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Novel Self-Configurable Positioning Technique for Multi-hop Wireless Networks
Hongyi Wu, Chong Wang,and Nian-Feng Tzeng
IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 13, NO. 3, JUNE 2005
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Outline Introduction Proposed self-configurable positioning
technique Euclidean distance estimation Coordinates system establishment
Simulation Conclusion
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Introduction Many application are need to know node
location Target tracking, routing…
We propose a self-configurable positioning technique
1. Euclidean distance estimation model
2. Coordinates system establishment Range-based GPS-free
AB
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Proposed self-configurable positioning technique – Euclidean distance estimation
This can be done off-line by each node or a central controller
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Euclidean distance estimation Assume the node distribution is uniform Euclidean distance d is given
(0,0) (d,0)
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Euclidean distance estimation The distance between node D and node i
(within S’s transmission range)
(0,0) (d,0)
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Euclidean distance estimation where Xi and Yi are random variables with a un
iform distribution
(0,0) (d,0)
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Euclidean distance estimation Accordingly, we can derive the density functio
n of Zi
(0,0) (d,0)
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Euclidean distance estimation Assume a node has the shortest
Euclidean distance to D
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Euclidean distance estimation Consequently, we can derive the pdf of Z
And obtain its mean value
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Euclidean distance estimation We draw an arc ACB with node D as the center
and as the radius
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Euclidean distance estimation Assuming node is uniformly distributed
along AC (or BC) We can obtain the first hop along the shortest
path from S to D
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Euclidean distance estimation
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Euclidean distance estimation Recursively applying the above method,
we can obtain the shortest path
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Euclidean distance estimation
This can be done off-line by each node or a central controller
r=0.25, network=1*1
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How to use the Euclidead distance estimation model Estimate the distance between A and B
A B1 2 3 4
ControlPacket
0
Include a route length field
Assume the control packet follow the shortest path
ControlPacket
0.17
0.17 0.12 0.1 0.18 0.2
ControlPacket
0.29
ControlPacket
0.39
ControlPacket
0.57
ControlPacket
0.77
DAB= 0.77
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How to use the Euclidead distance
DAB= 0.77
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Coordinates system establishment : Localize landmarks Each landmark flooding a control packet to
every one of all other landmarks In order to learn the Euclidean distance
L1 L2 … Li
L1 0 L21 … Li1
L2 L12 0 … Li2
… … … … …
Li L1i L2i … 0
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Coordinates system establishment: Localize landmarks1. The landmark with the lowest ID : (0, 0)2. The landmark with the second lowest ID : (X, 0)3. The landmark with the third lowest ID: negative Y
(0, 0)(LAB, 0)
(LacCos , - LacSin )
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Minimize the errors of the landmark’s coordination
(0, 0)
(LAB, 0)
(LacCos , - LacSin )
Minimize the error function:
Lij can be learned through the Euclidean distance estimation model
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Coordinates system establishment : Localize regular nodes Landmarks flooding control packet that
include their coordinates and length field
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Minimize the errors of the regular node’s coordination
Minimize the error function:
Lip can be learned through the Euclidean distance estimation model
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Locations of landmarks The more the landmarks, the higher the
accuracy But computational complexity increases
exponentially Simulation show that typical # of
landmark vary from 4 to 7 Locations of landmarks
We consider 4 landmarks in a 1*1 area Assume 4 landmark located at the vertices of a
square and has an edge of G
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Locations of landmarks
G = 0.5
1
1
0.5
(Xc,Yc)
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Locations of landmarks
G = 0.7G = 0.9
G = 0.7
1
1
0.7
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Selection of landmarks : a set of all landmark candidates
If the node is stability and power are high Each candidate node discovers the shortest path to
all other candidate nodes
Ci : Candidacy degree of node i. Lower value of C, higher probability to be selected as landmark
Si,j : the length of the shortest path from i to j
1
3 42
5
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Selection of landmarks
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Simulation parameters Use Matlab Assume a number (N=50 to 400) of nodes 1 * 1 unit area R=0.25 unit An average of about 10 to 80 neighbors
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Simulation: Node density V.S Euclidean distance estimation
N = 50 N = 100N = 400
Shortest path length
Euclidean distance
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Simulation: Node density V.S Coordinates system
N = 50 N = 100N = 400
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Simulation: Node density V.S Coordinates error
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The number of landmarks
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Conclusion We have proposed a self-configurable
positioning technique Do not depend on GPS Accuracy
We plan to implement the technique in real world