Kalman Filter-based Tracking of a Device-free PassiveEntity in Wireless Environments

Moustafa Seifeldin∗

Wireless Intelligent NetworksNile UniversityCairo, Egypt

moustafa.sefeldin@nileu.edu.egaelkeyi@nileuniversity.edu.eg

and Amr El-keyiCenter (WINC)

MoustafaDepartment of Computer

Alexandria UniversityAlexandria, Egypt

moustafa.youssef@ejust.edu.eg

YoussefScience and Engineering

and E-JUST

ABSTRACTDevice-free passive (DfP) localization has been recently proposedto allow localizing a stationary entity that neither carries a devicenor participates actively in the localization process. In this paper,we present a Kalman filter-based system that enables tracking acontinuously moving entity in a typical wireless environment richin multipath. The concept behind DfP tracking is that the receivedsignal strength at monitoring points in a wireless environment isinfluenced by any changes in the environment. These changes in-clude the movement of an entity, such as a human being, withinthe environment. This can be utilized to track an entity in manymilitary and civil applications. We evaluate the performance of oursystem by conducting experiments in a typical office environmentrich in multipath. Our results show that we were able to track apassive entity in a long corridor with a 1.2m median distance errorand a less than 4.6m distance error with probability one.

Categories and Subject DescriptorsH.m [Information Systems Applications]: Miscellaneous

General TermsAlgorithms, Experimentation, Measurement, Security

KeywordsDevice-free tracking, passive radio map

1. INTRODUCTIONWith the proliferation of mobile devices and context-aware ap-

plications, the need for localization technologies increases. Typicallocation determination systems require a device to be attached tothe tracked entity. These systems include infrared-based systems

∗Moustafa Seifeldin is currently affiliated with the Department ofElectrical and Computer Engineering, the University of Texas atAustin, Austin, TX 78712, USA.

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.WiNTECH’11, September 19, 2011, Las Vegas, Nevada, USA.Copyright 2011 ACM 978-1-4503-0867-0/11/09 ...$10.00.

Figure 1: Different components of a DfP system in a typicaloffice environment. Access Points transmit signals to standardlaptops and wireless-enabled desktops. Any laptop or desktopcan be used as an application server.

(IR) [1], the GPS system [2], ultrasonic-based systems [3] and RF-based systems [4]. Recently, we proposed the device-free passivelocalization (DfP) concept [5]. A DfP system tracks entities notcarrying any devices nor participating actively in the localizationprocess. This is particularly useful in applications such as intrusiondetection and tracking, border protection and smart homes automa-tion.

The concept of DfP systems is based on the fact that the exis-tence of an entity, e.g. a human, in a radio frequency (RF) envi-ronment affects the RF signals. This fact is true for a large bandof frequencies, including the common wireless technologies of to-day, such as WiFi and WiMax. A number of DfP systems havebeen proposed in literature based on different technologies includ-ing radar-based systems, e.g. [6], radio tomography-based systems,e.g. [7] and WiFi-based systems, e.g. [5]. WiFi-based DfP systemsare particularly interesting since WiFi access points are readily in-stalled in wireless local area networks. This increases the value ofthe wireless data network and allows wider deployability.

The components of a WiFi-based DfP system are signal transmit-ters, monitoring points (MPs) and an application server (AS) whichcarries out the processing and sets up different actions. Access

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points (APs) and stations used in typical WiFi deployments can rep-resent signal transmitters, whereas standard laptops and wireless-enabled desktops can represent MPs. An example of a DfP systemis shown in Figure 1.

This paper presents a WiFi-based DfP tracking system whichuses Kalman filtering to track a moving entity in typical environ-ments that are very rich in multipath, with high accuracy, using asmall number of streams, without any special hardware. A streamconsists of beacons sent by typical 2.4 GHz WiFi access points ev-ery 100 ms. In this paper, we focus on indoor environments thatare abundant of metals and other materials which affect the RF sig-nals propagation, causing severe multipath effects. RF signals aresubject to reflection, refraction, absorption and diffraction, whichinduce multipath fading. This alters the received signal strength(RSS) at the MPs, where it may increase or decrease. Moreover, RFsignals are also affected by noise, interference from other sourcesand interference between channels. Interference from other sourcesincludes radio-based transmission apparatus, microwave ovens, cord-less telephones and Bluetooth adapters. Figure 2 shows examplesof the RSS in controlled and real environments. It is clear from rawstreams and histograms that in real environments, the RSS has ahigher variability. Thus, tracking an entity indoors is challenging,especially for the DfP case.

1.1 ApproachTo perform tracking, we need to capture the relation between sig-

nal strength and distance. This relation is very complex in indoorenvironments. Thus, we use a “passive” radio map. A radio mapis a structure that stores information of the signal strength at dif-ferent locations in the area of interest. This is usually constructedonly once during an offline phase. Passive radio maps differ fromactive radio maps used in device-based active localization systems.Figure 3 demonstrates the difference between active and passiveradio maps construction. In a passive radio map, we have an aver-age value per raw data stream, as compared to an average value perAP. Also, a user does not carry any device when constructing thepassive radio map.

AP1 AP2

[Average AP2][Average AP1]

(a) Active

AP1 AP2

[Average AP2]

[Average AP1] [A

verage AP2]

[Average AP1]

(b) Passive

Figure 3: Differences between construction of active radiomaps and construction of passive radio maps.

During the online phase (when the entity is being tracked), weuse the RSS samples that MPs receive from APs, where we com-pare them to the constructed passive radio map in order to deter-mine the location of the tracked entity. We use deterministic tech-niques, in which we do the following. During the offline phase, werepresent the RSS of an AP at a certain location by a scalar value(we use the mean value of RSS samples). Then during the onlinephase, we estimate the location of the tracked entity as in [8], i.e.,given a signal strength vector z(l) at an unknown location l, theradio map location x returned by deterministic techniques is givenby:

x = argminx

√√√√nstrms∑i=1

(z(l)i − z(x)i)2 (1)

where nstrms is the number of available streams, and z(x)i is themean RSS value of stream i calculated during the offline phase atradio map location x.

Due to the noisy nature of the wireless environment, we refinethe RSS samples and estimates using a Kalman filter to enhancethe overall accuracy. Also the use of the Kalman filter allows thelocation estimates to have a continuous space as in the next section.Thus, the location estimate does not have to be one of the calibratedlocations.

Evaluation of the system in a typical wireless environment richin multipath, shows that we are able to track a passive entity witha 1.2m median distance error and a less than 4.6m distance errorwith probability one.

1.2 Paper OrganizationIn Section 2, we propose a technique to track a moving entity in

a certain area, and we use a Kalman filter to refine the estimates.We then evaluate the performance of our system in a typical envi-ronment rich in multi-path in Section 3. Section 4 presents a com-parison between our system and the relevant related work. Finally,Section 5 concludes the paper.

2. TRACKING A SINGLE MOVING ENTITYUSING KALMAN FILTER

We limit the application of our tracking system to corridors. Thisis due to the fact that, generally, in indoor environments, multipathhas a significant effect on the RSS. When a person (or more) ex-ists on the line of sight (LOS) between transmitter and receiver, heblocks only a few paths. Hence, his effect on the RSS is not signif-icant. However, in the corridors, a person blocks most of the pathsthat affect the RSS. Thus, we still deal with multipath, but we limitour applications to corridors.

In this section, we discuss modeling assumptions, then we dis-

44

cuss Kalman filter equations. Finally, we impose some heuristicconstraints to enhance the performance of our system.

2.1 Modeling AssumptionsConsider the system with dynamics:

2.1.1 State Transition

x(k + 1) = F x(k) + ν(k) (2)

where x(k) is the state vector at time instant k T , T is the samplinginterval, F is the state transition matrix, and ν(k) is the processnoise. The state vector x(k) is given by:

x(k) = [x1(k) x◦1(k)]

T (3)

where AT is the transpose of a matrix A, x1(k) and x◦1(k) respec-

tively denote the location of the human and his velocity at timeinstant k T . Note that we consider the case of corridors, and hence,the location and the velocity are one dimensional. Nevertheless,the techniques applied in this paper can be directly extended to thetwo-dimensional case. The state transition matrix F is given by:

F =

[1 T0 1

](4)

We consider a continuous white noise acceleration model. Thismodel assumes an object is moving with constant velocity. In prac-tice, the velocity at least undergoes slight changes. Such changescan be modeled by a zero mean white noise. The covariance of thediscrete-time process noise ν(k) is given by [9]:

Q = σ2proc

[13T 3 1

2T 2

12T 2 T

](5)

where σproc is the standard deviation of the process noise.

2.1.2 MeasurementThe measurement equation is given by

z(k + 1) = h(x1(k)) + w(k) (6)

where z(k) is an nstrms×1 vector containing the measured RSSof different streams during the online phase. h(x) is an nstrms × 1vector whose ith entry contains the loss in the RSS of the ith stream(compared to to the silence case where the entity is absent, butall the devices are still in their places) corresponding to the entitybeing at the location x1(k). In [9], the covariance of w(k), is givenby

R = (σ2meas)× Instrms×nstrms (7)

where σmeas is the standard deviation of w(k) and I is identitymatrix. The vector w(k) is the measurement noise vector which isassumed to be Gaussian with zero-mean and covariance given by[9]. Note that the values of h(x) at discrete grid points are availablefrom the radio map obtained during the offline phase.

2.2 Kalman Filter EquationsIn every iteration, Kalman filter first “predicts" the state using

the state estimate of the previous iteration. Then, it “updates" (orrefines) the state estimate using the new measurement. Thus, foreach new measurement, the filter carries out the following steps:

2.2.1 Apply State Prediction Equation

x(k + 1) = F x(k) (8)

where x is the estimated state vector at time instant k.

2.2.2 Apply Measurement Prediction Equation andEvaluate the Jacobians

Estimate the loss h(x1(k)) and its derivative H(x1(k)) using aradio map that yields the loss, h(x1(k)), and its derivative, H(x1(k)),for a certain location, x1(k). To build a radio map for the loss andits derivative, we use deterministic techniques, i.e, for each loca-tion, there is a certain value for the loss in RSS. First, we buildthe radio map for the loss in RSS in a calibration phase. Duringthis offline or calibration phase a person stands at certain locationsuniformly distributed along the length of the corridor. The RSSof each stream is recorded. We also record the RSS when nobodyexists in the corridor (silence period). We can simply get the loss inRSS at a certain location by subtracting the mean of RSS when theperson exists at this location from the mean of RSS of the silenceperiod. Thus, we have the loss in RSS only for certain locations(discrete values).

To get a continuous function for the loss in RSS, we approximatethe loss function at a point between two calibrated points by a lin-ear function. Assume a location x1(k) lies between two calibratedlocations xa and xb. The loss in RSS at location x1 is given by:

h(x1(k)) = h(xa) +x1 − xa

xb − xa(h(xb)− h(xa)) (9)

Second, we build the radio map for the derivative of the loss inRSS. Assume we have three consecutive calibrated locations xa,xb and xc. The derivative of the loss at location xb is given by:

H(xb) =

(H(xb)− H(xa)

xb − xa+

H(xc)− H(xb)

xc − xb

)/2 (10)

Thus, we have the derivative of the loss in RSS only for certainlocations (discrete values).

To get a continuous function for the derivative of the loss in RSS,again we use linearization. Assume a location x1(k) lies betweentwo calibrated locations xa and xb. The derivative of the loss inRSS at location x1 is given by:

H(x1(k)) = H(xa) +x1 − xa

xb − xa(H(xb)− H(xa)) (11)

H(k + 1) is an nstrms × 2 matrix. The first column of whichis found using a radio map, given the location x1(k), as mentionedabove. The second column is equal to the first column multipliedby the sampling time T .

2.2.3 State Covariance Prediction

P(k + 1|k) = F P(k|k) FT + Q (12)

2.2.4 Innovation Covariance

S(k+1) = H(k+1) P(k+1|k) H(k+1)T + R(k+1) (13)

2.2.5 Filter Gain

W(k + 1) = P(k + 1|k) H(k + 1)T S(k + 1)−1 (14)

2.2.6 Measurement Residual

ν(k + 1) = z(k + 1)− z(k + 1|k) (15)

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2.2.7 Update State Estimate

x(k + 1|k + 1) = x(k + 1|k) + W(k + 1) ν(k + 1) (16)

2.2.8 Update State Covariance

P(k+1|k+1) = P(k+1|k) − W(k+1) S(k+1) W(k+1)T

(17)

2.3 Heuristic ConstraintsWhen dealing with experimental data, we need to add some con-

straints that take into consideration the following:

• Topology of the building. This can help in avoiding any unre-alistic estimates such as estimating the location inside a wallor outside the building.

• Nature of tracked entity. Human beings move with a limitedvelocity.

• Any phenomena that may appear in the experimental data,yet not captured in our model, such as large fluctuations inRSS in real environments as discussed in Section 1.

2.3.1 Constraint on Estimated LocationFirst, estimates must be within the corridor. Any location esti-

mate should be within the range [min_coord, max_coord], wheremin_coord is the minimum coordinate that the moving entity canaccess in the corridor, and max_coord is the maximum coordinatethat he/she can access.

Second, since estimates at some locations (exactly at the lap-tops, where loss functions are discontinuous) lead the filter to giveextreme results, we should not get stuck at these points. Thus, weneed to introduce a little randomization.

To consider both of the points mentioned above, when the esti-mated location lies outside the range [min_coord, max_coord], we:(1) Initialize using last meaningful estimate +/- 0.1 meter*N (0, 1),where N (0, 1) is a Gaussian random variable with zero mean andunit variance.(2) Apply x1(k) = min{x1(k),min_coord}.(3) Apply x1(k) = max{x1(k),max_coord}.Steps 2 and 3 are used to ensure that the estimate lies in the coveredarea in the corridor.

2.3.2 Constraint on VelocityAbsolute value of the velocity of movement of the tracked entity

can be forced not to exceed a certain maximum value, vmax. Thisis achieved by adding the following steps after the state estimateupdate.

x◦1(k) = min{x◦

1(k), vmax}, if x◦1(k) ≥ 0 (18)

x◦1(k) = max{x◦

1(k),−vmax}, if x◦1(k) < 0 (19)

2.3.3 Constraint on Considered MeasurementsLet RSSmin denote the minimum value of RSS in the radio map

or the model of a certain stream, and RSSmax denote the maxi-mum value of RSS of this stream. Let nstd be a positive integer,usually of value equal to one or two. Based on the fact that weexpect the RSS of the online measurements to be within the range[ RSSmin , RSSmax dB], we add constraints on RSS to removeoutlier measurements, where we:(1) Drop any measurements out of the range [ RSSmin-nstd ×

σmeas , RSSmax+nstd × σmeas ]. When a sample of a certainstream is dropped, update the size of the measurement noise co-variance matrix accordingly:

R = (σ2meas)× Incons×ncons (20)

where ncons is the number of considered streams.(2) Force measurements within the range [ RSSmin-nstd ×σmeas

, RSSmin ] to be equal to RSSmin dB.(3) Force measurements within the range [ RSSmax , RSSmax +nstd × σmeas to be equal to RSSmax dB.(4) In case all measurements at one time instant are outside therange [ RSSmin-nstd ×σmeas , RSSmax+nstd ×σmeas ] , applystate prediction, but do not apply state update.

3. EXPERIMENTAL TESTBEDIn this section, we evaluate the performance of our proposed

system by conducting experiments in a typical office environment.First, we discuss the data collection method. Second, we discussthe experimental results.

3.1 Data Collection

Figure 4: The corridor in which tracking experiments werecarried out.

Figure 5: A cross section of the corridor in which tracking ex-periments were carried out.

46

Parameter Default valueσmeas 2 (dB)σproc 0.2 (m)

P (k)initial 30×I2×2 (m2)vmax 2 (m/s)nstd 1

Table 1: Kalman filter parameters used in tracking experiment

Technique 25th perc. 50th perc. 75th perc. 100th perc.Kalman 0.4m 1.2m 2.7m 4.6mRandom 2.3m

(5.8×)4.7m(3.9×)

7.7m(2.9×)

15.3m(3.3×)

Table 2: Comparison between different percentile values of dis-tance error for Kalman filter versus random estimator.

We conducted experiments in a corridor of 16.5 meters length,part of which is shown in Figure 4. The corridor is curved (manystreams have no clear LOS) and has a substantial amount of metals.Four laptops (MPs) and four access points (APs) were placed inthe corridor as shown in Figure 5. The laptops had wireless cardsattached to them. This provides a total of 16 streams. Two of themare useless since they belong to APs and MPS coinciding over eachother (MP1-AP1 and MP4-AP2), so the person cannot cut the LOS.Thus, 14 streams are used in the tracking process. All MPs (DellLatitude D830) are placed on disks at a height of 90 cm. AP1 andAP2 (Cisco Aironet 1130 AG Series) are placed at a height of 2 m,whereas AP3 and AP4 (Aruba AP-61) are attached to the ceilingwhose height is 2.6 m.

In the calibration (offline) phase, a person stands for 60 secondsat a certain location. RSS measurements are collected at a sam-pling rate of 10 samples per second (T = 100ms). The loss ata certain location equals the difference between the mean value ofRSS measurements when the person exists at this location and themean value of RSS measurements when nobody exists in the cor-ridor. We use linearization to obtain a continuous function for theloss in terms of location of human. We also use linearization toobtain a continuous function for the derivative of the loss (H) interms of location of the person.

For testing purpose (during the online phase), a person moveswith a constant velocity of 0.5 meters per second from MP1 (coordinate=0) towards MP4 (coordinate= 16.5m) as in Figure 5.

Kalman filter was run with parameters set to the values in Table1. Note that P (k) has dimensions (2 × 2) since the state vector isof length equal two.

3.2 Experimental ResultsFigure 6 shows the actual and estimated trajectories. The maxi-

mum distance error estimated by Kalman filter is 4.6 meters. Thedistance error of the location estimate compared to the actual lo-cation is shown in Figure 7 versus time. The performance of oursystem refined by Kalman filter is compared to a random estima-tor as a baseline. The random estimator just guesses any locationwithin the corridor as its estimate. Figure 7 shows also the CDF ofthe distance error. Table 2 summarizes the information in the CDFin Figure 7. Numbers between brackets indicate the degradation ofthe random estimates compared to Kalman filter estimates. UsingKalman filter to refine the estimates, we can track a passive entityin a corridor of 16.5m length with a 1.2m median distance error anda less than 4.6m distance error with probability one.

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Figure 7: Distance error of the location estimate, comparedto the actual location. The figure shows distance error versustime, as well as CDFs of distance error

4. RELATED WORKRecent device-free passive localization systems can be classified

into three classes: radar-based, imaging-based and WiFi-based sys-tems.

4.1 Radar-based systemsUltrawideband (UWB) radar systems provide “Through-wall"

detection and tracking. These systems can utilize impulse [6], frequency-modulated continuous-wave (FMCW) [10], stepped frequency [11],or noise [12] waveforms. These systems are very accurate, yet verycomplex. To provide less complexity a Doppler radar with a two-element receiver array is used [13]. This Doppler radar assumedthat no two targets have the same Doppler return, which is not validin case of human tracking since micro Doppler returns from thehuman arm and leg motions have a broad Doppler spread [14]. Afour-element array radar can also be used [15]. This latter combinesDoppler processing with software beamforming to resolve targetsalong both the Doppler and direction of arrival (DOA) space.

MIMO radar employs multiple transmit waveforms and have theability to jointly process the echoes observed at multiple receiveantennas ( [16] and references therein). MIMO radar elements

47

transmit independent waveforms giving an omnidirectional beam-pattern. Different waveforms are exploited in MIMO to enhanceperformance.

To sum up, radar-based systems provide accurate location es-timates, but require highly complex hardware which limits theirapplications.

4.2 Imaging-based systemsRadio Tomographic Imaging (RTI) is an emerging technology

[7]. It presents a linear model for using RSS measurements to ob-tain images of moving objects. The proposed system uses hundredsof raw data streams obtained from sensor nodes. The system mea-sures the attenuation in the transmitted signal rather than scatteringand reflection. Since this system is based on one path (LOS), itsaccuracy degrades as multipath components increase. To overcomemultipath, a higher density of nodes is used.

Wilson and Patwari presented variance-based RTI, which takesadvantage of the motion-induced variance of RSS measurements[17]. They Used a multipath model to show that RSS on a wirelesslink depends significantly on the power existing in multipath com-ponents traveling through the space which contains moving entities.They presented a statistical model relating variance to locations ofmovement. A Kalman filter is applied to the measurements to iter-atively track the location of a moving target. They present experi-mental results for through-wall imaging and tracking system using34 nodes over an area of 78 sq. foot.

In [18], measurement-based statistical models that can be used toestimate the locations of people using RSS measurements in wire-less networks was introduced. The author demonstrates, using ex-tensive experimental data, that changes in RSS measurements dueto human motion can be modeled by the skew-Laplace distribution.The parameters of the distribution are dependent on the position ofperson and on the amount of fading that a particular link experi-ences. To experimentally estimate the location of moving and sta-tionary people through walls, the author applies a particle filter anduse the skew-Laplace likelihood model.

Generally, the above systems use imaging techniques. This lim-its the applications due to privacy concerns.

4.3 WiFi-based SystemsThe concept of WiFi-based DfP localization was first introduced

in [5]. Experiments were set up in a highly controlled and small en-vironment. In addition, the user was allowed to move in only onedimension. Results show that the system can track the intruder’sposition with more than 86% accuracy in this limited controlledenvironment. These results proved the feasibility of the DfP lo-calization principle. This has been further extended to a real envi-ronment, but still in a very limited scale (a much smaller testbed),in [19]. We showed promising experimental results in [8] and [20]for a large-scale real environment for stationary entities.

Unlike previous work in the field, this work presents a DfP track-ing system which uses a Kalman filter to track moving entities intypical environments that are very rich in multipath, with high ac-curacy, using a small number of streams, without any special hard-ware.

5. CONCLUSIONS AND FUTURE WORKWe proposed a technique to track a continuously moving entity.

We evaluated the performance of the our system in a typical officebuilding rich in multipath. Using Kalman filter to refine the esti-mates, we can track a passive entity in a corridor of 16.5m lengthwith a 1.2m median distance error and a less than 4.6m distanceerror with probability one.

At present, we are extending the system in many ways where weconsider tracking multiple entities [20] and automatic generation ofthe passive radio map [21]. Also, possible future directions includefinding the optimum locations of APs and MPs, and analyzing theimpact of the dynamic changes in the environment as well as theimpact of the use of different hardware.

AcknowledgmentThis work is supported in part by a grant from the Egyptian Scienceand Technology Development Fund.

The authors would like to thank Dr. Ayman Naguib of Qual-comm Inc. for his valuable comments which helped enhance theperformance of our system.

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