IEEE TRANSACTIONS ON MOBILE COMPUTING 1 Robust ... - Utah …npatwari/pubs/robust_RTI_accepted.pdf · IEEE TRANSACTIONS ON MOBILE COMPUTING 1 Robust Estimators for Variance-Based

IEEE TRANSACTIONS ON MOBILE COMPUTING 1

Robust Estimators for Variance-BasedDevice-Free Localization and Tracking

Yang Zhao and Neal Patwari

F

Abstract—Device-free localization systems, such as variance-basedradio tomographic imaging (VRTI), use received signal strength (RSS)variations caused by human motion in a static wireless network to locateand track people in the area of the network, even through walls. How-ever, intrinsic motion, such as branches moving in the wind or rotatingor vibrating machinery, also causes RSS variations which degrade theperformance of a localization system. In this paper, we propose a newestimator, least squares variance-based radio tomography (LSVRT),which reduces the impact of the variations caused by intrinsic motion.We compare the novel method to subspace variance-based radio to-mography (SubVRT) and VRTI. SubVRT also reduces intrinsic noisecompared to VRTI, but LSVRT achieves better localization accuracy anddoes not require manually tuning additional parameters compared toVRTI. We also propose and test an online calibration method so thatLSVRT and SubVRT do not require “empty-area” calibration and thuscan be used in emergency situations. Experimental results from five datasets collected during three experimental deployments show that bothestimators, using online calibration, can reduce localization root meansquared error by more than 40% compared to VRTI. In addition, theKalman filter tracking results from both estimators have 97th percentileerror of 1.3 m, a 60% reduction compared to VRTI.

Index Terms—Wireless sensor networks, sensing, statistical signalprocessing

1 INTRODUCTION

Device-free localization (DFL) using radio frequency(RF) sensor networks is the use of channel measurementsbetween static radio transceivers deployed around anarea of interest to locate people and objects movingwithin it. DFL has particular application in securityand emergency applications, e.g., detecting intruders inindustrial facilities, and helping police and firefighterstrack people inside a building during an emergency[1]. In these scenarios, the people being located cannotbe expected to participate in the localization system bycarrying radio devices, thus standard radio localizationtechniques [2] are not useful.

Various RF measurements including ultra-wideband(UWB) and received signal strength (RSS) have beenproposed and applied to detect, locate and track ob-jects and people who do not carry radio devices inan environment [3], [4], [5], [6], [7], [8]. Compared

Y. Zhao is with General Electric Global Research Center, Niskayuna, NY; andN. Patwari is with the Department of Electrical and Computer Engineering,University of Utah, Salt Lake City, UT. This material is based upon worksupported by the National Science Foundation under Grant Nos. #0748206and #1035565. E-mails: [email protected] and [email protected].

to cameras and infrared sensing methods, RF sensorshave the advantage of penetrating non-metal walls andsmoke [1]. While UWB measurements are expensive, RSSmeasurements are inexpensive and available in standardwireless devices and have been used in different device-free localization studies with surprising accuracy [6], [9],[8]. These RSS-based localization methods essentially usea windowed variance of RSS measured on static links.For example, [8] deploys an RF sensor network arounda residential house and uses sample variance during ashort window to track people walking inside the house;[9] places RF sensors on the ceiling of a room, andtrack people using the received signal strength indicator(RSSI) dynamic, which is essentially the variance ofRSS measurements, with and without people movinginside the room. In this paper we focus on using RSSmeasurements to locate and track human motion. We usewindowed variance to describe the various functions ofRSS measurements recently used in different localizationand tracking studies [6], [9], [8], and we call themmethods for variance-based device-free localization.

This paper introduces and studies methods to makevariance-based DFL more robust to noise. For variance-based localization and tracking, variance can be causedby two types of motion: extrinsic motion and intrinsicmotion. Extrinsic motion is defined as the motion ofpeople and other objects that enter and leave the en-vironment. Intrinsic motion is defined as the motionof objects that are intrinsic parts of the environment,objects which cannot be removed without fundamentallyaltering the environment. If a significant amount ofwindowed variance is caused by intrinsic motion, then itmay be difficult to detect extrinsic motion. For example,rotating fans, leaves and branches swaying in wind,and moving or rotating machines in a factory all mayimpact the RSS measured on static links. Also, if RFsensors are vibrating or swaying in the wind, their RSSmeasurements change as a result. Even if the receivermoves by only a fraction of its wavelength, the RSSmay vary by several orders of magnitude as a resultof small-scale fading [10], [11]. We call variance causedby intrinsic motion and extrinsic motion, the intrinsicsignal and extrinsic signal, respectively. We consider theintrinsic signal to be “noise” because it does not relate toextrinsic motion which we wish to detect and track. One


example of intrinsic signal is shown in Figure 1, in whichthe RSS measurements are recorded during an “empty-area” offline calibration period, when tree branches andleaves sway strongly in wind [12]. Considering there isno human motion in the network, that is, no extrinsicmotion during the calibration, the high variations of RSSmeasurements are caused by intrinsic motion, in thiscase, wind-induced motion. To be practical, variance-based localization methods must identify and reduce theintrinsic signal.

0 20 40 60 80 100 120 140 160Sample index

90

85

80

75

70

65

60

55

50

45

RSS

(dB)

link1link2link3

Fig. 1: Intrinsic signal measurements: RSS measurementsfrom three links during an offline calibration period(when no people are present in the environment) ofone experiment, in which we observe significant wind-induced intrinsic motion.

In this paper, we propose and compare two estimatorsthat reduce the effect of intrinsic motion and improvethe robustness of VRTI [8] under noisy conditions. Thefirst estimator uses the subspace decomposition method,which has been used in spectral estimation, sensor arrayprocessing, and network anomaly detection [13], [14],[15], [16]. We apply this method to VRTI, which leadsto subspace variance-based radio tomography (SubVRT).SubVRT was introduced in [12], and is explored andtested in greater depth in this paper, and compared to asecond estimator which is first presented here.

The major contribution of this paper is to proposeand test a new robust estimator – least squares variance-based radio tomography (LSVRT). While both SubVRTand LSVRT are significantly more robust to intrinsic mo-tion than VRTI, one advantage of LSVRT over SubVRT isthat it does not require manual tuning of any additionalparameters compared to VRTI. In contrast, SubVRT hasa parameter k that must be manually set. Further, ex-perimental results show that LSVRT has consistentlybetter performance than SubVRT across all experimentsconducted for this paper.

Another contribution of this paper is the testing ofan online calibration procedure for SubVRT and LSVRT.An “empty-area” calibration (offline calibration) usingmeasurements recorded during a period without peoplein the network is effective for statistical characterization

of the intrinsic signal [12]. However, knowing when thearea is empty may not be possible in emergency situa-tions. To enable SubVRT and LSVRT in those situations,we propose an online calibration method in which RSSmeasurements are collected for statistical characteriza-tion of the intrinsic signal when the maximum pixelintensity of a radio tomographic image is low.

This paper presents new quantitative comparisons ofthe new methods with VRTI. Localization results fromfive data sets, collected during three experiments, showthat both estimators using online calibration can reducethe root mean squared error (RMSE) of the location esti-mate by more than 40% compared to VRTI. The LSVRTmethod proposed in this paper consistently outperformsSubVRT in localization accuracy across all experiments.A new experiment presented here shows that as the levelof intrinsic noise increases, the ability of both SubVRTand LSVRT to reduce the level of noise increases aswell. Further, we use the Kalman filter to track peopleusing localization estimates from SubVRT and LSVRT.The results show that tracking errors from SubVRT havea 97th percentile error of 1.4 m, a 65% improvementcompared to VRTI, while the 97th percentile error fromLSVRT is less than 1.2 m, a 70% improvement.

To summarize, in this paper we 1) introduce a new es-timator, least-squares variance-based radio tomography(LSVRT); 2) introduce a new online calibration methodwhich does require the user to know when the areaof interest is empty, 3) compare and evaluate SubVRTand LSVRT estimators by using data sets collected innew and past experiments in different environmentalconditions; and 4) quantify tracking improvements usinga Kalman filter in combination with SubVRT and LSVRT.

The rest of this paper is organized as follows: Sec-tion 2 formulates the subspace decomposition and leastsquares methods, and proposes an online calibrationmethod. Section 3 describes five data sets collected inthree experiments including new experiments first re-ported in this paper, Section 4 shows the experimentalresults, and Section 5 investigates the Kalman filtertracking. Related work is presented in Section 6, and theconclusion is given in Section 7.

2 METHODS

In this section, we describe variance-based radio tomo-graphic imaging (VRTI), a through-wall imaging methodintroduced in [8], which serves as a baseline for com-parison for our new methods. Then we extend theVRTI method by introducing the SubVRT and LSVRTestimators, and compare the two.

2.1 Problem statement

We assume an RF sensor network with N sensors (ra-dio transceivers) is deployed in an area of interest.We use zs,j to denote the coordinate of sensor j forj ∈ {1, . . . , N}. The deployment area has both extrinsic


motion and intrinsic motion, as defined in the Introduc-tion. The goal of all of the methods in this paper is toestimate an image of the presence of extrinsic motion.We discretize space into P pixels of a physical space anddefine x = [x1, . . . , xP ]T , where xi = 1 if extrinsic motionoccurs in pixel i, and xi = 0 otherwise. We denote thecenter coordinate of pixel i as zi.

To enable motion image estimation, each sensor mea-sures the RSS of packets received from many othersensors. We use sl,t to denote the RSS measured at nodeil sent by node jl at time t ∈ Z, where il and jl are thereceiver and transmitter number for link l, respectively.We assume L directional links measure RSS, where ingeneral, L ≤ N(N −1) since not all pairs of sensors maybe connected.

We denote the windowed RSS variance as:

yl,t =1

m− 1

m−1∑i=0

(sl,t − sl,t−i)2 (1)

where m is the length of the window, and sl,t =1m

∑m−1i=0 sl,t−i is the sample average in this window

period. We let y(t) = [y1,t, . . . , yL,t]T be the vector of

windowed RSS variance from all L links at time t. If wedo not need to represent time, we simplify the notationto y = [y1, . . . , yL]T .

We further use yc to denote the measurements col-lected during the calibration period, when no people arepresent in the environment; and we use yr to denote themeasurements from the real-time operation period.

We note two things. Transmit power does not affectyl,t because sl,t and sl,t−i in (1) are equally affectedby any change in transmit power. However, transmitpower must be high enough so that a receiver canreliably estimate RSS, that is, packets are received evenwhen a person obstructs the link. Next, we assume anychanges in transmit power are slow such that it can beconsidered constant within m samples so that the short-term changes in sl,t are due to the channel, not to thetransmitter.

2.2 Baseline Method: VRTIWork in [8] has shown the efficacy of a linear model thatrelates the motion image x to the RSS variance yr:

yr = Wx + n (2)

where n is an L-length noise vector including intrinsicmotion and measurement noise, and W is an L × Pmatrix quantifying how much of motion in each pixelimpacts each link measurement. The weighting of pixelp on link l is formulated as [8]:

Wl,p =1√dil,jl

{φ if dil,p + djl,p < dil,jl + dw

0 otherwise(3)

where dil,jl is the Euclidean distance between two sen-sors il, jl on link l located at zs,il and zs,jl ; djl,p is theEuclidean distance between sensor jl and zp, the center

coordinate of pixel p; dil,p is the Euclidean distancebetween sensor il and pixel p; dw is a tunable parametercontrolling the ellipse width, and φ is a constant scalingfactor. Essentially, column p of the W matrix describes amodel for how link variances are affected by a movingperson’s presence in pixel p.

VRTI is the method proposed in [8] to estimate imagex from the link measurements yr. Regularization is nec-essary for this ill-posed inverse problem, and Tikhonovregularization is used [8], which results in the imageestimator,

x = Π1yr

Π1 = (WTW + αQTQ)−1WT (4)

where α is a regularization parameter, and Q is theTikhonov matrix, which is calculated by using the dif-ference operations in both the vertical and horizontaldirections of an image, as discussed in [8]. One benefitof (4) is that Π1 does not need to be recomputed as longas the sensors are stationary.

The vector x has in element i the estimated motionin pixel i. Pixel i is centered at coordinate zi, and wedisplay an arbitrary motion image by plotting xi atcoordinate zi for each pixel i = 1, . . . , P .

The calculation of the projection matrix in (4) requiresthe inverse of a P×P matrix, which has complexity orderP 3. However, this is calculated once, and the real-timeestimation of x requires only one matrix multiply, whichuses at most LP operations.

2.3 Subspace decomposition methodThe subspace decomposition method has been widelyused in spectral estimation, sensor array processing, etc.[13], [16] to improve estimation performance in noise.It is closely related to principal component analysis(PCA), which is widely used in finding patterns in highdimensional data [17]. Essentially, it divides the space ofthe measurements into two orthogonal subspaces, onewe believe is very noisy and one that is not, and onlyuse the portion of the measurement which is containedin the latter subspace.

To find this subspace decomposition, we first estimatethe covariance matrix Cyc

as:

C∗yc

=1

M − 1

M−1∑t=0

(y(t)c − µc)(y

(t)c − µc)

T (5)

where M is the number of sample measurements, y(t)c

is the calibration measurement vector yc at time t, µc =1M

∑M−1t=0 y

(t)c is the sample average. Then, we perform

singular value decomposition (SVD) on C∗yc

:

C∗yc

= UΛUT (6)

where the unitary matrix U = [u1, . . . ,uL] and the diag-onal matrix Λ = diag {λ1, . . . , λL}. Right multiplying Uon both sides of (6), we have:

C∗ycui = λiui (7)


where ui is the eigenvector corresponding to the itheigenvalue λi. If the eigenvalues are in descending order,the first principal component u1 points in the directionof the maximum variance in the calibration measure-ments, the second principal component u2 points inthe direction of the maximum variance remaining inthe measurements, and so on. Examples of eigenvaluesfrom calibration measurements are shown in Figure 6 inSection 4.1. The first few eigenvalues are much largerthan the others, thus most of the variance in the calibra-tion measurements is in the subspace spanned by thesefew principal components. After obtaining eigenvaluesfrom calibration measurements, we decide how manyprincipal components, k � L, are necessary to capturethe majority of the variations (we discuss selection ofk in more detail in Section 4.3). In subspace decom-position, we will remove any part of the measurementvector y which falls in the subspace spanned by these kprincipal components, and by doing so, we eliminate alarge proportion of the intrinsic noise. Note that these kcomponents also contain portions of the extrinsic signaland so k should be kept as low as possible. Regardless,we describe the space spanned by the first k principalcomponents, U = [u1,u2, · · · ,uk], as the intrinsic signalsubspace; and we describe the space spanned by the nextL−k principal components, U = [uk+1,uk+2, · · · ,uL], asthe extrinsic signal subspace.

Once the two subspaces are constructed, we decom-pose the measurement vector y into two components –intrinsic signal component y and extrinsic signal com-ponent y:

y = y + y. (8)

The linearity of this approximation is by definition here,as the two subspaces are orthogonal by the propertiesof the SVD. However, linearity in RSS has been justifiedin prior literature [8], [18]. We also note that the “spatialcharacteristics” of intrinsic vs. extrinsic signal are fairlydifferent. For example, intrinsic signal caused by windappears at the same time everywhere in the area that hasbranches or bushes, for example, whereas people will nottend to be simultaneously moving in exactly those samepositions.

Since the principal components are orthogonal, theintrinsic signal component y and the extrinsic signalcomponent y can be formed by projecting y onto the in-trinsic subspace and the extrinsic subspace, respectively:

y = ΠIy = U UTy (9)

y = ΠEy = (I − U UT )y (10)

where ΠI = U UT is the projection matrix for the intrinsicsubspace, and ΠE = I − ΠI is the projection matrix forthe extrinsic subspace.

The key idea of SubVRT is to use the decomposedextrinsic signal component of the measurements in VRTI.We project the real-time measurement vector yr onto theextrinsic subspace to obtain the extrinsic signal compo-nent yr = (I − U UT )yr. Then, we replace yr in (4) with

yr and obtain the solution of SubVRT:

xSub = Π2yr

Π2 = (WTW + αQTQ)−1WT (I − U UT ). (11)

From (11), we see that the solution is a linear transforma-tion of the measurement vector. The transformation ma-trix Π2 is the product of the transformation matrix Π1 in(4) with the projection matrix for the extrinsic subspaceΠE : Π2 = Π1ΠE . Since the transformation matrix Π2 doesnot depend on instantaneous real-time measurements,it can be pre-calculated, and it is easy to implementSubVRT for real-time applications. Calculation of x fromyr requires LP multiplications and additions.

2.4 Least squares method

As shown above, SubVRT performs SVD on the covari-ance matrix of the calibration measurements. Here, weintroduce our LSVRT estimator formulated as a leastsquares (LS) solution, which uses the inverse of thecovariance matrix.

2.4.1 Formulation

To derive the least squares solution to the linear modelexpressed in (2), the cost function can be written as [19]:

J(x) = ‖Wx− yr‖2Cn+ ‖x− xa‖2Cx

(12)

= (yr −Wx)TC−1n (yr −Wx) + (x− xa)TC−1

x (x− xa)

where ‖n‖2Cnindicates weighted quadratic distance

nTC−1n n, Cn is the covariance matrix of the noise term

n, xa is the prior mean of x, and Cx is the covariancematrix of x.

Taking the derivative of (12) and setting it to zeroresults in the LSVRT solution:

xLS = (WTC−1n W + C−1

x )−1(WTC−1n yr + C−1

x xa). (13)

Since the prior information xa can be included in thetracking period, here we assume xa is zero, then (13)becomes:

xLS = Π3yr

Π3 = (WTC−1n W + C−1

x )−1WTC−1n . (14)

The LSVRT formulation can be also justified from aBayesian perspective. If we assume yr conditioned on xis Gaussian distributed with mean Wx and covariancematrix Cn, and x is Gaussian distributed with meanxa and covariance matrix Cx, then the maximum aposteriori (MAP) estimator, which maximizes p(x|yr),is equivalent to minimizing the cost function in (12).Under the same Gaussian assumption, the minimummean-squared error (MMSE) estimator is equivalent tothe MAP estimator. Thus the LS solution (13) can alsobe seen as the MAP or MMSE estimator under theseGaussian assumptions.


(a) Experiment 1 (b) Experiment 2

Fig. 2: Pictures of two experiments.

2.4.2 Covariance of Noise

For the LSVRT solution (13), the inverse of the covariancematrix Cn is needed. During the calibration period, weassume that there is no extrinsic motion in the signal, sox = 0 and yc = n. Thus Cn = Cyc .

Consider the inverse of the sample covariance matrixC∗

yc. From (6), The inverse of C∗

ycis given as,

[C∗yc

]−1 = UΛ−1UT (15)

where Λ−1 is a diagonal matrix with ith element 1/λi[13]. The problem is that C∗

ycis estimated using a sample

of size M , and M is typically less than L, the dimensionof the vector. Thus there will be at least L − M zeroeigenvalues λi in the SVD of the sample covariancematrix (equivalently, the rank of C∗

ycis at most M ). Thus

its inverse is not defined.For high dimensional covariance matrix estimation

problems, many regularized covariance matrix estima-tors have been proposed [20], [21]. Here, we use theLedoit-Wolf estimator, which is a linear combination ofthe sample covariance matrix and a scaled identity ma-trix, and is asymptotically optimal for any distribution[20]:

Cn = νµI + (1− ν)C∗yc

(16)

where C∗yc

is the sample covariance matrix of noisy cali-bration measurements yc, µ is the scaling parameter forthe identity matrix I , and ν is the shrinkage parameterthat shrinks the sample covariance towards the scaledidentity matrix. Again, since there is no extrinsic motionduring calibration period, that is, x = 0, thus yc = n, andwe approximate C∗

ycthat is also the sample covariance of

n. We follow [20] to automatically calculate parametersν and µ from the calibration measurements. From theBayesian perspective, this covariance matrix estimatorcan be seen as the combination of the prior informationand sample information of the covariance matrix.

We can rewrite (16) using (6) and the fact that UUT = Isince U is an orthogonal matrix:

Cn = νµUUT I + (1− ν)UΛUT = UDUT (17)

where D is a diagonal matrix with ith element νµ+ (1−

ν)λi. This form allows the inverse to be written as

C−1n = US−1UT (18)

where S−1 is a diagonal matrix with ith element1

νµ+(1−ν)λi. In this form, it is clear that with ν, µ > 0

there will be no divide-by-zero issues in the inverse ofthe estimated noise covariance matrix.

2.4.3 Covariance of ImageThe LSVRT solution also requires the covariance ma-trix Cx. As a means to generate a general statisticalmodel for Cx, we assume the positions of people inthe environment can be modeled as a Poisson process.Poisson processes are commonly used for modeling thedistribution of randomly arranged points in space.

Analysis of Poisson point processes leads to a co-variance function that is approximately exponentiallydecaying [22], and the exponential spatial covariancemodel is shown to be effective to locate people in anRF sensor network [23]. Thus, in this paper, we usean exponentially-decaying function as the covariancematrix of the human motion.

[Cx]i,j =σ2x

δexp

(−‖xj − xi‖l2

δ

)(19)

where σ2x is the variance of any element of the image

vector x, δ is a space constant, and ‖xj − xi‖l2 is theEuclidean distance between xi and xj .

2.5 Comparison of Two Methods

The SubVRT estimator and the LSVRT estimator areclosely related. Both build image estimators using the co-variance of the link variance measurements yc estimatedfrom calibration measurements. In this section, we showconnections between these two estimators.

Recall that SubVRT uses the SVD as given in (6). Wecan rewrite the extrinsic subspace projector (I − U UT )as USUT , where S is a diagonal matrix with its first kentries set to 0 and remaining entries set to 1. As such,the projection matrix for SubVRT can be written as:

Π2 = (WTW + αQTQ)−1WTUSUT . (20)


Next consider the LSVRT estimator from (14). Using(18), we can write the projection matrix for LSVRT as:

Π3 = (WTC−1n W + C−1

x )−1WTUS−1UT . (21)

Comparing the two, we see that S in (20) is replacedby S in (21). In LSVRT, the ith “principal component”ui (the ith column of U ) is weighted approximatelyby 1/λi, that is, one over the variance of noise in thatcomponent. When the variance λi is high, the componentis downweighted. In comparison in SubVRT, the ithprincipal component is weighted by 0 if the variance λiis one of the k highest; or 1 if not. Essentially, SubVRTapproximates 1/λi as 0 or 1, completely zeroing outsignals in the k noisiest dimensions and treating signalsin other dimensions equally. An advantage with LSVRTis that no parameter (like k in SubVRT) is required to betuned – recall that ν and µ are automatically determinedby the Ledoit-Wolf method.

From the former part of (20) and (21), we see thatthe LSVRT estimator includes C−1

n as a weight matrix inWTC−1

n W , while the SubVRT estimator just uses WTW .We also see that the inverse of the covariance matrix C−1

x

in the LSVRT solution plays the role of the regularizationterm αQTQ in the SubVRT solution.

In terms of computational complexity, both SubVRTand LSVRT require calculation of the SVD of an L × Lcovariance matrix, requiring on the order of L3 opera-tions. The Ledoit-Wolf estimation of covariance matrixadds additional complexity compared to the sample co-variance matrix calculation (5), which is used in SubVRT.However, these calculations are done once when thecalibration data has been collected. Real-time estimationof x requires only one matrix multiply which uses atmost LP operations, the same as VRTI.

2.6 Online CalibrationNote that the above SubVRT and LSVRT formulationsboth require calibration measurements to capture theintrinsic motion. In emergency applications, we cannotexpect to be able to perform calibration when the net-work area is empty.

We propose an online calibration method inspired bybackground subtraction techniques in the field of com-puter vision. Many background subtraction techniquesuse pixel-based features, such as pixel intensity, edges,for background modeling [24], [25]. For VRTI, we findthat the highest pixel intensities, when there are peoplemoving in the network area, are typically much higherthan those when no people are moving or present inthe network, i.e. pixel intensities of background noise.We propose to use pixel intensity to coarsely distinguishbetween times when a person is or is not present.

We denote the highest pixel intensities of VRTI imageswhen there are people in the network (foreground) andthere are no people (background) as xfq and xbq , respec-tively. An example of xbq and xfq time series is shownin Figure 3. We see that during the online period when

a person is walking inside the network (from sampleindex 160 to 440), all xfq values are above 0.5, while mostbackground pixel intensities xbq are below 0.5. We alsonotice that the xbq values from sample index 50 to 100are higher than those at other sample indexes. This isdue to the effect of high wind, that is, intrinsic motionfrom tree leaves and branches in a high wind periodcauses significant RSS variations. Thus the highest pixelintensities in this period are much higher than thosewhen the wind is not very strong.

0 50 100 150 200 250 300 350 400Sample index

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Max

imum

imag

e va

lue

Without peopleWith people

Fig. 3: Highest pixel intensities from VRTI with andwithout people moving in the network (using data fromExperiment 2).

Fig. 4: Flowchart of the online calibration method.

We assume that there will be some periods of timewhen there are no people moving and propose the fol-lowing procedure for online calibration. First, we run ourSubVRT or LSVRT estimator for incoming link measure-ment to find xq . Note that at the start when no calibrationmeasurements are available, both SubVRT and LSVRTestimators are replaced with VRTI. Whenever the highestpixel intensity xq is below a threshold, we record y asa calibration measurement. When there are more than athreshold number of calibration measurements 1, we usethem to update the estimator’s projection matrix accord-ing to SubVRT formulation (11) or LSVRT formulation(14). After we run the estimator, we calculate xq , and

1. we discuss the effect of all threshold values associated with thisonline calibration method in Section 4.2


repeat the procedure above. A flowchart of this onlinecalibration method is shown in Figure 4.

We note that online calibration suffers from a chicken-and-egg problem of estimating the extrinsic motionimage and knowing when the data is due solely tointrinsic motion. Sometimes intrinsic motion causes themax image intensity to be above the threshold, andthus that measurement is not included in the calibration.Rarely, extrinsic motion is such that image maximumis low, and it is included in the calibration. However,we show experimentally in Section 4.2 that as longas the threshold is set reasonably, sufficient calibrationmeasurements are recorded during intrinsic motion toenable SubVRT and LSVRT to be more robust to noise.

Further, online calibration requires that, at some pointduring the online calibration period, no people are mov-ing in the covered area. If people are always moving,then SubVRT and LSVRT would never be able to builda covariance model, and would revert to VRTI. In futurework, one might divide a large coverage area into sub-areas, and separately perform online calibration for eachsub-area. Alternatively, one may estimate where peopleare moving, draw large circles around their estimatedlocations, and then assume that links that do not inter-sect any circle are affected only by noise [26], and thenestimate the covariance matrix using known techniquesfor estimation with censored data [27]. However, theseideas are not explored in this paper.

2.7 Performance QuantificationTo quantify the performance of an image estimator, weuse the localization error in situations when one personis present. Multiple people can certainly be tracked usingradio tomography [28], [18], but localizing a single per-son is simple and is sufficient to quantitatively comparethe performance of different imaging estimators. Whena single person is present, her position z is estimated asthe center coordinate of the pixel with maximum value:

z = zq where q = arg maxp

xp (22)

where zq is the center coordinate of pixel q and xp is thepth element of image estimate x. Then, the localizationerror is defined as: eloc = ‖z− z‖l2 , where z is the actualposition of the person, and ‖ ·‖l2 indicates the Euclideannorm.

3 EXPERIMENTS

3.1 RF Sensor Network TestbedWe deploy a sensor network of ZigBee TelosB nodes asour testbed. All nodes are programmed with a TinyOStoken passing protocol called Spin [29]. At any particulartime, one node (the node with the token) broadcasts apacket, while all the other nodes measure the RSS of thereceived packet. A base station connected to a laptop alsooverhears the packet. The packet contains the transmitterid and a list of all of the RSS values that node has

recorded in the last round of Spin. The next node (onehigher in transmit id) takes the next turn broadcastinga packet. Nodes transmit in turn until all nodes havetransmitted, which completes one round of Spin, andthen the process repeats with the first node starting thenext round of Spin.

When round t of Spin completes, all pairwise mea-surements from the network have been overheard bythe base station and are recorded to {sl,t}l, and variancey(t) is computed. At this point, a real-time system wouldimmediately calculate an image estimate x that would becalculated from (4), (11) or (14). In our experiments, werecord {sl,t}l so that all methods can be tested across arange of parameters to show quantitative performancecomparisons in Section 4.

Note that the transmission interval between two nodesis set by the Spin protocol so that three link measure-ments are recorded each second to match the speedof human motion. For faster human motion, we canincrease the transmission frequency at the cost of morepower consumption. When a packet is not received,or if it fails the packet CRC check, we do not usethe RSS measurement for that packet. It is rare in ourexperimental network to see more than two packet dropsin a row, so such data loss causes less than one secondof delay on a link.

3.2 Experiment Location

In our experiments, thirty-four TelosB nodes are de-ployed outside the living room of a residential house.The living room is an addition, so the wall betweenthe kitchen and living room was originally an externalwall made of brick. The other walls are Hardy board (aconcrete and plastic composite) and wood. As shown inFigure 5, eight nodes are placed in the kitchen (on thecounter), six nodes are placed outside the windows ofthe living room. The other twenty nodes are all placedon polyvinyl chloride (PVC) stands outside the house.

3.3 Experiment Details

We use measurements from several data sets in thispaper. In all data sets, we first record data from the sen-sors during an empty-room calibration period. Next, aperson walks around a marked path (A-B-C-D as shownin Figure 15) in the living room at a constant speed ofabout 0.5 m/s, using a metronome and a metered pathso that the position of the person at any particular time isknown. A variety of intrinsic noise conditions are testedin three experiments:

• Experiment 1: We use the data set from the measure-ments conducted in March, 2009 reported by [8],which was performed in the same house with iden-tical setup, as our “Experiment 1”. Experiment 1 isperformed on a clear winter day with no wind. Asshown in our video [30] (a snapshot is shown inFigure 2a), there are no leaves on branches, and no


wind is observed during Experiment 1. The lack ofleaves or wind make this data set contain the leastintrinsic noise of any of those that we collected.For this experiment, have 47 seconds (M = 140) ofmeasurements collected during a calibration period.

• Experiment 2: We conduct another experiment at thesame house with identical setup on a windy day inMay, with leaves on the trees and long grass in theyard next to the house. From video recorded duringExperiment 2 (one snapshot is shown in Figure 2b),one can see that wind causes grass, leaves andbranches to sway [30]. The wind also causes thePVC stands supporting the nodes to move. For thisexperiment, we collect one minute (M = 170) ofmeasurements during a calibration period.

• Experiment 3: The first two experiments containedintrinsic motion that we did not control. In our finalexperiment, we attempt to control intrinsic motionusing four electric fans inside of the living room.The experiment is conducted on a windy summerday. The first data set (3a) is recorded with no fanson. The second data set (3b) is recorded with onerotating fan2 turned on. The third data set (3c) isrecorded with all four fans on. There are plants andobjects in the room which move somewhat when thefan blows on them. For each data set 3a, 3b, and 3c,we collect one minute (M = 170) of measurementsduring a calibration period.

0 2 4 6 8 10X (m)

�20

2

4

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Y (

m)

Living room

Kitchen

Door

Door

Camera

Tree

Nodes on stands

Nodes not on stands

Fig. 5: Map of tested area with node locations. A tree(shaded) is at the right side of the exterior. Video wasrecorded from camera location indicated.

4 RESULTS

4.1 Eigenvalues and eigen-networksWe propose in Section 2.3 that most of the intrinsic noisecan be contained within a low-dimensional subspace. Toverify this via experiment, we use PCA on the calibrationmeasurements from Experiments 1 and 2. The eigen-values of Cyc from these two experiments are shown

2. The fan is motor-controlled to change its facing direction, inaddition to rotating the fan blades.

Fig. 6: Scree plot.

0 2 4 6 8 10X (m)

0

2

4

6

8

Y (

m)

Fig. 7: First eigen-network: Links with u1l > 30% ofmaxl u1l.

in Figure 6. Because there is more intrinsic motion inExperiment 2, we see that the largest eigenvalue fromExperiment 2 is almost twice as large as that from Ex-periment 1. For Experiment 1, the first four eigenvaluesare much larger than the other eigenvalues, thus the sub-space spanned by the four corresponding eigenvectorscan capture most of the intrinsic signal. However, forExperiment 2, there are more large-valued eigenvalues.Thus more eigenvectors are necessary to capture themajority of the variations in the measurements.

Since each of the principal components used to con-struct the intrinsic subspace is an eigenvector of the co-variance matrix of the network measurements, and eachelement in an eigenvector is from an individual link,we refer these eigenvectors ui as “eigen-networks”. Thefirst eigen-network u1 = [u11, u12, · · · , u1L]T points inthe direction of the maximum variance of the calibrationmeasurements yc. We show the first eigen-network u1

graphically in Figure 7. We see the links with u1l valueshigher than 30% of the maximum value are all in thelower right side of the house. This is consistent withour observation that the leaves and branches on the treelocated to the right side of the house cause significanttemporal changes in the RSS measured on links likelyto propagate through the branches and leaves. Note


that links with high u1l values all have at least oneend point near the tree. In particular, links which arelikely to see significant diffraction around the bottom-right corner of the house have high u1l values. Theleaves and branches almost touch this corner, as seenin Figure 2b. Not only do these links measure high RSSvariance during the calibration period, they do so simul-taneously. That is, the fact that these links have highpositive u1l values indicates that when one of these linksexperiences increased RSS variance, the other links alsomeasure increased RSS variance. Thus, the first eigen-network u1 becomes a spatial signature for intrinsicmotion-induced RSS variance. When we see this linearcombination in yr, we should attribute it to intrinsic,rather than extrinsic motion. These observations aboutthe source of RSS variance on links support the idea thatintrinsic motion in the environment causes increased RSSvariance simultaneously on multiple links.

4.2 Localization resultsIn this section, we compare the performance of VRTI,SubVRT and LSVRT.

First, we compare in detail how LSVRT and VRTIperform in a particular segment of Experiment 2. TheVRTI estimates of Experiment 2 are shown in Figure 8.For clarity, we only show the actual/estimated positionswhen the person walks one round (out of the fourrounds) of the square. We show the last round becauseit is particularly affected by wind and thus illustratesthe effects of intrinsic noise on VRTI. In Figure 8, someVRTI estimates are greatly biased to the right side ofthe experimental area (i.e., five estimates > 4.0 m error).However, for LSVRT, the impact of intrinsic motion isgreatly reduced. As shown in Figure 9, the estimatesfrom LSVRT are more accurate than VRTI. There are noestimate errors larger than 2.0 m.

Note that some estimates are outside the house. Thealgorithms presented do not include any prior informa-tion of the house map or physical barriers which wouldprevent certain trajectories. Incorporation of such priorknowledge might be used to obtain better estimates, butat the expense of requiring more information to deploythe system.

Quantitatively, we next compare the localization errorsfrom VRTI, SubVRT and LSVRT for the full data sets.The comparison between VRTI and SubVRT is shownin Figure 9 of [12], and the comparison between VRTIand LSVRT is shown in Figure 10. The localization errorsfrom SubVRT are all below 1.8 m. For VRTI, there areseveral estimates with errors above 3.0 m. These largeerrors are due to the impact of intrinsic motion onstatic link measurements. Specifically, we compare thelocalization errors during a period with strong wind,from sample index 205 to 221, as shown in the insetof Figure 9 of [12]. During this period, the averagelocalization error from VRTI is 3.0 m, while the averageerror from SubVRT is 0.62 m, a 79% improvement, andfor LSVRT, it is only 0.50 m, a 83% improvement.

0 2 4 6 8 10X (m)

0

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m)

RF sensors

Known locations

Estimates

Fig. 8: Estimates from VRTI using measurementsrecorded when a person walks the last round of thesquare path in Experiment 2.

0 2 4 6 8 10X (m)

0

2

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8Y (

m)

RF sensors

Known locations

Estimates

Fig. 9: Estimates from LSVRT using the same measure-ments as used in Fig. 8.

0 50 100 150 200 250Sample index

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tion

est

imate

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ors

(m)

VRTI

LSVRT

206 208 210 212 214 216 218 2200

1

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Fig. 10: Estimate errors from VRTI and LSVRT.


Methods VRTI SubVRT LSVRTResults RMSE RMSE Improve RMSE ImproveExp. 1 0.70 0.65 7.0% 0.63 9.6%Exp. 2 1.26 0.74 41.3% 0.69 45.3%Exp. 3a 1.31 1.28 2.3% 1.10 16.0%Exp. 3b 1.44 1.15 20.1% 0.88 38.9%Exp. 3c 1.89 1.35 28.6% 1.0 47.1%

TABLE 1: Localization RMSEs (in meter) from VRTI,SubVRT and LSVRT.

Methods SubVRT LSVRTResults Online Offline Online OfflineExp. 1 0.66 0.65 0.64 0.63Exp. 2 0.77 0.74 0.70 0.69

Exp. 3a 1.31 1.28 1.07 1.10Exp. 3b 1.03 1.15 0.77 0.88Exp. 3c 1.32 1.35 0.99 1.0

TABLE 2: Localization RMSEs (in meter) from SubVRTand LSVRT using online and offline calibration.

We also compare the RMSE of the estimates, which isdefined as the square root of the average squared local-ization error over the course of the entire experiment.The RMSEs from all of the experiments are summarizedin Table 1. For Experiment 1, the RMSE from VRTI is0.70 m, while the RMSE from SubVRT is 0.65 m, a 7.0%improvement and the RMSE from LSVRT is 0.63 m, a9.6% improvement. For Experiment 2, the RMSE fromVRTI is 1.26 m, while SubVRT and LSVRT are morerobust to impact of intrinsic motion. The RMSE fromSubVRT is 0.74 m, a 41.3% improvement, and the RMSEfrom LSVRT is 0.69 m, a 45.3% improvement.

For the third experiment, the RMSEs are generallyhigher for all methods. We know that the small-scaleposition of sensors in the network can significantly affectoverall localization performance [31]. We suspect thatthis deployment had more links in deep fades.

The results from Experiment 3 show two things con-sistently:

1) LSVRT consistently has superior performance com-pared to SubVRT. The improvement in RMSEs forLSVRT are 14 to 19 percent better than SubVRT foreach of 3a, 3b, and 3c, as seen in Table 1.

2) Compared to data set 3a in which no fans were on,the improvement in RMSE increases as the quantityof intrinsic motion increases (as more fans areturned on) in 3b and then in 3c. The improvementincreases in 3b compared to 3a, and in 3c comparedto 3b, as seen in Table 1.

We believe that during the one-minute calibration forExperiment 3a, there was very little wind present, eventhough there was wind later while the person wasmoving in the room. As a result, for Experiment 3a,SubVRT and LSVRT show small reductions in RMSEcompared to VRTI.

Finally, we compare the localization RMSEs fromSubVRT and LSVRT using online and offline calibra-tion methods in Table 2. We see that the RMSEs fromboth estimators using online calibration are very similar

Param. Value Descriptionα 100 Regularization parameterm 4 Window length to calculate variancek 4/40 Principal components, Exp. 1 / Exp. 2, 3σ2x 0.001 Image variance parameterσ2w 2 Process noise parameterσ2v 5 Measurement noise parameter

TABLE 3: Parameters in VRTI, SubVRT, LSVRT andKalman filter.

Methods VRTI SubVRT LSVRTResults RMSE RMSE Improve RMSE ImproveExp. 1 0.66 0.57 13.6% 0.57 13.6%Exp. 2 1.21 0.72 40.5% 0.66 45.5%

Exp. 3a 1.17 1.15 1.7% 0.98 16.2%Exp. 3b 1.31 0.98 25.2% 0.79 39.7%Exp. 3c 1.86 1.33 28.5% 0.99 46.8%

TABLE 4: Tracking RMSEs (in meter) from VRTI, Sub-VRT and LSVRT.

to those using offline calibration for all experiments.Remember that in our online calibration method, weperform calibration only after enough measurements arecollected, as described in Section 2.6. We find as long asthe number of measurements used in the calibration isabove 100 (which corresponds to about 30 seconds) theperformance of both estimators using online calibrationis significantly better than VRTI. Thus, we choose thethreshold of the number of calibration measurements tobe 100 in our tests. We note that a result is that newintrinsic noise conditions, for example a new weathercondition, would take at least the duration of the cali-bration (here, 30 s) before the system properly reducedits intrinsic noise.

0.2 0.3 0.4 0.5 0.6 0.7 0.8Threshold

0.60

0.65

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0.75

0.80

0.85

0.90

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RMSE

(m)

Experiment 1Experiment 2

Fig. 11: RMSEs vs. pixel intensity threshold values.

Also recall that we use an intensity threshold value inonline calibration. Here, we test the effect of this thresh-old on the localization accuracy. We choose differentthreshold values and show RMSEs from Experiments 1and 2 in Figure 11. We see that as long as the thresholdvalue is in the range of 0.3 to 0.8, RMSE is not sensitiveto its value. For values < 0.3, very little data will beavailable for estimation of the covariance matrix. Forthresholds > 0.8, many data points from the period with


20 22 24 26 28 30 32 34Number of nodes

0.5

1.0

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2.0

2.5

3.0

3.5

4.0RM

SE (m

)VRTISubVRTLSVRT

Fig. 12: Localization RMSEs from Experiment 1 vs. numberof nodes.

a person present are included, which can lead SubVRTand LSVRT to learn to ignore data corresponding toactual people in the area, and lead to increased RMSE.When the threshold is between 0.3 and 0.8, there issufficient intrinsic noise and little extrinsic noise, whichallows the two methods to reduce the RMSE. FromFigure 3, we see that all highest pixel intensity valueswith people in the network are above 0.5, thus we simplychoose the threshold value to be 0.5 in our tests.

We note that adaptive thresholding for determiningwhen an area is empty has been developed for mean-based RTI [28], but is not directly applicable to VRTI be-cause people disappear when they stop moving. Futurework could explore applying such adaptive methodsin applications in which image intensities are unpre-dictable.

In sum, our SubVRT and LSVRT estimators usingonline calibration achieve approximately equivalent lo-calization accuracy compared to using offline calibration.

4.3 Discussion

The parameters that we use in VRTI, SubVRT and LSVRTare listed in Table 3. We show the effect of the numberof nodes on these three algorithms. We also discuss theeffects of the number of principal components k andthe image variance parameter σ2

x on the performancesof SubVRT and LSVRT, respectively.

To see the effect of node number on the localizationperformance, we run VRTI, SubVRT and LSVRT algo-rithms using RSS measurements from only a randomlychosen subset N less than the 34 total nodes used inExperiment 1. For example, when we use N = 20 nodes,we randomly choose 20 of the measured nodes, andthen run our algorithms using the RSS measurementscollected between pairs of these 20 nodes. For each N ,we repeat the above procedure 100 times, and eachtime calculate the RMSEs of the position estimates. Theaverage RMSEs and the RMSE standard deviations ofthe three algorithms from Experiment 1 are shown in

Figure 12, for N = 20 to 34 (a node density of 0.27 per m2

to 0.47 per m2). We find if we only use 26 nodes (L = 650)to cover this 9 m by 8 m area, the average RMSEs fromthree algorithms are all above 2 m. Comparing resultsfrom N = 26 vs. N = 32, the RMSE reduces by a factor of3−3.6 for the three methods. For all methods, increasingN may lead to diminishing returns beyond N = 32. Wealso find that the performance of LSVRT is consistentlybetter than SubVRT and VRTI independent of numberof nodes.

An important parameter for SubVRT is the numberof principal components used to construct the intrin-sic subspace. As discussed in Section 2.3, the first kcomponents are used to calculate the projection matrixfor the intrinsic subspace ΠI . If k = 0, ΠI = 0, thenΠ1 = Π2, SubVRT is simplified to VRTI. The RMSEsof SubVRT using a range of k are shown in Figure 13.Since the first eigen-network u1 captures the strongestintrinsic signal, when k = 1, the RMSE of Experiment 2decreases substantially from 1.26 m to 0.82 m. Since Ex-periment 1 has less intrinsic motion, the RMSE decreasesfrom 0.70 m when k = 0 to 0.65 m when k = 4, a lesssubstantial decrease. We note that as k increases, moreand more information in the measurement is removed,and the RMSE stops decreasing dramatically, and evenincreases, at certain k. This is because when k becomesvery large, the information removed also contains a greatamount of signal caused by extrinsic (human) motion.Thus, the performance of SubVRT could be degradedif k is chosen to be too large. The parameter k isa tradeoff between removing intrinsic motion impactand keeping useful information from extrinsic motion.For experiments without much intrinsic motion, suchas Experiment 1, we choose a small k. However, forExperiment 2, with strong impact from intrinsic motion,we use a large k. As listed in Table 3, we use k = 4 andk = 40 for all experiments.

0 20 40 60 80 100k

0.6

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SE (

m)

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Fig. 13: Localization RMSEs vs. principal component numberk.

An advantage of LSVRT over SubVRT is that LSVRTcan change its parameters automatically based on cali-bration measurements, thus we do not need to manually


Fig. 14: Localization RMSEs vs. σ2x.

tune parameters like k in SubVRT. Thus, we only in-vestigate parameter σ2

x in LSVRT, which plays the samerole of the regularization parameter α in SubVRT. FromFigure 14, we see the RMSE from LSVRT reaches theminimum at 0.63 m, when σ2

x = 0.001 and m = 4. How-ever, the localization RMSEs from LSVRT are shallowfunctions of σ2

x in the range from 10−4 to 10−1. Thatis, LSVRT is not very sensitive to this regularizationparameter in a wide range. Another advantage of LSVRTis that its localization accuracy is higher than SubVRT forall five experiments, as listed in Table 1. As discussed inSection 2.4, the inverse of the covariance matrix Cx isused as the regularization term in the LSVRT formula-tion. This regularization scheme provides better smooth-ing of the images, compared to the regularization term(difference operations of the image) in VRTI and SubVRTformulations. Thus, the motion images from LSVRT aregenerally cleaner than those from VRTI and SubVRT,and LSVRT has even better localization accuracy thanSubVRT.

5 TRACKING

In this section, we apply a Kalman filter to the local-ization estimates shown in Section 4.2 to better estimatemoving people’s positions over time. Then, we comparethe tracking results from VRTI with those from SubVRTand LSVRT, and show that the Kalman filter trackingresults from SubVRT and LSVRT are more robust to largelocalization errors.

5.1 Kalman filter

In the state transition model of the Kalman filter, weinclude both position (Px, Py) and velocity (Vx, Vy) inthe Cartesian coordinate system in the state vector s =[Px, Py, Vx, Vy]T , and the state transition model is:

s[t] = Gs[t− 1] + w[t] (23)

where w = [0, 0, wx, wy]T is the process noise, and G is:

G =

1 0 1 00 1 0 10 0 1 00 0 0 1

. (24)

The observation inputs r[t] of the Kalman filter are thelocalization estimates from VRTI, SubVRT or LSVRT attime t, and the observation model is:

r[t] = Hs[t] + v[t] (25)

where v = [vx, vy]T is the measurement noise, and H is:

H =

[1 0 0 00 1 0 0

]. (26)

In the Kalman filter, vx and vy are zero-mean Gaussianwith variance σ2

v , wx and wy are zero-mean Gaussianwith variance σ2

w [32]. The parameters σ2v and σ2

w ofthe measurement noise and process noise are listed inTable 3.

5.2 Tracking resultsWe use the Kalman filter described above to track thepositions of the person. The tracking results of Experi-ment 2 from SubVRT and LSVRT are shown in Figure 15.We see that for Experiment 2, with significant intrinsicmotion, the Kalman filter tracking results using SubVRTand LSVRT estimates generally have errors less than 1meter. The tracking results from LSVRT, proposed inthis paper, are even better than those from SubVRT. Thecumulative distribution functions (CDFs) of the trackingerrors from Experiment 2 are shown in Figure 16. We seethat the Kalman filter tracking results from VRTI havemany more large errors than SubVRT and LSVRT. ForVRTI, 97% of the tracking errors are less than 3.91 m,while 97% of the tracking errors from SubVRT are lessthan 1.36 m, a 65.2% improvement. For LSVRT, 97% ofthe errors are less than 1.15 m, a 70.6% improvementcompared to VRTI. We use the 97th percentile of errorsto show the robustness of the tracking algorithm tolarge errors, and the CDFs show the tracking resultsfrom SubVRT and LSVRT are more robust to these largeerrors.

We also compare the RMSEs of the tracking resultsfrom VRTI, SubVRT and LSVRT, which are listed inTable 4. For Experiment 1, the tracking RMSEs fromSubVRT and LSVRT are both 0.57 m, a 13.6% improve-ment compared to the RMSE of 0.66 m from VRTI.For Experiment 2, the tracking RMSE from SubVRT isreduced by 40.5% to 0.72 m compared to 1.21 m RMSEfrom VRTI, and the RMSE from LSVRT is reduced by45.5% to 0.66 m. We note that the tracking RMSEs fromVRTI, SubVRT and LSVRT of Experiment 2 are bothlarger than Experiment 1 due to the impact of intrinsicmotion. However, for VRTI the tracking RMSE fromExperiment 2 has a 83.3% increase compared to Experi-ment 1, while for SubVRT and LSVRT, they only increase


26.3% and 15.8%, respectively. For the data sets recordedduring Experiment 3, the tracking errors from LSVRTare all below 1 meter. Overall, the tracking RMSEs fromSubVRT and LSVRT are more robust to intrinsic motionthan VRTI, with LSVRT performing better than SubVRT.Also, the performance gain vs. VRTI increases as thequantity of intrinsic motion increases.

(a)0 2 4 6 8 10

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Tracking estimates

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Fig. 15: Kalman filter tracking results of Experiment 2from SubVRT (a) and LSVRT (b).

0 1 2 3 4 5 6Tracking error (m)

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20

40

60

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Freq

uenc

y (%

)

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Fig. 16: CDFs of tracking errors.

6 RELATED WORK

For device-free localization (DFL) of people in wirelesssensor networks, different measurements, algorithmsand frameworks have been proposed [6], [9], [8], [33],[34]. For RSS-based localization, we may divide methodsinto fingerprint-based and model-based algorithms. Likefingerprint-based real-time location service (RTLS) sys-tems, fingerprint-based device-free localization methodsuse a database of training measurements, and estimatea person’s location by comparing a measurement takenduring the online phase with the training measurementdatabase [35], [36], [37], [38]. To collect one trainingmeasurement, a person stands in one position while linkmeasurements are made, and associates the collecteddata with her known coordinate. Several such measure-ments are made throughout the area of interest. Oneactive area of research is developing tracking methodsfor multiple people which do not require an exponentialincrease in the number of training measurements thatmust be made [36]. Another area is the use of channelstate information (instead of RSS) for fingerprint-basedDFL [37], [38]. Finally, significant research addressesfingerprint-based activity recognition rather than local-ization alone [39], [40]. Since fingerprint-based methodsrequire a person to perform training at many knownlocations inside the area of interest, it is not suitable inemergency scenarios in which presence in the area ofinterest is dangerous.

Model-based algorithms [8], [23], [41], [42], [43], [44],[45], [18], [26] require a model for the relationship be-tween changes in RSS as a function of people’s positions.With this forward model, these methods solve localiza-tion as an inverse problem. Model-based algorithms typ-ically require 1) calibration measurements taken whenthe area is empty of people, and 2) known node co-ordinates. However, VRTI does not require calibration,and methods have been developed to learn the “empty”condition of each link [25], [45]. Regarding 2), node self-localization methods such as GPS may provide sufficientnode localization for RTI [46]; additionally, a model-based algorithm may simultaneously perform device-free localization and improve the node location estimates[18].

Radio tomographic imaging (RTI) is a particular typeof model-based algorithm which describes a statistic ofthe measured RSS as a linear combination of the effectcaused by each pixel in an area. Mean-based RTI relateslink attenuation to the loss due to people or objectsin the environment [23], [43], but does not performwell in non-LOS multipath-rich environments. Further,static building structure (walls and open areas) can bemapped [47]. Variance-based RTI (VRTI) [8] relates linkattenuation to motion in the environment, and does notrequire any calibration. As such, it is well-suited foremergency applications. However, VRTI cannot locatepeople if they stand still without any motion, and it issensitive to other motion in the environment, as shown


in this paper.Bistatic radar can be used to detect and locate motion

from behind walls using bistatic WiFi signals inside ofthe building [48]. Monostatic or multi-antenna through-wall radar systems [49], [50] operate with one or veryfew devices, but use specialized receivers and requireGHz of bandwidth.

In this paper, we apply subspace decomposition andleast squares-based formulations to reduce the impactof intrinsic noise in VRTI. We note that noise reductionwould presumably benefit both fingerprint-based andmodel-based algorithms, and future work may applythese techniques to other device-free localization meth-ods.

7 CONCLUSION

In this paper, we propose to use subspace decompositionand least squares methods to reduce noise for variance-based device-free localization and tracking. We discusshow intrinsic motion, such as leaves moving in thewind, increase measured RSS variance in a way thatis “noise” to a localization system. Our new estimatorLSVRT outperforms SubVRT in localization accuracy,and it requires tuning of fewer parameters comparedto SubVRT. We also propose a new online calibrationmethod so that both SubVRT and LSVRT can use real-time online measurements to perform calibration insteadof using “empty-area” offline calibration measurements.We perform new experiments to better investigate theeffect of intrinsic motion and the performance of SubVRTand LSVRT. Experimental results show that SubVRTand LSVRT can reduce localization RMSE by more than40%, and our online calibration method achieves similarlocalization accuracy as offline calibration. We furtherapply a Kalman filter on SubVRT and LSVRT estimatesfor tracking and show that SubVRT and LSVRT are morerobust to large errors than VRTI.

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Yang Zhao received the B.S. from ShandongUniversity (2003), the M.S. from the Beijing Uni-versity of Aeronautics and Astronautics (2006),and the Ph.D. from the University of Utah (2012),all in Electrical Engineering. He was a researchassistant at the Sensing and Processing AcrossNetworks (SPAN) lab of the University of Utahfrom 2009 to 2012. He was a research internat the Human Computer Interaction (HCI) groupof Microsoft Research Asia during the springof 2012. Since 2013, he has been a research

engineer at Software Sciences and Analytics (SSA) organization ofGeneral Electric Global Research Center in Niskayuna, New York. Hisresearch interests include signal processing, sensor networks, machine-to-machine.

Neal Patwari received the B.S. (1997) and M.S.(1999) degrees from Virginia Tech, and thePh.D. from the University of Michigan, Ann Arbor(2005), all in Electrical Engineering. He was aresearch engineer at Motorola Labs, Florida,between 1999 and 2001. He is an AssociateProfessor in the Department of Electrical andComputer Engineering at the University of Utah.He directs the Sensing and Processing AcrossNetworks (SPAN) Lab, which performs researchat the intersection of statistical signal processing

and wireless networking. Neal is also the Director of Research atXandem Technology. He has received best paper awards from theIEEE Signal Processing Magazine (2009), SenseApp (2012), and IPSN(2014), and the 2011 University of Utah Early Career Teaching Award.He is an associate editor of the IEEE Transactions on Mobile Computing.

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IEEE TRANSACTIONS ON MOBILE COMPUTING 1 Robust ... - Utah …npatwari/pubs/robust_RTI_accepted.pdf · IEEE TRANSACTIONS ON MOBILE COMPUTING 1 Robust Estimators for Variance-Based