48
A li ti & Th Applications & Theory Azadeh Kushki [email protected] Professor K N Plataniotis Professor K.N. Plataniotis Professor A.N. Venetsanopoulos

Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

  • Upload
    others

  • View
    2

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

A li ti & ThApplications & Theory

Azadeh [email protected]

Professor K N PlataniotisProfessor K.N. PlataniotisProfessor A.N. Venetsanopoulos

Page 2: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Presentation Outline2

Part I: The case for WLAN positioning

2

HistoryApplicationsO i & h llOverview & challenges

Part II: TheoryMemoryless positioningTracking A cognitive design

Page 3: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

P I Th C f WLAN P i i iPart I: The Case for WLAN Positioning

HiHistoryApplications Overview & challenges

Page 4: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Positioning4

Objective:

4

Determine physical coordinates of a mobile terminal

Historical perspective:St di d id l f th t fi d dStudied widely for the past five decadesLimited to military/civilian target tracking & navigationnavigation

Renewed interest: mobile computingRenewed interest: mobile computing

Page 5: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Mobile Computing5

Motivated by advances in wireless that allow ti h ti

5

computing anywhere, anytime

Mobility has led to new needsLocation-dependent resource & information needs

Mobility has sparked new applicationsLocation-based services

Page 6: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Location-Based Services6

Radio/map information

Position informationNetwork Provider

6

Position information

Authentication

Network Provider

Location-based management

Location server

Resource allocation

Friend Finder services

Proactive resource deployment

Social networking

U t d t t

Content ProviderGeo-tagging/geo-blogging

Location metadata

User generated content

Location-based information

Geo-tagging/geo-blogging

Content server

Page 7: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Location-Based Services7

250

300

7

100

150

200Number of subscribers(Millions)

0

50

100

2007 2008 2011

5

6

7

8

1

2

3

4

5Revenue in $

(Billions)

0

1

2007 2008 2011

Figures obtained from Gartner.

Page 8: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Positioning Technology8

Motivation:

8

To enable location-based service, accurate and timely location information is needed

Example technologies:Global positioning systemGlobal positioning systemCellular-based methods

In this talk, we focus on positioning in indoor environmentsenvironments

Page 9: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Indoor Positioning9

Motivation:

9

GPS & cellular systems provide limited coverage in indoors

Objective:D t i h i l di t f d t i Determine physical coordinates of a pedestrian carrying a wireless device in an indoor environmentenvironment

Page 10: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Indoor Positioning Solutions1010

Technology Accuracy Cost Complexity Invasive

RFID 10 M di L YRFIDs <10m Medium Low Yes

Visual centimeters High High YesVisual surveillance

centimeters High High Yes

Radio (WLAN) <10m Low Low No( )tracking

Page 11: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

WLAN Tracking: Basic Idea11

WLAN radio signal features depend on distance b t i & t itt

11

between receiver & transmitter

Measure signal features to determine locationTime of Arrival

d ff f lRequire additional

Time difference of ArrivalAngle of ArrivalR i d Si l St th (RSS)

Require additional hardware

Received Signal Strength (RSS)

Page 12: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

RSS-Based Tracking: Motivation12

Inexpensive

12

No additional hardware needed

ScalableUbiquitous deployment

Non-invasiveRequires cooperation of mobile device

Page 13: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

The Setup13

Pedestrian carries a WLAN-capable device

13

L access points 3

Unknown positions

1

)(2 kr)(3 kr

)(4 kr

)(1 kr )(kr L

Mobile measures RSS vector at time k

TL krkrk )](,),([)( 1 L=r

Page 14: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

The Problem14

Given a sequence of RSS measurement over time

14

)}(,),1({)( kk rrR L=

Estimate a sequence of position estimates

)(ˆ,),1(ˆ kpp L

Page 15: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Technical Challenges15

Functional form of RSS-position relationship ll k

15

generally unknownSevere multipath, shadowingP ti d l i ffi i t t d ib Propagation models insufficient to describe spatial variations

A. Kushki, K.N. Plataniotis, A.N. Venetsanopoulos, “Indoor Positioning with Wireless Local Area Networks”, in the Encyclopedia of Geographical Information Sciences, 2008.

Page 16: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Technical Challenges16

RSS measurements depend on unpredictable i t l f t

16

environmental factorsMoving people, doors, humidity, etc.

RSS t ti t fi d RSS measurements vary over time at fixed locationsVariations do not obe ell kno n distrib tionsVariations do not obey well-known distributions

Page 17: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Location Fingerprinting17

Characterize RSS-position dependency through t i i b d th d

17

training-based method

yConstruct a radio map

( ) ( ){ })()( FF R ( ) ( ){ })(,,,)(, NN pFppFp L11 R =

Tyx ][ h i

N: Number of anchor points

Tyi

xi pp ][=ip : anchor point

[ ])()1()( nii rrpF L=i : fingerprint matrix

x

n: Number of RSS samples per anchor points

[ ])()1()( nii rrpF i : fingerprint matrix

Page 18: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Outline of Solutions18

Kernel density estimation for fingerprinting-b d iti i

18

based positioning

N t i I f ti FiltNonparametric Information FilterImprove positioning accuracy by incorporating knowledge of pedestrian motion dynamicsknowledge of pedestrian motion dynamics

Cognitive design to deal with unpredictable RSS Cognitive design to deal with unpredictable RSS variations through sensor selection

Page 19: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

P t II ThPart II: Theory

M l i i iMemoryless positioningTracking A cognitive design Conclusion and future work

Page 20: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Memoryless Positioning20

Objective: given an RSS measurement, d t i iti ti t

20

determine a position estimate

)(kr )(ˆ kp?)(kr )(kp?

Optimality criterion: minimum mean square

Radio map

error (MMSE)

}||)()({||minarg)(ˆ 2kkEk ppp (( −= }||)()({||minarg)( kkEk ppp p(

Page 21: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

MMSE Estimation21

MMSE estimate is given as

21

)}(|)({)(ˆ kkEk rpp = ( )∫= )()(|)()( kdkkfk prpp

unknown

Approximate the posterior density

unknown

HistogramKernel density estimator

N

∑∑ =≈ N

i i

N

i ii

w

wk

1

1)(ˆp

p

A. Kushki, K.N. Plataniotis, A.N. Venetsanopoulos, “Kernel-based Positioning in Wireless Local Area Networks”, IEEE Transactions on Mobile Computing, 6(6), pp.689-705, 2007.

∑ =i i1

Page 22: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Memoryless MMSE Estimator22

RSS observationRadio map

22

RSS rep extraction

11pw)1(1r

)(1 nr1r

+ )(ˆ krpRSS rep

KDE

)(1 nr

)1(r pextraction

NNw p)1(Nr

)(nNrNr

Temporal processing Spatial processing

n: Number of RSS samples per anchor points

( )rΣrr ,);( ii kw N=N: Number of anchor points

Page 23: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Performance Evaluation23

Evaluation data collected in a real office

23

RSS measured using public software on a laptop

4646m

42

Performance measure: root mean square

42m

positioning error

Page 24: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Test Conditions24

Capture environmental variations

24

Training & testing sets collected on different daysOrientation mismatch

Two motion scenarios consideredStationary user

352 test cases (44 locations)

Mobile userMobile user34 paths

Page 25: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Experimental Results2525

Method Stationary user(Average RMSE)

Mobile user(Average RMSE)

Complexity

KNN 3.18m 5.85m O(dN)

Histogram 3.22m 5.68m O(bdN)

Kernel Density 2.90m 5.70m O(dN)

n: Number of RSS samples per anchor pointsd: Number of access pointsb: Number of histogram bins

N: Number of anchor pointsn: Number of RSS samples per anchor points

Page 26: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

P t II ThPart II: Theory

M l i i iMemoryless positioningTracking A cognitive design Conclusion and future work

Page 27: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Tracking27

Objective: given the RSS observation record, d t i iti i ti t ti

27

determine positioning estimates over time

Dynamic model

)(ˆ kp?)}(,),1({)( kk rrR L= )(p?

Radio map

)1(ˆ,),0(ˆ −kpp L

)}(,),({)(

Exploit knowledge of pedestrian motion

Radio map

dynamics to refine RSS-based estimates

Page 28: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Tracking28

Traditional approach: Bayesian filtering

28

Estimate the hidden state of system given observable RSS measurements Kalman filter & extensions particle filterKalman filter & extensions, particle filter

Challenge:Challenge:Lack of an explicit relationship between RSS & positionspositionsComputational complexity

A. Kushki, K.N. Plataniotis, A.N. Venetsanopoulos, “Nonparameteric Techniques for Pedestrian Tracking in Wireless Local Area Networks”, to appear in the Handbook on Sensor and Array Processing.

Page 29: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Bayesian Filtering: State Vector29

Contains all variables needed to describe the l ti f th t t f t

29

evolution of the state of a systemIn general, many parameters needed to describe pedestrian motionpedestrian motion

Simplifying assumption: In indoor office spaces Simplifying assumption: In indoor office spaces, movements constrained by physical structure

Page 30: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

The State Vector30

Assuming linear motion, define the state vector

30

where,])()()()([)( Tyyxx kvkpkvkpk =x

kkpkp yx time at scoordinate pedestrian is )]()([ kkpkp time at scoordinate pedestrian is )]()([kkvkv yx time at velocity pedestrian is )]()([

The dynamic model is )()()1( kkk ωFxx +=+

Initial state:System matrix: F,System noise: )0()( Qω k N

),(~)0( 00 Pxx ,N

System noise: ).0(~)( Qω ,k N

Page 31: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

MMSE Tracking31

MMSE estimate of the state is defined as

31

}||)()({||minarg)(ˆ 2kkEk xxx x(

( −=

MMSE estimate is given as

)}(|)({)|(ˆ kkEkk Rxx =

( )∫ ( )∫= )()(|)()( kdkkfk xRxx

unknown

Page 32: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Bayesian Filtering32

Estimate the posterior density recursively in two t

32

stepsPredictionC tiCorrection

prediction correctionprediction correctionEstimate at k-1 Predicated

estimate at kEstimate at k

Dynamic model Measurement model Dynamic model Measurement model RSS observation

Page 33: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Bayesian Filtering: Prediction33

Use the dynamic model to predict the state i th i ti t

33

given the previous estimate

)1|(ˆ)1|1(ˆ → kkkk xx )1|()1|1( −→−− kkkk xx

Since a linear-Gaussian dynamic model is assumed, prediction is the same as traditional K l filt i gKalman filtering

Page 34: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Bayesian Filtering: Correction34

Use measurements to refine predicted estimate

34

Requires measurement model that relates RSS observations to the stateobservations to the state

Explicit measurement model not available in Explicit measurement model not available in fingerprinting!

The Nonparametric Information (NI) Filter

A. Kushki, K.N. Plataniotis, A.N. Venetsanopoulos, “Cognitive Dynamic Radio Tracking in Indoor Wireless Local Area Networks”, submitted to the IEEE Transactions on Mobile Computing.

Page 35: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

The Nonparametric Information Filter35

)1|1(ˆ −− kkx )1|1( −− kkPRSS observationRadio map

35

Dynamic modelMemoryless estimator

)1|( −kkP)(ˆ krx )(krP

Dynamic modelMemoryless estimator

)1|(ˆ −kkx )|(

NI filter

)(r )(r )|(

)|(ˆ kkx )|( kkP

( ))(ˆ)()1|(ˆ)1|()|()|(ˆ 11 kkkkkkkkkk rxPxPPxr

−− +−−=)()1|()|( 111 kkkkk −−− +−=

rPPP

Page 36: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Experimental Results36

Method Stationary user(Average RMSE)

Mobile user(Average RMSE)

Complexity

36

(Average RMSE) (Average RMSE)

Memoryless 2.90m 5.70m O(dN)

Kalman filter 2.75m 5.41m O(dN)

Particle filter 2.44m 5.16m O(dNNpart)

NI filter 2.29m 4.58m O(dN)

N: Number of anchor pointsd: Number of access points

Npart: Number of particles (Npart =1000)

All filters use same memoryless estimator

p

All filters use same motion model

Page 37: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

P t II ThPart II: Theory

M l i i iMemoryless positioningTracking A Cognitive design Conclusion and future work

Page 38: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

A Cognitive Design38

Motivation:

38

NI filter builds its knowledge of the environment through RSS observations & radio mapConditions during tracking may be different than Conditions during tracking may be different than those learned from fingerprints

Objective: Mitigate adverse effects of unpredictable Mitigate adverse effects of unpredictable environmental variations

Page 39: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

A Cognitive Design39

Basic idea:

39

Proactively adapt sensing and estimation parameters based on predicated operating conditionsconditions

Approach: adaptive radio scene analysisApproach: adaptive radio scene analysisAnchor point selection

RSS-position relation is many-to-manyRSS position relation is many to many

Access point selection Number of available access points >>3p

Page 40: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Adaptive Radio Scene Analysis40

Determine region of interest (ROI) using f db k

40

feedbackUse only anchor points in ROI for positioningE l t i t l ti it i ROIEvaluate access point selection criterion over ROI

A. Kushki, K.N. Plataniotis, A.N. Venetsanopoulos, “Cognitive Dynamic Radio Tracking in Indoor Wireless Local Area Networks”, submitted to the IEEE Transactions on Mobile Computing.

Page 41: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

The Cognitive Design4141

Anchor point selection

State Prediction

Outlier Mitigation

Memorylessestimator

State Estimation

PositionEstimate

Mitigation

Access Point selection

Adaptive Scene Analysis NI filter

RSS observationRadio map

Two levels of feedbackLocal (NI filter)Gl b l (S l i )Global (Scene analysis)

Page 42: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Experimental Results42

Method Stationary user Mobile user Complexity

42

(Average RMSE) (Average RMSE)

Memoryless 2.90m 5.70m O(dN)

NI filter 2.29m 4.58m O(dN)( )

NI filter + anchor point selection 2.31m 3.96m O(dN’)

NI filter + anchor point selection + access point selection

2.07m 2.51m O(dN’) access point selection

d N b f i t

N’: Number of selected anchor points (N’<N)N : Number of anchor pointsd : Number of access points

Page 43: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Example4343

Page 44: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

P t II ThPart II: Theory

M l i i iMemoryless positioningTracking A cognitive design Conclusion and future work

Page 45: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Conclusions45

Location-based services (LBS) emerging area ith i ifi t i l i t

45

with significant commercial impact

WLAN positioning is an enabling technology for indoor LBS

I i & l blInexpensive & scalable

A li it d b lit f g ti Accuracy limited by quality of propagation channel

Use of motion dynamics sensor selectionUse of motion dynamics, sensor selection

Page 46: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Future Directions46

Fusion of multiple technologies to provide li bl iti i i i d / td

46

reliable positioning in indoor/outdoor environments

GPS radio videoGPS, radio, video

Privacy security an anonymity in positioning Privacy, security, an anonymity in positioning systems

Page 47: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Related Publications47

A. Kushki, K.N. Plataniotis, "Nonparametric Techniques for Pedestrian Tracking in Wireless Local Area Networks", to appear in Handbook on Sensor

47

and Array Processing, S. Haykin and K.J.R. Liu, Eds., IEEE-Wiley, 2009.

A. Kushki, K.N. Plataniotis, A. N. Venetsanopoulos, "Indoor Positioning with Wireless Local Area Networks (WLAN)", in the Encyclopedia of Geographical I f ti S i S Sh kh d H Xi Ed S i 566 571 Information Science, S. Shekhar and H. Xiong, Eds., Springer, pp.566-571, 2007.

A. Kushki, K.N. Plataniotis, A.N. Venetsanopoulos, "Kernel-based Positioning in Wireless Local Area Networks" IEEE Transactions on Mobile Computing in Wireless Local Area Networks , IEEE Transactions on Mobile Computing, 6(6), pp.689-705, 2007.

A. Kushki, K.N. Plataniotis, and A.N. Venetsanopoulos, "Sensor Selection for Mitigation of RSS-based Attacks in Wireless Local Area Network Positioning", Mitigation of RSS based Attacks in Wireless Local Area Network Positioning , in the proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 2065-2068, 2008.

Page 48: Aliti Applications & Theory - IEEE Canada · compu ti ting anyw h here, any time Mobility has led to new needs ... 2007 2008 2011 Figures obtained from Gartner. Positioning Technology

Th k Y

C t t d h k hki@i

Thank You.

Contact: [email protected]