Download - Lost in Space or Positioning in Sensor Networks

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

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