Lost in Space or Positioning in Sensor Networks Michael O’Dell Regina O’Dell Mirjam Wattenhofer Roger Wattenhofer
Dec 21, 2015
Lost in Spaceor
Positioning in Sensor Networks
Michael O’DellRegina O’Dell
Mirjam WattenhoferRoger Wattenhofer
RealWSN 2005 Positioning in Sensor Networks 2
Positioning
• What is positioning (a.k.a. localization)?– Deduce coordinates– GPS “software version”
• Why positioning?– Sensible sensor networks– Heavy/costly localization hardware– Geometric routing benefits
• Idea:– (Small) set of anchors– Others: location = f(network,communication,measurements)
RealWSN 2005 Positioning in Sensor Networks 5
Positioning – As We See It
• Models of Sensor Networks
• Positioning Algorithms
• Hardware Description
• Experiments
• Lessons
• Future Work
Theory
Practice
RealWSN 2005 Positioning in Sensor Networks 7
Models of Sensor Networks
• Unit Disk Graph (UDG)– [Clark et al, 1990]– Widely used abstraction
• Quasi-Unit Disk Graph (qUDG)– [Krumke et al, 2001]– [Barriere et al, 2003]– [Kuhn et al, 2003]– More realistic?
• “well-behaved” ) allow proofs
1
1
d
?
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Available Information
• T[D]oA:time– GPS– Cricket [Priyantha et al, 2000]
• RSS: signal strength– RADAR [Bahl, Padmanabhan, 2000]
• Imply distance
• AoA: angle– APS using AoA [Niculescu, Nath, 2003]
• Relative distance to anchors– APiT [He et al, 2003]
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Positioning Algorithms
• Based on (q)UDG– (sometimes) provable statements– Abstraction ) rough idea
• Virtual Coordinates Algorithm [Moscibroda et al, 2004]– Linear programming– Complex, time-consuming– 100-node network: several minutes on desktop
• GHoST, HS [Bischoff, W., 2004]– Dense networks– Optimal in 1D– UDG crucial
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Positioning Algorithms… cont’d
• APS [Niculescu, Nath, 2001 & 2003]– Hop or distance based– Given distance estimate, use GPS triangulation– Least-squares optimization– Isotropic network helpful
• General graphs– Given inter-node distances– Also: Internet graph (latencies)
• Example: Spring Algorithms– Internet: Vivaldi [Dabek et al, 2004]– Ad hoc [Rao et al, 2003]
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Spring Algorithm
• Most practical?• Originally: graph drawing• Idea
– Edge = spring– Rest length = distance– Embedding = minimal power configuration
• Algorithm– Steepest descent, numerical methods– Simple:
• New position = average of neighbors• Iterate
Local vs. global
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Our View = Assumptions
• Minimal hardware– Low storage– Low computing power– Basic RSS measurements
• Short range– Few meters– (RADAR: building – several dekameters)
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Hardware Description
• ESB– scatterweb.com– 32kHz CPU– 2kB RAM– Sensors and actuators
• RSS:– Indirectly via packet loss
• New version:– Actual RSS measurable at receiver
• “Battery with Antenna”
Desktop:
– 3GHz– 512MB– Factor 105
RealWSN 2005 Positioning in Sensor Networks 15
“software version” RSS
• Older ESB (software) version– @sender: vary transmission power
• Via potentiometer controlling current to tranceiver
• Value s between 0 and 99
• Write s into packet
• Repeat x times
– @receiver: count number received packets• per s
– Measurement: packet loss• Requirement
– Distance increase → power increase– Correlation: to be determined
• New version (software):– Direct read out
Future work!
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Experiment 1 – “Laboratory”
• Power vs. Distance– A sends at power level s– x = 100 times– d = 1..120cm
• Minimum• 90%
A B
ds
0
5
10
15
20
25
1 11 21 31 41 51 61 71 81 91 101 111 121
Distance (in cm)
Min
imu
m P
ow
er R
ecei
ved
0
5
10
15
20
25
30
35
1 11 21 31 41 51 61 71 81 91 101 111 121
Distance (in cm)
po
wer
at
90%
of
pac
kets
rec
eive
d
Coffee machine?
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Original Algorithm
• Spring Embedding– Good for “easy” networks
• Power-to-distance– Inverse of previous experiments
• Results– Unusable!
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Experiment 2 – “Room”
• Localization in the plane– Rectangle: 4m x 3m– 4 anchors: corners– Test node: inside
• Each anchor Ai
– Send packet s = 0..99– Next anchor
• Test node N– Record packets received
A0 A2
A3 A1
N15: 278
14: 365
16: 302
11: 139
RealWSN 2005 Positioning in Sensor Networks 19
Experiment 2 – “Room” … Results
Anchor 1
0
100
200
300
400
500
600
700
800
900
1 11 21 31 41 51 61 71 81 91
Received Power
Fre
qu
ency
Anchor 1
0
50
100
150
200
250
300
1 6 11 16 21 26 31 36
Minimum Power Received
Fre
qu
ency
Anchor 1
0
50
100
150
200
250
300
1 6 11 16 21 26 31 36
Minimum Power Received with/without Obstacles
Fre
qu
ency
Anchor 1
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Hole Size
Fre
qu
ency
anchor distance avg. min power
A2 1.39 11
A0 2.78 15
A1 3.02 16
A3 3.65 14
(without obstacles)
RealWSN 2005 Positioning in Sensor Networks 20
Experiment 3 – “Network”
• 9 nodes in a room– Distances: 1..6m
• 1 sender at a time– Send 1 packet at each level– Others: record minimum received– Report previous minima
• Round robin
• Minima:– Good approximation– Storage: save factor 100 per round
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Experiment 3 – “Network” … Results
• Error– Almost 30 units for same distance– Exp. 1: “nicer” curve
• Longer range effects?
• Symmetry!Symmetry
0
100
200
300
400
500
600
700
800
900
1 6 11 16 21 26 31 36
Minimum Power Received
Fre
qu
ency
Symmetry
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6
Rounded Diffence in Average Minimum Received Power
Fre
qu
ency
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600
Distance (in cm)
Ave
rag
e M
inim
um
Po
wer
Rec
eive
d
RealWSN 2005 Positioning in Sensor Networks 22
Lessons
• Average minimum– Stable– Good approximation– Saves storage
• Symmetric links
• Power versus Distance– Strongly environment dependant– Measurements between two nodes
Not generalizable
• RSSI in sensor networks: good, but not for “reasonable” localization
RealWSN 2005 Positioning in Sensor Networks 23
Future Work
• Here: more questions than answers
• Hardware RSS measurements– Indication given by reviewer
• Same experiments – different hardware– Same results/trend?
• Long range vs. short range
• More environments
• New models
mica2:
in progress
Similar results