IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 5, OCTOBER 2018 4031

WiBall: A Time-Reversal Focusing Ball Methodfor Decimeter-Accuracy Indoor Tracking

Feng Zhang , Student Member, IEEE, Chen Chen , Student Member, IEEE,

Beibei Wang , Senior Member, IEEE, Hung-Quoc Lai, Yi Han,

and K. J. Ray Liu , Fellow, IEEE

Abstract—With the development of the Internet of Thingstechnology, indoor tracking has become a popular applicationnowadays, but most existing solutions can only work in line-of-sight scenarios, or require regular recalibration. In this paper, wepropose WiBall, an accurate and calibration-free indoor track-ing system that can work well in non-line-of-sight based on radiosignals. WiBall leverages a stationary and location-independentproperty of the time-reversal focusing effect of radio signals forhighly accurate moving distance estimation. Together with thedirection estimation based on inertial measurement unit and loca-tion correction using the constraints from the floorplan, WiBallis shown to be able to track a moving object with decimeter-levelaccuracy in different environments. Since WiBall can accommo-date a large number of users with only a single pair of devices, itis low-cost and easily scalable, and can be a promising candidatefor future indoor tracking applications.

Index Terms—Indoor tracking, radio signals, speed estimation,time-reversal transmission.

I. INTRODUCTION

W ITH the proliferation of the Internet of Things applica-tions, indoor positioning and indoor navigation (IPIN)

has received an increasing attention in recent years. Technavioforecasts the global IPIN market to grow to $7.8 billion by2021 [1], and more than ever before, enterprises of all sizesare investing in IPIN technology to support a growing listof applications, including patient tracking in hospitals, assetmanagement for large groceries, workflow automation in largefactories, navigation in malls, appliance control, etc.

Although global positioning system can achieve good accu-racy with a low cost in outdoor real-time tracking, such agood balance between the cost and performance has not beenrealized for indoor tracking yet [2].

Manuscript received December 12, 2017; revised June 7, 2018; acceptedJuly 1, 2018. Date of publication July 10, 2018; date of current versionNovember 14, 2018. (Corresponding author: Feng Zhang.)

F. Zhang, B. Wang, and K. J. R. Liu are with the Department ofElectrical and Computer Engineering, University of Maryland at College Park,College Park, MD 20742 USA, and also with the R&D Department, OriginWireless, Inc., Greenbelt, MD 20770 USA (e-mail: fzhang15@umd.edu;bebewang@umd.edu; kjrliu@umd.edu).

C. Chen was with the Department of Electrical and Computer Engineering,University of Maryland at College Park, College Park, MD 20742 USA, andwas also with the R&D Department, Origin Wireless Inc., Greenbelt, MD20770 USA. He is now with Pinterest, Inc., San Francisco, CA 94103-4904USA (e-mail: cc8834@umd.edu).

H.-Q. Lai and Y. Han are with the R&D Department, Origin Wireless,Inc., Greenbelt, MD 20770 USA (e-mail: quoc.lai@originwireless.net;yi.han@originwireless.net).

Digital Object Identifier 10.1109/JIOT.2018.2854825

In this paper, we propose WiBall, a wireless system forindoor tracking, that can work well in both non-line-of-sight (NLOS) and line-of-sight (LOS) scenarios and is robustto environmental dynamics as well. WiBall estimates theincremental displacement of the device at every moment, andthus, it can track the trace of the device in real time. WiBalladopts a completely new paradigm in the moving distanceestimation, which is built on the proposed discovered physicalphenomenon of radio signals. In the past, the moving distanceestimation can be done by analyzing the output of IMU thatis attached to the moving object. Accelerometer readings areused to detect walking steps and then, the walking distance canbe estimated by multiplying the number of steps with the stridelength [3]. However, pedestrians often have different stridelengths that may vary up to 40% even at the same speed, and50% with various speeds of the same person [4]. Thus, calibra-tion is required to obtain the average stride lengths for differentindividuals, which is impractical in real applications and thushas not been widely adopted. The moving distance can also beestimated by analyzing radio signals that are affected by themovement of the device. Various methods have been proposedbased on the estimation of the maximum Doppler frequency,such as level crossing rate methods [5], covariance-basedmethods [6], [7], and wavelet-based methods [8]. However,the performance of these estimators is unsatisfactory in prac-tical scenarios. For example, the approach in [7] can onlydifferentiate whether a mobile station moves with a fast speed(≥ 30 km/h) or with a slow speed (≤ 5 km/h).

In WiBall, a new scheme for moving distance estimationbased on the time-reversal (TR) resonating effect [9], [10]is proposed. TR is a fundamental physical resonance phe-nomenon that allows people to focus the energy of a transmit-ted signal at an intended focal spot, both in the time and spatialdomains, by transmitting the TR waveform. The research ofTR can be traced back to the 1950s when it was first utilized toalign the phase differences caused by multipath fading duringlong-distance information transmissions. The TR resonatingeffect was first observed in a practical underwater propagationenvironment [11] that the energy of a transmitted signal canbe refocused at the intended location because by means of TRthe RX recollects multipath copies of a transmitted signal ina coherent matter.

In this paper, we present a new discovery that the energydistribution of the TR focusing effect exhibits a location-independent property, which is only related to the physical

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4032 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 5, OCTOBER 2018

parameters of the transmitted EM waves. This is because thenumber of multipath components (MPCs) in indoors is solarge that the randomness of the received energy at differentlocations can be averaged out as a result of the law of largenumbers. Based on this location-independent feature, WiBallcan estimate the moving distance of the device in a com-plex indoor environment without requiring any precalibrationprocedures. To cope with the cumulative errors in distanceestimation, WiBall incorporates the constraints imposed bythe floorplan of buildings and corrects the cumulative errorswhenever a landmark, such as a corner, hallway, door, etc.,is met. Combining the improved distance estimator and themap-based error corrector, the proposed WiBall is shown to beable to achieve decimeter-level accuracy in real-time trackingregardless of the moving speed and environment.

The rest of this paper is organized as follows. Section IIintroduces the related works. Section III introduces the systemarchitecture of WiBall followed by a discussion on the TRprinciple for distance estimation. Section IV presents an IMU-based moving direction estimator and a map-based localizationcorrector, which can correct the accumulated localization error.Experimental evaluation is shown in Section V and Section VIconcludes this paper.

II. RELATED WORKS

Existing solutions for indoor tracking can be classi-fied into four categories: 1) vision-based; 2) audio-based;3) radio-based; and 4) inertial measurement unit (IMU)-based.Vision-based approaches, such as camera [12], laser [13],infrared [14], etc., suffer from high cost of deployment andequipment, sophisticated calibrations and limited coverage,although a very high accuracy can be achieved. The acoustic-based schemes [15] can only cover a limited range and arenot scalable to a large number of users. The performance ofradio-based approaches, such as RADAR [16], RFID [17], andUWB localization systems [18], [19], is severely affected bythe NLOS multipath propagation which is unavoidable for atypical indoor environment. The localization accuracy of IMU-based methods [3], [4] is mainly limited by the poor estimationof moving distance and the drifting of the gyroscope.

Due to the wide deployment of WiFi in indoors, vari-ous indoor localization systems based on WiFi have beenproposed, as summarized in Table I. In general, these workscan be classified into two categories: 1) modeling-basedapproach and 2) fingerprinting-based approach. The featuresutilized in these approaches can be obtained either from theMAC layer information, e.g., receive signal strength indicator(RSSI) readings and the timestamps of the received packetsat the receiver (RX), or from the PHY information, e.g., thechannel state information (CSI).

In the modeling-based schemes, either thedistance [20]–[23], or the angle [24]–[26] between ananchor point and the device can be estimated and the devicecan be localized by performing geometrical triangulation. Thedistance between the anchor point and the device can be esti-mated from the decay of RSSI [27] or from the time of arrival(ToA) of the transmitted packets which can be extracted from

TABLE IBRIEF SUMMARY OF TYPICAL WIFI-BASED APPROACHES

the timestamps of the received packets [28]. The angle inbetween can be obtained by examining the features of the CSIreceived by multiple receive antennas, and then, the angle ofarrival (AoA) of the direct path to the target can be calculated.ToA-based methods typically require synchronization betweenthe anchor point and the device and thus are very sensitive totiming offsets [29]; AoA-based methods require an array ofphased antennas which are not readily available in commercialWiFi chips [25]. Recently, a decimeter-level tracking system,Widar, is proposed in [30] and [31], however, the system canonly work in a small area with the constraint of LOS. Themain challenges for the modeling-based approaches are theblockage and reflection of the transmitted signal since onlythe signal coming from the direct path between the anchorpoint and the device is useful for localization.

The fingerprinting-based schemes consist of an offline phaseand an online phase. During the offline phase, features asso-ciated with different locations are extracted from the WiFisignals and stored in a database; in the online phase, the samefeatures are extracted from the instantaneous WiFi signals andcompared with the stored features so as to classify the loca-tions. The features can be obtained either from the vector ofRSSIs [27], [32], or the detailed CSI [33]–[35] from a specificlocation to all the anchor points in range. A major drawbackof the fingerprinting-based approaches lies in that the featuresthey use are susceptible to the dynamics of the environment.For example, the change of furniture or the status of doorsmay have a severe impact on these features and the databaseof the mapped fingerprints need to be updated before it canbe used again. In addition, the computational complexity ofthe fingerprinting-based approaches scales with the size of thedatabase and thus they are not feasible for low-latency applica-tions, especially when the number of the collected fingerprintsis large.

In sum, the performance of most existing solutions forindoor localization degrades dramatically under NLOS con-ditions, which are common usage scenarios though. Evenwith a significant overhead in the manual construction ofthe database, the fingerprinting-based approaches still fail toachieve a decimeter-level accuracy. Therefore, indoor location-based services are not provided as widespread as expectednowadays, which motivates us to design a highly accurateand robust indoor tracking system even without requiringspecialized infrastructure.

III. TR FOCUSING BALL METHOD FOR

DISTANCE ESTIMATION

In this section, we first introduce the overall system archi-tecture of WiBall and the TR radio system. Then, we derive theanalytical normalized energy distribution of the TR focal spot.

ZHANG et al.: WiBALL 4033

Fig. 1. Illustration of the tracking procedure.

We show that the normalized energy distribution is location-independent and can be used to estimate distance. Last, wediscuss the TR-based distance estimator.

A. Overview of WiBall

WiBall consists of a transmitter (TX) broadcasting beaconsignals periodically to all the RXs being tracked. WiBall esti-mates the paths that the RX travels, i.e., the location of theRX �x at time ti is estimated as

�x(ti) = �x(ti−1) + ��(ti) (1)

where �x(ti−1) represents the location of the RX at the previoustime ti−1 and �(ti) is the incremental displacement. The mag-nitude of ��(ti), denoted as d(ti), and the angle of ��(ti),denoted as θ(ti), correspond to the moving distance and thechange of moving direction of the RX from ti−1 to ti, respec-tively. As shown in Fig. 1, the location of the RX at time tn iscomputed based on the accumulative displacements from timet0 to tn and the initial start point �x(t0).

WiBall estimates the moving distance d(ti) based on theTR resonating effect, which can be obtained from the CSImeasurements at the RX. The estimation of θ(ti) is based onthe angular velocity and gravity direction from IMU, which isa built-in module for most smartphones nowadays.

B. TR Radio System

Consider a rich-scattering environment, e.g., an indooror metropolitan area, and a wireless transceiver pair eachequipped with a single omnidirectional antenna. Given a largeenough bandwidth, the MPCs in a rich-scattering environ-ment can be resolved into multiple taps in discrete-time andlet h(l; �T → �R0) denote the lth tap of the channel impulseresponse (CIR) from �T to �R0, where �T and �R0 denotes the coor-dinates of the TX and RX, respectively. In the TR transmissionscheme, the RX at �R0 first transmits an impulse and the TXat �T captures the CIR from �R0 to �T . Then the RX at �T simplytransmits back the time-reversed and conjugated version of thecaptured CIR, i.e., h∗(−l; �R0 → �T), where ∗ denotes complexconjugation. With channel reciprocity, i.e., the forward and

(a)

(b) (c)

Fig. 2. TR prototype and the environment of the measurement, the TRRSdistribution in the spatial domain, and the normalized energy of the receivedsignal at the focal spot �R0 in the time domain. (a) TR prototype and channelprobing platform. (b) TRRS in spatial domain. (c) TRRS in time domain.

backward channels are identical [35], the received signal atany location �R when the TR waveform h∗(−l; �R0 → �T) istransmitted can be written as [39]

s(l; �R) =

L−1∑

m=0

h(m; �T → �R)

h∗(m − l; �R0 → �T)(2)

where L is the number of resolved multipaths in the envi-ronment. When �R = �R0 and l = 0, we have s(0; �R) =∑L−1

m=0 |h(m, �T → �R0)|2 with all MPCs added up coherently,i.e., the signal energy is refocused at a particular spatial loca-tion at a specific time instance. This phenomenon is termedas the TR spatial-temporal resonating effect [40], [41].

To study the TR resonating effect in the spatial domain, wefix time index l = 0 and define the TR resonating strength(TRRS) between the CIRs of two locations �R0 and �R asthe normalized energy of the received signal when the TRwaveform for location �R0 is transmitted

η(h(�R0

), h

(�R))

=

∣∣∣∣∣∣∣∣∣∣

s(0; �R)

√L−1∑

l1=0|h(

l1; �T → �R0)|2

√L−1∑

l2=0|h(

l2; �T → �R)|2

∣∣∣∣∣∣∣∣∣∣

2

(3)

where we use h(�R) as an abbreviation ofh(l; �T → �R), l = 0, . . . , L − 1, when �T is fixed. Notethat the range of TRRS is normalized to be [0, 1] and TRRSis symmetric, i.e., η(h(�R0), h(�R)) = η(h(�R), h(�R0)).

We built a pair of customized TR devices to measure theTRRS at different locations, as shown in Fig. 2(a). The devicesoperate at f0 = 5.8 GHz ISM band with 125 MHz bandwidth,and the corresponding wavelength is λ = c/f0 = 5.17 cm. TheRX is placed on a 5 ×5 cm square area above a channel prob-ing table with 0.5 cm resolution, and the center of the squareis set to be the focal spot �R0. The TRRS distribution around �R0

4034 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 5, OCTOBER 2018

Fig. 3. Illustration of the polar coordinates in the analysis.

in the spatial domain and the normalized received energy at �R0in the time domain are shown in Fig. 2(b) and (c), respectively.As we can see from the results, the received energy is con-centrated around �R0 both in spatial and time domains almostsymmetrically, which shows that a bandwidth of 125 MHz isable to achieve the TR resonating effect in a typical indoorenvironment.

C. Energy Distribution of TR Focal Spot

Assume that all the EM waves propagate in a far-field zone,and then each MPC can be approximated by a plane EM wave.For the purpose of illustration, the receive antenna is placed inthe origin of the space and each MPC can be represented by apoint in the space whose coordinate is determined by its AoAand propagation distance, e.g., the point A, as shown in Fig. 3,where r stands for the total traveled distance of the MPC, θ

denotes the direction of arrival of the MPC, and G(ω) denotesthe power gain with ω = (r, θ). In a rich-scattering environ-ment, we can also assume that ω is uniformly distributed inthe space and the total number of MPCs is large. When a ver-tically polarized antenna is used, only the EM waves with thedirection of electric field orthogonal to the horizontal planeare collected. Then, the received signal is just a scalar sum ofthe electric field of the impinging EM waves along the verti-cal direction. In the sequel, without loss of generality, we onlyconsider the TRRS distribution in the horizontal plane sinceits distribution in the vertical plane is similar.

For a system with bandwidth B, two MPCs would be dividedinto different taps of the measured CIR as long as the differ-ence of their ToA is larger than the sampling period 1/B,that is, any two MPCs with a difference of their traveled dis-tances larger than c/B can be separated. With a sufficientlylarge system bandwidth B, the distance resolution c/B of thesystem is so small that all of the MPCs with significant energycan be separated in the spatial domain, i.e., each significantMPC can be represented by a single tap of a measured CIR.Assume that the distribution of the energy of each MPC isuniform in direction θ , i.e., the distribution of G(ω) is onlya function of r. Then the energy of MPCs coming from dif-ferent directions would be approximately the same when the

number of MPCs is large. Mathematically, for any point �R ina source-free region with constant mean electric and magneticfields, the CIR when a delta-like pulse is transmitted can bewritten as [39]

h(t; �T → �R)

=∑

ω∈�

G(ω)q(t − τ(ω))ei(

2π f0(t−τ(ω))−φ(ω)−�k(ω)·�R)

(4)

where q(t) is the pulse shaper, τ(ω) = r/c is the propagationdelay of the MPC ω, f0 is the carrier frequency, � is the setof MPCs, φ(ω) is the change of phase due to reflections, and�k(ω) is the wave vector with amplitude k = c/f0. Accordingly,the lth tap of a sampled CIR at location �R can be expressed as

h(l; �T → �R)

=∑

τ(ω)∈[lT− T

2 ,lT+ T2

)G(ω)q(�τ(l, ω))e

i(

2π f0�τ(l,ω)−φ(ω)−�k(ω)·�R)

(5)

where T is the channel measurement interval and �τ(l, ω) =lT − τ(ω) for l = 0, 1, . . . , L − 1. When the TR waveformh∗(−l; �R0 → �T) is transmitted, the corresponding receivedsignal at the focal spot �R0 can be written as

s(0; �R)

=L∑

l=1

∣∣∣∣∣∣∣

∑

τ∈[lT− T

2 ,lT+ T2

)G(ω)q(�τ(l, ω))ei(2π f0�τ(l,ω)−φ(ω))

∣∣∣∣∣∣∣

2

.

(6)

Equation (6) shows that the MPCs with propagation delaysτ(ω) ∈ [lT − (T/2), lT + (T/2)) for each l would be mergedinto one single tap, and the signals coming from different tapswould add up coherently while the MPCs within each sam-pling period T would add up incoherently. It indicates thatthe larger the bandwidth, the larger the TR focusing gain thatcan be achieved, since more MPCs can be aligned and addedup coherently. When the bandwidth is sufficiently large, thereceived signal at each point �R can be approximated as

s(0; �R) ≈

L∑

l=1

|G(ω)q(�τ(l, ω))|2e−i�k(ω)·(�R−�R0). (7)

When a rectangular pulse shaper is used, i.e., q(t) = 1 fort ∈ [ − (T/2), (T/2)) and q(t) = 0 otherwise, under the abovesymmetric scattering assumption the received signal s(0; �R)

can thus be approximated as

s(0; �R) =

∑

ω∈�

|G(ω)|2e−i�k·(�R−�R0)

≈∫ 2π

0P(θ)e−ikd cos(θ)dθ

= PJ0(kd) (8)

where the coordinate system in Fig. 3 is used, � standsfor the set of all significant MPCs, J0(x) is the zeroth-orderBessel function of the first kind, and d is the Euclidean dis-tance between �R0 and �R. Here we use a continuous integral

ZHANG et al.: WiBALL 4035

(a)

(b)

Fig. 4. Distributions of TRRS. (a) Comparison of the TRRS distributionbetween experimental results and the theoretical result. Experiments 1 and 2correspond to Location 1 and Location 2, respectively, in Fig. 2(a).(b) Illustration of the proposed TR-based speed estimation algorithm.

to approximate the discrete sum and P(θ) = P denotes thedensity of the energy of MPCs coming from direction θ .For �R = �R0, it degenerates to the case of d = 0 and thuss(0; �R0) ≈ P. Since the denominator of (3) is the product ofthe energy received at two focal spots, it would converge to P2.At the same time, the numerator is approximately P2J2

0(kd) asdiscussed above. As a result, the TRRS defined in (3) can beapproximated as

η(h(�R0

), h

(�R)) ≈ J20(kd). (9)

In the following, since the theoretic approximation of theTRRS distribution only depends on the distance between twopoints, we use η(d) = J2

0(kd) to stand for the approximationof TRRS between two points with distance d.

To evaluate the above theoretic approximation, we also builta mobile channel probing platform equipped with steppingmotors that can control the granularity of the CIR mea-surements precisely along any predefined direction. Extensivemeasurements of CIRs from different locations have been col-lected in the environment shown in Fig. 2(a). Fig. 4(a) showstwo typical experimental results measured at Location 1 andLocation 2 with a separation of 10 m as shown in Fig. 2(a).The distance d away from each predefined focal spot increasesfrom 0 to 2λ with a resolution of 1 mm. The measured TRRS

(a) (b)

(c)

Fig. 5. Numerical simulations of the distributions of TRRS with varyingbandwidth. (a) 40 MHz bandwidth. (b) 125 MHz bandwidth. (c) 500 MHzbandwidth.

distribution functions agree with the theoretic approximationquite well in the way that the positions of the peaks and valleysin the measured curves are almost the same as those of thetheoretic curve. Although Locations 1 and 2 are far apart, themeasured TRRS distribution functions exhibit similar dampingpattern when the distance d increases.

We also observe that the measured TRRS distribution func-tions are far above 0. This is due to the contribution of thedirect path between the TR devices. Therefore, the energydensity function P(θ) in (8) consists of a term which is sym-metric in direction due to NLOS components and another termwhich is asymmetric in direction due to LOS components. Asa result, the TRRS is indeed a superposition of J2

0(kd) andsome unknown function which is the result of the asymmetricnormalized energy distribution of MPCs in certain directions.Since the pattern of J2

0(kd), embedded in the TRRS distri-bution function, is location-independent, we can exploit thisfeature for speed estimation.

A numerical simulation using a ray-tracing approach isalso implemented to study the impact of bandwidth on TRRSdistribution. In the simulation, the carrier frequency of thetransmitted signals is set to be 5.8 GHz. Two hundred scat-terers are uniformly distributed in a 7.5 by 7.5 m square area.The reflection coefficient is distributed uniformly and inde-pendently in (0, 1) for each scatterer. The distance betweenthe TX and RX is 30 m and the RX (focal spot) is set to bethe center of the square area. Fig. 5 shows the distributionsof TRRS around the focal spot when the system bandwidth40 MHz, 125 MHz, and 500 MHz, respectively. As we can seefrom the results, as the bandwidth increases, the distribution ofTRRS in the horizontal plane becomes more deterministic-likeand converges to the theoretical approximations.

D. TR-Based Distance Estimator

Since the shape of the TRRS distribution function η(d) ≈J2

0(kd) is only determined by the wave number k which is

4036 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 5, OCTOBER 2018

Fig. 6. Empirical probability density for time intervals between adjacentpackets.

independent of specific locations, it can be utilized as an intrin-sic ruler to measure distance in the space. Consider that anRX moves along a straight line with a constant speed v start-ing from location �R0, and a TX keeps transmitting the TRwaveform corresponding to �R0 at regular intervals. Then, theTRRS measured at the RX is just a sampled version of η(d),which would also exhibit the Bessel-function-like pattern, asillustrated in Fig. 4(b).

Take the first local peak of η(d) for example. The corre-sponding theoretical distance d1 is about 0.61λ according tothe Bessel-function-like pattern. In order to estimate the mov-ing speed, we only need to estimate how much time t it takesfor the RX to reach the first local peak starting from point�R0. We use a quadratic curve to approximate the shape of thefirst local peak. Combining the knowledge of the timestampsof each CIR measurement, t can be estimated by the vertex ofthe quadratic curve. Therefore, we obtain the speed estimationas v = (0.61λ)/t, and then, the moving distance can be cal-culated by integrating the instantaneous speed over time. Onething to note is that as long as the rate of CIR measurement isfast enough, it is reasonable to assume that the moving speedis constant during the measurement of the TRRS distribution.For example, in Fig. 4(b) the duration is about 0.16 s.

In practice, the channel is not measured with a uniforminterval and the empirical probability density function ofthe time interval between adjacent channel measurements isshown in Fig. 6. To overcome the imperfect channel samplingprocess, we combine multiple realizations of the TRRS dis-tribution function measured at adjacent time slots to increasethe accuracy of the estimation of t. For the ith measurement,first find the data points near the first local peak (ti,j, yi,j),i = 1, . . . , N, j = 1, 2, 3, as shown in Fig. 4(b), where Nis the number of TRRS distribution functions obtained withinthe window of channel measurements. Then fit the data pointswith a quadratic regression model yi,j = α +βti,j + γ t2i,j + ei,j,

and thus estimation of the elapsed time is t = −βLS/(2γLS),where βLS and γLS are the least-square estimators of β andγ , respectively. Different reference points can be used as well,such as the first local valley, the second local peak, and so on,to increase the accuracy of estimation. Therefore, the movingdistance at time t can be estimated as d(t) = v(t)�t, where �tdenotes the time duration between the current packet and theprevious packet. The procedures of the proposed TR-based dis-tance estimator has been summarized in the flowchart shownin Fig. 7.

Fig. 7. Flowchart of the TR-based distance estimator.

Fig. 8. Transforming the rotation of RX into the moving direction inhorizontal plane.

Note that besides taking advantage of TR spatial focusingeffect, the proposed distance estimator also exploits the phys-ical properties of EM waves and thus does not require anyprecalibration, while the estimator presented in our previouswork [40] needs to measure the TRRS spatial decay curve inadvance.

IV. MOVING DIRECTION ESTIMATION AND

ERROR CORRECTION

In this section, we introduce the other two key componentsof WiBall: 1) the IMU-based moving direction estimator and2) the map-based position corrector.

A. IMU-Based Moving Direction Estimator

If the RX is placed in parallel to the horizontal plane,the change of moving direction can be directly measuredby the readings of the gyroscope in the z-axis, i.e., θ(ti) =ωz(ti−1)(ti − ti−1), where ωz(ti−1) denotes the angular veloc-ity of the RX with respect to z-axis in its local coordinatesystem at time slot ti−1. However, in practice, the angle ofthe inclination between the RX and the horizontal plane isnot zero, as shown in Fig. 8, and WiBall needs to transformthe rotation of the RX into the change of the moving direc-tion in the horizontal plane. Since the direction of the gravity�g/‖�g‖ can be estimated by the linear accelerometer, the rota-tion of the RX in the horizontal plane, which is orthogonal tothe �g/‖�g‖, can be obtained by projecting the angular velocityvector �ω = ωxx + ωyy + ωzz with respect to its local coordi-nate system onto the direction �g/‖�g‖. Therefore, the change

ZHANG et al.: WiBALL 4037

Fig. 9. Two possible estimated paths and the ground truth path.

of moving direction θ(ti) is obtained as

θ(ti) = �ωT(ti−1)�g(ti−1)

‖�g(ti−1)‖ · (ti − ti−1) (10)

where �ω(ti−1) and �g(ti−1) denote the vector of angular velocityand the gravity at time ti−1, respectively.

B. Map-Based Position Corrector

Since WiBall estimates the current location of the RX basedon the previous locations, its performance is limited by thecumulative error. However, for typical indoor environments,there are certain constraints in the floorplan which can be uti-lized as landmarks and thus, the cumulative errors may becorrected correspondingly as long as a landmark is identified.For example, Fig. 9 shows a T-shaped corridor and two pos-sible estimated paths are illustrated in the figure. The movingdistance of path #1 is underestimated and that of path #2 isoverestimated, while the dotted line corresponds to the groundtruth path. Both of the estimated traces would penetrate thewall in the floorplan if the errors are not corrected, whichviolates the physical constraints imposed by the structure ofthe building. In these two cases, a reasoning procedure can beimplemented and WiBall tries to find the most possible paththat can be fitted to the floorplan where all the border con-straints imposed by the floorplan are satisfied. Therefore, thecumulative errors of both the distance estimations and direc-tion estimations can be corrected when a map-based positioncorrection is implemented.

V. PERFORMANCE EVALUATION

To evaluate the performance of WiBall, various experimentsare conducted in different indoor environments using the pro-totype as shown in Fig. 2(a). In this section, we first evaluatethe performance of the TR-based distance estimator. Then, theperformance of WiBall in tracking a moving object in two dif-ferent environments is studied. At last, the impact of packetloss and system window length on the proposed system is alsodiscussed.

A. Evaluations of TR Distance Estimator

The first experiment is to estimate the moving distance of atoy train running on a track. We put one RX on a toy train asshown in Fig. 10(a) and place one TX about 20 m from the RXwith two walls between them. The sampling period between

(a)

(b)

Fig. 10. Tracking the speed of the toy train. (a) Toy train and the train trackused in the experiment. (b) Estimated speed of the toy train over time.

adjacent channel measurement is set to T = 5 ms. CIRs arecollected continuously when the toy train is running on thetrack. We also set an anchor point as shown in Fig. 10(a) onthe train track and collect the CIR when the train is at theanchor. The TRRS values between all the measured CIRs andthe CIR of the anchor are computed and shown in Fig. 10(b).The peaks in the red line indicate that the train passes theanchor three times. The estimated length of the track for thissingle loop is 8.12 m and the error is 1.50%, given the actuallength of the train track is 8.00 m. The train slows down whenit makes turns due to the increased friction and then speedsup in the straight line. This trend is reflected in the speedestimation shown by the blue curve. To show the consistencyof the distance estimator over time, we collect the CIRs for100 laps in total and estimate the track length for each lapseparately. The histogram of the estimation results is shownin Fig. 11. The mean of the estimation error is about 0.02 mand the standard error deviation is about 0.13 m, which showsthat the estimation is consistent even over a long period.

The second experiment is to estimate the human walkingdistance. One RX is put on a cart and one participant pushesthe cart along the line from point A to point B shown inFig. 2(a) with an approximately constant speed of 1 m/s. Tocontrol the walking speed, the participant uses a timer andlandmarks placed on the floor during the experiment. In theupper panel of Fig. 12(a), for each time t, the TRRS valuesbetween the CIR measured at time t and those measured at

4038 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 5, OCTOBER 2018

Fig. 11. Histogram of the estimated track lengths for a total of 100experiments.

(a)

(b)

Fig. 12. Human walking speed/distance estimation. (a) Speed estimation fora controlled human walking speed (1m/s). (b) Results for walking distanceestimation.

time t − �t, where �t ∈ (0 s, 0.16 s], are plotted along thevertical axis. As we can see from the figure, when the per-son moves slowly (e.g., at the beginning or the end of theexperiment), the time differences between the local peaks ofthe measured TRRS distribution along the vertical axis aregreater than that when the person moves faster. In addition, fort ∈ [0.5 s, 3.5 s], the asymmetric part of the density functionP(θ) of the energy of MPCs is more significant compared to

the case when t ∈ [3 s, 9.5 s] and thus the pattern of J2(kd) isless obvious than the latter one. The bottom panel of Fig. 12(a)shows the corresponding walking speed estimation. The actualdistance is 8 m and the estimated walking distance is 7.65 m,so the corresponding error is 4.4%. The loss of performanceis from the blockage of signals by the human body, whichreduces the number of significant MPCs.

We further let the participant carry the RX and walk for adistance of 2 m, 4 m, 6 m, 8 m, 10 m, and 12 m, respec-tively. The ground-truth travel distances are measured by alaser distance meter. For each ground-truth distance, the exper-iment is repeated 20 times with different paths and the walkingspeed does not need to be constant. The results are shown inFig. 12(b), where the 5, 25, 75, and 95th percentiles of theestimated distances for each actual distance are plotted fromthe bottom line to the top line for each block. We find thatwhen the ground-truth distance is small, the error tends to belarge. This is mainly because the participant could introduceadditional sources of errors which are uncontrollable, such asnot following the path strictly, shaking during walking, and notstopping at the exact point in the end. When the distance isshort, the impact of this kind of error can be magnified greatly.However, when the walking distance is large, the impact of theuncontrollable errors on the estimation result is insignificant.

B. Estimated Traces in Different Environment

We evaluate the performance of indoor tracking usingWiBall in two sets of experiments. In the first set of experi-ments, a participant walks inside a building with a large openspace. He carriers the RX with him and walks from point Aon the second floor to point B on the first floor, as shownin Fig. 13(a). The TX is placed closed to the middle of thepath on the second floor. The dimension of the building isaround 94 m × 73 m. Although the moving distance of thefirst segment of the path is overestimated, the estimated pathis corrected when the participant enters the staircase leadingto the first floor.

In the second set of experiments, the participant walksinside an office environment. Fig. 13(b) demonstrates atypical example of the estimated traces in a typical officeof a multistory. One RX is put on a cart and the participantpushes the cart along the route from point A to point B, asillustrated in the figure. The dimension of the environmentis around 36.3 m × 19 m and the placement of the TX isalso shown in the figure. As we can see from the figure,the estimated path matches the ground truth path very wellbecause the cumulative errors have been corrected by theconstraints from the floorplan.

C. Statistical Analysis of Localization Error

To evaluate the distribution of the localization errors,extensive experiments have been conducted in the same officeenvironment shown in Fig. 13(b). The participant pushes thecart with the RX on the cart, following the route as shown inFig. 14.

The RX starts from Point A and stops at different locationsin the route shown in Fig. 14. The lengths of the chosen paths

ZHANG et al.: WiBALL 4039

(a)

(b)

Fig. 13. Experiment results in different environments. (a) Estimated path in abuilding with a lot of open space. (b) Estimated path in an office environment.

Fig. 14. Route for the evaluation of statistical errors.

are 5, 21, 25, 30, 40, 64, and 69 m, respectively, and the end ofeach path is marked with two green circles. For each specificpath, the experiment is repeated for 25 times. The estimationerror for different paths has been analyzed through empiricalcumulative distribution function, as shown in Fig. 15. Based onthe results, the median of the estimation error for the selectedpaths is around 0.33 m, and the 80 percentile of the estimationerror is within 1 m. Therefore, WiBall is able to achieve asubmeter median error in this complex indoor environment.

Fig. 15. Empirical CDF of localization error.

(a) (b)

Fig. 16. Impact of packet loss on the accuracy of distance estimation.(a) Sample mean of the distance estimation. (b) Standard deviation of thedistance estimation.

D. Impact of Packet Loss on Distance Estimation

In the previous experiments, WiBall operates on a vacantband and the packet loss rate can thus be neglected. However,in practice, the RF interference from other RF devices operatedon the same frequency band will increase the packet loss rate.Since WiBall relies on the first peak of the TRRS distributionfor distance estimation, enough samples need to be collectedso as to estimate the first peak accurately, and a high packetloss can affect the peak estimation and thus increase distanceestimation error.

To study the impact of RF interference, a pair of RF devicesis configured to operate in the same frequency band of WiBallto act as an interference source, and we run the tracking systemfor 100 times with the ground-truth distance being 10 m. Whenthe interfering devices are placed closer to the transmissionpair of WiBall, WiBall encounters a higher packet loss rate.Therefore, to obtain various packet loss rates, the interferingdevices are placed at different locations during the experi-ment. The average estimated distance and standard deviationof the estimation under different packet loss rates are shownin Fig. 16. It is seen that a large packet loss rate would leadto an underestimation of the moving distance and increase thedeviations of the estimates.

E. Impact of Window Length on Distance Estimation

In the following, the impact of window length on theperformance of the proposed TR-based distance estimator isstudied. One implicit assumption of the proposed estimator

4040 IEEE INTERNET OF THINGS JOURNAL, VOL. 5, NO. 5, OCTOBER 2018

Fig. 17. Impact of window length in terms of speed estimations.

is that the speed of the moving device is constant within theobservation window of channel measurements. The length ofthe observation window should be at least 0.61 λ/v, where vis the actual speed of the device. Furthermore, more samplesof channel measurements will also improve the accuracy of tas described in Section III-D. Therefore, the window length isan important system parameter of WiBall.

In the following experiments, one RX is put on a toy trainwhose speed can be tuned and remains constant during eachexperiment. One TX is placed in two different locations: 1) anLOS location where the RX is within the fields of vision of theTX and 2) an NLOS location where the direct path betweenthe RX and TX is blocked by walls. The TX keeps transmit-ting packets with a uniform interval of 5 ms. Two experimentsare conducted for each location of the TX with two differentspeeds of the toy train, 0.72 m/s and 0.63 m/s, respectively,and each experiment lasts 10 min. The 5th and 95th percentilesand the sample mean of the estimated speed have been shownin Fig. 17 with different window lengths. It can be observedthat when the window length is smaller than 30 samples, thespeed estimates have a bias for the both cases; when the win-dow length is greater or equal to 30 samples, the bias is closeto 0 and the range of the estimates becomes stable. In addition,a higher accuracy can be achieved when the TX is placed inthe NLOS location.

VI. CONCLUSION

In this paper, we propose WiBall, which offers an accu-rate, low-cost, calibration-free, and robust solution for INIPin indoor environments without requiring any infrastructure.WiBall leverages the physical properties of the TR focusingball in radio signals, such as WiFi, LTE, 5G, etc., to estimatethe moving distance of an object being monitored and doesnot need any specialized hardware. It is shown through exten-sive experiments that WiBall can achieve a decimeter-levelaccuracy. WiBall is also easily scalable and can accommodatea large number of users with only a single access point orTX. Therefore, WiBall can be a very promising candidate forfuture indoor tracking systems.

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Feng Zhang (S’12) received the B.S. andM.S. degrees from the Department of ElectronicEngineering and Information Science, University ofScience and Technology of China, Hefei, China, in2011 and 2014, respectively. He is currently pursu-ing the Ph.D. degree at the Department of Electricaland Computer Engineering, University of Marylandat College Park, College Park, MD, USA.

His current research interests include wirelesssensing, statistical signal processing, and wirelessindoor localization.

Mr. Zhang was a recipient of the Distinguished TA Award from theUniversity of Maryland at College Park the State Scholarship from theUniversity of Science and Technology of China.

Chen Chen (S’15) received the B.S. and M.S.degrees from the Department of Microelectronics,Fudan University, Shanghai, China, in 2010 and2013, respectively, and the Ph.D. degree from theDepartment of Electrical and Computer Engineering,University of Maryland College Park at CollegePark, College Park, MD, USA in 2017.

He was with Origin Wireless, Inc., Greenbelt,MD, USA. He is currently with Pinterest, Inc.,San Francisco, CA, USA.

Dr. Chen was a recipient of multiple honors andawards, including the Chinese Government Award for Outstanding StudentsAbroad in 2017, the Best Student Paper Award of IEEE ICASSP 2016, theLitton Industries Fellowship from the University of Maryland at CollegePark in 2015, the Distinguished Graduate Student Teaching Award from theUniversity of Maryland at College Park in 2014, and the Excellent GraduateStudent of Shanghai in 2013.

Beibei Wang (SM’15) received the B.S. degree(Highest Hons.) in electrical engineering from theUniversity of Science and Technology of China,Hefei, China, in 2004, and the Ph.D. degree in elec-trical engineering from the University of Marylandat College Park, College Park, MD, USA, in 2009.

She was with the University of Marylandat College Park, as a Research Associate from2009 to 2010, and with Qualcomm Research andDevelopment, San Diego, CA, USA, from 2010 to2014. Since 2015, she has been with Origin Wireless

Inc., Greenbelt, MD, USA, where she is currently a Chief Scientist. She co-authored Cognitive Radio Networking and Security: A Game-Theoretic View(Cambridge Univ. Press, 2010). Her current research interests include wirelesscommunications and signal processing.

Dr. Wang was a recipient of the Graduate School Fellowship, the FutureFaculty Fellowship, the Dean’s Doctoral Research Award from the Universityof Maryland at College Park, and the Overview Paper Award from the IEEESignal Processing Society in 2015.

Hung-Quoc (Quoc) Lai received the B.S. (cumlaude), M.S., and Ph.D. degrees from the Universityof Maryland at College Park, College Park, MD,USA, in 2004, 2006, and 2011, respectively, all inelectrical engineering.

He was a Technical Lead in research and devel-opment of multiple-input multiple-output and coop-erative communications with U.S. Army RDECOMCERDEC, Aberdeen Proving Ground, MD, USA.In 2013, he joined Origin Wireless, Inc., Greenbelt,MD, USA, where he is a founding member and

currently the Vice President of Engineering, which develops advanced timereversal wireless technologies for use in a wide variety of applications ofindoor positioning/tracking, monitoring, security, radio human biometrics,wireless power transfer, and 5G communications.

Dr. Lai is a Gates Millennium Scholar.

Yi Han received the B.S. degree (Highest Hons.)in electrical engineering from Zhejiang University,Hangzhou, China, in 2011, and the Ph.D. degreefrom the Department of Electrical and ComputerEngineering, University of Maryland at CollegePark, College Park, MD, USA, in 2016.

He is currently the Wireless Architect with OriginWireless, Inc., Greenbelt, MD, USA. His currentresearch interests include wireless communicationand signal processing.

Dr. Han was a recipient of the Class A Scholarshipfrom Chu Kochen Honors College, Zhejiang University, in 2008 and the BestStudent Paper Award of IEEE ICASSP in 2016.

K. J. Ray Liu (F’03) was named a DistinguishedScholar–Teacher of the University of Maryland atCollege Park, College Park, MD, USA, in 2007,where he is a Christine Kim Eminent Professorof Information Technology. He leads the MarylandSignals and Information Group, conducting researchencompassing broad areas of information and com-munications technology with a recent focus on wire-less AI.

Dr. Liu was a recipient of the 2016 IEEELeon K. Kirchmayer Award on graduate teaching

and mentoring, the IEEE Signal Processing Society 2014 Society Award,the IEEE Signal Processing Society 2009 Technical Achievement Award,the Highly Cited Researcher Award by Web of Science, the 2017 CEATECGrand Prix Award for his invention of the time-reversal machine by OriginWireless Inc., teaching and research recognitions from the University ofMaryland at College Park, including the University-Level Invention of theYear Award, the College-Level Poole and Kent Senior Faculty TeachingAward, the Outstanding Faculty Research Award, and the Outstanding FacultyService Award, all from A. James Clark School of Engineering, and over adozen of Best Paper Awards. He has also served as the Editor-in-Chief of theIEEE Signal Processing Magazine. He is the IEEE Technical Activities VicePresident-Elect. He was the President of IEEE Signal Processing Society,where he has served as the Vice President (Publications and Board ofGovernor), and a member of the IEEE Board of Director as the DivisionIX Director. He is a Fellow of the AAAS.