Minimal Transmission Power asDistance Estimation

for Precise Localization in Sensor Networks

Jan Blumenthal, Dirk TimmermannUniversity of Rostock

IWCMC, Vancouver2006/07/06

2

Focus of Presentation

• Preconditions– Hundreds of sensor nodes are

randomly deployed– Position initially unknown

• Why do we need localization?– Measurement requires position– Example: Self organization, self

healing, geographic routing

• Problem Statement– Localization needs distance

information– How to measure distances ?

Flood prevention by dikeobservation

3

Distance Estimation with RSSI in Theory

• Energy of signal decreases with distance d

• Sensor node measures energy of received signal

• Compared to a reference voltage• Received Signal Strength

supported by hardware– Cheap and always available

20

4R

R SS

P G GP d

λπ

⎛ ⎞= ⎜ ⎟⎝ ⎠

[ ]2

0( ) [ ] 10 log 20 log( )4R S R SP d dBm P dBm G G dλπ

⎡ ⎤⎛ ⎞= + ⋅ − ⋅⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦

distance d [m]R

ecei

ved

Sign

al S

tren

gth

[dB

m]

Measured RSS1

d1

Power Relations:

PTX Transmission PowerPRX Received PowerGTX Gain at SenderGRX Gain at Receiverd Distanceλ0 Wave length

20

4RX

RX TXTX

P G GP d

λπ

⎛ ⎞= ⎜ ⎟⎝ ⎠

4

Distance Estimation with RSSI in Theory II

20

4RX

RX TXTX

P G GP d

λπ

⎛ ⎞= ⎜ ⎟⎝ ⎠

0

4RX TX TX

RX

TX

RX

G G PdP

PkP

λπ

=

=

20

4R

R SS

P G GP d

λπ

⎛ ⎞= ⎜ ⎟⎝ ⎠

distance d [m]R

ecei

ved

Sign

al S

tren

gth

[dB

m]

Measured RSS1

d1

PTX Transmission PowerPRX Received PowerGTX Gain at SenderGRX Gain at Receiverd Distanceλ0 Wave length

Friis‘ Equation:

max TXd P∼

Rearrange

~

5

RSSI on Chipcon CC1010

- graph not stable- high variance

0

50

100

150

200

250

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72Distance [m]

Rec

eive

d Si

gnal

Str

engt

h

6

RSSI in Theory and in Reality

Transmitter Receiver

RSSI

Message Message

RSSI in Theory

0

50

100

150

200

250

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72

RSSI in Reality

Result: In Reality, distances based on RSSI are inaccurate.

Y Y

dMax. Transmission

Power

Approach: Minimal Transmission Power

8

Approach

Assumption:– Max. transmission power– Measuring RSSI is inaccurate

caused by• Measuring principle• Hardware effort

Approach:– Stepwise increasing transmission

power PTX

– In case of reception of a message the transmission power PTXspecifies a distance d

– Utilize only smallest transmission power Distance d

• Moving graph• Find crossing

with x-axisPTXMax

PTX

dMax d

• Measuring PRX• Recalculation of d

PRX

Distance d ddMax

PTXPTXMax

PTX_1

PTX_2

9

Finding the Distance

• Transmission power PTX is controlled via Special Function Register SFRTX

• SFRTX of tranceiver is transmitted with every message

• Distance d is calculated out of smallest SFRTX

Example (Scatterweb)• SFRTX tunable in range 0..100 (300m)• SFRTX(16±4) → d=2m

SFRTX=11

2m

SFRTX=14 SFRTX=16

Transmitting node (Beacon)

Receiving sensor node

10

Relation between Transceiver and SFRTX

Approximated transfer function H(x) of tranceiver (npn transistor)

Message

Transmission Power

YTransmitter

PTX

SFRTX

4TX

SFRkPTX ⋅=≈

Special Function Register to control transmitter

11

Relation between Distance and SFRTXPTX = Transmission PowerSFRTX = Transmission RegisterPRX = Received Powerd = distance

SFRTX

d

Already known:

Transmitter Y

Adjust Transmission Power via Special Function Register SFRTX

SFRTX

MessagePTX

max TXd P∼~

4TX

SFRkPTX ⋅=≈

2

2

4

TX

RXTX

SFRd

PkSFRd

=

⎟⎠⎞

⎜⎝⎛=πλ

≈

dSFRTX =≈

12

Min. Transmission Power

Message Message

• Distance d can be easly calculated from transmitted SFRTX

• Smaller estimation error compared to RSSI

Theory

d

Min. SFRTXTransmission Power

SFRTX

Y YTransmitter Receiver

d

Min. SFRTX

Reality

PTX 4TX

SFRkPTX ⋅=≈

13

Measurement Results: Scatterweb

0

5

10

15

20

25

30

35VarianzMinVarianzMaxMittelwert

Min. SFRTX of sensor nodes based on Scatterweb (indoor, ideal conditions, 40 samples each)

0 50 400100 150 200 250 300 350

Min. VarianceMax. VarianceAverage

We know, in theory: dSFRTX =≈

Distance dij between sender and receiver [cm]

Min

. Tra

nsm

issi

on P

ower

[SFR

TX]

14

Linearized Measurements

0

100

200

300

400

500

600

700

800

900

5 30 55 80 105 130 155 180 205 230 255 280 305 330 355 380

Min

. Tra

nsm

issi

on P

ower

[SFR

TX²]

Distance dij between sender and receiver [cm]

Linear Regressionf(x)=mx+n• m=1.3• n=0

• Create linear equation• Linearize graph by squaring d• Determine raising of graph• Combine final equation

Theory:

dmSFR

dSFR

TX

TX

⋅=

≈2

≈

15

Measurement Results: Scatterweb

0

5

10

15

20

25

30

5 25 45 65 85 105 125 145 165 185 205 225 245 265 285 305 325 345 365 385

Distance d ij between sender and receiver [cm]

Min

. tra

nsm

issi

on p

ower

[SFR

TX]

Average min. transmission power

Average min. transmission power plus standard deviation

Average min. transmission power minus standard deviation

Regression 1.3TX ijSFR d= ⋅

dSFRTX ⋅= 3.12

3.1

2TXSFRd =dSFRTX ⋅= 3.1

Example Application

17

Example Application with Scatterweb

Localization Algorithm:Weighted Centroid Localization (WCL)

– simple and fast calculation– small memory footprint– acceptable positioning error

Jan Blumenthal, Frank Reichenbach, Dirk Timmermann: Precise Positioning with a Low Complexity Algorithm in Ad hoc Wireless Sensor Networks, PIK - Praxis der Informationsverarbeitung und Kommunikation, Vol.28 (2005), Journal-Edition No. 2, S.80-85, ISBN: 3-598-01252-7, Saur Verlag, Deutschland, June 2005

Jan Blumenthal, Frank Reichenbach, Dirk Timmermann: Position Estimation in Ad hoc Wireless Sensor Networks with Low Complexity (Slides), Joint 2nd Workshop on Positioning, Navigation and Communication 2005 (WPNC 05) & 1st Ultra-Wideband Expert Talk 2005 (05), S.41-49, ISBN: 3-8322-3746-1, Hannover, Deutschland, March 2005

References:

Task:Determine position of moving sensor node

Immobile beacons

Mobile sensor node

Sensor network

18

Weighted Centroid Localization (WCL)

Approach:- Positioning by centroid determination

Pi´ (CGLCD)- Improved precision by weighting

measured distance dix using wij()

( )1

1

( , )''( , )

b

ij jj

i b

ijj

w B x yP x y

w

=

=

⎛ ⎞⋅⎜ ⎟

⎝ ⎠=⎛ ⎞⎜ ⎟⎝ ⎠

∑

∑ wij = Weight of distance Bj and node ib = Number of beaconsBj(x,y)= Position of beacons j

1

1'( , ) ( , )n

i jj

P x y B x yn =

= ∑

WCL

CGLCD ''( , )iP x y'( , )iP x y

1B 2B

3B4B

4id3id

2id1id

( , )iP x y

Immobile beacons

Mobile Sensor Node

19

Weight-based on Distances

( )1

ij g

ij

wd

=

Weight wij() depends on measured distance between beacon and sensor node.

Definition of Weight:

How to determine dij?

( )1

1

( , )''( , )

b

ij jj

i b

ijj

w B x yP x y

w

=

=

⎛ ⎞⋅⎜ ⎟

⎝ ⎠=⎛ ⎞⎜ ⎟⎝ ⎠

∑

∑

Optimal: g=3

20

Operations on Beacons

Max. transmission power sent ?

Increase round number

Send message with own position, transmission power and round number

Increase transmission power and wait one time slot

no

yes

Adjust transmitter with current transmission power

Reset transmission power

• Beacons are sensor nodes with already known position• Send out messages with own position and currently adjusted SFRTX

21

Operations on Sensor Nodes

Higher round number ?

New min. trans-mission power ?

Store beacons’ position, round number and transmission powerReject message

no

yes

no

yes

Waiting for messages

New beacon position received ?yes

no

Beacon message received ?

yes

no

• Sensor nodes do not know own position

• Calculate distance and positions out of received messages

22

Reduce high Oscillating Measurements

Control Loop

Calculate averaged min. transmissionpower e.g.,

PTX aPTX

0.25 0.75TX TX TXaP aP P= ⋅

Higher round number ?

New min. trans-mission power ?

Store position, round number and transmission powerReject message

no

yes

no

yes

Waiting for messages

New beacon position received ?yes

no

Beacon message received ?

yes

no

23

Demonstrator Show• 4 beacons at all corners, one unknown node was moved• Localization error: 0.3m• Notation:

– P12 : current transmission power is 12– aP10: averaged transmission power is 10

Scatterweb

SpyGlass (University of Luebeck) Field size = 2x2 m

http://rtl.e-technik.uni-rostock.de/~bj/movies/PositionEstimationUsingMinimalTransmissionPower.mpg

24

Discussion

Remarks• based on circular transmission range• concurrent channel access through hidden terminal

problem• numerous sources of interferences (sensor nodes,

steel girders, obstacles)• noticeable delays caused

– increasing transmission power– round counting

Advantages of min. Transmission Power• simple distance estimation• easy to implement• more accurate than RSSI

25

Conclusion

Essentials • Wireless sensor networks require localization of

sensor nodes• Most distance estimations are inaccurate especially in

indoor use

New approach to estimate a distance• Minimal transmission power

Proof of concept• Higher resolution and smaller variances than RSSI• Example application combined with Weighted

Centroid Localization (WCL)

Thank you!

www.sensornetworks.org