Reasonable Resolution of Finger-print Wi-Fi

Radio Map for Dense Map Interpola-tion

University of Seoul

Wonsun Bong, Yong Cheol Kim

Auckland, New ZealandJanuary 13-16, 2014

The 2014 FTRA International Symposium on Frontier and Innovation in Future Computing and Communications

Overview

Introduction Previous Works on Wi-Fi Based Localization Fingerprint Localization and Radio Map DPS (Discontinuity Preserving Smoothing)

Adaptive Smoothing Derivation of Reasonable Resolution of Map Experimental Results

Comparison with other interpolation methods Comparison with full density radio map

Conclusions

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Introduction : Indoor Localization Service

IndoorGeo-Service

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With GPS-like indoor navigation, • Find restroom in a department store • Find the gate in an airport• Receive deals from retailers

upon entering into a shop

COEX

MALL

GPS

GPS signal cannot reach inside of building

Previous Works on Wi-Fi Based Localization

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Signal Strength

Empirical

Radio Map

Propagation Model Triangulation

Fingerprinting

RSS is a indicator of distance from source.

Pattern matching of measured RSS

with the RSS patterns in the radio map

RSS = Received Signal Strength

Google Indoor Maps

2005. 02 Google Maps Released (for PC) 2008.10 Google Maps Application (for Smart Phones) 2011.11 Google Indoor Maps Application (for Smart

Phones)

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locations of Wi-Fi APs are collected by the same vehicles which collect street view im-age data.

Available in some locations in Europe, Canada, U.S.A. and Japan. (mostly airports, large stores and hotels) 

Google Indoor Map

San Francisco Airport (2nd floor)

Localization Using Wi-Fi Signal

Triangulation Fingerprinting

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Triangulation

Ideal Triangulation

Estimated Position of MD (Mobile Device)

AP 1AP 2

AP 3

AP 4

AP 1AP 2

AP 3

AP 4

Actual Position of MD

Least Mean-Squared Triangulation:with Estimation Errors

strength signal measured from distance :

determined be postion to thefrom distance :

Minimize 233

222

211

i

i

d

r

drdrdr

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Path Loss Model

XWAFwr

rnrPrP

00 log10)()(

100

101

102

-55

-50

-45

-40

-35

-30

-25

-20Real Measurements of RSSI over Hallway

meter

RS

SI [

dB

m]

n attenuatio random:

factor.n attenuatio wall:

exponent losspath :

X

WAF

nMD

P(r)AP

r

r0

P(r0)Pt

100

101

102

-55

-50

-45

-40

-35

-30

-25

-20RSSI by Path Loss Model (n=1.6)

meter

RS

SI [

dB

m]

Measured RSSI : -40 dBm

Distance is 10 meters.

Ideal Model Real RSS

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Fluctuations of RSS by Perturbation of Wi-Fi Signal

MD

P(r)AP

r Wall

Perturbing ObjectsAttenuation Reflection of Wave

Accurate Model is Hard to Obtain.

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Fingerprint Localization

AP 1 AP 2

AP 3

AP 4

Estimated Position of MD (Mobile Device)

Actual Position of MD

APof

jj

iji RSSRSSd

#

1

2' )(

Similarity Measure:

Euclidean distance between RSS vectors

device mobile of vector RSS :

point gridth -at vector RSS :

'RSS

iRSS i

Measure RSS at each grid

Create Radio Map

Measure RSS at MD Position

Find the most similar RSS pattern

ORGet the avg. of K similar

patterns (K-NN)

Offline Step

OnlineStep

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DPS: Discontinuity Preserving

Smoothing Why is DPS Required in Radio Map? Adaptive Smoothing Using Wall Information Experimental Results

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Interpolation of Low Density Radio Map• The cost of radio map is high• Interpolation of a coarse map into a dense one re-

duces cost.

Problems with Radio Map Interpolation • The measured RSS exhibits discontinuity at barri-

ers, especially at the wall boundaries.• An interpolation simply fits the measured data into

a parametric curve

discontinuity of RSS is not well preserved.• An interpolated map has low accuracy near a wall.

Interpolation of Radio Map

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The path loss model and the actual data have a large differ-ence, especially at the wall boundaries.

Preserving Discontinuity

Measured RSS : Considerable drop at wall boundary

• 19 dBm (side A) • 16 dBm (side B).

But path loss model does not handle discontinuity

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IDW(Inverse Distance Weight)• A linear interpolation with weights

dependent on the distance• No means of accommodating the

RSS discontinuity around walls.

Kriging• A linear sum of measured RSS of

surrounding RPs. • The coefficients are determined by

spatial correlation of signal strength.

• Kriging does not provide means of handling the wall discontinuity.

Previous Works on Radio Map Interpolation (1)

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• Voronoi Tessellation• Based on path loss model• Grouping of RPs are guided

by Voronoi tessellation of second order.

• Estimated parameters reflect the local property of the cell which holds just two RPs.

• There is no preventing of a cell having two RPs at oppo-site sides of a wall.

Previous Works on Radio Map Interpolation (2)

M. Lee and D. Han, ”Voronoi Tessellation Based Interpolation Method for Wi-Fi Radio Map Construction,” IEEE Communications Letters, Vol. 16 , Issue: 3, pp.404-407. March, 2012

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Motivations and Scope of this Work

Motivation of this Paper• To interpolate a low-density radio map into a high-density

map which preserves RSS discontinuity at wall boundaries• To present a closed form solution of reasonable resolution

of radio map • To reduce the cost in the off-line stage of fingerprint radio

map, which involves data measurement and calibration Scope of this Work

• To apply adaptive smoothing for the DPS functionality in the interpolation of low density radio map

• To examine the lower bound of sampling density which achieves comparable performance

• To compare the above experimental lower bound of sam-pling density and the derived resolution of reasonable ra-dio map

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Discontinuity Preserving Interpolation from Sparse Data• Regularization-based methods have been developed• Not applicable to Radio map interpolation

Adaptive Smoothing• Simple smoothing technique • Fluctuation is reduced and skeleton is preserved

Original signal Adaptively smoothed signal

Proposed DPS : Adaptive Smoothing

P. Saint-Marc and J. Chen, ”Adaptive Smoothing: A General Tool for Early Vision,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. l3, No. 6, June, 1991

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Interpolation is almost separately performed on both sides of the wall

Interpolated value of RSS is affected mainly by those which lie on the same side of the.

Adaptive smoothing accommodates barrier.

Adaptive Smoothing of RSS across Walls

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RSS(dBm) : Wall

: Measured

: DPS

: Path loss model

Adaptive Smoothing

Room with AP

(Wall information fully used)

Real RSS Data: Wall Layout Information in Interpo-lation

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Kernel In Adaptive Smoothing

If a wall lies between two RPs’, then the weight is very small two RPS have little impact on the smoothing process. This way, the office layout information is effectively utilized in the reconstruction of full density radio map.

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p = 10 two RPs are separated by a wallP = 1 two RPs are on the same side of a wall

),()1,(

gradient vertical

),(),1(

gradient horizontal

)()(

)()(

yxsyxs

yxsyxs

tt

tt

Reasonable Resolution of Radio Map (1)

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RSS fluctuation affects positional accuracy.• (difference of RSS at ) corresponds to

radial difference.

• Measurement error of RSS • Error in Radio map can be decreased by taking the aver-

age of N measurements.• RSS on MD side is measured only once or twice.

• Radio map with too fine resolution is not needed.• Error of 1.5 dBm corresponds to 1.9 meter error.

RSS0rr

)( 110100

n

r

RSS

rd

Reasonable Resolution of Radio Map (2)

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Map resolution worth efforts of measurement• A reasonable value of radio map would be of the

order of positional error resulting from RSS fluc-tuation.

• : reasonable resolution of radio map

: standard deviation of RSS over time

• .

mapR

)( 110100 n

map

RSS

rR

RSS

Reasonable Resolution of Radio Map (3)

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0.5 1 1.5 2 2.50.5

1

1.5

2

2.5

3

3.5

RSS Std. Dev (dBm)

Po

sitio

na

l Err

. (m

ete

r)

Positional Err w.r.t. RSS Std.Dev.

Reasonable resolution w.r.t. std. dev. of RSS

Environment• Sixth floor of IT-Building in Univ. of Seoul

RP : grid of 1.2m by 1.2m (# of RP = 145 )

Index AP-1 AP-2 AP-3 AP-4

σ [dBm] 1.21 1.68 1.51 1.47

Variation of RSS in 80 measurements.

Standard deviation of Measured RSS

RSS Measurement• At all RPs, measure RSS 100 times

during 200 secs.• The average is taken to reduce the effect of random fluctuation.

(noise power reduced to 10 %)

Experiments with Real RSS Data

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• RSS vectors of all 145 RPs are randomly selected with a sampling density varying from 10% to 95% in 5 % step.

• We constructed a series of low density(10% 95%) radio ∼map to find the lower bound of sampling density.

• DPS outperforms IDW-interpolation and Voronoi-based interpolation.

Fingerprint Localization with Real RSS Data (1)

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Observations: • With sampling density ≥ 35%, accuracy approaches the

original full density map.• With sampling density ≥ 60%, DPS-interpolated map is

even better than the original full density map.• In continuous spatial smoothing, the random fluctuation

gets further reduced. higher accuracy in localization.• For the other two methods, the effect of spatial smooth-

ing is weak.

Fingerprint Localization with Real RSS Data (2)

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27 / 20

• The average error decreases as the sampling density increases.

Improvement w.r.t. sampling density

Fingerprint Localization with Real RSS Data (3)

0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

3-NN

Sampling density(%)

erro

r(m)

Voronoi

Adaptive Smooth

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Radio map for fingerprint localization has high cost.• Discontinuity preserving smoothing can be used to

generate a high density map. Advantage of interpolated radio map

• RSS measurement can be reduced to 35%. • With sampling density >= 60%, better than the origi-

nal full density map Reasonable resolution of radio map

• Rmap is of the order of positional error of RSS mea-surement.

• Fits well with the experimental results.

Conclusions

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