition of the support of the dierential equivalent
soure, whih satises the inverse sattering equation (2), starting from the measurements
of
ξtot (rm)
,
m= 1, ..., S −1
. This is possible in a
W SN
-infrastrutured environment sine
the nodes at hand are simple and heap devies that give an indiret estimate of the eld
value through the
RSS
index. Aordingly, the
RSS
is measured at the
m
-th node
when the
s
-th no de is transmitting by onsidering both the target-free senario [
ξinc
s(rm)
knowledge℄ and the presene of targets within
D
[
ξtot
s(rm)
knowledge℄ and the dierential
eld
ξsct
m,s =ξtot
s(rm)−ˆ
ξinc
s(rm)
ould be used for the inversion proedure.
However, it is worth to take into aount that the p ower radiated by the
W SN
nodes an
vary due to several fators (e.g., battery level of the
W N S
nodes, environmental ondi-
tions) thus blurring the data aquisition and, onsequently, ompliating the solution of
the inverse problem at hand. To overome this drawbak, the inversion is statistially re-
ast as the denition of the probability that a target is lo ated in a position of
D
starting
from the knowledge of
ξsct
m,s
,
s= 1, ..., S
,
m= 1, ..., S
,
m6=s
. The arising lassiation
problem is then solved by means of a suitable
SV M
-based approah. Suh a strategy al-
lows one to improve the generalization apability of the loalization and traking system
sine it is less sensitive to the instantaneous variations of the measurements by virtue of
the underlying probabilisti model. Moreover, it is also able to deal with senarios not
onsidered in the training phase as well as to perform the real time traking of multiple
targets. More speially, the proposed approah works as follows. The region
D
where
the targets are lo oked for is partitioned into a grid of
C
ells entered at
rc
,
c= 1, ..., C
.
Eah
c
-th ell is haraterized by its state,
χc
, whih an be either empty (
χc=−1
) or
6

oupied (
χc= 1
) whether a target (i.e., the orresponding dierential equivalent soure)
is present or absent. Moreover, the probability that a target belongs to the
c
-th ell,
αc=P r {χc= 1|(Γ, c)}
, is given by
αc=1
1 + exp npHhϕ(Γ, c)i+qo, c = 1, ..., C
(5)
where
Γ = nξsct
m,s;s= 1, ..., S;m= 1, ..., S;m6=no
, and
p
,
q
are unknown parameters to
be determined [23℄. In (5), the funtion
ϕ(·)
is a non-linear mapping from the data of
the original input spae,
Γ
, to a higher dimensional spae (alled
feature spae
) where the
data are more easily separable through a simpler funtion (i.e., the hyperplane
H
).
The hyperplane
H
is o-line dened throughout the
training phase
by exploiting the
knowledge of a set of
T
known examples where both the input data (
Γ
,
t= 1, ..., T
) and
the orresp onding maps (
χt={χc,t;c= 1, ..., C }
,
t= 1, ..., T
) are available. Usually, a
linear deision funtion is adopted
Hhϕ(Γ, c)i=w·ϕ(Γ, c) + b, c = 1, ..., C
(6)
w
and
b
being an unknown normal vetor and a bias o eient, respetively.The deision
funtion parameters unequivoally dene the deision plane and are omputed in the
training phase by minimizing the following ost funtion
Ψ (w) = kwk2
2+λ
PT
t=1 C(t)
+
T
X
t=1
C(t)
+
X
c=1
η(t)
c++λ
PT
t=1 C(t)
−
T
X
t=1
C(t)
−
X
c=1
η(t)
c−
(7)
subjet to the separability onstraints
w·ϕ(Γ, c) + b≥1−η(t)
c+, c = 1, ..., C
w·ϕ(Γ, c) + b≤η(t)
c−−1, c = 1, ..., C
(8)
where
λ
is a user-dened hyperparameter [24℄ that ontrols the trade-o between the
training error and the model omplexity to avoid overtting. Moreover,
η(t)
c+
and
η(t)
c−
are
the so-alled
slak variables
related to the mislassied patterns. They are introdued
beause the training data are usually not ompletely separable in the feature spae by
7

means of a linear hyperplane.
The minimization of (7) is performed following the guidelines detailed in [17℄ and also
exploiting the so-alled kernel trik method [23℄.
3 Experimental Validation
The feasibility and the eetiveness of the proposed approah have been assessed through
an extensive exp erimental validation arried out in b oth indoor and outdo or senarios
(Fig. 2). The nodes have b een plaed at xed p ositions
rs= (xs, ys)
,
s= 1, ..., S
, on the
perimeter of the investigation area
D
. In all experiments, the region
D
has b een assumed
having the same size (
−20λ≤x≤20λ
and
−12λ≤y≤12λ
) whatever the senario at
hand,
λ
being the free-spae wavelength of the wireless signals transmitted by the nodes
(e.g.,
f= 2.4GHz
), and
S= 6
Tmote Sky nodes have been used to obtained a suitable
trade-o between the omplexity of the sensor network (i.e., the number of sensor nodes)
and the eieny of the system (i.e., the sampling rate) while guaranteeing a omplete
overage of
D
(i.e., eah sensor node is onneted at least to another node of the network in
ase of target-free senario). Although the same topology has been adopted for outdo or
as well as indoor situations, two dierent trainings of the
SV M
-based approah have
been performed sine the arising eletromagneti phenomena signiantly dier (e.g., the
eletromagneti interferenes). Otherwise, the alibration of training examples (
T
), the
separation hyperplane
H
(
λ
), and the disretization of the investigation area (
C
) has been
performed only one, namely for the outdo or ase, sine the format of the data pro essed
by the
SV M
does not hange. More in detail, the following setup has b een onsidered:
T∈[100,700]
with step
∆T= 100
,
λ= 10i
,
i={0,1,2,3}
, and
C∈[15,960]
from a
rough disretization with
C= 5 ×3
ells of dimension
4λ×4λ
to the nest one having
C= 40 ×24
ells of dimension
λ×λ
. These values have been alibrated with referene to
single-target experiments by evaluating the behavior of the loalization error dened as
ρ=rxact
j−xest
j2+yact
j−yest
j2
ρmax
(9)
where
ract
j=xact
j, yact
j
and
rest
j=xest
j, yest
j
are the atual and estimated p ositions of the
8

target,
ρmax
being the maximum admissible loation error. As for the test ase at hand,
it turns out that
ρmax =qX2
D+Y2
D
and
rest
j
has been alulated from the probability
map aording to the following relationships
xest
j=PC
c=1 αcxc
PC
c=1 αc
yest
j=PC
c=1 αcyc
PC
c=1 αc
.
(10)
Figure 3 gives the normalized values of the loation indexes obtained for dierent ombi-
nations of the ontrol parameters. Eah plot refers to the variation of a ontrol parameter
keeping onstant the others (
Topt = 500
,
λopt = 100
,
Copt = 60
).
As far as the
SV M
training phase is onerned, the referene measurements have b een
rst olleted in the target-free senarios [i.e.,
ˆτ(r) = 0 ⇒ξsct
m,s = 0
,
m, s = 1, ..., S
,
m6=s
℄. Suessively, the sets of
RSS
measurements [i.e.,
RSSm,s (t)
,
m, s = 1, ..., S
,
m6=s
,
t= 1, ..., T
℄ have been olleted with the target loated at
T
dierent positions,
rj= (xj, yj)
,
j= 1, .., T
, randomly seleted within
D
to over as uniformly as possible
the whole area under test. Conerning the required omputational time, the burden of
the training phase grows proportionally with the number of training samples and the
disretization of
D
from a minimum of
3×102[s]
when
T= 100
,
C= 15
up to a
maximum of
104[s]
(i.e., almost three hours) when
T= 700
,
C= 960
.
As regards the
SV M
test step, both single (
J= 1
) and multiple (
J= 2
) target trak-
ing problems have been onsidered. Sine o-the-shelf sensor no des are used for these
experiments, they allow to obtain one
RSS
measurement eah
5×10−2[s]
. Therefore,
onsidering the situation where eah no de has to ollet a
RSS
measurement for all other
S−1
nodes, the maximum aquisition time is
2 [s]
. The system is then able to proess
the data and dene a lo alization map
αc
,
c= 1, ..., C
, in
0.1 [s]
using a
3GHz
PC with
2GB
of RAM.
The rst experiment deals with the outdoor traking of a single human being moving inside
D
. Figure 4 shows the probability map estimated when the target is at
ract
1= (−16λ, 8λ)
.
9

The irle gives the atual p osition. Two dierent ases have b een onsidered. More
speially, Figure 4(
a
) shows the probability map assuming that the same exp eriment
has been taken into aount in the training phase. Dierently, the map in Fig. 4(
b
) has
been obtained the example not belonging to the training data set. It is worth noting that
the target is orretly loalized in both maps sine the enter of the target lies within the
region with higher probability. The same exp eriment has been suessively onsidered for
the indo or senario. The results of the
SV M
-based lo alization pro ess are shown in Fig.
5. As for the previous test, the results when the same example has been either onsidered
[Fig. 5(
a
)℄ or not [Fig. 5(
b
)℄ in the training phase have been reported. As expeted, the
values of the loalization errors inrease whatever the training beause of the omplexity
of the eletromagneti interations arising from the presene of the walls (i.e., multiple
reetions) in indoor environments. Nevertheless, the region with high probability still
ontains the atual position of the target thus demonstrating a good degree of reliability
of the approah also in this ase.
Let us now onsider a single target moving outdoor inside
D
along the straight line shown
in Fig. 6. The
RSS
values have been measured at
6
dierent time instants, but it is worth
to point out that the aquisition time an be further shortened to reah an almost real-
time traking. The samples of the loalization maps and the estimated path are reported
in Fig. 7 and Fig. 6, resp etively. As it an b e observed, there is a good mathing
between the atual path and the estimated one assessing the eetiveness of the approah
in real-time proessing, as well. The same analysis has b een arried out for the indoor
ase. Although the moving target is quite arefully loalized, the result in Figure 8 and
the loation indexes in Tab. I onrm the higher omplexity of traking the target as
ompared to the outdoor ase.
In order to deal with the traking of multiple targets, the
SV M
lassier has been trained
with a mixed data-set ontaining examples with one (
T1
examples with
J= 1
) and two
(
T2
examples with
J= 2
) targets. Sine
T=T1+T2
examples have been used also for the
single-target training, some experiments have been arried out to analyze the dep endene
of the loalization on the p erentage of training samples from
T1
and
T2
. The probability
10

maps in Fig. 9 show that the position of one target an be orretly loated although a
smaller set of single-target examples has b een used for the training phase (i.e.,
T1< T2
).
Vie versa, a larger numb er of example is needed for an eetive loalization of the two
targets as pointed out by the maps in Fig. 10 and quantied by the loation indexes
in Tab. II. Suh a behavior was exp eted sine the number of dierent ombinations
with two targets is higher if ompared to the single-target ase. Therefore,
T1= 150
and
T2= 350
examples have b een suessively used for the training phase of the following
traking exp eriments.
As representative examples, two dierent situations with
J= 2
have b een dealt with.
In the former, one target (
j= 1
) is moving within
D
while the other (
j= 2
) remains
immobile in the same position. Instead, both targets are moving in the seond example.
The atual trajetory and the estimated one are shown in Fig. 11 and Fig. 12, respe-
tively. Whatever the example at hand, a quite areful indiation on the position and path
followed by the targets has been obtained as further onrmed by the average values of
the lo alization errors (outdoor:
ρ1= 0.070
,
ρ2= 0.061
- indo or:
ρ1= 0.101
,
ρ2= 0.070
).
4 Conlusions
In this work, the loalization and traking of passive targets have been addressed by ex-
ploiting the
RSS
values available at the nodes of a
W SN
. The problem at hand has
been reformulated into an inverse soure one aimed at reonstruting the supp ort of an
equivalent soure generating a perturbation of the wireless links among the
W SN
nodes
equal to that due to the presene of targets within the monitored area. The inversion
has been faed with a learning-by-examples approah based on a
SV M
lassier devoted
to determine a map of the
a-posteriori
probability that a dierential equivalent soure is
present within the investigation domain. Exp erimental results have assessed the eetive-
ness and reliability of the proposed approah in dealing with the traking of single and
multiple human b eings b oth in indo or and outdo or environments.
11

Referenes
[1℄ C.-Y. Chong and S. P. Kumar, Sensor networks: evolution, opportunities, and hal-
lenges,
Pro. IEEE
, vol. 91, no. 8, pp. 1247-1256, Aug. 2003.
[2℄ Z. Li, W. Dehaene, and G. Gielen, A 3-tier UWB-based indoor loalization system
for ultra-low-power sensor networks
IEEE Trans. Wireless Commun.
, vol. 8 , no. 6,
pp. 2813-2818, Jun. 2009.
[3℄ G. Latsoudas and N. D. Sidiropoulos, A fast and eetive multidimensional saling
approah for node loalization in wireless sensor networks,
IEEE Trans. Geosi.
Remote Sens.
, vol. 55, no. 10, pp. 5121-5127, Ot. 2007.
[4℄ C.-T. Huang, C.-H. Wu, Y.-N. Lee and J.-T. Chen, A novel indoor RSS-based
position loation algorithm using fator graphs,
IEEE Trans. Wireless Commun.
,
vol. 8, no. 6, pp. 3050-3058, Jun. 2009.
[5℄ K. Pahlavan, X. Li, and J. P. Makela, Indoor geoloation siene and tehnology,
IEEE Commun. Mag.
, vol. 40, no. 2, pp. 112-118, Feb. 2002.
[6℄ A. Catovi, and Z. Sahinoglu, The Cramer-Rao bounds of hybrid TOA/RSS and
TDOA/RSS loation estimation shemes,
IEEE Commun. Lett.
, vol. 8, no. 10, pp.
626-628, Ot. 2004.
[7℄ X. Li, RSS-based lo ation estimation with unknown pathloss model,
IEEE Trans.
Wireless Commun.
, vol. 5, no. 12, pp. 3626-3633, De. 2006.
[8℄ X. Li, Collaborative loalization with reeived-signal strength in wireless sensor net-
works,
IEEE Trans. Veh. Tehnol.
, vol. 56, no. 6, pp. 3807-3817, Nov . 2007.
[9℄ F. Cabrera-Mora and J. Xiao, Preproessing tehnique to signal strength data of
wireless sensor network for real-time distane estimation,
2008 IEEE Int. Conf.
Robotis Automation
, Pasadena, CA, USA, May 19-23, 2008, pp. 1537-1542.
12

[10℄ M. Saxena, P. Gupta, B. N. Jain, Experimental analysis of RSSI-based loation
estimation in wireless sensor networks,
2008 IEEE Conf. Commun. System Software
and Midd leware (COMSWARE)
, Bangalore, India, pp. 503-510, Jan. 2008.
[11℄ W. Butler, Design onsiderations for intrusion detetion wide area surveillane
radars for p erimeters and b orders,
2008 IEEE Int. Conf. Teh. Homeland Seurity
,
Waltham, MA, USA, May 12-13, 2008, pp. 47-50.
[12℄ A. S. Bugaev, V. V. Chapurski, S. I. Ivashov, V. V. Razevig, A. P. Sheiko, and I. A.
Vasilyev, Through wall sensing of human breathing and heart beating by monohro-
mati radar,
2004 Int. Conf. Ground Penetrating Radar
, Delft, Netherlands, Jun.
21-24, 2004, vol. 1, pp. 291-294.
[13℄ P. Withington, H. Fluhler, and S. Nag, Enhaning homeland seurity with advaned
UWB sensors,
IEEE Mirow. Mag.
, vol. 4, no. 3, pp. 51- 58, Sept. 2003.
[14℄ F. Viani, L. Lizzi, P. Roa, M. Benedetti, M. Donelli, and A. Massa, Ob jet traking
through RSSI measurements in wireless sensor networks,
Eletron. Lett.
, vol. 44, no.
10, pp. 653-654, 2008.
[15℄ A. H. El Zooghby, C. G. Christo doulou, and M. Georgiopulos, A neural network-
based smart antenna for multiple soure traking,
IEEE Trans. Antennas Propag.
,
vol. 48, no. 5, pp. 768-776, May 2000.
[16℄ M. Donelli, F. Viani, P. Ro a, and A. Massa, An innovative multiresolution ap-
proah for DOA estimation based on a supp ort vetor lassiation,
IEEE Trans.
Antennas Propag.
, vol. 57, no. 8, pp. 2279-2292, Aug. 2009.
[17℄ A. Massa, A. Boni, and M. Donelli, A lassiation approah based on SVM for
eletromagneti subsurfae sensing,
IEEE Trans. Geosi. Remote Sens.
, vol. 43, no.
9, pp. 2084-2093, Sep. 2005.
[18℄ Q. Liu, X. Liao, and L. Carin, Detetion of unexplo ded ordnane via eient semisu-
pervised and ative learning,
IEEE Trans. Geosi. Remote Sens.
, vol. 46, no. 9, pp.
2558-2567, Sep. 2008.
13

[19℄ E. Pasolli, F. Melgani, and M. Donelli, Gaussian proess approah to buried ob jet
size estimation in GPR images,
IEEE Geosi. Remote Sens. Lett.
, vol. 7, no. 1, pp.
141-145, Sep. 2009.
[20℄ F. Viani, P. Meaney, P. Roa, R. Azaro, M. Donelli, G. Oliveri, and A. Massa,
Numerial validation and experimental results of a multiresolution SVMbased
lassiation proedure for breast imaging,
Pro. 2009 IEEE APS Int. Symp.
,
Charleston, SC, USA, June 15, 2009, pp. 1-4.
[21℄ W. C. Chew,
Waves and Fields in Inhomogeneous Media
. New York: Van Nostrand
Reinhold, 1990.
[22℄ A. Ishimaru,
Eletromagneti Wave, Propagation, Radiation and Sattering
. Engle-
wood Clis, NJ: Prentie-Hall, 1991.
[23℄ V.Vapnik,
Statistial Learning Theory
. New York, USA: Wiley, 1998.
[24℄ K. Morik, P. Brokhausen, and T. Joahims, Combining statistial learning with a
knowledge-based approah - A ase study in intensive are monitoring,
1999 Int.
Conf. Mahine Learn. (ICML 1999)
, June 27-30, 1999, Bled, Slovenia, pp. 268-277.
14

(a)
(b)
Fig. 1 -
Equivalent Traking Problem
- Sketh of (
a
) the traking senario and (
b
) the
equivalent inverse problem.
15

XD
YD
x
y
(xc, yc)
(xs, ys)
D
W SN node
(a)
(xs, ys)
(xact
j, yact
j)
W SN node
(b)
Fig. 2 -
Problem Geometry
- Plots of (
a
) the outdoor and (
b
) the indoor environments
with
W SN
-based traking system.
16

2
4
6
8
10
12
14
16
18
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Localization Error, ρ [x102]
Normalized Parameter Value
T/Tmax - [Tmax=700]
λ/λmax - [λmax=1000]
C/Cmax - [Cmax=960]
Fig. 3 -
Calibration
- Loalization error as a funtion of the
SV M
ontrol parameters:
T
(
λ= 100
,
C= 60
),
λ
(
T= 500
,
C= 60
), and
C
(
T= 500
,
λ= 100
).
17

−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(a)
(b)
Fig. 4 -
Single-target loalization - Outdoor Senario
- Probability maps of the
investigation region
D
obtained when the test data (
a
) belongs and (
b
) does not b elong
to the training data set.
18

−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(a)
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(b)
Fig. 5 -
Single-target loalization - Indoor Senario
- Probability maps of the
investigation region
D
obtained when the test data (
a
) belongs and (
b
) does not b elong
to the training data set.
19

-12
-8
-4
0
4
8
12
-20 -16 -12 -8 -4 0 4 8 12 16 20
y/λ
x/λ
Real
Estimated
Fig. 6 -
Single-target traking - Outdoor Senario
- Atual and estimated trajetories.
20

−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(a) (b)
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(c) (d)
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(e) (f)
Fig. 7 -
Single-target traking - Outdoor Senario
- Sreenshots of the probability map
of the investigation region
D
aquired during the target motion
.
21

-12
-8
-4
0
4
8
12
-20 -16 -12 -8 -4 0 4 8 12 16 20
y/λ
x/λ
Real
Estimated
Fig. 8 -
Single-target traking - Indoor Senario
- Atual and estimated trajetories.
22

−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(
a
) (
b
)
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(

) (
d
)
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(
e
) (
f
)
Fig. 9 -
Single-target loalization - Outdoor Senario
(
T1∈[0,500]
,
T2∈[0,500]
,
λ= 100
,
C= 60
) - Probability maps of the investigation region
D
when using (
a
)
100
%
T1
and
0
%
T2
, (
b
)
80
%
T1
and
20
%
T2
, (

)
60
%
T1
and
40
%
T2
, (
d
)
40
%
T1
and
60
%
T2
,
(
e
)
20
%
T1
and
80
%
T2
, and (
f
)
0
%
T1
and
100
%
T2
of samples in the training phase.
23

−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(
a
) (
b
)
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(

) (
d
)
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
−20 20
12
0.0 1.0
−12
x/
λ
y/
λ
Pr
{χ
=+1 |
Γ

}
(
e
) (
f
)
Fig. 10 -
Multiple-targets loalization - Outdoor Senario
(
T1∈[0,500]
,
T2∈[0,500]
,
λ= 100
,
C= 60
) - Probability maps of the investigation region
D
when using (
a
)
100
%
T1
and
0
%
T2
, (
b
)
80
%
T1
and
20
%
T2
, (

)
60
%
T1
and
40
%
T2
, (
d
)
40
%
T1
and
60
%
T2
,
(
e
)
20
%
T1
and
80
%
T2
, and (
f
)
0
%
T1
and
100
%
T2
of samples in the training phase.
24

-12
-8
-4
0
4
8
12
-20 -16 -12 -8 -4 0 4 8 12 16 20
y/λ
x/λ
Target 1 - Real
Target 1 - Estimated
Target 2 - Real
Target 2 - Estimated
Fig. 11 -
Multiple-targets traking - Outdoor Senario
- Atual and estimated
trajetories.
25

-12
-8
-4
0
4
8
12
-20 -16 -12 -8 -4 0 4 8 12 16 20
y/λ
x/λ
Target 1 - Real
Target 1 - Estimated
Target 2 - Real
Target 2 - Estimated
Fig. 12 -
Multiple-targets traking - Outdoor Senario
- Atual and estimated
trajetories.
26

Outdoor I ndoor
T ime I nstant ρ ρ ×ρmax [λ]ρ ρ ×ρmax [λ]
1 0.071 3.32 0.209 9.76
2 0.070 3.30 0.131 6.09
3 0.060 2.78 0.115 5.38
4 0.057 2.67 0.048 2.23
5 0.045 2.09 0.089 4.15
6 0.074 3.46 0.140 6.53
Average Error :ρ0.063 2.94 0.122 5.69
Tab. I -
Single-target traking
- Loalization errors for the outdoor and the indo or
senarios.
27

Sing le T arg et M ultiple T arg et
j= 1 j= 1 j= 2
ρ ρ ×ρmax [λ]ρ ρ ×ρmax [λ]ρ ρ ×ρmax [λ]
(a) 0.044 2.07 0.217 10.12 0.158 7.37
(b) 0.059 2.77 0.196 9.14 0.135 6.31
(c) 0.093 4.34 0.151 7.02 0.074 3.44
(d) 0.150 6.98 0.149 6.96 0.062 2.91
(e) 0.262 12.23 0.063 2.93 0.106 4.94
(f) 0.357 16.67 0.031 1.46 0.063 2.93
Tab. I I -
Multiple-targets loalization - Outdoor Senario
- Loalization errors for the
single and multiple target ase.
28