chapter 9: localization & positioninghscc.cs.nthu.edu.tw/~sheujp/lecture_note/sensys-ch9... ·...
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98/5/25 1
Chapter 9: Localization & Positioning
J. P. Sheu
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
98/5/25 2J. P. Sheu
Overview
• Properties of localization and positioning procedures
• Basic approaches• Trilateration• Single-hop schemes• Multihop schemes
98/5/25 3J. P. Sheu
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
98/5/25 4J. P. Sheu
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, …
98/5/25598/5/25 5J. P. Sheu
Overview
• Properties of localization and positioning procedures• Basic approaches• Trilateration• Single-hop schemes• Multihop schemes
98/5/25 6J. P. Sheu
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
98/5/25 7J. P. Sheu
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:
98/5/259
Length known
Angle φ 1
Angle φ 2(x = 2, y = 1)
(x = 8, y = 2)
(x = 5, y = 4)
r1
r2
r3
98/5/25 9J. P. Sheu
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”
98/5/251098/5/25 10J. P. Sheu
Estimating distances – RSSI
• Received Signal Strength Indicator– Send out signal of known strength, use received signal
strength and path loss coefficient to estimate distance
1198/5/25 11J. P. Sheu
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
98/5/25 12J. P. Sheu
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!
98/5/251398/5/25 13J. P. Sheu
Estimating distances – RSSI
98/5/2514
DistanceDistance Signal strength
PD
F
PD
F
PDF of distances in a given distance
98/5/25 14J. P. Sheu
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
98/5/25 15J. P. Sheu
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
98/5/251698/5/25 16J. P. Sheu
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
98/5/25 17J. P. Sheu
Overview
• Properties of localization and positioning procedures• Basic approaches• Trilateration• Single-hop schemes• Multi-hop schemes
98/5/25 18J. P. Sheu
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
98/5/25 20J. P. Sheu
Trilateration as matrix equation
• We get
• Rewriting as a matrix equation:
98/5/25 21=3
J. P. Sheu
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,
98/5/252298/5/25 22J. P. Sheu
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:
98/5/25 23J. P. Sheu
Overview
• Properties of localization and positioning procedures• Basic approaches• Trilateration• Single-hop schemes• Multihop schemes
98/5/25 24J. P. Sheu
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
98/5/25 25J. P. Sheu
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
98/5/252698/5/25 26J. P. Sheu
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
98/5/25 27J. P. Sheu
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
98/5/252898/5/25 28J. P. Sheu
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
98/5/252998/5/25 29J. P. Sheu
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
98/5/25 30J. P. Sheu
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
98/5/253198/5/25 31J. P. Sheu
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
98/5/2532
A
B C
D
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33
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
98/5/25 J. P. Sheu
34
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
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00011100
00011000
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anchor node normal node
1
2
98/5/25 J. P. Sheu
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
98/5/253598/5/25 35J. P. Sheu
Single-hop localization
• Using angle of arrival information
98/5/253698/5/25 36J. P. Sheu
Overview
• Properties of localization and positioning procedures• Basic approaches• Trilateration• Single-hop schemes• Multihop schemes
98/5/25 37J. P. Sheu
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
98/5/25 38
X
B
A
C
J. P. Sheu
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
98/5/2539
X
B
A
C98/5/25 39J. P. Sheu
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)
98/5/2540
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B
A
C98/5/25 40J. P. Sheu
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
anchor98/5/25
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
98/5/25 42J. P. Sheu
Iterative multilateration
98/5/25 43
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I: II:
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J. P. Sheu
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
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98/5/25 45J. P. Sheu
Collaborative multilateration
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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 46J. P. Sheu
Collaborative multilateration
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
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
Probabilistic position description
98/5/254998/5/25 49J. P. Sheu
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
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