1

Ad Hoc Positioning System (APS)Using AOA

Dragos¸ Niculescu and Badri NathINFOCOM ’03

Seoyeon KangSeptember 23, 2008

2

Outline

• Introduction• Angle of arrival(AOA) theory• Ad hoc positioning system(APS) algorithm• Error control• Simulation• Future work & conclusion

3

Introduction

• Ad hoc networks• Challenges• Background• Problem definition

4

Ad hoc networks

• Decentralized wireless network• Each node is willing to forward data for other nodes• Each node acts as a router• Large number of unattended nodes

with varying capability– Ranging, compass, AOA, etc.

5

Challenges

• Cost of deployment• Capability and complexity of nodes• Routing without the use of large conventional

routing table• Etc.

6

Challenges

• Availability of position would enable routing without the use of large routing tables

• How to get position information– Using capabilities

• How to export capabilities in network

7

Background

• Orientation– Heading– Defined by the angles it forms with the axes of a reference

frame

NORTH

8

Background

• Angle of arrival(AOA)– To sense the direction from which a signal is received– By knowing ranges x1, x2, and distance L

– The node can infer the orientation Θ

Ultrasound receiver x1

x2

9

Background

• Related works with other capabilities– Time of arrival(TOA)– Time difference of arrival(TDOA)– Signal strength

• Based on AOA– Less computational resources and infrastructures

10

Problem definition

• How all nodes determine their orientation and position in an ad-hoc network where only a fraction of the nodes have positioning ca-pabilities, under the assumption that each node has the AOA capability

11

AOA theory

• Terms• Problem definition• Finding headings• Finding positions– Triangulation using AOA

12

Terms

• Bearing– Angle measurement with respect to another object

• Radial– Reverse bearing– Angle under which an object

is seen from another point

13

Problem definition

• Given imprecise bearing to neighbor – By AOA capability

• A small fraction of the nodes have self position-ing capability– Landmarks

• Find headings and positions for all nodes

14

Finding headings

A’s heading :

15

Finding positions

• Triangulation using AOA• Given– Positions for the vertices of a triangle– Angles at which an interior point “sees” the vertices

Reduction to trilateration

16

• Review of trilateration• Given– Positions for the vertices of a triangle– Distances to vertices

Finding positions

17

• For each pair of landmarks – Create an trilateration– A triangulation problem of size n a trilateration problem of size

Finding positions

18

• Using triplets of landmarks– trilateration problems of size 3

• Less memory

D(x,y)

Finding positions

L1

L2

L5L4

L3

19

APS(ad hoc positioning system) Algorithm

• Concepts of original APS– Information is forwarded in a hop by hop fashion– Each node estimates position based on landmarks

• Extend to angle measurements– DV-Bearing– DV-Radial

20

Orientation forwarding

• DV-Bearing

21

Orientation forwarding

• DV-Radial

22

Orientation forwarding

• Tradeoffs between DV-Bearing and DV-Radial

23

Network density

• What kind of node density is needed in order to achieve a certain condition with high probability

24

Error control

• Bearing measurements are affected by errors• Forwarding may amplify and compound smaller errors

into larger errors

25

Limiting the propagation of packets

• Set TTL to limit error propagation

26

Threshold to eliminate triangles

• Ignore small angles• Tradeoff – coverage vs. positioning error

27

Elimination of outliers

• Compute centroid and remove outliersthen recompute

28

Simulation

• Isotropic topology1000nodesAvg. degree=10.5Gaussian noise20% landmarksThreshold 0.35(≈ 20˚)DV-Bearing TTL=5DV-Radial TTL=4

29

Positioning error

• 1.0 means that the position is one hop away from true position

30

Bearing error

• How forwarding method compounds and propa-gates error

31

Heading error

• Error in the absolute orientation averaged over all nodes

32

Coverage

• Percentage of regular nodes which are able to resolve for a position

33

Tracking example

34

Future work

• Extension to mobility– A moving landmark provides more information

• Error estimation – Transmitting of the error estimation with DV data– Weights for each landmark

• Multimodal sensing– With compasses and accelerometers

35

Summary

• A method that infers position and orientationin ad hoc network with only few landmarks– Orientation forwarding

• DV-Bearing and DV-Radial

– Triangulation using AOA

• Advantages– Do not require additional infrastructures– Less computational resources– Scalable

36

Thank you