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98/5/25 1
Chapter 9: Localization & Positioning
J. P. Sheu
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Goals of this chapter
• Means for a node to determine its physical position with respect to some coordinate system (50, 27) or symbolic location (in a living room)
• Using the help of – Anchor nodes that know their position– Directly adjacent– Over multiple hops
• Using different means to determine distances/angles locally
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Overview
• Properties of localization and positioning procedures
• Basic approaches• Trilateration• Single-hop schemes• Multihop schemes
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Properties of localization and positioning procedures
• Physical position or logical location– Coordinate system: position– Symbolic reference: location
• Absolute coordinate: anchors are required• Centralized or distributed computation• Scale (indoors, outdoors, global, …)• Limitations: GPS for example, does not work indoors
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Properties of localization and positioning procedures
• Metrics– Accuracy
• how close is an estimated position to the real position?
– Precision • for repeated position determinations, how often is a
given accuracy achieved?– Costs, energy consumption, …
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Overview
• Properties of localization and positioning procedures• Basic approaches• Trilateration• Single-hop schemes• Multihop schemes
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Main approaches (information sources)
• Proximity: a node wants to determine its position or location in the proximity of an anchor
• (Tri-/Multi-) lateration and angulation– Lateration : when distances between nodes are used– Angulation: when angles between nodes are used
• Scene analysis: the most evident form of it is to analyze pictures taken by a camera
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Main approaches (information sources)
• Proximity– Using information about a node’s neighborhood.
• Exploit finite range of wireless communication• E.g.: easy to determine location in a room with infrared
(room number announcements)
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Main approaches (information sources)
• (Tri-/Multi-)lateration and angulation– Using geometric properties – Lateration: distances between entities are used– Angulation: angle between nodes are used:
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Length known
Angle φ 1
Angle φ 2(x = 2, y = 1)
(x = 8, y = 2)
(x = 5, y = 4)
r1
r2
r3
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Main approaches (information sources)
• Scene analysis – Analyze characteristic properties of the position of a
nods in comparison with premeasured properties• Radio environment has characteristic “fingerprints”
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Estimating distances – RSSI
• Received Signal Strength Indicator– Send out signal of known strength, use received signal
strength and path loss coefficient to estimate distance
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Estimating distances – RSSI
• Problem: Highly error-prone process : – Caused by fast fading, mobility of the environment– Solution: repeated measurement and filtering out
incorrect values by statistical techniques
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Estimating distances – RSSI
• Problem: Highly error-prone process: – Cheap radio transceivers are often not calibrated
• Same signal strength result in different RSSI• Actual transmission power different from the intended power• combination with multipath fading • Signal attenuation along an indirect path is higher than along a
direct path
– Solution: No!
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Estimating distances – RSSI
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DistanceDistance Signal strength
PD
F
PD
F
PDF of distances in a given distance
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Estimating distances – other means
• Time of arrival (ToA)– Use
• time of transmission, • propagation speed, to compute distance
– Problem: Exact time synchronization• Usually, sound wave is used • But propagation speed of sound depends on
temperature or humidity
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Estimating distances – other means• Time Difference of Arrival (TDoA)
– Use two different signals with different propagation speeds
• Compute difference between arrival times to compute distance
• Example: ultrasound and radio signal (Cricket System)– Propagation time of radio negligible compared to
ultrasound
– Problem: expensive/energy-intensive hardware
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Determining angles• Directional antennas
– Node mount a directional antennas• Supporting infrastructure anchors
– Multiple antennas mounted on a device at known separation
• Measuring the time difference between a signal’s arrival at the different antennas
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Overview
• Properties of localization and positioning procedures• Basic approaches• Trilateration• Single-hop schemes• Multi-hop schemes
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Trilateration
• Assuming distances to three points with known location are exactly given
• Solve system of equations (Pythagoras!)
– (xi , yi) : coordinates of anchor point i,– ri distance to anchor i– (xu, yu) : unknown coordinates of node
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Trilateration
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=3
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Trilateration as matrix equation
• We get
• Rewriting as a matrix equation:
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Trilateration with distance errors• What if only distance estimation ri
0 = ri + εi 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 square of the of Euclidean norm expression
– (note that for all vectors v)
• Look at derivative with respect to x, set it equal to 0:
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Overview
• Properties of localization and positioning procedures• Basic approaches• Trilateration• Single-hop schemes• Multihop schemes
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Single-hop localization
• Active Badge – Uses diffused infrared as transmission medium – Exploits the natural limitation of infrared waves by walls as
a delimiter for its location granularity– A badge periodically sends a globally unique identifier via
infrared to receivers, at least one of which is installed in every room
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Single-hop localization• Active office
– use ultrasound– with receivers placed at well-known position, mounted in
array at the ceiling of a room; – devices for which the position is to be determined act as
ultrasound senders– Process:
• Central controller sends a radio containing the devices ‘s address
• The devices upon receiving this radio message, sends out a short ultrasound pulse
• The receiver array compute the difference of the arrival time of the radio and ultrasound pulse
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Single-hop localization
• RADAR – Scene analysis techniques– Both the anchors and the mobile device can be used to
send the signal, which is then measured by the counterpart device(s)
• Cricket– Combines radio wave and ultrasound pulses to allow
measuring of the TDoA
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Single-hop localization
• Overlapping connectivity – Without any numeric range measurement– Use connectivity to a set of anchors – The underlying assumption is that transmissions from an
anchor can be received within a circular area of known radius
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Single-hop localization
• Overlapping connectivity – Process:
• Anchor nodes periodically send out transmissions identifying themselves
• A node has received these announcements, it can determine that it is in the intersection of the circles
• Suppose node knows about all the anchors– Anchor announcements are not received implies that
the node is outside the respective circles
– Problem: • accuracy depends on the number of anchors
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Single-hop localization• Approximate point in triangle
– By pure connectivity information– Idea: decide whether a node is within or outside of a
triangle formed by any three anchors
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Single-hop localization
• Approximate point in triangle (APIT)– Inside a triangle:
• irrespective of the direction of the movement, the node must be closed to at least one of the corners of the triangle
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Single-hop localization
• Approximate point in triangle – Outside a triangle:
• There is at least one direction for which the node’s distance to all corners increases
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A
B C
D
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APITAPIT• Approximation: Normal nodes test only directions
towards neighbors
A
C
1
23
4
M
B
A
CB
A. Inside Case B. OutSide Case
1
23
4
M
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APIT (cont.)APIT (cont.)
• Grid-Based Aggregation– Narrow down the area where the normal node can
potentially reside
-1-1-10011100
-1-1-10122200
0-1-10112211
00-10112210
0001111100
0001110100
0001000000
-1-1-10000
-1-10100
0-1011
00-1010
00011100
00011000
0001100000
anchor node normal node
1
2
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Single-hop localization
• Approximate point in triangle – However, moving a sender node to determine its
position is hardly practical !
– Solution:
inquire all its neighbors about their distance to the given three corner anchors
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Single-hop localization
• Using angle of arrival information
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Overview
• Properties of localization and positioning procedures• Basic approaches• Trilateration• Single-hop schemes• Multihop schemes
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Multihop range estimation• How to estimate range to a node to which no direct
radio communication exists? – No RSSI, TDoA, …– But: Multi-hop communication is possible
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X
B
A
C
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Multihop range estimation
• Idea 1: Count number of hops, assume length of one hop is known (DV-Hop)– Start by counting hops between anchors, divide known
distance
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B
A
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Multihop range estimation
• Idea 2: If range estimates between neighbors exist, use them to improve total length of route estimation in previous method (DV-Distance)
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B
A
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J. P. Sheu 41
DV-Based Scheme
• Must work in a network which is dense enough• DV-hop approach used the hop of the shortest
path • to approximately estimate the distance between
a • pair of nodes• Drawback: Requires lots of communicationsanchor
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Discussion• number of anchors
– Euclidean method increase accuracy as the number of anchors goes up
– The “distance vector”-link methods are better suited for a low ratio for anchors
• Uniformly distributed network– Distance vector methods perform less well in anisotropic
networks– Euclidean method is not very sensitive to this effect
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Iterative multilateration
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(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
J. P. Sheu
![Page 44: Chapter 9: Localization & Positioninghscc.cs.nthu.edu.tw/~sheujp/lecture_note/sensys-ch9... · 2015. 8. 14. · Single-hop localization • Active Badge –Uses diffused infrared](https://reader035.vdocuments.site/reader035/viewer/2022081615/5fd645801ebee64d243d36b3/html5/thumbnails/44.jpg)
Iterative multilateration
• Assume some nodes can hear at least three anchors (to perform triangulation), but not all
• Idea: – let more and more nodes compute position estimates,– spread position knowledge in the network
• Problem: – Errors accumulate– When not all nodes in the network will have three
nodes with position estimates
98/5/25 44J. P. Sheu
![Page 45: Chapter 9: Localization & Positioninghscc.cs.nthu.edu.tw/~sheujp/lecture_note/sensys-ch9... · 2015. 8. 14. · Single-hop localization • Active Badge –Uses diffused infrared](https://reader035.vdocuments.site/reader035/viewer/2022081615/5fd645801ebee64d243d36b3/html5/thumbnails/45.jpg)
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
98/5/25 45J. P. Sheu
Collaborative multilateration
![Page 46: Chapter 9: Localization & Positioninghscc.cs.nthu.edu.tw/~sheujp/lecture_note/sensys-ch9... · 2015. 8. 14. · Single-hop localization • Active Badge –Uses diffused infrared](https://reader035.vdocuments.site/reader035/viewer/2022081615/5fd645801ebee64d243d36b3/html5/thumbnails/46.jpg)
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
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(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
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(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
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(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
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(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
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(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
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(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
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(18,20)
(38,5)
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(?,?)
(?,?)
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C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(?,?)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(?,?)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(?,?)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
(2,10)
(8,0)
(18,20)
(38,5)
(22,2)
(30,12)
(12,14)
A B
C
I: II:
III: IV:
98/5/25 46J. P. Sheu
Collaborative multilateration
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Iterative multilateration• Solution 1: Participating nodes
– Have at least three anchors or other participating nodes as neighbors
• Solution 2: Sound– Have at least three independent references to anchor
nodes– The path to the anchors have to be edge-disjoint.
• Discussion: – solution 2 is suited to low anchor ratios
98/5/254798/5/25 47J. P. Sheu
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Probabilistic position description• Similar idea to previous one, but accept problem that
position of nodes is only probabilistically known– Represent this probability explicitly, use it to compute
probabilities for further nodes
98/5/25 48Distance
J. P. Sheu
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Probabilistic position description
98/5/254998/5/25 49J. P. Sheu
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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)
98/5/25 50J. P. Sheu
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Impact of anchor placement
• A preference for anchor to be placed on the perimeter of a given area– Solution 1:
Mobile entity is wandering around the given area • Measuring position error
– Solution 2:
Anchors try to estimate the positioning error• Decide where an additional anchor should be placed
98/5/25 51J. P. Sheu