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Distributed Selection of References for Localization in
Wireless Sensor Networks
Dominik Lieckfeldt, Jiaxi You, Dirk TimmermannInstitute of Applied Microelectronics and Computer Engineering
University of Rostock, 18119 Rostock, GermanyEmail: {dominik.lieckfeldt, jiaxi.you}@uni-rostock.de
Outline
2WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
1. Introduction Localization in Sensor Networks Sources of errors regarding localization
2. Selecting references for localization Finding a criteria for selection Description of the algorithm
3. Simulation results
4. Summary and conclusions
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Localization in Wireless Sensor Networks
• Why? Mapping of location ↔ sensor data
• Problem: Nodes randomly deployed GPS not on every node possible
• Solution: Few nodes with GPS → Beacons Remaining nodes → Unknowns
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 3
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Baseline Algorithm for Localization
4WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
1. Phase Refinement
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Unknown
Beacon
TX range
Reference/Beacon
Sources of Error
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 5
Error Systematic Random
RF Shadowing, orientation of antenna Noise , Fading (interference)
Hardware Tolerances Noise
EnvironmentTemperature, Humidity, Location of References
(Geometry )-
• Selection of beacons that contribute most to accurate localization Distributed Beacon Selection1
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
• Theory of Estimation Comparison of estimators based on
variance of estimates Fundamental lower bound on Variance
→ Cramer-Rao-Lower-Bound (CRLB)
• Here: Use CRLB as selection criteria
6WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
Finding a Selection Criteria
Need 3 reference points for localization!
Need 3 reference points for localization!??
CRLBCRLB
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
CR
LB
subset
Selection using CRLB
Inequality of Cramér and Rao• Poses lower bound on variance of any
estimator
• CRLB for localization based on: Time-of-Arrival (ToA) or received signal
strength (RSS) derived by Patwari et al.2
• RSS:
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 7
23
4
12,1d
3,1d
4,1d
Distances
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
… path loss coefficient… deviation of RSS… true parameter… estimated parameter
• Example: 2 references, 1 unknown
8
0 0.1 0.2 0.3 0.41
10
100
Distance/ [rad]
CR
LB
no
rmal
ized
linearcircular
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
Reference Unknown
Impact of Geometry on CRLB
Linear vector
Circular vector
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Distributed Selection Procedure
9WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
• Phase I: Inquiry send by unknown All beacons compute
response probability
( … maximal tx range)
TDMA: Beacon i responds with probability and broadcasts its position and estimated distance
End condition:– One beacon has
responded
Need 5 reference points for
localization.
Need 5 reference points for
localization.
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Distributed Selection Procedure
10WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
• Phase II: After first response:
– Use estimated distances and position of first responder to avoid collinear beacons
– How? Utilize CRLB
End condition:– 2 beacons have
responded
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Distributed Selection Procedure
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 11
• Phase III: Recalculation of
based on previous responses and on CRLB
Reference i responds with probability
End condition:– Sufficient number of
references has responded
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Performance Metrics
• Error of location estimates:
• Power-Error-Product (PEP):
• Simple Energy Model (TDMA):
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 12P
EP
More
effi
cient
More
effi
cient
PEP schematic
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
= 0.3 mJ
= 0.81 mJ
2 4 6 8 10 12 144
6
8
10
12
14
16
18
number of references in subset
loc
ati
on
err
or
[m]
Local-DistanceLocal-CRLBLocal-CRLB with circle ruleGlobal-DistanceGlobal-CRLB
13WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
Simulation Results (RSS)Reference
Unknown
Distance-based
CRG-based 2 4 6 8 10 12 1410
-1
100
101
102
103
number of references in subset
PE
P [
mJ
]
Local-CRLBLocal-CRLB with circle ruleLocal-Distance
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
2 4 6 8 10 12 140.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
number of references in subset
loc
ati
on
err
or
[m]
Local-DistanceGlobal-DistanceLocal-CRLBLocal-CRLB with circle ruleGlobal-CRLB
14WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
Simulation Results (TOA)Reference
Unknown
2 4 6 8 10 12 1410
-2
10-1
100
101
number of references in subset
PE
P [
mJ
]
Local-CRLBLocal-CRLB with circle ruleLocal-Distance
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Distance-based
CRG-based
15WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
• Contribution: Analysis of distributed algorithms for selecting
references for localization Investigation of error of localization Comparison regarding Power-Energy-Product
• Conclusions: Use of CRLB can improve selection regarding
accuracy Convergence of CRLB-based algorithms
should be improved to increase energy efficiency
Introduction > Selecting References > Simulations > ConclusionIntroduction > Selecting References > Simulations > Conclusion
Questions?
- Thank you for your attention -
Literature:1 Lieckfeldt, D; You, Jiaxi; Timmermann, D.: “An algorithm for distributed for
distributed beacon selection”, IEEE PerSeNS, 20082 Patwari, N.; O. Hero III, A.; Perkins, M.; Correal, N. & O'Dea, R.: “Relative location
estimation in wireless sensor networks“, IEEE TSP, 2003
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 17
LocalizationLocalization Wireless Sensor NetworksWireless Sensor Networks
Accuracy Limited resources
Auswahl von ReferenzenAuswahl von Referenzen
CRLBCRLBDistanceDistance
Introduction > Selecting References > Simulations > Conclusion
Summary
Formeln
I
XTEXT
2
Var
XT
22
1
2 1
2
2,1
2,1
,,1
2
2,1
rss )~()~(E1
yyxx
dd
dd
d
bCRLB
N
i
N
ij ji
jiji
N
ij
2
rss
p
10ln
10
n
b
pn
rssx
x~
iPresp
2
tx
,1resp 1
d
dP ii
id ,1txd
iRCRLB
RCRLBiRCRLBPi
resprss
resprssresprssresp
)(
T
i
yyxxT
e1
22 )~()~(1
eΔEPEP
M
ii
i
ntδEtΔE
EnEntntδE
1
(i)tx
tx(i)txrx
(i)tx
(i)tx
),()(
)(),(
txE
rxE
Beacon Selection: CRLB explained
19
CRLBCRLB
Error model of RSS
measurements
Error model of RSS
measurements
Number of beacons
Number of beacons GeometryGeometry
Lower bound on variance of
position error
Lower bound on variance of
position errorRSS [dBm]
Pro
ba
bili
ty
Motivation > SotA > Beacon Selection > Conclusion
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
-5 0 2.5-2.5 5 x
Cramer-Rao-Lower-Bound
-5 0 2.5-2.5 5 x
-5 0 2.5-2.5 5
0
0.2
0.4
x
Pro
bab
ilit
y
• Beispiel 1 Dimension Wahre Position: x=0 Fehlerhafte Positionsschätzungen PDF der Positionsschätzungen Standardabweichung -> intuitives Maß um Fehler zu
charakterisieren
20
22rss )ˆ()ˆ(E yyxxCRLB
2
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
Unknown Reference Beacon/Reference Tx range
Baseline Algorithm for Localization
21WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
1. Phase Refinement
23
4
12,1d
3,1d
4,1d
24,1
241
241
23,1
231
231
22,1
221
221
)()(
)()(
)()(
dyyxx
dyyxx
dyyxx
y
x
),( 11 yx
Localization in WSN > Distributed Beacon Selection > Conclusion
Distributed Selection Procedure
22WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
• Phase I: Inquiry sent by unknown References calculate
response probability
TDMA: Reference i response with probability
After first response:– Utilize CRLB to avoid
collinear references
iPant2
tx
,1ant 1
d
dP ii
iPant
Need 5 reference points for
localization.
Need 5 reference points for
localization.
Introduction > Selecting References > Simulations > Conclusion
Distributed Selection Procedure
WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 23
• Phase II: Recalculation of
based on the decrease of CRLB
Reference i response with probability
End condition:– Sufficient number of
references has responded
iPant
iRCRG
RCRGiRCRGPi
antrss
antrssantrssant
)(
iPant
Introduction > Selecting References > Simulations > Conclusion
Drahtlose Sensornetzwerke
• Definition: Netz aus kleinsten Knoten Zufällige Positionierung Drahtlose Kommunikation Erfassung von Umwelt-
parametern
• Eigenschaften: Ressourcenarm Fehleranfällig
• Anwendungsbereiche:
Analyse, Beobachtung, Überwachung24WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"
Einleitung > Positionsbestimmung > Auswahlverfahren > Zusammenfassung