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


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


2010

212

220

2101

2cos

RR

RRR


Location Calculation


31,111

111

111

N

zzyyxx

zzyyxx

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

jjjj

jjjj

jj

j


Location Calculation


11,

2

21

21

21

N

r

r

r

r

C

Nj

jj

jj

j

j

jjsjTjj

Tj

Ts CRBAAAn

1

Example

15

14

1

11

16

9

8

12

5

3

102

17

4

19

13

18

7

6

20

21

22

24

25

26

23

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


Example

15

14

1

11

16

9

8

12

5

3

102

17

4

19

13

18

7

6

20

21

22

24

25

26

23

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


Example

15

14

1

11

16

9

8

12

5

3

102

17

4

19

13

18

7

6

20

21

22

24

25

26

23

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

15

14

1

11

16

9

8

12

5

3

102

17

4

19

13

18

7

6

20

21

22

24

25

26

23

0)0,0,0(

)0,0,( 90d

x

y

z

12

2

)0,0,0(

)0,0,( 6,24d

z

x

y


Positioning algorithm


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


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


21 , f1

2

Simulation Results

Node Num=40, Xloc=87m, Yloc=36m, Zloc=8m, Rs=50m

1-hop Neighbors

2-hop Neighbors


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


Simulation Results

Node Num=80, Xloc=110m, Yloc=45m, Zloc=10m, Rs=100m


Simulation Results


QUESTION: Which percentage of the sensor nodes is able to find their physical location after running the location discovery procedure?

Coverage


Simulation Results


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


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


3D Position Determination Hasti AhleHagh Professor. W.R. Michalson.

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