Lost in Space or Positioning in Sensor Networks Michael O’Dell Regina O’Dell Mirjam Wattenhofer...

Lost in Spaceor

Positioning in Sensor Networks

Michael O’DellRegina O’Dell

Mirjam WattenhoferRoger Wattenhofer

RealWSN 2005 Positioning in Sensor Networks 2

Positioning

• What is positioning (a.k.a. localization)?– Deduce coordinates– GPS “software version”

• Why positioning?– Sensible sensor networks– Heavy/costly localization hardware– Geometric routing benefits

• Idea:– (Small) set of anchors– Others: location = f(network,communication,measurements)


Sensor Networks


Our Perspective

Theory Practice


Positioning – As We See It

• Models of Sensor Networks

• Positioning Algorithms

• Hardware Description

• Experiments

• Lessons

• Future Work

Theory

Practice


Part I: Theory


Models of Sensor Networks

• Unit Disk Graph (UDG)– [Clark et al, 1990]– Widely used abstraction

• Quasi-Unit Disk Graph (qUDG)– [Krumke et al, 2001]– [Barriere et al, 2003]– [Kuhn et al, 2003]– More realistic?

• “well-behaved” ) allow proofs

1

1

d

?


Available Information

• T[D]oA:time– GPS– Cricket [Priyantha et al, 2000]

• RSS: signal strength– RADAR [Bahl, Padmanabhan, 2000]

• Imply distance

• AoA: angle– APS using AoA [Niculescu, Nath, 2003]

• Relative distance to anchors– APiT [He et al, 2003]


Positioning Algorithms

• Based on (q)UDG– (sometimes) provable statements– Abstraction ) rough idea

• Virtual Coordinates Algorithm [Moscibroda et al, 2004]– Linear programming– Complex, time-consuming– 100-node network: several minutes on desktop

• GHoST, HS [Bischoff, W., 2004]– Dense networks– Optimal in 1D– UDG crucial


Positioning Algorithms… cont’d

• APS [Niculescu, Nath, 2001 & 2003]– Hop or distance based– Given distance estimate, use GPS triangulation– Least-squares optimization– Isotropic network helpful

• General graphs– Given inter-node distances– Also: Internet graph (latencies)

• Example: Spring Algorithms– Internet: Vivaldi [Dabek et al, 2004]– Ad hoc [Rao et al, 2003]


Spring Algorithm

• Most practical?• Originally: graph drawing• Idea

– Edge = spring– Rest length = distance– Embedding = minimal power configuration

• Algorithm– Steepest descent, numerical methods– Simple:

• New position = average of neighbors• Iterate

Local vs. global


Our View = Assumptions

• Minimal hardware– Low storage– Low computing power– Basic RSS measurements

• Short range– Few meters– (RADAR: building – several dekameters)


Part II: Practice


Hardware Description

• ESB– scatterweb.com– 32kHz CPU– 2kB RAM– Sensors and actuators

• RSS:– Indirectly via packet loss

• New version:– Actual RSS measurable at receiver

• “Battery with Antenna”

Desktop:

– 3GHz– 512MB– Factor 105


“software version” RSS

• Older ESB (software) version– @sender: vary transmission power

• Via potentiometer controlling current to tranceiver

• Value s between 0 and 99

• Write s into packet

• Repeat x times

– @receiver: count number received packets• per s

– Measurement: packet loss• Requirement

– Distance increase → power increase– Correlation: to be determined

• New version (software):– Direct read out

Future work!


Experiment 1 – “Laboratory”

• Power vs. Distance– A sends at power level s– x = 100 times– d = 1..120cm

• Minimum• 90%

A B

ds

0

5

10

15

20

25

1 11 21 31 41 51 61 71 81 91 101 111 121

Distance (in cm)

Min

imu

m P

ow

er R

ecei

ved

0

5

10

15

20

25

30

35

1 11 21 31 41 51 61 71 81 91 101 111 121

Distance (in cm)

po

wer

at

90%

of

pac

kets

rec

eive

d

Coffee machine?


Original Algorithm

• Spring Embedding– Good for “easy” networks

• Power-to-distance– Inverse of previous experiments

• Results– Unusable!


Experiment 2 – “Room”

• Localization in the plane– Rectangle: 4m x 3m– 4 anchors: corners– Test node: inside

• Each anchor Ai

– Send packet s = 0..99– Next anchor

• Test node N– Record packets received

A0 A2

A3 A1

N15: 278

14: 365

16: 302

11: 139


Experiment 2 – “Room” … Results

Anchor 1

0

100

200

300

400

500

600

700

800

900

1 11 21 31 41 51 61 71 81 91

Received Power

Fre

qu

ency

Anchor 1

0

50

100

150

200

250

300

1 6 11 16 21 26 31 36

Minimum Power Received

Fre

qu

ency

Anchor 1

0

50

100

150

200

250

300

1 6 11 16 21 26 31 36

Minimum Power Received with/without Obstacles

Fre

qu

ency

Anchor 1

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Hole Size

Fre

qu

ency

anchor distance avg. min power

A2 1.39 11

A0 2.78 15

A1 3.02 16

A3 3.65 14

(without obstacles)


Experiment 3 – “Network”

• 9 nodes in a room– Distances: 1..6m

• 1 sender at a time– Send 1 packet at each level– Others: record minimum received– Report previous minima

• Round robin

• Minima:– Good approximation– Storage: save factor 100 per round


Experiment 3 – “Network” … Results

• Error– Almost 30 units for same distance– Exp. 1: “nicer” curve

• Longer range effects?

• Symmetry!Symmetry

0

100

200

300

400

500

600

700

800

900

1 6 11 16 21 26 31 36

Minimum Power Received

Fre

qu

ency

Symmetry

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6

Rounded Diffence in Average Minimum Received Power

Fre

qu

ency

0

5

10

15

20

25

30

35

40

45

0 100 200 300 400 500 600

Distance (in cm)

Ave

rag

e M

inim

um

Po

wer

Rec

eive

d


Lessons

• Average minimum– Stable– Good approximation– Saves storage

• Symmetric links

• Power versus Distance– Strongly environment dependant– Measurements between two nodes

Not generalizable

• RSSI in sensor networks: good, but not for “reasonable” localization


Future Work

• Here: more questions than answers

• Hardware RSS measurements– Indication given by reviewer

• Same experiments – different hardware– Same results/trend?

• Long range vs. short range

• More environments

• New models

mica2:

in progress

Similar results

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Lost in Space or Positioning in Sensor Networks Michael O’Dell Regina O’Dell Mirjam Wattenhofer...

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