Positioning in Ad-Hoc Networks - A Problem Statement Jan Beutel Computer Engineering and Networks Lab Swiss Federal Institute of Technology (ETH) Zurich.

Positioning in Ad-Hoc Networks-

A Problem Statement

Jan BeutelComputer Engineering and Networks Lab

Swiss Federal Institute of Technology (ETH) Zurich

June 20, 2001

Computer EngineeringComputer Engineeringand Networks Laboratoryand Networks Laboratory

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Jan Beutel, March 26, 2001Jan Beutel, March 26, 2001

Network Scenarios

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Positioning: Environment

• Stationary and Dynamic Environments

• Graph Connectivity

– Node Clusters

– Node Depletion

• Variance in

– Initial Position Estimates

– Range Estimates

• Map Data, Lookup Tables

• Multiple Link Reception Capability of Nodes

• Low Duty Cycle Radio Frontend

• Incorporate Positioning System in Communication Framework

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Positioning: The Problem

• Finding the position of networking nodes

Relative vs. Absolute Positioning Mode

Reference Positions, Map

Database

Other Networking Nodes, Distance and Geometric

Constellation

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Positioning: Definitions

• anchor node knows its location at start of algorithm

• unknown node does not know its location

• settled node has discovered its location

• neighborhood all nodes within one hop

• Context dependent on Positioning Mode

– Absolute Coordinates (Xi,Yi) Position

– Relative Coordinates (xi-X0,yi-X0) Orientation, Topology

– Range Value ri Proximity to Neighbors

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Positioning: Granularity

• Granularity of Solution Depends on– Network population (nodes/area)– Geometric constellation (Dilution of Precision)– Amount of settled nodes (convergence)– Dynamics in networking nodes (network links/area)– Bounds of the geometric solution

• Coarse Grain Positioning– Cell based proximity– Coarse topology discovery– Low precision coordinates– Invariants

• Fine Grain Positioning– High precision coordinates– Orientation

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Existing Solutions

• Cell Based Identification

• Triangulation to Base Stations (AOA, TDOA, TOA, RSSI, Carrier Phase…)– Global Positioning System– Radar/VOR– Mobile Phones

• Depending on Uni-/Bi-directional Communication Link

• Probability Spaces• Mapping to RF Reference Mappings• Event Based• Topology Information

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Radio Ranging Methods

TOA – time of arrival

Carrier phase

AOA – angle of arrival

Signal strength

TDOA – time distance of arrival

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Positioning Scenarios

• Initialization– Problem: Convergence

• Iteration– Single connected graphs– No dynamics– Problem: Large Amount of Data

• Motion– Multiple disconnected graphs– Mobile nodes– Additional metric incorporated– Problem: Distributed System

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Algorithms for Positioning

• Case: No Anchors available

Idea: Reuse High Connectivity

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Redundant Triangulation

Iteration on 25 individual ranges with 50% each

0 0.5 10

0.2

0.4

0.6

0.8

1

Delaunay Mesh of 25 Networked Nodes

x

0 0.5 10

0.2

0.4

0.6

0.8

1

Solution on 25 Ranges and 50% Error

x

0 0.5 10

0.2

0.4

0.6

0.8

1

50 Solutions and Mean

x

0.4 0.45 0.5 0.55 0.60.4

0.45

0.5

0.55

0.6

Zoom on Error

x

dx 0.0054

dy 0.0058

1% error

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Triangulation on Real Data

• Application to Wavelan RSSI data shows good average

Solution• Iterative triangulation• Overload systems• Influence of

geometric DOP• Include

environmental information

Yielding sub meter DOP

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Algorithms for Positioning

• Case: Anchors available

Idea: Propagate Reference Data

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Establishing Initial Position Estimates

• Assumption Based Coordinates (ABC)

• n0 assumed to be at (0,0,0)

• n1 assumed to be at (r01,0,0)

r01 = RSSI range between n0 and n1

• n2 at (

Assumptions:

• n3 at (

Assumption:

r012 + r03

2 - r132

2r01

, r032-x3

2-y32 )

r032 – r23

2 + x22 + y2

2 - 2x2x3

2r01

,

r012 + r02

2 - r122

2r01

, r022-x2

2 , 0)x

y

z

n0 n1

n2

n3• positive square root• z2 = 0

• positive square root

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The TERRAIN Algorithm

• Triangulation via Extended Range and Redundant Association of Intermediate Nodes

• ABC algorithm creates maps

• Target node waits to beincluded in 3 maps

• Extended rangescalculated fromrespective maps

• Triangulation bytarget node basedon extended ranges

• Iterate network-widetriangulation

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radio range

extended range

intermediate node

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Status

• Simulations yielding first results– Redundant triangulation works well– Range error impacts more than initial position– Initialization/Convergence a problem

• Testbed in setup phase– Smart it’s – BTnode– Multihop BT Prototype

• Simulation with real data in preperation

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Algorithms for Positioning using Bluetooth

• Appropriate HCI Commands and Events– Find Neighbors

• HCI_INQUIRY

– Classify Neighbors• HCI_READ_REMOTE_SUPPORTED_FEATURES

– Continuity in Neighbors• HCI_READ_CLOCK_OFFSET• HCI_READ_CONNECTION_ACCEPT_TIMEOUT• HCI_READ_PAGE_TIMEOUT• HCI_READ_LINK_SUPERVISION_TIMEOUT• HCI_READ_FAILED_CONTACT_NUMBER

– Find Ranges • HCI_READ_RSSI

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Bluetooth RSSI Samples Free Space

-25

-20

-15

-10

-5

0

5

10

15

201

30

59

88

11

7

14

6

17

5

20

4

23

3

26

2

29

1

32

0

34

9

37

8

40

7

43

6

46

5

49

4

52

3

55

2

58

1

61

0

63

9

66

8

69

7

72

6

75

5

78

4

81

3

84

2

87

1

90

0

92

9

95

8

98

7

10

16

10

45

Samples/Distance

RS

SI

Series1

Series2

S

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Bluetooth RSSI Samples Office Space

-25

-20

-15

-10

-5

0

5

10

15

201 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103

109

115

121

127

133

139

145

151

157

163

169

175

181

187

193

199

Samples/Distance

RS

SI

Series1

Series2

Series3

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Wavelan 802.11b RSSI Samples

-120

-100

-80

-60

-40

-20

0

20

40

60

80

-3 -2 -1 0 0 1 2 3 4 5 6 6 7 8 9 10 11 12 12 13 14 15 16 17 18 18 19 20 21 22

Distance [m]

Sig

na

l an

d N

ois

e L

ev

el [

dB

m]

LSNR Avg

LSL Avg

LNL Avg

RSNR Avg

RSL Avg

RNL Avg

Path Loss 1/r 2̂

Path Loss 1/r 4̂

Positioning in Ad-Hoc Networks - A Problem Statement Jan Beutel Computer Engineering and Networks Lab Swiss Federal Institute of Technology (ETH) Zurich.

Documents

error slide

positioning case

networked nodes x

geometric constellation

topology information

distributed system slide

high connectivity slide

beutel computer engineering