3D Position Determination Hasti AhleHagh Professor. W.R. Michalson.
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Transcript of 3D Position Determination Hasti AhleHagh Professor. W.R. Michalson.
3D Position Determination
Hasti AhleHagh
Professor. W.R. Michalson
Outline
Problem Formulation
Location Estimation
Location Discovery in Presence of Errors
Deployment Problem
Future Work
Conclusion
Objective
Calculate a node location by
combining distances from its
neighbors
Optimize the quality of solution
while guarantees the coverage
Establish accurate location of
all nodes by combining
information from four far away
anchor nodes.
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Input
-
-
- for pair if
Output
- determine
-
-
Graph Model
),,( zyxLEd
iii zyx ,,
EVG ,
iiii zyxV ,,
ije ji VV &sij RR
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Coordinate System Selection:
Calculation of a Node Position:
Coordinate System
0,0, zyipx ppdp
0),sin(),cos( ziqyiqx qdqdq
2222 2)( wskwwskwwskwks rdrdrdd
2222 2 osT
okks dskdskd
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
2010
212
220
2101
2cos
RR
RRR
Calculation of a Node Position:
Location Calculation
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
31,111
111
111
N
zzyyxx
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zzyyxx
zzyyxx
A
jNjNjN
jjjjjj
jjjjjj
jjj
j
11,.2
1
222
21
221
21
221
21
221
N
rxx
rxx
rxx
rxx
B
NjjN
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jj
j
Calculation of a Node Position:
Location Calculation
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
11,
2
21
21
21
N
r
r
r
r
C
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Ts CRBAAAn
1
Example
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11
16
9
8
12
5
3
102
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0)0,0,0(
)0,0,( 90d
x
y
z
12
2
x
y
z
)0,0,0(
)0,0,( 6,24d
)0,sin,cos( 0,100,10 dd
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Example
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5
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102
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0)0,0,0(
)0,0,( 90d
x
y
z
12
2
x
y
z
)0,0,( 6,24d
)0,sin,cos( 0,100,10 dd
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Example
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1
11
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9
8
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5
3
102
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4
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0)0,0,0(
)0,0,( 90d
x
y
z
12
2
)0,sin,cos( 0,100,10 dd
Problem Formulation . Error Free Location Discovery . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
xy
z
Example
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9
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5
3
102
17
4
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0)0,0,0(
)0,0,( 90d
x
y
z
12
2
)0,0,0(
)0,0,( 6,24d
z
x
y
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Positioning algorithm
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Positioning algorithm
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Positioning algorithm
a1
b11 b12 b13
c112
c111
c113
b122
b121
b123
b122
b121
b123
a2
b21 b22 b23
c212
c211
c1213
c222
c221
c223
b232
b231
b233
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
QUESTION: What is the error function where is the
error in distance measurements and is the error in the
nodes location ?
distributed localization -> simulation study
error function has almost the same behavior for each n-hop
neighbor
Error Propagation
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
21 , f1
2
Simulation Results
Node Num=40, Xloc=87m, Yloc=36m, Zloc=8m, Rs=50m
1-hop Neighbors
2-hop Neighbors
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
QUESTION: What is the cause of error in the network?
Propagation of error
Some error in the rotation angle cause a considerable error in
node location
Sources of Error
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Simulation Results
Node Num=80, Xloc=110m, Yloc=45m, Zloc=10m, Rs=100m
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Simulation Results
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Simulation Results
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Simulation Results
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
QUESTION: Which percentage of the sensor nodes is able to find their physical location after running the location discovery procedure?
Coverage
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Simulation Results
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Deploying atomic tri-lateration procedure for calculating the
position of a node in the presence of noisy information
Adding node with GPS information and study error
propagation and coverage with percolation
Evaluate the effect of error in input distance on the output
location calculation
Add optimization algorithms to the location discovery
Future Work
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion
Here we addressed location discovery by deploying
geometric and graph theory
We developed Monte Carlo simulation to identify the network
scalability
Evaluated the effect of error in input distance on the output
location calculation
Conclusion
Problem Formulation . Location Estimation . Location Discovery in Presence of Errors . Deployment Problem . Future Work . Conclusion