ARTI: An Adaptive Radio Tomographic Imaging System

15 Pages·2017·1.78 MB·English

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ARTI: An Adaptive Radio Tomographic
Imaging System
Ossi Kaltiokallio, Riku Ja¨ntti Senior Member, IEEE and Neal Patwari Member, IEEE
Abstract—Radio tomographic imaging systems use received multipath waves interact with the environment and the people
signal strength measurements between static wireless sensors within it [2], [6], [7], [8], [4], [9].
to image the changes in the radio propagation environment
There are two widely used approaches to model RSS and
in the area of the sensors, which can be used to localize a
to perform localization: fingerprinting [10], [11], [12], and
person causing the change. To date, spatial models used for
such systems are set a priori and do not change. Imaging and model-based approaches [13], [14], [15], [16]. Fingerprinting
tracking performance suffers because of the mismatch between methods require a database of training data labelled with
the model and the measurements. Collecting labelled training a person’s location, as the person moves to each possible
data requires intensive effort, and the data degrades quickly
location in the area. During runtime, the current set of RSS
as the environment changes. This paper provides a means for
measurements are compared to those in the database to esti-
a radio tomographic imaging system to bootstrap to improve
its spatial models using unlabelled data, iteratively improving mate the current location. Instead of location-labelled training
itself over time. A collection of tracking filters are presented data,model-basedapproachesuseanapriorispatialstatistical
to improve the accuracy of image and coordinate estimates. model for the changes in RSS with respect to the locations
This paper presents an online method to use these estimates
of the sensors and person. Localization is typically performed
to instantaneously update spatial model parameters. Further, a
via imaging [13], [14] or sequential Monte Carlo [16], [17]
smoothing method is presented to fine-tune the model with a
given finite latency. The development efforts are evaluated using methods. With sufficient labelled training data, fingerprinting
simulationsandvalidatedwithreal-worldexperimentsconducted methods are able to achieve high accuracy, although perfor-
in three different environments. With respect to another state- mance degrades exponentially as the environment is altered
of-the-artradiotomographicimagingsystem,theresultssuggest
[12]. Model-based approaches can be deployed quickly, but
thatthepresentedsystemincreasesthemediantrackingaccuracy
the mismatch between the a priori model and the actual RSS
bytwofoldinthemostchallengingenvironmentandbythreefold
when the model parameters are trained using the smoothing changesobservedasafunctionoflocationresultsindegraded
method. performance. The paper focuses on model-based approaches
and we refer to them as RF tomography systems.
In this paper, we present Adaptive Radio Tomographic
I. INTRODUCTION Imaging (ARTI), a model-based approach which bootstraps
In received signal strength (RSS)-based device-free local- to improve its model over time. There is a chicken-and-
ization (DFL) systems, a wireless network is deployed in an egg problem in adapting link RSS models: location estimates
area to be monitored. Each device in the network broadcasts using generic a priori models are variable and inaccurate,
packets and stores the RSS received from the other devices yet finding an accurate model for any particular link requires
in the network. When people are located or move in the accuratelocationestimatesaslabelsforRSSdata.ARTIsolves
environment, they modify the way radio signals propagate, this problem by applying a combination of 1) filtering for
which is observed in the RSS measurements of the sensors in the RF tomographic imaging and tracking estimates, 2) RSS
waysthatcanbeusedtolocateandmonitorthem[1].Since,in modeling, and 3) new online and batch-processing algorithms
this type of system, the only source of information is the RSS toadjustmodelparameters.TheresultisthatARTIovercomes
provided by the radio module of the nodes, the transceivers the need for location-labelled training data and is capable of
are commonly referred to as sensors, and the network as a providing extremely accurate localization.
radiofrequency(RF)sensornetwork[2].Asanexample,such ARTI operates as illustrated in Fig. 1. In short, the system
systems have been exploited for residential monitoring [3], acquires RSS measurements ˜r from S sensors of the wireless
ambientassistedliving[4],andmilitarypurposes[5].Accurate network and weights the measurements in the adaptive mea-
localization is dependent on an accurate model for RSS surement unit. The weighted and mean-removed RSS mea-
measurements. However, the way in which RSS is a function surements y are inputted to the RTI unit to form a discretized
of the locations of people is highly variable, dependent on the propagation field image zi of the monitored area. Thereafter,
environment, the frequency channel, and the way in which ziarefilteredandtheperson’spositionztisestimatedfromthe
filteredimagesxi.AKalmanfilterisusedtotrackevolutionof
Copyright (c) 2015 IEEE. Personal use of this material is permitted. thetarget’sstatext whichisusedbytheonlineestimatorunit
However, permission to use this material for any other purposes must be
torecursivelyestimatethereferenceRSSvalueµandexpected
[email protected].
Ossi Kaltiokallio and Riku Ja¨ntti are with the Department of Communi- directionofRSSchangew.Thesmoothing/batch-trainingunit
cations and Networking, Aalto University, School of Electrical Engineering, calculates smoothed estimates of xi and xt which are then
Espoo,Finland(email:{name.surname}@aalto.fi).
used by a batch-training algorithm to estimate parameters of
Neal Patwari is with University of Utah, Department of Electrical and
ComputerEngineering.email:[email protected] the system.
2
$&,$’, (
% % %
SMOOTHING / BATCH-TRAINING
,"
! !
$&
Online %
RF sensornetwork estimator
#
,"
! !
#"! Adaptive ! !" Image !" Estimate !" Target $!%
measurement RTI
KF position KF
unit
!"#$,%!"#$ #!"$%,&!"$%
Fig. 1: System overview of ARTI
TABLE I: Major notations
amoredetailedspatialmodeltorelatetheRSSmeasurements
toperson’skinematicstate,geometryandelectricalproperties.
Parameter Description
In this paper, we develop an image filter for RTI that is
r˜l,c(k) RSSoflinklonchannelcattimek
used to track evolution of the propagation field. In this way,
µl,c andwl,c ReferenceRSSandweightofmeasurementsystem
yk InputmeasurementvectortoRTIattimek informationhowthepersonalteredthepropagationfieldatthe
zi andzt Imageandlocationmeasurement previoustimeinstantcanbeincludedtothetrackingalgorithm.
k k
xi andxt Estimateofimageandtargetstates Also, smoothing filters are presented so that the entire time
k k
φl,c andλl,c ParametersofRSSmodelforlinklandchannelc horizon can be taken into account when estimating unknown
FandH Transitionandmeasurementmatrix states of the system.
QandV Processandmeasurementnoise
Imaging based approaches typically rely on a Kalman filter
to track evolution of the target state, that is, coordinates and
The rest of the paper is organized as follows. In the velocity of the person [9], [18], [19], [20], [21]. In this paper,
followingsection,therelatedworkisdiscussed.Thereafter,the a Kalman filter is also used to track the image state. This
requiredbackgroundinformationisintroducedandmotivation improves the quality of noisy images, it enables to control the
for the work is presented. In Section IV, the components of delayinimageestimatesandwellknownsmoothingfilterscan
ARTI are presented. In Section V, the conducted experiments be used to enhance the images even further. Imaging systems
are presented, experimental findings are discussed and the that use RSS variance [18], [21], kernel distance methods
systemperformanceisevaluatedusingsimulations.InSection that use short- and long-term RSS histograms [19], [20], and
VI,thedevelopmenteffortsarevalidatedusingdatafromthree channel diversity methods that average the RSS across the set
different environments and thereafter, conclusions are drawn. of used channels [8], [9] all introduce a significant delay in
In Table I, major notations of the paper are summarized. the images because the measurements are based on a window
of RSS samples. Using RTI and the image filter, the system
II. RELATEDWORK canbedesignedsothatthedelayintheimagesissmallerthan
with the aforementioned methods.
RF tomography systems commonly localize the person
using an imaging approach referred to as radio tomographic The used spatial model relates RSS measurements to the
imaging (RTI) [13], [14] or with a Bayesian inference ap- person’s location, geometry and electrical properties and it
proachwhichistypicallysolvedusingsequentialMonteCarlo dictatestheperformanceofRFtomographysystems.RTIuses
methods (SMC) [17], [7]. The benefit of RTI is that it is averysimplisticmodelthatonlyrequiresknowledgeaboutthe
computationally efficient, it provides a global solution and size of the sensitivity region [13]. On the other hand, SMC
the used spatial model only requires information regarding methods typically rely on more detailed empirical models
the size of the elliptic region where the person influences the such as the exponential [17], magnitude [22] or exponential-
RSS, which we call the sensitivity region. As a drawback, the Rayleigh [23] models. Theoretical models have also been
temporal RSS changes are not accounted for in the tracking developed based on diffraction theory [15], [16] and single-
algorithm and information can be lost in the two-step process bounce reflections [24]. If the model parameters are properly
tofirstestimatetheimageandthenthelocation.Thebenefitof tunedandinline-of-sight(LoS)conditions,ithasbeenshown
SMC is that the temporal evolution of the measurements are thatSMCmethodsoutperformRTI[17]andthemoredetailed
directly related to the kinematic state of the person. However, the model is, the higher the tracking accuracy is [24], [23],
SMCiscomputationallymoredemanding,itonlygivesalocal [16].However,manyoftheaforementionedmodelshavebeen
solutionthatcanconvergetoawrongtrajectoryanditrequires derived and validated only in LoS conditions and exploiting
3
them in challenging environments is difficult. The reason The sensors communicate in TDMA fashion and the trans-
being, as the person obstructs the imaginary line connecting missionsequenceisbasedonthesensors’built-inIDnumbers.
the TX-RX pair, which we call the link line, the RSS can One TDMA cycle consists of S transmissions, one from each
increaseorremainunchangedratherthandecrease[8],[4],[9]. sensor. After the cycle, the sensors switch synchronously to
In addition, the sensitivity region is unique for different links the next frequency channel found in a list predefined by the
[9]. These two empirical findings contradict with the models user and a new TDMA cycle is started. The TDMA cycles
presented in literature because they commonly assume: i) a are sequential, and a transmission from each sensor on each
decrease in RSS is observed when the link line is obstructed; channel forms a communication round consisting of S · C
ii) the parameter that tunes size of the sensitivity region is transmissions. After the communication round, the sensors
assumed constant. To overcome this limitation, we extend the switch to the first frequency channel on the list and a new
exponential model in the context of RTI by estimating the communication round is started.
magnitude and direction of RSS change online and use batch-
training to fine-tune parameters of the model. This approach B. Radio Tomographic Imaging
is shown to be extremely effective, enabling high accuracy
The objective of RTI is to estimate changes in the prop-
tracking in very difficult environments.
agation field of the monitored area and to locate the person
In order for RF sensor networks to function, they require
causing the change. This objective is fulfilled by monitoring
accesstocalibrationdata,i.e.,RSSmeasurementsthatarenot
thechangesinRSSandformingadiscretizedpropagationfield
altered by the presence of a person. Typically, measurements
image using a projection matrix.
aregatheredduringavacantperiodandmeanofthecalibration
Themean-removedRSSmeasurementsforlinklonchannel
data is used as the reference RSS value during operation1.
c can be expressed as
However, it is not always possible to collect such calibration
data, and the reference value can also change over time rl,c(k)=r˜l,c(k)−µl,c(k). (1)
[3], [4], [25], [19]. In related literature, an exponentially
where r˜ (k) is the measured RSS and µ (k) the reference
l,c l,c
weighted moving average (EWMA) has been used to update
RSS value. In the discretized RTI model, it is assumed that
the reference value and to make the system adaptive [3], [7],
r (k) is a linear combination of the changes in each voxel
l,c
[19]. The drawback of using EWMA is that if the person
plus noise [14]
remains stationary for a long time period, the EWMA will
N
slowlyconvergetothecurrentvalueandthepersonwillblend (cid:88)
r (k)= [a ·b (k)]+η (k), (2)
in to the noise of the estimated images making localization l,c l,n n,c l,c
n=1
impossible [3], [19]. This issue has been addressed by only
where b is the RSS change in voxel n on channel c, a
updatingthereferenceRSSforlinksthatarefarawayfromthe n,c l,n
the weight of voxel n for link l, N the number of voxels
person [4] or by identifying the links that are not altered by
and η (k) the measurement noise. The weighting how each
theperson[7],[25].Weexpandtheworkin[4]bydeveloping l,c
voxel n impacts the RSS change of each link l is described
a logic that makes the decision about parameter update. If
by a geometrical ellipse model
the conditions are satisfied, the reference RSS is estimated
online using EWMA and only links that are far away from al,n =d−l 1/2·e−∆l,n/λ, (3)
the estimated position are updated. On the other hand, when
the person is close to the link line, the magnitude of RSS where dl = (cid:107)ptlx −prlx(cid:107) is the link length and (cid:107)·(cid:107) denotes
changeisestimatedusingEWMAandbasedonthevalue,the the Euclidean norm, ∆l,n =(cid:107)ptlx−pn(cid:107)+(cid:107)prlx−pn(cid:107)−dl is
used measurement model is updated. excess path length of voxel n with respect to link l and λ is
decay rate of the model defining sensitivity region of the link.
Variousweightingmodelshavebeenproposedintheliterature
III. BACKGROUND and the readers are referred to [26], [27] and the references
A. Preliminaries therein for details about other weighting options.
RTI systems that exploit channel diversity weight the chan-
We consider scenarios where S wireless sensors are de-
nel measurements using
ployed in the monitored area. Each sensor broadcasts and
receivespacketsfromothersensorofthenetwork.Thesensors yl,c(k)=wl,c(k)·rl,c(k), (4)
formLuniquelinksthatareprogrammedtocommunicateover where w (k) is a scalar weight2. When all links of the RF
l,c
C channels. A link is represented with a 2-tuple (l,c) where l
sensornetworkareconsidered,thechangesinthepropagation
is the link and c the channel identifier. The monitored area is
field can be modeled as
discretizedusingagridofN voxels.Thepositionofvoxelnis
denoted as pn =[xn yn]T where xn and yn are coordinates yc(k)=Abc(k)+ηc(k), (5)
of the voxel. Correspondingly, the coordinates of TX and RX where y ∈ RL×1 and η ∈ RL×1 are the weighted
of link l are denoted as ptlx and prlx in corresponding order. measuremcents and noise of tche L links, b ∈ RN×1 is the
c
1The reference value is not always the mean. For example, [7] uses a 2Typically, RTI systems reduce a link’s multi-channel RSS measurements
Gaussian distribution and [19] uses a long-term RSS histogram to describe toascalarvaluebyweightingandaveraging,i.e.,yl(k)= C1 (cid:80)Cc=1wl,c(k)·
thereferenceRSSmeasurements. rl,c(k)[8],[3],[4].
4
4 15
3
] 10
m
[ 2
∆
5
1
]
B
0 d
[ 0
S
8 S
R
B] 4 -5 r (∆),c=17
d l,c
[ 0 g (∆),c=17
S l,c
S -4 -10 rl,c(∆),c=22
R -8 gl,c(∆),c=22
-15
0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1
sample [k] ∆ [m]
(a)RSSvs.time (b)RSSvs.∆
Fig. 2: r (k) and g (k;θ ) as a function of time in (a) and as a function of ∆ in (b)
l,c l,c l,c
radio tomographic image to be estimated, and A ∈ RL×N where θ = (cid:2)φ λ (cid:3) are parameters of the model for
l,c l,c l,c
is the weight matrix where each column represents a single whichφ definesthemagnitudeanddirectionofRSSchange
l,c
voxel of the image and each row the weight of each voxel for when the person is on the link line and λ is a parameter
l,c
that particular link. Estimating the image vector b given y that controls the decay rate with respect to excess path length
c c
isanill-posedinverseproblemandaregularizedleast-squares ∆ (k). As an example, r and g for two different channels
l l,c l,c
estimator is given by [28] of the same link are illustrated as a function of time in
zi(k)=Πy (k), Fig. 2a and as a function of ∆ in Fig. 2b. For channel
c
(6) 17, φ = −4.106 and λ = 0.068 whereas for channel 22,
Π=(cid:0)ATA+γC−1(cid:1)−1AT, φ = 8.147 and λ = 0.035. Since the model parameters
where γ is a regularization parameter which can be tuned differbetweenlinksandchannels,usingfixedvaluesforthem
to emphasize either the prior on the image covariance or limits the achievable accuracy of RF tomography systems.
the measurement. The elements of covariance matrix C are To overcome this limitation, we develop an online estimator
calculated using an exponential spatial decay [28] for φl,c in this paper and update the weigthing in Eq. (4)
correspondingly. Moreover, batch-training is used to fine-tune
{C} =e−(cid:107)pm−pn(cid:107)/δ, (7)
m,n the estimates of φ and λ which can then be used in the
l,c l,c
where δ is the correlation distance, and m and n denote the future.
voxel indexes. Alternative regularization methods are possible
[29] and improved linear estimators can be developed when IV. METHODOLOGY
better noise models are available [21].
From the estimated image zi(k)∈RN×1, a person can be A. Linear State Space Models
localized by finding voxel n with highest intensity Todefinetheproblemoftracking,considerevolutionofthe
state sequence given by
zt(k)=[x y ]T, where n=argmax zi(k). (8)
n n
x =Fx +q , (10)
In this paper, we only consider localizing a single person. k k−1 k−1
Multiple target tracking is not within the scope of this paper,
where x is state of the system at time step k, F the
k
and the readers are referred to [30], [31] and the references
transition matrix describing dynamics of the system and
therein for further details. However, we wish to point out that
q ∼ N (0,Q ) the process noise. The objective of
k−1 k−1
ARTI enhances the accuracy of the images and it would also
tracking it to recursively estimate x from measurements
k
increase the performance of RTI systems that are capable of
localizing more than one person. zk =Hxk+vk, (11)
where H is the measurement model matrix and v ∼
C. Motivation k
N (0,V ) the measurement noise.
In related literature, the mean-removed RSS measurements k
In this paper, we track both the state of the voxels and
are commonly modeled using an exponential model [17]
target. The voxel state is composed of voxel intensity and
gl,c(k;θl,c)=E[rl,c(k)] its derivative. The target state is composed of the person’s
(9)
gl,c(k;θl,c)(cid:44)φl,c·e−∆l(k)/λl,c, location and velocity. Such systems can be modeled using a
5
Algorithm1:ARTIalgorithm
fork=1:K Attimeinstantk
zik=Πyk, whereyk=wc◦[˜rc(k)−µc] Formmeas.andcomputeimageusing(6)
[xi, Pi]=kalmanfilter(xi , Pi , zi) Estimateimagestatewith(17)and (18)
k k k−1 k−1 k
ztk=[xn yn]T, wheren=argmax Hixik Estimatepositionfromfilteredimage
[xt, Pt]=kalmanfilter(xt , Pt , zt) Estimatetargetstatewith(17)and (18)
k k k−1 k−1 k
if(cid:107)ztk−HtFtxtk−1(cid:107)<Tn and(cid:107)[x˙tk y˙kt](cid:107)>Ts Conditionmeas.residualandspeedonthresholds
[φc, µc, wc]=estimator(φc, µc, [xtk ykt]T) UpdatereferenceRSSandweightusedin(1)and(4)
end
end
Algorithm2:[φc, µc, wc]=estimator(φc, µc, pk)
forl=1:L Forlinkl
∆ =(cid:107)ptx−p (cid:107)+(cid:107)prx−p (cid:107)−(cid:107)ptx−prx(cid:107) Computeexcesspathlength
l l k l k l l
if∆l≤2λ, φl,c=αφl,c+(1−α)(r˜l,c(k)−µl,c),end Personisclosetolinkline,updateφl,c
if∆l>2λ, µl,c=αµl,c+(1−α)r˜l,c(k),end Personisfarawayfromlinkline,updateµl,c
wl,c=sgn{φl,c}
end
◦denoteselement-wisevectorproduct,(cid:107)·(cid:107)theEuclideannorm,(·)T thetransposeandsgn{·}thesignfunction
discrete white noise acceleration (DWNA) model where the Thereafter, the state and covariance are updated when mea-
first derivative of the system is perturbed with a zero-mean surement z becomes available using the following recursion
k
white acceleration sequence. The transition matrix, process
S =HP−HT +V
noise and measurement model of a single dimension DWNA k k
K =P−HTS−1
model are [32, Ch. 6] k k k (18)
(cid:20)1 dt(cid:21) (cid:20)1dt3 1dt2(cid:21) (cid:20)1(cid:21)T xk =x−k +Kk(zk−Hx−k)
F = 0 1 Q= 132dt2 2dt H= 0 (12) Pk =P−k −KkSkKTk.
where dt is the sampling interval. The equations to compute covariance Pk and Kalman
The image state can be expressed as gain Kk are independent of the measurements implying that
(cid:20)xi xi ... xi (cid:21) the sequence could be calculated beforehand and that they
xi = 1 2 N , (13) convergetoaconstant,i.e.,P →PandK →K.Thus,the
x˙i x˙i ... x˙i k k
1 2 N N voxels can share the same covariance matrix while having
where xi denotes intensity and x˙i intensity change rate of independent states. This allows us to compute the prediction
j j
voxel j. The transition matrix, measurement model, and noise and update stages using matrix multiplies and additions, and
processes of the imaging system are the inversion in Eq. (18) is calculated only once. This reduces
Fi =F, Qi =qiQ, Hi =H, Vi =vi. (14) the computational overhead notably with respect to a solution
with N independent filters running in parallel.
Respectively, the target state can be expressed as In the experiments, the image filter is initialized using
xt =[xt x˙t yt y˙t]T, (15) the first created image and the change rate is set to zero,
i.e., xi = (cid:2)zi 0N×1(cid:3)T. The covariance is initialized as
where xt and yt denote position and x˙t and y˙t velocity of Pi =1I2×2, w1here I is a unit matrix. Correspondingly, the
1
the target in the Cartesian coordinate system. The transition
target state is initialized using the position estimate of the
matrix, measurement model, and noise processes of the target
first image given by Eq. (8) and velocity is set to zero, i.e.,
system are xt =(cid:2)x 0 y 0(cid:3)T with covariance Pt =I4×4.
(cid:20) F 02×2(cid:21) (cid:20) Q 02×2(cid:21) 1 j j 1
Ft = Qt =qt
02×2 F 02×2 Q C. Online Estimator
(16)
(cid:20) H 01×2(cid:21) (cid:20)vt 0(cid:21) Itiswellknownthatthesteady-statechannelcharacteristics
Ht = Vt = . change in time if the surrounding environment is altered
01×2 H 0 vt
[1], [7], [25]. In long-term deployments and in domestic
environments this is inevitable as doors and windows can
B. Kalman Filter
be opened or closed, daily commodities are consumed and
In case F and H are linear, time-invariant and the noise
moved, and furniture might be relocated or replaced [3], [4],
sequencesq andv Gaussian,theKalmanfilteryieldsthe
k−1 k [12]. Under such conditions, it is mandatory to estimate the
optimal solution to the tracking problem in the least squares
reference RSS µ online. We have also identified that if
sense. The recursion of the filter can be divided into the l,c
φ used in Eq (9) is known for each channel and link,
prediction stage [32, Ch. 5.2] l,c
it significantly improves the system performance. Since the
x−k =Fxk−1 (17) model defined in Eq. (3) only requires knowledge about size
P− =FP FT +Q. of the sensitivity region, we do not need to know the exact
k k−1
6
value of φ , it is sufficient to know the expected direction recursion [34]. The prediction step of the information filter is
l,c
of RSS change when the person obstructs the link line. Thus, given by
we estimate φl,c online and set the weight used in Eq. (4) Kbk =Mbk+1(cid:0)Mbk+1+Q−1(cid:1)−1
as wl,c (cid:44) sgn{φl,c}, where sgn{·} denotes the sign function. m− =FT (cid:0)I−Kb(cid:1)mb (20)
The pseudocode of ARTI is presented in Algorithm 1 and the k k k+1
M− =FT (cid:0)I−Kb(cid:1)Mb F,
online estimator for µl,c and φl,c in Algorithm 2. k k k+1
The logic to update µl,c and φl,c is straightforward. First, whereIistheidentitymatrix.Theinformationvectormb and
we compute the measurement residual (cid:107)ztk−HtFtxtk−1(cid:107) and information matrix Mbk are updated using k
onlyupdatetheparametersifthecurrentpositionmeasurement
mb =m−+HTR−1z
is inline with the kinematic model estimate. Small residual k k k (21)
values indicate that the state estimate can be trusted. Second, Mb =M−+HTR−1H.
k k
the parameters are updated only when the target is moving.
The smoothed state estimate x˜ and covariance P˜ is a
If the person is stationary, the current location estimate can k k
combination of the forward and backward filter outputs
be inaccurate which would lead to incorrect estimates of µ
l,c
and φl,c. In this case, the future location estimates would also G =P M−(cid:0)I+P M−(cid:1)−1
k k k k k
contain this error. If the two conditions hold, µ is updated
l,c P˜ =(cid:0)(P )−1−M−(cid:1)−1 (22)
when the person is far away from the link line (∆l > 2λ). k k k
Otherwise,φ isupdatedtocapturetheexpecteddirectionof x˜ =(I−G )x +P˜ m−,
l,c k k k k k
RSS change when the person is near the link line (∆ ≤2λ).
l wherex andP aretheKalmanfilterestimatesforthemean
In the experiments, the reference RSS is initialized using k k
µ (0) = 1 (cid:80)0 r˜ (k), where r˜ (k) are gathered andcovarianceandm−k andM−k arethepredictedinformation
l,c T+1 k=−T l,c l,c vector and information matrix. As in RTSS, recursion starts
during an initial training period when the monitored area is
fromthelasttimestepK withinitialestimatesx˜ =x and
vacant. In Section VI-D, we discuss the scenario where µl,c P˜ =P . K K
is initialized without a training period. The weight used in K K
In this paper, three different algorithms for smoothing the
Eq. (4) is initialized as w (0)=sgn{φ } and φ =−1e−3.
l,c 0 0 state estimates are considered and they are presented in the
The initial value of φ is selected negative because it is more
0 following. The algorithms output smoothed estimates of the
likely that attenuation is measured when the person obstructs target state x˜t and covariance P˜t.
the link line (see Section V-B and Table III) and a value close k k
1) RTSS-target(RTSS-T): Thestateestimatesofthetracked
to zero is used so that the estimate changes its sign rapidly if
target are smoothed using RTSS. The state space models
φ >0.
l,c are given in Eqs. (15) and (16) and the state estimate and
covariance used in Eq. (19) are x =xt and P =Pt.
k k k k
D. Smoothing Filters 2) RTSS-image and target (RTSS-IT): The estimated im-
ages are smoothed using RTSS. The state space models
Sometimes, it is of interest to estimate states of the system
are given in Eqs. (13) and (14) and the state estimate and
for each time instant k conditioned on all the measurements
covariance used in Eq. (19) are x =xi and P =Pi. After
up to time step K, where K > k. This problem can be k k k k
smoothing the images, new position estimates are calculated
solved with Bayesian smoothing, which in general, improves
from the smoothed images and a Kalman filter is used to
thestateestimatesanddecreasesthecovariance.OneBayesian
track the target state xt and covariance Pt. Thereafter, the
smoother is the discrete-time Kalman smoother, also known k k
target state and covariance are smoothed with RTSS as in the
as the Rauch-Tung-Striebel smoother (RTSS) and it can be
previous algorithm to obtain x˜t and P˜t.
used for computing smoothed estimates of the model given in k k
Eq. (10). The smoothed state estimate x˜ and covariance P˜ 3) TFS-image and target (TFS-IT): The algorithm is the
k k same as presented in Algorithm 1 with three differences.
can be calculated with the following recursion [33, Ch. 8]
First, the recursion runs backward in time starting from time
P− =FP FT +Q sample K. Second, the image Kalman filter is replaced by
k+1 k
G =P FT(P− )−1 the information filter given in Eqs. (20) and (21) and by the
k k k+1 (19) TFSgiveninEq.(22).Theinitialestimatesoftheinformation
x˜ =x +G (x˜ −Fx )
k k k k+1 k filter are mb = 02×N and Mb = 02×2 [34]. Third, the
K K
P˜k =Pk+Gk(P˜k+1−P−k+1)GTk, targetKalmanfilterusesthepositionestimatescalculatedfrom
the smoothed images. At the end of the recursion, the state
wherex andP aretheKalmanfilterestimatesforthemean
k k estimates of the tracked target are smoothed using RTSS to
and covariance, and G is the smoother gain at time step k.
k obtain x˜t and P˜t. This algorithm differs notably from the
ThedifferencebetweentheKalmanfilterandRTSSisthatthe k k
other two since µ and φ are re-estimated in the backward
recursion in the filter moves forward whereas in the smoother l,c l,c
recursion.
backwards.Inthesmoother,recursionstartsfromthelasttime
step K with initial estimates x˜ =x and P˜ =P .
K K K K
E. Training
Anotherpossibilityforsmoothingistouseatwofilterbased
smoother(TFS)inwhichaKalmanfilterisusedintheforward Training parameters of the exponential model requires the
recursion and an information filter is used in the backward mean-removed RSS measurements r (k) and excess path
l,c
7
(a)Openenvironment(Ex.1) (b)Apartmentdeployment(Ex.2and3) (c)Through-wallscenario(Ex.4)
Fig.3:Thethreeexperimentenvironments.Experimentallayoutoftheapartmentandthrough-wallenvironmentsareillustrated
in Fig. 9
TABLE II: Experimental Parameters
length ∆ (k) of the person with respect to link l. Using the
l
smoothed target state estimates x˜t, ∆ (k) with respect to
k l Parameter Value Description
location of the person p =Htx˜t is calculated as
k k p 0.1524 Voxelwidth[m]
γ 500 Regularizationparameter
∆l(k)=(cid:107)ptlx−pk(cid:107)+(cid:107)prlx−pk(cid:107)−(cid:107)ptlx−prlx(cid:107). (23) RTI δ 2 Correlationdistance[m]
(cid:2) (cid:3) λ 0.05 Excesspathlength[m]
Given r (k) and ∆ (k), parameters θ = φ λ of
l,c l l,c l,c l,c R α 0.90 SmoothingfactorofEWMA
O
the exponential model can be estimated by minimizing the MAT Tr 1.0 Residualthreshold[m]
cost function ESTI Tv 0.2 Velocitythreshold[m/s]
qi 1.0 Processnoiseofimagefilter[dB/s2]
K
J(θl,c)=(cid:88)[rl,c(k)−gl,c(k;θl,c)]2, (24) LTERS vqti 02..003 PMroeacse.ssnoniosieseofofimtaarggeetfifiltletrer[d[mB]/s2]
k=1 FI vt 0.5 Meas.noiseoftargetfilter[m]
whereg (k;θ )istheexponentialmodeldefinedinEq.(9).
l,c l,c
In this paper, we use a Nelder-Mead simplex algorithm [35]
to find the minimum of J(θ ). channelsasexplainedinSectionIII-A.Ineachpacket,thesen-
l,c
The trained parameters are used when re-initializing the sors include their ID and the most recent RSS measurements
system.Inotherwords,φ isusedastheinitialestimateinthe of the packets received from other sensors of the network. If
l,c
online estimator, i.e., φ = φ and w (0) = sgn{φ }. On a packet is dropped, the next sensor in the schedule transmits
0 l,c l,c 0
the other hand, λ is substituted with λ in Eq. (3) to update after a backoff time, thus increasing the network’s tolerance
l,c
the weighting for each link, channel and voxel. Thereafter, Π to packet drops. The communication protocol is explained in
is calculated using Eq. (6) and the projection matrix becomes further detail in [4].
unique for each frequency channel. As an example, r and In experiment 1, shown in Fig. 3a, 30 sensors are deployed
l,c
g with the trained model parameters is illustrated in Fig. 2. on the perimeter of an open area (70 m2). The sensors are
l,c
For channel 17, φ = −4.106 and λ = 0.068 and these placed on podiums at a height of one meter. The sensors are
l,c l,c
values are used for this channel and link when re-initializing programmed to communicate on channels 11, 17, 22, and 26
the system. so as to cover the entire span of available frequencies. During
the test, a person walks at constant speed along a rectangular
V. EXPERIMENTS path and the trajectory is covered twice. Markers are placed
inside the monitored area for the test person to follow, while
In this section, the experimental setting and conducted
a metronome is used to set a predefined walking pace. In this
testsareintroduced.Thereafter,empiricalfindingshowmodel
way, each collected RSS measurement can be associated to
parameters φ and λ differ between links and environments is
the true location of the person.
presented. At the end of the section, the presented system is
In experiments 2 and 3, shown in Fig. 3b, 33 sensors are
numerically evaluated using simulations.
deployedinasingle-floor,single-bedroomapartment(58 m2).
Mostofthesensorsareattachedonthewallsoftheapartment,
A. Experiment Description
while a few of them are placed elsewhere, e.g., on the edge
The used wireless sensors are Texas Instruments CC2531 of a marble counter in the kitchen or on the side of the
USB dongles, operating at the maximum transmit power refrigerator. The antennas of the sensors are detached from
(+4.5 dBm) [36]. The IEEE 802.15.4 standard [37] specifies the walls by a few centimeters to enhance the localization
16 channels (c∈[11,...,26]) within the 2.4 GHz ISM band accuracy [3]. In experiment 2, the sensors are programmed
and they are 5 MHz apart, having a 2 MHz bandwidth. The to communicate on channels 15, 20, 25, and 26 in order to
sensorscommunicateinTDMAfashiononmultiplefrequency avoid the interference generated by several coexisting Wi-Fi
8
Open env.
1 1
y y
t t
bili0.8 bili0.8
a a
b b Apartment
o o
pr0.6 pr0.6 Through-wall
e e
ativ0.4 Apartment Through-wall ativ0.4
ul ul
m Open env. m
u u
C0.2 C0.2
0 0
-15 -10 -5 0 5 10 0 0.2 0.4 0.6 0.8 1
φ λ
(a)CDFofφ (b)CDFofλ
Fig. 4: Empirical CDFs of φ and λ in the three environments illustrated with markers and dashed lines. In the figures, fitted
models are illustrated with solid color lines.
TABLE III: Distribution parameters
networks found in the neighboring apartments, which would
increasethefloornoiselevel[38].Inexperiment3,thesensors
µ σ ν a b
φ φ φ λ λ
areprogrammedtocommunicateonall16frequencychannels.
Open -1.5537 3.5885 10.0298 0.0772 0.7951
In both experiments, a person is either standing still at a Apartment -2.2998 4.9506 8.7467 0.0891 0.7076
predefinedlocationorwalksfromonelocationtoanotherwith Through-wall -0.2644 2.1330 3.9600 0.1158 0.6112
constant speed. The trajectory is covered once.
Experiment 4 differs from the other experiments since it
is a through-wall experiment as shown in Fig. 3c. In the parameterbλ.Theempiricalandfitteddistributionsareshown
experiment, 33 sensors are deployed around a lounge room, in Fig. 4 and distribution parameters are given in Table III.
outsidethewallsoftheroom,coveringanareaof86 m2.The The results are inline with our understanding how the
sensors are set on podiums at a height of one meter and they signal strength behaves in various environments. In open
areprogrammedtocommunicateonall16frequencychannels. environments and when the distance between the transceivers
In the experiment, a person walks along a predefined path at is small, it is expected that the RSS measurements attenuate
constant speed. The path is covered six times. as the person obstructs the LoS. In the open and apartment
Onaverage,thetimeintervalbetweentwoconsecutivetrans- environments, µφ is much smaller than it is in the through-
missions is dt =t −t =2.9 ms. If S =30 and C =4 wall experiment. This indicates that it is much more likely
k k k−1
as in Ex. 1, one TDMA cycle lasts dt = 30·dt = 87 ms that attenuation will be measured in the open and apartment
c k
and one communication round dt = 4·dt = 348 ms. The environments when the person is in between the transceivers.
r c
image and target filters use dt = dt . Parameters used in the In addition, it is more likely in these environments that the
c
experiments are given in Table II. person has a larger effect on the link and therefore, σφ is
larger. In the through-wall environment, it is likely that a link
isnotaffectedbythepersonorthatthechangeinRSSissmall
B. Experimental Findings
whenthepersonisclosetothelinklineyieldingasmallshape
Togetan understanding howparametersφ and λ oftheex- parameter σφ. To note, the sensor distances are on average
ponentialmodeldefinedinEq.(9)varybetweendifferentlinks smaller in the apartment experiment (d¯=4.43 m) than in the
andenvironments,g (k;θ )isfittedtor (k)usingknown openenvironment(d¯=6.28 m)andtherearemanylinksthat
l,c l,c l,c
location of the person. Links that were not intersected by the have LoS communication. Thus, it is understandable why µφ
personduringtheexperimentareomittedfromtheevaluation. is smaller and σφ is larger in the apartment environment.
Thereafter,well-knownprobabilitydistributionarefittedtothe Size of the spatial region where the person influences the
empirical distributions to find the best match. The empirical RSS is defined by λ. In the open environment, multipath
distribution of φ closely follows a non-standardized Student’s propagation is not as severe as in the other two environments
t-distribution φ ∼ T(µ ,σ ,ν ) with location parameter µ , andthepersonmainlyeffectstheLoSsignal.Thus,λissmall
φ φ φ φ
scale parameter σ and shape parameter ν . Correspondingly, and it does not vary much between the different links. In
φ φ
the empirical distribution of λ closely follows a Weibull cluttered environments, multipath propagation is common and
distributionλ∼W(a ,b )withscaleparametera andshape the person can also alter the RSS by affecting the multipath
λ λ λ
9
TABLE IV: Median (and 95th percentile) localization errors in centimeters
Ex.1 Ex.2 Ex.3 Ex.4
CDRTI 31.99(100.19) 18.79(56.84) 15.74(69.83) 181.15(628.35)
E
LIN ARTIw/oonlineest. 31.26(128.92) 18.47(64.42) 17.59(68.05) 200.59(488.49)
N
O ARTI 19.82(47.75) 10.30(25.40) 10.41(27.52) 72.91(378.49)
CDRTI,RTSS-T 22.94(66.13) 15.79(45.72) 14.78(62.93) 151.62(463.70)
D
HE ARTI,RTSS-T 14.33(36.10) 8.07(19.30) 6.96(18.67) 66.02(256.74)
OOT ARTI,RTSS-IT 10.09(31.64) 8.40(19.26) 6.81(16.06) 27.69(279.62)
M
S ARTI,TFS-IT 7.81(25.62) 7.82(17.30) 6.14(13.18) 13.93(38.75)
componentsimpingingonthereceiverantenna.Thisincreases
50
size of the spatial region where the person influences the link
and therefore, λ is larger and deviates more in the apartment 40
and through-wall environments.
] 30
%
[
w 20 Ex.1,open
ǫ
Ex.2,apt. (C=4)
C. Numerical Evaluation
10 Ex.3,apt. (C=16)
In this subsection, the presented system is numerically Ex.4,through-wall
0
evaluated using the same sensor positions and trajectories as 100 101 102 103
in the experiments. In the simulations, the RSS measurements Sample [k]
are generated using the exponential model given in Eq. (9)
Fig. 5: Error of estimating w .
and the measurements are corrupted by i.i.d. Gaussian noise, l,c
i.e., η (k) ∼ N(0,σ2) where σ = 2. Parameters of the
l,c η η
exponential model are drawn from φ ∼ T(µ ,σ ,ν ) and
φ φ φ
where w˜ = sgn{φ } and φ ∼ T(µ ,σ ,ν ). Now, the
λ ∼ W(a ,b ) using the distribution parameters given in m m m φ φ φ
λ λ percentage error of wˆ can be calculated using
TableIIIandtheyareassumedi.i.d.foreachlinkandchannel.
Since no temporal statistical model is known for the changes M (cid:40)
inRSSovertimeduetochangesintheenvironmentotherthan (cid:15)w = 10M0% · (cid:88) 1m, 1m = 01 oifthw˜emrw(cid:54)=isewˆm (25)
people,thereferenceRSSvalueisassumedtobeconstantand m=1
known (µl,c = −45 dB) and it is not updated by Algorithm and it is illustrated in Fig. 5 as a function of time for the
2 during simulations. The presented system is evaluated with differentexperiments.Intheopenandapartmentexperiments,
respect to channel diversity RTI (CDRTI) which averages the the initial estimates is incorrect for approximately 33% of
measurements across the entire set of used channels, i.e., the links whereas in the through-wall experiment for 45%
yl(k)=−C1 (cid:80)Cc=1r˜l,c(k)−µl,c(k). indicating that the through-wall environment is significantly
The simulation results are given in Table IV where the more challenging than the others. The figure also reveals
median and 95th percentile localization errors are reported in that higher sampling rate of the channel increases the con-
centimeters for the different experiments. On average, CDRTI vergence rate of wˆ which is visible by comparing (cid:15) of
w
achieves comparative accuracy as the presented system w/o the apartment experiments. The sampling rate is four times
online estimation. This is understandable, since the Kalman higher in Ex. 2 w.r.t. Ex. 3. In the experiments, the average
filter used for enhancing the images essentially acts as a low- numberofsamplestheonlineestimatorhastoestimatew is
l,c
(cid:2) (cid:3)
pass filter, i.e., averaging the RSS measurements on the dif- 14.03 17.76 5.49 10.95 for Ex. 1−4 in corresponding
ferent channels (CDRTI) is equivalent to forming the images order. Thus, using channel diversity is a tradeoff between
individually for each channel and then averaging the images sampling rate and available information. A large number of
together.Inthisrespect,processnoisevalueoftheimagefilter channels is beneficial for localization purposes because the
qi can be viewed as a smoothing parameter. Using a small probability increases that at least one of the channels follows
value (qi (cid:28) 1) corresponds to averaging a large number of themodel.However,thecostofdoingsoisthelowersampling
successive images together whereas for large values (qi >1), rate for each channel which inevitably effects performance of
only the most recent images are taken into account. the online estimator.
With online training enabled, ARTI outperforms CDRTI in Accuracyofthedifferentsmoothingfiltersarealsogivenin
every experiment because w is recursively estimated. For Table IV. In general, smoothing increases the accuracy of the
l,c
CDRTI,anincreaseinRSSisanindicationthatapersonisnot state estimates because the entire time horizon is taken into
in between the transceivers which is incorrect if φ >0. For account. RTSS-T improves the localization accuracy mainly
l,c
ARTI, the same increase can be informative and indicate the because the effect of outliers is reduced and lag induced by
person’s location correctly if w ≡ sgn{φ }. Let us group the target tracking Kalman filter is compensated for. RTSS-
l,c l,c
w of links that were intersected during the experiment into IT decreases the error even more because the images, from
l,c
a column vector wˆ of size M×1, where M is the number of which the positions are estimated, are enhanced. In addition,
crossed links. For these links, we define the true weight as w˜, RTSS-IT removes lag of the image filter which is significant
10
d
ure
Meas
d
Filtere
d
he
ot
mo
S
k=91 k=92 k=93 k=94
Fig. 6: The measured zi, filtered xi and smoothed x˜i propagation field images in Ex. 1. In the figures, the true position of
k k k
the person is illustrated with a circle and the position estimate zt using a cross
k
if the person is moving. Removing delay of the image filter fade level RTI (FLRTI). FLRTI weights the different chan-
is clearly visible in the open and through-wall experiments nels based on their fade level and averages the measure-
where the person is continuously in motion. TFS-IT results ments across the entire set of used channels, i.e., y (k) =
l
to the best accuracy. The algorithm not only removes the −1 (cid:80)C wˆ (r˜ (k)−µ (k)),wherewˆ isthefadelevel
C c=1 l,c l,c l,c l,c
lag in image and position estimates, but it also improves the based weight [4].
estimates of w and µ in the backward recursion yielding In Ex. 3−4, qi = 0.1 because in these experiments the
l,c l,c
better measurements y from which the images are created. number of used channels is four times greater than in Ex.
k
This is especially important in challenging environments and 1−2. Using a lower qi value implies that the confidence in
when the experiment duration is relatively short as is the case the model is increased and reactiveness to new measurements
in the through-wall experiment. isdecreasedwhichisdesirablewhenall16frequencychannels
It can be concluded that in ideal environments (φ (cid:28)0), are used.
l,c
channel diversity, the presented image filter and adaptive
estimatordonotimprovethesystemperformancesignificantly.
A. Quantitative evaluation
The real benefits start to be visible as µ → 0 and there are
φ
The presented system comprises of three significant ad-
linksforwhichφ >0.Inclutteredandchallengingenviron-
l,c
vancementstoincreasetheaccuracyandperformanceofstate-
ments,suchasthethrough-wallexperiment,theimportanceof
of-the-art RTI systems. First, the images are filtered using a
channeldiversityincreasesandthesystemperformancecanbe
Kalmanfilter.Thisisbeneficialbecausenowthepreviousstate
significantly improved by using the presented image filter and
of the propagation field xi is taken into account. In past
online estimator. Furthermore, the state estimates can always k−1
works,itisnotconsideredhowthepersonalteredthepropaga-
be improved using the presented smoothing filters.
tionfieldattheprevioustimeinstantandvaluableinformation
islost.Thesecondbenefitoftheimagefilteristhattheimages
VI. EXPERIMENTALVALIDATION canbeenhancedusingwellknownsmoothingfilters.Thethird
In this section, the development efforts are first quan- advantage is that the system can be designed so that the delay
titatively evaluated after which performance of the system in xi is significantly lower than in systems that combine the
k
is presented. Thereafter, model parameters φ and λ for RSS measurements on different channels by weighting and
l,c l,c
the different links and channels are estimated using data averaging [4], [8]. Averaging the channel measurements over
from the experiments. After the model parameters are es- the set of used channels inevitably introduces a delay in zi
k
timated using batch-training, the system performance is re- which also effects zt. Length of this delay is determined by
k
evaluated. In this section, ARTI is evaluated with respect to parameters of the system such as transmission interval of the