GPS-free Positioning in Ad-Hoc Networks Yu-Min Tseng.

GPS-free Positioning in Ad-Hoc NetworksGPS-free Positioning in Ad-Hoc Networks

Yu-Min Tseng

TargetTarget

Not rely on GPSNot rely on GPS Use the distances between nodes to build Use the distances between nodes to build

a relative coordinate systema relative coordinate system Distance measurement methodDistance measurement method

• Signal strength methodSignal strength method• Angel of Arrival (AOA) methodAngel of Arrival (AOA) method• Time of Arrival (TOA) methodTime of Arrival (TOA) method

Build Local Coordinate SystemBuild Local Coordinate System

Build Local Coordinate SystemBuild Local Coordinate System

Detect one-hop neighbors (KDetect one-hop neighbors (K ii))

Measure the distances to one-hop neighbors (DMeasure the distances to one-hop neighbors (D ii))

Send KSend Ki i && DDi i to all one-hop neighborsto all one-hop neighbors

Choose node p & qChoose node p & q Local View Set for node i as a set of nodes LVSLocal View Set for node i as a set of nodes LVSii(p,q)(p,q)

K Kii such that , node i can compute the such that , node i can compute the

location of node jlocation of node j

iLVSj

),(LVS arg q) (p, iC)q,(p

maxikk

kk qp

Coordinate System DirectionCoordinate System Direction

ki

axis-ymirror ki

Coordinate System DirectionCoordinate System Direction

ki

Coordinate System DirectionCoordinate System Direction

ki

ikj

ikj

ki

ikj

ikj

if

if

angel correction the

necessary NOT is mirroring

and or

and

angel correction the

necessary is mirroring

and or

and

j

j

j

j

Coordinate System DirectionCoordinate System Direction

Coordinate SystemCoordinate System

ProblemProblem The motion of node The motion of node ii will cause that all the will cause that all the

nodes have to re-compute their positionsnodes have to re-compute their positions Cause a large inconsistencyCause a large inconsistency Only used in small area networks, low mobilityOnly used in small area networks, low mobility

SolutionSolution Compute the center of the coordinate systemCompute the center of the coordinate system Message broadcastMessage broadcast Stable coordinate systemStable coordinate system

Location Reference GroupLocation Reference Group

Location Reference Group (LRG)Location Reference Group (LRG) The density of the nodes in the LRG is the The density of the nodes in the LRG is the

highest in the networkhighest in the network Network center is a relative position Network center is a relative position

dependent on the topology of the LRGdependent on the topology of the LRG Average speed of LRG center is much smaller Average speed of LRG center is much smaller

than the average speed of nodesthan the average speed of nodes

Location Reference GroupLocation Reference Group

How to obtain the LRG centerHow to obtain the LRG center Every node broadcast hello packet to its n-hop Every node broadcast hello packet to its n-hop

neighborhood to obtain node IDs, their mutual neighborhood to obtain node IDs, their mutual distances, the directions of their coordinate systemsdistances, the directions of their coordinate systems

Compute positions of the n-hop neighborsCompute positions of the n-hop neighbors Compute the n-hop neighborhood centersCompute the n-hop neighborhood centers

odneighborho hop-nin nodes ofnumber m

, c , c yx

m

jm

j yx

Location Reference GroupLocation Reference Group

Compute n-hop neighborhood direction as Compute n-hop neighborhood direction as average of coordinate system directionsaverage of coordinate system directions

Compute density factorCompute density factor• Density factor is the ratio between the number of Density factor is the ratio between the number of

nodes & the size of the observed areanodes & the size of the observed area

Location Reference GroupLocation Reference Group

Location Reference GroupLocation Reference Group

How to maintain the LRGHow to maintain the LRG Every node broadcast hello packet to its n-Every node broadcast hello packet to its n-

hop neighborhood to obtain node IDs, their hop neighborhood to obtain node IDs, their mutual distances, the directions of their mutual distances, the directions of their coordinate systems (same as init)coordinate systems (same as init)

Compare the n-hop neighbors list with the list Compare the n-hop neighbors list with the list of the LRG membersof the LRG members• The node that is a n-hop neighbor of LRG master The node that is a n-hop neighbor of LRG master

& the highest number of LRG nodes still in its n-& the highest number of LRG nodes still in its n-hop neighborhood is elected to be the new LRG hop neighborhood is elected to be the new LRG mastermaster

Location Reference GroupLocation Reference Group

• If the node doesn’t have the LRG master in its n-If the node doesn’t have the LRG master in its n-hop neighborhood, and the node doesn’t receive hop neighborhood, and the node doesn’t receive the new position information issued by LRG the new position information issued by LRG master, it starts the init proceduremaster, it starts the init procedure

Location Reference GroupLocation Reference Group

If we finds at least 3 modes have same topology in both C1 & C2, then adjust the direction of C2 to direction of C1

SimulationSimulation

DrawbackDrawback

Relative positioningRelative positioning When the reference moves, positions have When the reference moves, positions have

to be recomputed for nodes that have not to be recomputed for nodes that have not movedmoved

If intermediate nodes move, fixed nodes If intermediate nodes move, fixed nodes depending on them also have to depending on them also have to recompute positionrecompute position

Ad Hoc Positioning SystemAd Hoc Positioning System

At least 3 nodes (called landmarks) are At least 3 nodes (called landmarks) are GPS enhancedGPS enhanced

An arbitrary node has estimates to a An arbitrary node has estimates to a number (>= 3) of landmarks, it can number (>= 3) of landmarks, it can compute its own position in the plaincompute its own position in the plain

Use propagation method, all nodes infer Use propagation method, all nodes infer their distance to landmarkstheir distance to landmarks

Complexity of signaling is driven by the Complexity of signaling is driven by the number of landmarks, and by the average number of landmarks, and by the average degree of each nodedegree of each node

DV-Hop propagation methodDV-Hop propagation method

Each node maintain a table {XEach node maintain a table {X ii,Y,Yii,h,hii} & } &

exchanges updates only with its neighborsexchanges updates only with its neighbors The correction a landmark (XThe correction a landmark (X ii,Y,Yii) computes is ) computes is

j landmarks all,,)()( 22

jih

yyxxc

i

jiji

i

DV-Hop propagation methodDV-Hop propagation method

5.1726

40100 :1

L

42.1652

7540 :2

L

90.1556

00157 :3

L

Assume A gets its correction from L2, its estimate distance to the 3 landmarks would be: to L1, 3x16.42 ; to L2, 2x16.42 ; to L3, 3x16.42

Then plugged into the triangulation procedure to get an estimate location

DV-distance propagation methodDV-distance propagation method

Similar to DV-hop methodSimilar to DV-hop method Measured by using radio signal strength & Measured by using radio signal strength &

is propagated in meters rather than in is propagated in meters rather than in hopshops

Less coarse than DV-hop methodLess coarse than DV-hop method Not all hops have same sizeNot all hops have same size

Sensitive to measurement errorsSensitive to measurement errors

Euclidean propagation methodEuclidean propagation method

AB AC BC are known by estimation, and known by node A

The estimated distance of AL is obtained by applying Pithagora’s generalized theorem in triangles ACB BCL ACL

It is possible that A is on the different side of BC A’, the choice is made by voting or by examining relation with other common neighbors of B and C

SummarySummary

Setup Setup coordinate by coordinate by perimeter nodesperimeter nodes

Setup Setup coordinate by coordinate by every nodeevery node

Setup Setup coordinate by coordinate by landmarkslandmarks

GPSGPS No GPS.No GPS. No GPS.No GPS. Landmarks Landmarks need GPS.need GPS.

Coordinate Coordinate systemsystem

AbsoluteAbsolute RelativeRelative AbsoluteAbsolute

FloodingFlooding When initWhen init LRG need LRG need broadcast all,broadcast all,

Other nodes Other nodes broadcast n-hopbroadcast n-hop

PropagationPropagation