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Achieving Centimeter Accuracy Indoor Localizationon WiFi
Platforms: A Frequency Hopping Approach
Chen Chen, Student Member, IEEE, Yan Chen, Senior Member, IEEE,
Yi Han, Student Member, IEEE,Hung-Quoc Lai, and K. J. Ray Liu,
Fellow, IEEE
Abstract—Indoor positioning systems are attracting more andmore
attention from the academia and industry recently. Amongthem,
approaches based on WiFi techniques are more favorablesince they
are built upon the WiFi infrastructures available inmost indoor
spaces. However, due to the bandwidth limit in main-stream WiFi
systems, the indoor positioning system leveragingWiFi techniques
can hardly achieve centimeter localization accu-racy under strong
non-line-of-sight conditions, which is commonfor indoor spaces. In
this paper, we present a WiFi-based indoorpositioning system that
achieves centimeter accuracy in non-line-of-sight scenarios by
exploiting the frequency diversity viafrequency hopping. During the
offline phase, the system collectschannel state information from
multiple channels at locations-of-interest. Then, the channel state
information are post-processed tocombat the synchronization errors
and interference. The channelstate information from multiple
channels are then combinedinto location fingerprints via bandwidth
concatenation and ina database. During the online phase, channel
state informationfrom an unknown location are formulated into the
locationfingerprint and is compared against the fingerprints in
thedatabase using the time-reversal resonating strength. Finally,
thelocation is determined by the calculated time-reversal
resonatingstrengths. Extensive experiment results demonstrate a
perfectcentimeter accuracy in an office environment in
non-line-of-sightscenarios with only one pair of single-antenna
WiFi devices.
Index Terms—WiFi, indoor localization, channel state
infor-mation, time-reversal, resonating strength.
I. INTRODUCTION
Global Positioning System (GPS) is an outdoor positioningsystem
that provides real-time location information under allweather
conditions near the Earth’s surface, as long as thereexists an
unobstructed line-of-sight (LOS) from the device toat least four
GPS satellites [1]. On the other hand, accurateindoor localization
is highly desirable, since nowadays peoplespend much more time
indoor than outdoor. A high accuracyindoor positioning system (IPS)
can enable a wide varietyof applications, e.g., providing museum
guides to tourists bylocalizing their exact locations [2], or
supplementing userswith location information in shopping malls [3].
Unfortunately,the GPS signal cannot provide reliable location
informationindoor, since it is severely attenuated by the walls in
thebuilding and scattered by numerous reflectors in an
indoorenvironment.
All the authors are with Origin Wireless, Inc., Greenbelt, MD
20770 USA.Chen Chen, Yi Han, and K. J. Ray Liu are also with the
Department ofElectrical and Engineering, University of Maryland
College Park, CollegePark, MD 20742 USA (e-mail: {cc8834, yhan1990,
kjrliu}@umd.edu). YanChen is also with University of Electronic
Science and Technology of China,Chengdu, Sichuan, China (e-mail:
[email protected]). Hung-Quoc Lai iswith Origin Wireless Inc.
(e-mail: [email protected]).
Many research efforts have been devoted to the developmentof
accurate and robust IPSs. According to the technologiesadopted,
these IPSs can be further classified into two classes,i.e.,
ranging-based and fingerprint-based [4]. For the ranging-based
methods, at least three anchors are deployed into theindoor
environment to triangulate the device through measur-ing the
relative distances between the device to the anchors.The distances
are generally obtained from other measurements,e.g., received
signal strength indicator (RSSI) and time ofarrival (TOA).
RSSI-based ranging methods [5]–[7] utilizesthe path-loss model to
derive the distance and can typicallyachieve an accuracy of 1 ∼ 3m
on average under LOSscenarios, while TOA-based ranging methods
retrieve the TOAof the first arrived multipath component from the
channelimpulse response (CIR). To achieve a fine timing
resolution,TOA-based methods require a large bandwidth, which
isavailable with ultra-wideband (UWB) techniques. With UWB,the
localization accuracy is 10 ∼ 15cm in a LOS setting [8],[9].
On the other hand, the fingerprint-based approaches harnessthe
naturally existing spatial features associated with
differentlocations, e.g., RSSI, CIR, and channel state
information(CSI), where CSI is a fine-grained information readily
avail-able in WiFi systems that portraits the environment. In
theseschemes, fingerprints of different locations are stored in
adatabase during the offline phase. In the online phase,
thefingerprint of the current location is compared against thosein
the database to estimate the device location. In [10]–[12],RSSI
values from multiple access points (APs) are utilizedas the
fingerprint, leading to an accuracy of 2 ∼ 5m. Theaccuracy is
further improved to 0.95 ∼ 1.1m by taking CSIsas the fingerprint
[13]–[15]. In [16], Zhung-Han et al. obtainCIR fingerprints under a
bandwidth of 125 MHz and calculatethe time-reversal (TR) resonating
strength as the similaritymeasure among different locations, which
gives an accuracyof 1 ∼ 2cm under non-line-of-sight (NLOS)
scenarios.
Summarizing the ranging-based and fingerprint-basedschemes, we
find that
1) The accuracy of the ranging-based methods are sus-ceptible to
the correctness of the physical rules, e.g.,path-loss model, which
degrades severely in the complexindoor environment. The existence
of large number ofmultipath components and blockage of obstacles
inindoor spaces impair the precision of the physical rules.
2) The fingerprint-based methods, which can work understrong
NLOS environment, require a large bandwidth foraccurate
localization. Since the maximum bandwidth of
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the mainstream 802.11n is 40 MHz, IPSs utilizing WiFitechniques
cannot resolve enough independent multipathcomponents in the
environment. The shortage of avail-able bandwidth introduces
ambiguities into fingerprintsassociated with different locations,
and thus degrades thelocalization accuracy. On the other hand, a
bandwidth aslarge as 125 MHz that leads to centimeter accuracy
[16]can only be achieved on dedicated hardware and incursadditional
costs in deployment.
Is there any approach that can achieve the centimeter
local-ization accuracy using WiFi devices in an NLOS
environment?The answer is affirmative. In [17], Chen et al. present
an IPSthat achieves centimeter accuracy using one pair of
single-antenna WiFi devices under strong NLOS conditions
usingfrequency hopping. The IPS obtains CSIs and formulateslocation
fingerprints from multiple WiFi channels in the offlinephase, and
calculates TR resonating strengths for localizationin the online
phase. However, interference from other WiFinetworks might corrupt
the fingerprint, which is neglectedin [17]. To deal with the
interference, in this work, weintroduce an additional step of CSI
sifting. Moreover, weutilize CSI averaging to mitigate the impact
of channel noiseand refine the fingerprint. Additionally, we
provide much moredetails and analysis on the experiment results. In
comparisonwith the existing works, the proposed method embraces
themultipath effect and is infrastructure-free since it is built
uponthe WiFi networks available in most indoor spaces.
The main contributions of this work can be summarized
asfollows:• We propose an IPS that can achieve centimeter
accuracy
in an NLOS environment with one pair of single-antennaWiFi
devices. The proposed IPS eliminates the impactof interference from
other WiFi networks through theprocess of CSI sifting.
• Leveraging the frequency diversity, we demonstrate thata large
effective bandwidth can be achieved on WiFidevices by means of
frequency hopping to overcome theissue of location ambiguity issue
on traditional WiFi-based approaches.
• We conduct extensive experiments in a typical
officeenvironment to show the centimeter accuracy within anarea of
20cm×70cm under strong NLOS conditions.
The rest of the paper is organized as follows. In Section II,we
introduce the TR technique and the channel estimation inWiFi
systems. In Section III, we elaborate on the proposedlocalization
algorithm. In Section IV, we present the experi-ment results in a
typical office environment. Finally, we drawconclusions in Section
V.
II. PRELIMINARIES
In this part, we introduce the background of the TR tech-nique
and the channel estimation schemes in WiFi systems.
A. Time-Reversal
TR is a signal processing technique capable of mitigatingthe
phase distortion of a signal passing a linear time-invariant
(LTI) filtering system. It is based upon the fact that when
theLTI system h(t) is concatenated with its time-reversed
andconjugated version h∗(−t), the phase distortion is
completelycancelled out at a particular time instance.
A physical medium can be regarded as LTI if it
satisfiesinhomogeneity and invertibility. When both conditions
hold,TR focuses the signal energy at a specific time and at a
par-ticular location, known as the spatial-temporal focusing
effect.Such focusing effect is observed experimentally in the field
ofultrasonics, acoustics, as well as electromagnetism
[18]–[21].Leveraging the focusing effect, TR is applied
successfully tothe broadband wireless communication systems
[22].
Fig. 1 shows the architecture of the TR communication sys-tem
consisting of two phases, namely, channel probing phaseand
transmission phase. Here, we assume that transceiverA intends to
send some data to transceiver B. During thechannel probing phase,
transceiver B sends an impulse signalto transceiver A, and
transceiver A extracts the CIR basedon the impulse signal,
time-reverses, and takes conjugate ofthe CIR to generate a
waveform. During the transmissionphase, transceiver A convolves the
transmitted signal withthe waveform and sends to transceiver B. In
this process,the channel acts as a natural matched filter due to
the time-reversal operation. The TR focusing effect could be
observedat a specific time instance and only at the exact location
oftransceiver B.
In virtue of the high-resolution TR focusing effect, in
thiswork, we utilize TR as the signal processing technique to
mea-sure the similarity among fingerprints of different
locations.
Fig. 1. The architecture of TR wireless communication
system.
B. Channel Estimation in WiFi systems
In a WiFi system adopting the orthogonal frequency-division
multiplexing (OFDM), the transmitted data symbolsare spread onto
several subcarriers to improve the robustnessof the wireless
communication against frequency-selectivefading. Assuming a total
of K usable subcarriers and denotethe transmitted data symbol on
the k-th subcarrier with indexuk as Xuk , the received signal on
subcarrier uk, denoted byYuk , takes the form as [23]
Yuk = HukXuk +Wuk , k = 1, 2, · · · ,K, (1)
where Huk is the CSI on subcarrier uk and Wuk is the
complexGaussian noise on subcarrier uk.
To facilitate channel estimation, two identical
sequencesconsisting of predetermined data symbols, known as the
long
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CSI
Acquisition
?No Yes
Fingerprint
Database
Fingerprint
Generation
Fingerprint
Database
Calculating
Resonating
StrengthLocalization
Fig. 2. Flowchart of the algorithm.
training preamble (LTP), are appended before the actual
dataframes. Therefore, given known LTP data symbols Xuk,0, theCSI
Huk can be estimated by [24]
Ĥuk =YukXuk,0
, k = 1, 2, · · · ,K. (2)
Eq. (2) is only valid in the absence of synchronizationerrors.
In practice, synchronization errors cannot be neglectedand they
introduce additional phase rotations into Ĥuk . Thesynchronization
errors are mainly composed by (i) channelfrequency offset (CFO) �
caused by the misalignment ofthe local oscillators at the WiFi
transmitter and receiver (ii)sampling frequency offset (SFO) η due
to the mismatchbetween the sampling clock frequencies at the WiFi
transmitterand receiver (iii) symbol timing offset (STO) ∆n0 caused
bythe imperfect timing synchronization at the WiFi receiver.
In the presence of the aforementioned synchronization er-rors,
the CSI associated with the i-th LTP, denoted as Ĥuki ,can be
rewritten as [25]
Ĥuki = Hukej2π(βiuk+αi) +Wi,uk , k = 1, 2 · · · ,K , (3)
where
αi =
(1
2+iNs +Ng
N
)� (4)
βi =∆n0N
+
(1
2+iNs +Ng
N
)η (5)
are the initial and linear phase distortions respectively. N
isthe size of Fast Fourier Transform (FFT), Ng is the lengthof the
cyclic prefix, Ns is the total length of one OFDMframe with length
N +Ng , and Wi,uk is the estimation noiseon subcarrier uk for the
i-th LTP, which can be modeled ascomplex Gaussian noise [26].
III. PROPOSED ALGORITHM
A. Calculation of the TR Resonating Strength in
FrequencyDomain
In the proposed IPS, the similarity of locations are measuredby
the TR resonating strength between their fingerprints. Inthis
section, we provide details of TR resonating
strengthcomputation.
Given two time-domain CIRs ĥ and ĥ′, with ĥ =[ĥ[0], ĥ[1], ·
· · , ĥ[L− 1]]T and ĥ′ defined similarly, where Tis the transpose
operator, the resonating strength between ĥand ĥ′ is calculated
as [16]
γCIR[ĥ, ĥ′] =
maxi
∣∣∣(ĥ ∗ ĝ) [i]∣∣∣2〈ĥ, ĥ〉〈ĝ, ĝ〉
, (6)
where ∗ denotes the convolution operator, ĝ is the
time-reversed and conjugate version of ĥ′, and 〈x,y〉 is the
innerproduct operator between vector x and vector y, expressed
byx†y. Here, (·)† is the Hermitian operator. Notice that, the
com-putation of γCIR[ĥ, ĥ′] removes the impact of STO by
search-ing all possible index i across the output of
∣∣∣(ĥ ∗ ĥ′) [i]∣∣∣. Itcan be shown that 0 ≤ γCIR[ĥ, ĥ′] ≤
1.
Since the convolution in time domain is equivalent to theinner
product in frequency domain [27], the TR resonat-ing strength can
be calculated using CSIs, the frequency-domain counterparts of
CIRs. Given two CSIs Ĥ =[Ĥu1 , Ĥu2 , · · · , ĤuK ]T and Ĥ′
defined similarly, and assumethat the synchronization errors are
mostly mitigated, the TRresonating strength in frequency domain is
given by
γ[Ĥ, Ĥ′] =
∣∣∣∑Kk=1 ĤukĤ ′uk ∣∣∣2〈Ĥ, Ĥ〉〈Ĥ′, Ĥ′〉
. (7)
It is straightforward to prove that 0 ≤ γ[Ĥ, Ĥ′] ≤ 1, andγ[Ĥ,
Ĥ′] = 1 if and only if Ĥ = CĤ′ where C 6= 0 is anycomplex
scaling factor. Therefore, the TR resonating strengthcan be
regarded as a measure of similarity between two CSIs.
B. Indoor Localization Based on TR Resonating Strength
The proposed localization algorithm consists of an offlinephase
and an online phase. The details of the two phases areillustrated
in Fig. 2 and are elaborated below.
1) Offline Phase: In the offline phase, the CSIs are mea-sured
at D channels, denoted by f1, f2, · · · , fd, · · · , fD, and atL
locations-of-interest, denoted by 1, 2, · · · , `, · · · , L.
Assumethat a total of N`,fd CSIs are measured from the first
andsecond LTPs at location ` and channel fd, we write the CSImatrix
as
Ĥi [`, fd] =[Ĥi,1[`, fd] · · · Ĥi,m[`, fd] · · · Ĥi,N`,fd
[`, fd]
],
(8)where m = 1, 2, · · · , N`,fd is the realization index,i ∈
{1, 2} is the LTP index, and Ĥi,m[`, fd] =[Ĥu1i,m[`, fd] · · ·
Ĥ
uki,m[`, fd] · · · Ĥ
uKi,m[`, fd]]
T with Ĥu1i,m[`, fd]standing for the m-th CSI of the i-th LTP
on subcarrier uk,and at location `, channel fd.
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Fig. 3. An example of CSI post-processing, channel fingerprint
generation, and location fingerprint generation.
The location fingerprint is generated from Ĥi [`, fd].
Theprocess contains 4 steps, which are presented below.
1. CSI SanitizationThe captured CSIs must be sanitized so as to
mitigate theimpact of initial and linear phase distortions shown in
(3).First of all, we estimate the residual CFO and SFO from
thechannel estimation using [28]
Ωukm [`, fd] =[Ĥuk1,m[`, fd]
]∗× Ĥuk2,m[`, fd]
= ej2πNsN φuk |Huk1,m[`, fd]|2sinc
2 (πφuk) + ψukm [`, fd], (9)
where φk = � + ηk, sinc2 (πφk) ≈ 1 since πφuk is small,and ψukm
[`, fd] contains all cross terms. Therefore, φuk can beestimated
by
φ̂uk = ] [Ωukm [`, fd]] , (10)
where ][X] is the angle of X measured in radians. Compen-sating
φ̂uk gives
H̃uki,m[`, fd] = Ĥuki,m[`, fd]e
−jπφ̂uk e−j2πNg+(i−1)Ns
N φ̂uk (11)
Substituting (11) into (8) and writing the updated Ĥi [`, fd]in
(8) as H̃i [`, fd], we take the average of H̃1 [`, fd] andH̃2 [`,
fd] as H̃ [`, fd] =
(H̃1 [`, fd] + H̃2 [`, fd]
)/2.
After the removal of residual CFO and SFO, the STO stillremains
to be compensated. Write
H̃ [`, fd] =[H̃1[`, fd] · · · H̃m[`, fd] · · · H̃N`,fd [`,
fd]
], (12)
where H̃m[`, fd] = [H̃u1m [`, fd] · · · H̃ukm [`, fd] · · ·
H̃uKm [`, fd]]Tis the CSI vector for the m-th realization on usable
sub-carriers after CFO/SFO correction. Denote Aukm [`, fd] =]{H̃ukm
[`, fd]
}as the angle of H̃ukm [`, fd], we perform phase
unwrapping on Aukm [`, fd] to yield A′ukm [`, fd]. The slope
of
A′ukm [`, fd] is linear with STO if we disregard the noise
and
interference. To estimate the slope, we perform a
least-squarefitting on A
′ukm [`, fd] expressed by
∆̂n0 =N∑Kk=1 [(uk − u)]
[A′ukm [`, fd]−A
]2π∑Kk=1 [uk − u]
2, (13)
where u =∑Kk=1 ukK and A =
∑Kk=1 A
′ukm [`,fd]
K . Therefore,H̃ukm [`, fd] is compensated as
Ȟukm [`, fd] = H̃ukm [`, fd]e
−juk∆̂n0 2πN . (14)
The compensated CSI matrix is denoted by
Ȟ [`, fd] =[Ȟ1[`, fd] · · · Ȟm[`, fd] · · · ȞN`,fd [`,
fd]
]. (15)
2. CSI SiftingDue to the presence of other WiFi devices in the
envi-ronment, some CSI measurements might suffer from
largeinterference from the traffic of nearby WiFi devices or
radio-frequency systems, and should be excluded from
furthercalculations. The interference introduces random noise
ontothe CSIs and impairs the CSI qualities. To combat the
in-terference, firstly, we use Ȟm[`, fd] to calculate the N`,fd
×N`,fd resonating strength matrix R`,fd , where Ȟm[`, fd] =[Ȟu1m
[`, fd] · · · Ȟukm [`, fd] · · · ȞuKm [`, fd]
]Twith γ[·, ·] defined
in (7). The (i, j)-th entry of R`,fd is
[R`,fd ]i,j = γ[Ȟi[`, fd], Ȟj [`, fd]
]. (16)
Secondly, we compute the column-wise average of R`,fddenoted as
Oj with j = 1, 2, · · · , N`,fd , given by
Oj =1
N`,fd − 1∑
i=1,2,··· ,N`,fdi 6=j
[R`,fd ]i,j . (17)
Finally, we remove the j′-th column of Ȟ [`, fd] if Oj′ ≤ τ
,where τ is a threshold.
We assume that the number of remaining CSIs after CSIsifting is
N ′`,fd , and the corresponding index of the remainingCSIs are t1,
· · · , tm, · · · , tN ′`,fd .
3. CSI AveragingAt location `, for channel fd, we generate the
averaged CSIS [`, fd] = [S
u1`,fd· · ·Suk`,fd · · ·S
uK`,fd
]T with dimension K×1 as
S [`, fd] =1
N ′`,fd
N ′`,fd∑m=1
Ȟtm [`, fd] ·Wm , (18)
where · stands for the element-wise dot product between
twovectors. Wm is a K × 1 vector represented as
Wm =[wm[`, fd] wm[`, fd] · · · wm[`, fd]
]T, (19)
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5
where wm[`, fd] = ej(][Ȟu1t1 [`,fd]]−][Ȟ
u1tm
[`,fd]]). The pur-pose of introducing Wm is to match the initial
phases ofȞtm [`, fd] with m > 1 to the first realization Ȟt1
[`, fd], sothat Ȟtm [`, fd] can be accumulated coherently, and the
noisevariance contained in Ȟtm [`, fd] is reduced by N
′`,fd
timesconsequently.
4. Bandwidth ConcatenationAt location `, we obtain the
fingerprint vector with dimensionDK×1 by concatenating the averaged
CSIs from all channels{fd}d=1,2,··· ,D as
G[`] =[ST [`, f1]V1 · · ·ST [`, fd]Vd · · ·ST [`, fD]VD
]T,
(20)
where Vd = e−j]
[Su1`,fd
]is introduced to nullify the initial
phases of different ST [`, fd].Fig. 3 demonstrates an example of
the fingerprint generation
procedure. As can be observed from Fig. 3, the CSI
post-processing effectively removes the phase distortions caused
bythe synchronization errors. The CSI averaging combines dif-ferent
realizations coherently, and the bandwidth concatenationassociates
two averaged CSI into the location fingerprint.
Since we concatenate all available bandwidths from D chan-nels,
we achieve a much larger effective bandwidth denotedby We = DW ,
where W is the bandwidth per channel.
2) Online Phase: The CSIs from an unknown location areformulated
into the location fingerprint in the same manneras described in the
offline phase. Assume that the locationfingerprint from the unknown
location `′ is given by G[`′], theresonating strength between
location `′ and location ` is com-puted as γ [G[`],G[`′]]. Define
`? = argmax
`=1,2,··· ,Lγ [G[`],G[`′]],
the estimated location ˆ̀′ takes the form
ˆ̀′ =
{`?, if γ [G[`?],G[`′]] ≥ Γ0, Otherwise ,
(21)
where Γ is a tunable threshold. Notice that, in case ofγ
[G[`?],G[`′]] < Γ, the proposed IPS fails to localize thedevice,
and the algorithm returns 0 to imply an unknownlocation.
In Fig. 4, we show an example of location fingerprintsgenerated
at two different locations in different colors. Foreach location,
we formulate 5 location fingerprints. As wecan see, the differences
among the location fingerprints atthe same location are minor,
while the differences of locationfingerprints between the two
different locations are much morepronounced.
IV. EXPERIMENT RESULTS
A. Experiment Settings
Fig. 5 shows the setups of the experiments with details
givenbelow.
1) Environment: The experiments are conducted in a typi-cal
office suite composed by a large and a small office roomin a
multi-storey building. The two office rooms are blockedby a wall.
In addition to the two large desks, the indoor spaceis filled with
other furniture including chairs and computers,which are not shown
in Fig. 5 for brevity.
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Fig. 4. A snapshot of location fingerprint after bandwidth
concatenationgenerated at two different locations.
RX
TX
Door
Fig. 5. Experiment settings.
2) Devices: Two Universal Software Radio Peripherals(USRPs) [29]
are deployed as the WiFi transmitter and receiverrespectively. For
both devices, the bandwidth of each channelis configured as W = 10
MHz. The USRP transmitter sendsWiFi signals compatible with
802.11a/g/p, while the USRPreceiver performs timing and frequency
synchronization, chan-nel estimation, equalization, and data frame
decoding. CSIswith correctly decoded data frames are recorded. The
twoUSRPs perform frequency hopping to the next channel
simul-taneously after a sufficient number of CSIs are obtained
onthe current channel.
3) Details of Measurement: The WiFi transmitter is placedon a
rectangular measurement structure in the small room. TheWiFi
receiver is placed on the table of the larger room.
The stepsize of the frequency hopping is configured as W =10
MHz. We measure the frequency band from 4.9 to 5.9 GHz.The total
number of channels D equals 100, and the effectivebandwidth We is
thus 1 GHz.
CSIs from L = 75 different locations are measured on
thestructure within an area of 70cm×20cm. The measurementresolution
is 5cm, i.e., the distance between two adjacentlocations is 5cm.
For each of the 75 locations, we formulateM = 5 location
fingerprints.
B. Metrics for Performance Evaluation
We consider the CSIs collected in the experiment as inputto the
fingerprint generation procedure in the online phase,
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3500
0.2
0.4
0.6
0.8
1
Testing Index
100 200 300
Tra
inin
g I
nd
ex
50
100
150
200
250
300
3500
0.2
0.4
0.6
0.8
1
(a) (b) (c) (d)
Fig. 6. Resonating strength matrix under different We.
Resonating Strength
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pe
rce
nt
(%)
0
20
40
60
80
100
Resonating Strength
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pe
rce
nt
(%)
0
1
2
3
4
5
Diagonal Avg 0.989 Std 0.086 Med 0.999 Max 1.000 Min 0.197
Off-diagonal Avg 0.662 Std 0.208 Med 0.695 Max 0.992 Min
0.000
Resonating Strength
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pe
rce
nt
(%)
0
20
40
60
80
100
Resonating Strength
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pe
rce
nt
(%)
0
1
2
3
4
5
6
Diagonal Avg 0.990 Std 0.042 Med 0.998 Max 1.000 Min 0.660
Off-diagonal Avg 0.400 Std 0.152 Med 0.397 Max 0.863 Min
0.013
(a) We = 10 MHz (b) We = 40 MHz
Resonating Strength
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pe
rce
nt
(%)
0
20
40
60
80
100
Resonating Strength
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pe
rce
nt
(%)
0
2
4
6
8
Diagonal Avg 0.989 Std 0.026 Med 0.997 Max 0.999 Min 0.837
Off-diagonal Avg 0.357 Std 0.099 Med 0.358 Max 0.698 Min
0.024
Resonating Strength
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Perc
ent (%
)
0
10
20
30
40
50
60
Resonating Strength
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Perc
ent (%
)
0
5
10
15
20
25
Diagonal Avg 0.988 Std 0.010 Med 0.992 Max 0.998 Min 0.944
Off-diagonal Avg 0.341 Std 0.037 Med 0.341 Max 0.498 Min
0.207
(c) We = 120 MHz (d) We = 1000 MHz
Fig. 7. Histogram of diagonal and off-diagonal entries under
different We.
Resonating Strength0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Cu
mu
lative
De
nsity F
un
ctio
n
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Diag., Eff. BW = 10 MHz
Diag., Eff. BW = 20 MHz
Diag., Eff. BW = 40 MHz
Diag., Eff. BW = 80 MHz
Diag., Eff. BW = 120 MHz
Diag., Eff. BW = 300 MHz
Diag., Eff. BW = 500 MHz
Diag., Eff. BW = 1000 MHz
Off-Diag., Eff. BW = 10 MHz
Off-Diag., Eff. BW = 20 MHz
Off-Diag., Eff. BW = 40 MHz
Off-Diag., Eff. BW = 80 MHz
Off-Diag., Eff. BW = 120 MHz
Off-Diag., Eff. BW = 300 MHz
Off-Diag., Eff. BW = 500 MHz
Off-Diag., Eff. BW = 1000 MHz
Fig. 8. Cumulative density functions of diagonal and
off-diagonal entries ofthe resonating strength matrix under
different We.
and store all CSIs into the fingerprint database. For
evalu-ation purpose, we assume that the same CSIs are obtainedin
the offline phase. Denote the m-th location fingerprintformulated
at location ` as Gm[`], we calculate the resonatingstrength matrix
R with the (i, j)-th entry of R given byγ[Gm[`],Gn[`
′]], where m = Mod(i,M)+1, ` = i−m−1M +1,n = Mod(j,M) + 1, and
`′ = j−n−1M + 1. Here, Mod is themodulus operator. Notice that,
[R]i,j = 1 if i = j. Here, i istermed as the training index, while
j is termed as the testingindex.
We define the entries of R calculated from CSIs obtainedat the
same locations as the diagonal entries, while thosecalculated using
CSIs obtained from different locations asthe off-diagonal entries.
We demonstrate the histograms andcumulative density functions for
the diagonal and off-diagonalentries.
-
7
Effective Bandwidth100 200 300 400 500 600 700 800 900
Re
so
na
tin
g S
tre
ng
th
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
DiagonalOff-Diagonal
Fig. 9. Mean and standard deviation of the diagonal and
off-diagonal entriesof the resonating strength matrix under
different We.
Effective Bandwidth100 200 300 400 500 600 700 800 900
Γ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
100% true positive rate, 0% false positive rateAt least 95% true
positive rate, at most 5% false positive rate
Fig. 10. Threshold Γ under different We to achieve (i) PTP =
100% andPFP = 0% (ii) PTP ≥ 95% and PFP ≤ 5%.
Based on R, we evaluate the localization performancesusing the
metrics of the true positive rate, denoted as PTP,and the false
positive rate, denoted as PFP. PTP is definedas the probability
that the IPS localizes the device to itscorrect location, while PFP
captures the probability that theIPS localizes the device to a
wrong location, or fails to localizethe device.
In the performance evaluation, the CSI sifting parameter τis set
as 0.8.
C. Performance Evaluation
Resonating Strength Matrix under Different WeFig. 6 demonstrates
R with We ∈ [10, 40, 120, 1000] MHz.We observe that when We = 10
MHz, there exists many largeoff-diagonal entries in R, indicating
severe ambiguities amongdifferent locations. When the total
bandwidth We increases,the ambiguities among different locations
are significantly
eliminated, while the resonating strengths within the
samelocation are almost unchanged.Distribution of Diagonal and
Off-diagonal Entries underDifferent WeFig. 7 visualizes the
distribution of the diagonal and off-diagonal entries of R with
different We ∈ [10, 40, 120, 1000]MHz using histograms. Statistics
of the diagonal and off-diagonal entries are shown as well. As we
can see, the resonat-ing strengths at the same location are
identical with differentWe, implying high stationarity of the
proposed IPS. On theother hand, the off-diagonal entries are more
suppressed andapproaches a Gaussian-like distribution when We
increases.We also observe an enlarged gap between the diagonal
andoff-diagonal entries when We increases, indicating a
betterseparability among different locations. The increase of We
alsoreduces the variations of diagonal and off-diagonal entries,as
shown by the decreasing standard deviations. Moreover, alarge We
removes the outliers in the diagonal entries: whenWe = 10 MHz, the
minimum value of diagonal entries is0.197, while the minimum value
increases to 0.944 whenWe = 1000 MHz. Thus, a large We improves the
robustnessof the IPS against outliers.Cumulative Density Functions
of Diagonal and Off-diagonal Entries under Different WeIn Fig. 8,
we demonstrate the cumulative density func-tions of diagonal and
off-diagonal entries with We ∈[10, 20, 40, 80, 120, 300, 500, 1000]
MHz. As can be seen fromthe figure, a large We reduces the spread
of both the diagonaland off-diagonal entries, which agrees with the
results shownin Fig. 7.Mean and Standard Deviation Performances
under Differ-ent WeFig. 9 depicts the impact of We on the mean and
standarddeviation performances for both diagonal and
off-diagonalentries. The upper and lower bars indicate the ±σ
boundswith respect to the average, where σ stands for the
standarddeviation. We conclude that: a large We improves the
distinc-tion among different locations, but also reduces the
variationof resonating strengths at the same locations as well as
amongdifferent locations. In other words, a large We makes the
IPSperformance more stable and predictable.Threshold Γ Settings
under Different WeFig. 10 depicts the smallest threshold Γ under We
=[20, 60, 100, · · · , 1000] MHz to achieve (i) PTP = 100% andPFP =
0% (ii) PTP ≥ 95% and PFP ≤ 5%. We observe adecreasing in Γ when We
is larger, which can be justified bythe fact that the gap between
the diagonal and off-diagonalentries enlarges when We becomes
larger. When We = 20MHz, the IPS fails to achieve PTP = 100% and
PFP = 0%.Fig. 10 also implies that we can achieve a perfect
5cmlocalization if Γ is chosen appropriately.
D. Discussion of Experiment Results
Based on the experiment results, we conclude that a largeWe is
imperative for the robustness, stability, and performanceof the
proposed IPS. By formulating the location fingerprintthat
concatenates multiple channels, the proposed IPS achieves
-
8
0 5 10 15 20 25 30 35 40 45 500
5
10
15
20
25
30
35
40
45
50
x−axis (mm)
y−
axis
(m
m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 11. TR resonating strength near the intended location with
a measurementresolution of 0.5cm.
a perfect centimeter localization accuracy in a NLOS
environ-ment with one pair of single-antenna WiFi devices.
Notice that the localization accuracy is limited by the5cm
resolution of the measurement structure. In an
additionalexperiment, we refine the measurement resolution to
0.5cm.The TR resonating strengths near the intended location
isshown in Fig. 11 with We = 125 MHz, which demonstratethat the
localization accuracy can reach 1 ∼ 2cm in an NLOSenvironment.
V. CONCLUSION
In this paper, we present a WiFi-based IPS that exploitsthe
frequency diversity to achieve centimeter accuracy forindoor
localization. The proposed IPS fully harnesses thefrequency
diversity by CSI measurements on multiple channelsvia frequency
hopping. Impacts of synchronization errors andinterference are
mitigated by CSI sanitization, sifting, andaveraging. The averaged
CSIs of different channels are thenconcatenated together into
location fingerprints to augmentthe effective bandwidth. The
location fingerprints are storedinto a database in the offline
phase, and are used to calculatethe TR resonating strength in the
online phase. Finally, theproposed IPS determines the location
based on the resonatingstrengths. Extensive experiment results of
measurements on a1 GHz frequency band demonstrate the centimeter
localizationaccuracy of the proposed IPS in a typical office
environmentwith a large effective bandwidth.
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