Wireless Embedded Systems (0120442x) Localization
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Transcript of Wireless Embedded Systems (0120442x) Localization
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Network Kernel Architectures
and Implementation(01204423)
Localization
Chaiporn [email protected]
Department of Computer EngineeringKasetsart University
Materials taken from lecture slides by Karl and Willig
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Overview Basic approaches Trilateration Multihop schemes
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Localization & positioning Determine physical position or
logical location Coordinate system or symbolic
reference Absolute or relative coordinates
Metrics Accuracy Precision Costs, energy consumption, …
http://www.mathsisfun.com/accuracy-precision.html
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Main Approaches Based on
information source Proximity (Tri-/
Multi-)lateration and angulation
Scene analysis Radio environment
has characteristic “signatures”
Length known
Angle 1
Angle 2
(x = 2, y = 1)
(x = 8, y = 2)
(x = 5, y = 4)
r1
r2
r3
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Estimating Distances – RSSI Compute distance from Received
Signal Strength Indicator
Problem: Highly error-prone process
Distance
PD
F
DistanceSignal strength
PD
F
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Estimating Distances – Others Time of arrival (ToA)
Use time of transmission, propagation speed, time of arrival to compute distance
Time Difference of Arrival (TDoA) Use two different signals with different
propagation speeds Example: ultrasound and radio signal
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Determining Angles Directional antennas
Multiple antennas Measure time difference between
receptions
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Range-Free Techniques Overlapping connectivity
Approximate point in triangle
?
?A
B
C
D
F
G
E
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Overview Basic approaches Trilateration Multihop schemes
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Trilateration Assuming distances to
three points with known location are exactly given
Solve system of equations(x1,y1)
(x2,y2)
(x3,y3)
(xu,yu)
r1r2
r3
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Trilateration as Matrix Equation Rewriting as a matrix equation:
Example: (x1, y1) = (2,1), (x2, y2) = (5,4), (x3, y3) = (8,2), r1 = 100.5 , r2 = 2, r3 = 3
3
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Trilateration with Distance Errors What if only distance estimation ri' = ri + i
available? Use multiple anchors
Overdetermined system of equations
Use (xu, yu) that minimize mean square error, i.e,
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Minimize Mean Square Error
Look at derivative with respect to x, set it equal to 0:
Normal equation Has unique solution (if A has full rank),
which gives desired minimal mean square error
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Example: Distance Error Anchors' positions and measured
distances:
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(x,y) r
(2,1) 5
(5,4) 1
(8,2) 4
(3,1) 2
(7,5) 3
(2,8) 7
(4,6) 4
7.2
5.5x̂
Solve bAxAA TT ˆ
0.5
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Overview Basic approaches Trilateration Multihop schemes
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Multihop Range Estimation No direct radio communication exists
Idea 1: Count number of hops, assume length of one hop is known (DV-Hop)
Idea 2: If range estimates between neighbors exist, use them Improve total length of route estimation
in previous method (DV-Distance)
X
B
A
C
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Iterative Multilateration
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Probabilistic Position Description Position of nodes is only probabilistically
known Represent this probability explicitly Use it to compute probabilities for further
nodes
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Conclusions Determining location or position is a
vitally important function in WSN, but fraught with many errors and shortcomings Range estimates often not sufficiently
accurate Many anchors are needed for
acceptable results Anchors might need external position
sources (GPS) Multilateration problematic
(convergence, accuracy)