localization11 aug 09

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Shinsuke Hara, Ph. D.Gradate School o f Engineering, Osaka City University

11/August/2009

[email protected]

Localization-1

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Contents of Shins seminar

Whats localization?Why localization now?Context-aware servicesLocation-based servicesImportance of localizationCategoryPrinciple

Performance bounds

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Whats localization?

To estimate the 2-dimensional or 3-dimensionallocation of a target, such as a mobile user and node

Location estimationPositioning

Localization (technical term in robotics)

Ranging is to estimate (measure) the distancebetween a pair of transceivers

Usually, localization is based on multiple rangingwith different known locations, such as basestations and anchor nodes

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Assumptions for localization

Some nodes are available whose locations areknown in advance, which are called referencenodesor anchor nodes. In this seminar, we callthem anchor nodes.

From a target node, anchor nodes can get someinformation related to the distance to the targetnode

Examples are: TOA (time of arrival), TDOA (timedifference of arrival), AOA (angle of arrival), RSSI(received signal strength indication, receivedpower) and so on


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Anchornode #3

Anchornode #1

Anchornode #4Target node

Anchornode #2

1=g(d1)

TOA (time of arrival)

2=g(d2)

3=g(d3)

4=g(d4)

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How can we measure TOA? (1)

One-Way Ranging (synchronization, the same

clock among nodes)

time

time

0

0

Anchor node

Target node

d=cc: speed of light (3.0x108 m/s)

Establishment of the synchronization is very difficult!

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Round trip time measurement

time

time

0Anchor node

Target node

Td(known in advance)

TR

=(TR-Td)/2

d=c

8tt

t

0

1

0

1Anchornode

(A)

Targetnode(B)

TTA

TTA

TRB

TTB

TTB

TRB

TRA


Two-Way Ranging


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TTA+=TR

B+tTR

A-t=TTB+ 2)()( BR

BT

AT

AR

p

TTTTt

TWR does not need synchronization !


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Anchornode #3

Anchornode #1


Anchornode #2

TDOA (time difference of arrival)

21=2-1 31=3-1

41=4-1

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How can we measure TDOA?

Anchor nodes are synchronized and can talkwith each other

time

time

0

0

Anchor node 1

Anchor node 2

time

1

2

21=2-1

Target node

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Anchornode #3

Anchornode #1 Anchor

node #4

Target node

Anchornode #2

AOA (angle of arrival )

2

1

3

4


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How can we measure AOA?

A target node or anchor nodes need to havearray antenna

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Pros and cons of TOA, TDOA and AOA

Their performance has been long believed to bemuch better (than RSSI)They do not work in non-line-of-sight (NLOS)environments (tall buildings and people walkingaround)TWR or synchronization is required for TOAArray antenna is required for AOA

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Anchornode #3

Anchornode #1


Anchornode #2

P1=f(d1)

RSSI (received signal strength indication)

P2=f(d2)

P3=f(d3)

P4=f(d4)

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RSSI is easily measurable

Cellularphones

Wireless LANterminals

Many current wireless communication standardssupport RSSI measurement

IEEE 802.15.4

LQI (link quality indicator)8bit resolution,-173dBm to 82dBm(1dB step)


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Pros and cons of RSSI

Its performance has been long believed to bemuch worse (than TOA), because of fadingand shadowingThey can work even in NLOS environmentsIt is simply implementableOWR is easily possible

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Why localization now?

What are the paradigms of next generation mobilecommunication systems?

1G system: analogue (1980s)2G system: digital (1990s)3G system: multimedia (2000s)4G system: heterogeneous network & system

and context-aware services

5G system: green, learning,

The word of contextmeans the overall situation in which an eventoccurs (The American Heritage Dictionary)

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NGN

ADSL WLAN

WiMAX

CPU capabilit y

Traffic load condition

Channel bandwidth

Indoor

Outdoor

In motion

Stationary

3G

Context in communicationsmeans the overall situationsurrounding any parts of the entities in a communication system

Context-aware services

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What is an essential difference of wireless from wired?

End device (terminal) can move aroundThe location is worth estimatingServices with the location information are uniqueonly for wireless

Location-based services


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Location-based services (1/3)

Switch your cellphones to sleepmode

My cell phoneisautomaticallyswitched to sleepmode

My cell phonei sautomatically switchedto vibration modewhen getting on asilencecart

(a) School (b) Transportation

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You areapproaching toagood French restaurant My cell phoneis

automaticallyswitched off whenentering atheater

(c) Navigation andadvertisement

(d) Theater


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(e) Resource management

My current basestation is busy withhandling a lot of traffic, but my nextbasestation which I can reach in afewseconds is not busy. So the systemhas just decided not to assign a channelwith lower datarateto mein thecurrentcell and to assign channel with muchhigher dataratein thenext cell


(f) Advice

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Importance of localization (1/4)

GPS (Global Positioning System)Cellular (3G, 4G)WMAN (WiMAX)WLAN (WiFi)

WPAN (Bluetooth)WSN (Zigbee, UWB)

RF-ID (Passive, Active)

Providing a variety of location-based services depends onthe accuracy of the estimated location of a target (node, cellphone and so on)

To localize a target more accurately, we can use any kindsof wireless systems

WiMAX

GPS

RF-ID

WiFi

Zigbee

Bluetooth


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[1] G. Y. Delisle, Location Awareness and Positioning Methods for LocationBased Services in Wireless Communication Networks,IEEE VTC 2006-Fall.

From always best connected to always best

located [1]


References

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Wireless Enhanced 911 (FCC Third Order)

Base station-based localization: error67%)error95%)

GPS-based localization: error67%)error95%)

All terminals are not equipped with GPS receiversCellular base stations and GPS satellites are not availablein indoor environments

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Increasing number of sessions in international conferencesIncreasing number of special issues in international journalsSpecialized conferences

Specialized projects

MELT 2008 (The 1st ACM International Workshop onMobile Entity Localization and Tracking in GPS-less

Environments), San Francisco, CA, USA, 19 Sep. 2008WPNC 2009 (The 6th Workshop on Positioning,

Navigation and Communication, Leibniz, Germany, 19Mar. 2009

WHERE (Wireless Hybrid Enhanced Mobile RadioEstimators), FP7-ICT-2007-1, 01.01.2008-30.06.2010,5.551 Million Euros

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Category

Range-freeAPS [1]

Range-based

Deterministic (fingerprinting)

Probabilistic

RADAR [2]Parametric

Non-parametric

ML, LS, MAP

BP-iterative

BP [3]

[1] D.Niculescu and B.Nath, Ad hoc positioning system (APS), IEEE Globecom2001, pp.2926 2931, Nov. 2001.

[2] P.Bahl and V.Padmanabhan, RADAR: An in-building RF-based user locationand tracking system,IEEE Infocom2000, pp.775 - 784 Mar. 2000.

[3] A.T.Ihler, et al., Nonparametric belief propagation for self-localization of sensornetworks,IEEE J SAC, vol.23, no. 4, pp.809-819, Apr. 2005.

References


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Range-free localization (APS)

Anchor #1Anchor #2

Anchor #3Anchor #4

Anchor #5

3 hops

3 hops

3 hops

4 hops

5 hops

Target

The location of a target is estimated with the knownlocations of anchor nodes and the numbers of hops tothem 30

Problems of APS

Hop count does not correspond to physicaldistance

The localization performance is very badThey believe ranging is difficult (ranging function isrealized in current wireless communicationstandards)

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Deterministic localization (RADAR)

a b c d

Anchor #1

Anchor #2

Anchor #3

RSSI (received signal strength indication)=received power

Database[a, -20, -34, -50][b, -21, -32, -65][c, -34, -11, -45]

RSSI at Anchor #1

[?, -33, -15, -22]

Find thebestmatching

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Problems of RADAR

Exhausted pre-measurement for making databaseis requiredOnce the room layout is changed, the currentdatabase becomes useless, so a new measurement

is requiredTo include the effect of moving objects intodatabase is difficult


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Principle of localization

Targetnode

Targetnode

Mobile

terminal

Unknownlocation

(x, y, z)

Anchornode

Accesspoint

Basestation

Knownlocation

(xn, yn, zn)

WSNWLANCellular

N>kfor the k-dimensional localization problemn=1, , N

Mn: measurement vector at the n-th anchor node for a target

Mn=[Mn1, , MnL], L: the number of measurements for the target

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What is the measurement?

The measurement is related to the location of the target node,(x, y, z), such as

TOA (Time Of Arrival)TDOA (Time Difference Of Arrival) [1]AOA (Angle Of Arrival) [2]RSSI (Received Signal Strength Indication, received power)

Localization: to estimate the location of the target node,=(x, y, z)

Ranging: to estimate the distance to the target node

Note:

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An example of TOA-based method (1/2)

2-dimensional localization: z=0, zn=0(parameter) vector to be estimated: =(x, y)One-shot measurement: L=1Measurement TOAn: Mn=tn (the propagation time

between the mobile terminal andthe n-thbase station

Distance: nn ctd

c=3.0x108 m/sec

[1] N. Priyantha, et al., CRICKET location-support system,Proc. ACM MOBICOM,Aug. 2003.

[2] H. Kawano and M. Kawano, Development of a pedestrian navigation systemworking on the 2.4 GHz band,11th World Congress on Intelligent TransportSystems,Oct. 2004 (http://www.radio-com.jp/rcs_technology.html).

References

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Basestation 4

Basestation 1

Basestation 2

Mobile terminal =(x, y)

Basestation 3

d1

d3 d2

d4

NLOS

An example of TOA-based method (2/2)

Localization is based on several ranging from differentplaces (base stations)

NLOS: non-line-of-sight


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How can we localize the target?

p42

p14

p12

The target must belocated at theweight of thetrianglep42-p12-p14

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ctn

LS (Least Squares) estimation (1/2)

find which minimizes

2

1 |)(

~

|)( N

nnn dde

),( yxLS estimation problem [1]

22 )()( nn yxxx

n-th true distance: 22 )()()),(( nnn yyxxyxd

n-th square (ranging) error:2|)(

~|)( nnn dde

Sum of the square errors: )()(1

N

nnee

Note:

LS estimation is a nonlinear minimization problemLS estimation does not care about the distribution ofdn

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LS (Least Squares) est imation (2/2)

d4)(4 d

Basestation 4

2444 |)(|)( dde

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ML (Maximum Likelihood) estimation (1/2)

Assume that dn has a known conditional probability densityfunction (pdf) for a given :)(nd

)|())(|( nnn dpddp

The likelihood function on =(x, y) is given by

N

n

ndpl1

)|()(


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find which maximizes),( yxML estimation problem [1]

ML (Maximum Likelihood) estimation (2/2)

N

n

ndpL1

)|(log)(

Note:

ML estimation is a nonlinear minimization problemML estimation does not care about the distribution of

Log-likelihood function on

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MAP (Maximum A Posteriori) estimation

Assume that has a knownpdf: p()

By Bayes theorem

(|()(

(|()|( pdp

dp

pdpdp n

n

nn

find which maximizes),( yxMAP estimation problem [2]

N

nndpMAP

1

)(log)(

Note:

ML estimation is a nonlinear minimization problem

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A Gauss ian case

Assume that tn contains a Gaussian distributed error thus dnalso contains a Gaussian distributed error [3]:

2

2

2

))(~

(

2

1)(

~|( d

nn dd

d

nn eddp

find which maximizes),( yx

ML estimation problem

ML

N

n d

nn Cdd

L

1

2

2

2

))(~

()(

Therefore,

find which minimizes),( yx

)())(~

( 2

1

eddN

n

nn

LS estimationproblem !

N

n d

nn ddN

d

N

n

nn eddpl1

2

2

2

))((

1 2

1))(

~|()(

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Concluding remarks

LS and ML estimations are classical frequentistapproacheswhereas MAP is a Bayesian approach

The concept of MAP estimation is totally different from that ofML estimation (The Bayesian approach gives a related butconceptually different treatment of the parameter estimation

problem (LS and ML) [1])

Only for a Gaussian case, LS estimation becomes equivalentto ML estimation

The localization performance depends on how accurately wecan knowp(dn|) andp(), that is, the channel propagationcharacteristicand the system layout

[1] L. Ljung, System Identification: Theory for the User, Prentice-Hall, 1999.[2] C.M. Bishop, Pattern Recognition and Machine Learning, Springer, 2006.[3] N. Patwari, et al., Relative location estimation in wireless sensor networks,

IEEE Trans. Signal Process., vol.51, no.8, pp.2137-2148, Aug. 2003.

References


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Performance bounds

Target node location: (x, y, 0) (unknown)Unknown parameter: =(x, y)Anchor node location: (xn, yn, zn) (known) (n=1, , N)Measurement (RSSI, TOA and so on): Mn (L=1)

True distance between the target and n-thanchor node:

probability density function (pdf) ofMn given :Log-likelihood function on for the n-thanchor node: L

n

()

222 )0()()()( nnnn zyyxxd

))(|(log)( nnn dMpL

nd ))(|( nn dMp

)(nd

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Log-likelihood function on : L()

Fishers information matrix is defined as [1]

N

nnn

N

nn dMpLL

11

)(~

|(log)()(

2221

1211

2

22

2

2

2

)()(

)()(

)(JJ

JJ

LyLxy

Lyx

Lx

EJ F

Taking into consideration:

0)(

~)(

n

n

d

LE

Cramer-Rao lower bound for ML estimation (1/6)

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We have

y

d

x

dJJ

y

dJ

x

dJ

nN

n

nn

N

n

nn

N

n

nn

)(~

)(~

)(

)(~

)(

)(~

)(

12112

1

2

22

1

2

11

where

2

2

)(~

)()(

n

nn

d

LE


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Defining the inverse matrix ofJFas IF():

1121

1222

211222112221

1211

1

1

)()(

JJ

JJ

JJJJII

II

JI FF

the Cramer-Rao lower bound on the ML estimation errorvariance is given by

2

11

2

1

2

1 1

22

22112

)(~

)(~)(

)(~)(

)(~)(

)(~)(

)(~)(

)]var()min[var()(

N

nn

n

n

nn

N

nn

nn

N

nn

nn

N

n

N

nn

nn

n

nn

CRLB

d

yy

d

xx

d

yy

d

xx

d

yy

d

xx

IIyx



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0

x

z

y

(x, y, 0)

(xn, yn, zn)

(xn, yn, 0)

n

n

From the target node to the n-thanchor node, define the elevationangle and the direction angle on thex-yplane as n and n, respectively

nd~


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The Cramer-Rao lower bound can be re-written as

N

i

N

ijji

ji

ji

N

nn

n

CRLB

1 1 22

2

1 2

2

coscos

)(sin)()(

cos

1)(

)(

Note:

when the target and anchor nodes are on a line(1=2=, , =N)

)(2CRLB


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For L measurements case, the Cramer-Rao lower boundcan be re-written as

1

1 1 22

2

1 2

2

coscos

)(sin)()(

cos

1)(

)(

L

LN

i

N

ijji

ji

ji

N

nn

n

CRLB


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Assuming we know a priori knowledge on the location ofthe target node asp(), the priori information matrix iscalculated as

)(log)(log

)(log)(log

)(

2

22

2

2

2

py

pxy

p

yx

p

xEJ P

Bayesian Cramer-Rao lower bound for MAP estimation (1/2)


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the Bayesian Cramer-Rao lower bound on the MAPestimation error variance is given by

DefiningJT()=JF()+JP() and its inverse matrix as IT():

2221

12111

''

'')()(

II

IIJI TT

22112 '')]var()min[var()( IIyxBCRLB

Note:

When no priori knowledge on the targets location is available,the BCRLB (MAP estimation) becomes equivalent to theCRLB (ML estimation), because JP()=0

[1] H.L.VanTrees, Detection, Estimation, and Modulation Theory, Part I, JohnWiley & Sons, 1968.

References

Bayesian Cramer-Rao lower bound for MAP estimation (2/2)

localization11 aug 09

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