Ad hoc and Sensor Networks Chapter 9: Localization

1
Ad hoc and Sensor NetworksChapter 9
Localization positioning

• Holger Karl

2
Outline

• Introduction
• AHLoS
• Ad-Hoc Localization Systeme and overview
• Atomic Multilateration
• Iterative Multilateration
• Collaborative Multilateration
• Performance evaluation
• Conclusion

3
Introduction What is Localization

• A mechanism for discovering spatial relationships
  among objects

4
Introduction here, It is Location discovery
for nodes

• Given a network of sensor nodes where a few nodes
  know their location how do we calculate the
  location of the nodes?

5
Introduction Why need this kind of
localization? Motivation

• Support Location Aware Applications
• Track Objects
• Report event origins
• Evaluate network coverage
• Assist with routing, GF
• Support for upper level protocols.
• GPS is not practical
• Not work Indoors or if blocked from the GPS
  satellites
• Spends the battery life of the node
• Issue of the production cost factor of GPS
• Increase the size of sensor nodes

6
Introduction Two phases

• Location discovery approaches consist of two
  phases Ranging phase, Estimation phase
• Ranging phase (distance estimation)
• Each node estimate its distance from its
  neighbors
• Estimation phase (distance combining)
• Nodes use ranging information and beacon node
  locations to estimate their positions

7
Introduction phases 1 Ranging phase

• Distance measuring methods
• Signal Strength
• Uses RSSI readings
• Time based methods
• ToA, TDoA
• Used with radio, acoustic, ultrasound
• Angle of Arrival (AoA)
• Measured with directive antennas or arrays

8
Introduction phases 2 Estimation phase

• Hyperbolic Trilateration
• Triangulation
• Multi-lateration
• Considers all available beacons

9
Introduction Related work

• Outdoor
• Automatic Vehicle Location (AVL)
• Determine the position of police cars
• Use ToA, Multi-lateration
• Global Positioning System (GPS) LORAN
• GPS24 NAVSTAR satellites
• LORAN ground based beacons instead of satellites
  
• Time-of-flight, trilateration
• Mobile phone position
• Cellular base station transmits beacons
• Use TDoA, Multi-lateration

10
Introduction Related work

• Indoor
• RADAR system
• Track the location of users within a building
• RF strength measurements from three fixed base
  stations
• Build a set of signal strength maps
• Mathing the online readings from the maps
• Cricket location support system
• Use Ultrasound from fixed beacons
• Multi-lateration
• The Bat system
• Node carries an ultrasound transmitter
• Multi-lateration

11
Introduction Ranging characterization

• Received Signal Strength
• RF signal attenuation is a function of distance
• Inconsistent Model because of environment fading
  and shadowing effects and the altitude of the
  radio antenna
• A Model is derived by obtaining a least square
  fit for each power level

12
Introduction Ranging

• ToA using RF and Ultrasound
• The time difference between RF and ultrasound
• To estimate the speed to sound, perform a best
  line fit

13
Introduction Discussion

• Does ToA suffer from the environment changes?
• Obstacles, interference to ToA?
• Extra work to identify the pairs of Radio Signal
  and Ultrasound pulse.
• Constraints Ultrasound range on the Medusa nodes
  used is about 3 meters (11-12 feet), the
  ultra-range of second generation of Medusa is
  about 10-15 meters, far less than the
  communication radius (30-100m)
• Any other comments?

14
Outline

• Introduction
• AHLoS
• Ad-Hoc Localization Systeme and overview
• Atomic Multilateration
• Iterative Multilateration
• Collaborative Multilateration
• Performance evaluation
• Conclusion

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AHLoS Ad-Hoc Localization Systeme

• Ranging phase (distance estimation)
• ToA
• Estimation phase (distance combining)
• Multilateration

16
AHLoS Overview

• Some percentage of nodes knows their positions
• Beacon nodes
• Nodes with known positions
• Broadcast their locations to their neighbors
• Unknown nodes
• Nodes with unknown positions
• Use ranging information and beacon node locations
  to estimate their positions
• Once knows its location, becomes a beacon node
• Atomic, Iterative, and Collaborative
  Multilateration

17
Outline

• Introduction
• AHLoS
• Ad-Hoc Localization Systeme and overview
• Atomic Multilateration
• Iterative Multilateration
• Collaborative Multilateration
• Performance evaluation
• Conclusion

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AHLoS Atomic Multilateration

• Requirement
• Atomic multilateration can take place if the
  unknown node is within one hop distance from at
  least three beacon nodes. The node may also
  estimate the ultrasound propagation speed if four
  or more beacons are available
• Topology for atomic multilateration

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AHLoS Atomic Multilateration
What we know 1. The location of Three or more
beacons N1,N2,N3, 2. Ti0, the time from
beacon Ni to unknown node 0 for ultrasound
propagation What we want to get The location
of the unknown node 0 How to get the location
Make the difference between
the measured distance and estimated Euclidean
distance to be as small as possible. Method
used The minimum mean square estimate (MMSE),
let F to be as small as possible
(Equation 3)
(Equation 4)
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AHLoS Incorrectness 1 in Atomic Multilateration
The goal is let F(X0,Y0,S) in equation 4 to be as
small as possible
(Equation 4)
We should have
(Equation 40)
Here, equation 5 is generated by setting
0
So it has
(Equation 5)
If equations 5 have solutions, they are solutions
to equation 4. BUT equations 5 may not have
solutions, because Ti0 is a measured value,
equations 5 can not be guaranteed to have
solutions on the measured values Ti0.
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AHLoS Incorrectness 2 in Atomic Multilateration
Look at the solution of the system of equations
(Equation A)
(Equation B)
How to get it?
In the process, one important assumption is
If
doesnt exist. We can not use the method
,
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AHLoS Incorrectness 3 in Atomic Multilateration
3 beacons are not enough to get a unique solution
with unknown speed s.
In the left figure, d1x, d2x, d3x are
distance But in the equations, distance is
unknown, Another variable is introduced, the
ultrasound Propagation speed s. There are only 3
equations with x, y square factors and unknown s.
3 beacons are not enough to get a unique
location solution with unknown speed s.
1
d1x
d3x
X
3
d2x
2
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AHLoS Atomic Multilateration Example 1
EXAMPLE
Conditions Three beacons N1(0,1),N2(0,-1),N3(2,0)
One unknown node N0 The time of the ultrasound
propagation From N1 to N0, it is sqrt(2) s From
N2 to N0, it is sqrt(2) s From N3 to N0, it is 1
s Test Using the algorithm on the paper to see
if we can get the coordinates of N0 or some other
interesting results.
N1(0,1)
N3(2,0)
1
N0(1,0)
N2(0,-1)
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AHLoS Atomic Multilateration Example 1
EXAMPLE
From equation above, we have
N1(0,1)
Equation N1
Equation N2
N3(2,0)
1
Equation N3
N0(1,0)
N1 N3 and N2 N3 , we have
N2(0,-1)
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AHLoS Atomic Multilateration Example 1
EXAMPLE
N1(0,1)
N3(2,0)
1
N0(1,0)
N2(0,-1)
We can not directly use the solution provided by
the paper.
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AHLoS Atomic Multilateration Example 1
EXAMPLE
From equations above, we have
Equation e1
N1(0,1)
Equation e2
Equation e3
N3(2,0)
1
Eliminating
Equation e4
N0(1,0)
Equation e5
Equation e6
From Equation e4,e5, we have
N2(0,-1)
From Equation e5,e6, we have
Equation e7
From Equation e3,e5,e6 we have
Equation e8
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AHLoS Atomic Multilateration Example 1
EXAMPLE
Equation e6
N1(0,1)
Equation e7
Equation e8
N3(2,0)
1
From Equation e6,e7,e8, we have 2 sets of results
N0(1,0)
N2(0,-1)
OR
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AHLoS Atomic Multilateration Example 1
Taking the algorithm on the paper 3 beacons are
not enough to get a unique solution with unknown
speed s.
N1(0,1)
N3(2,0)
1
N0(7,0)
N0(1,0)
N2(0,-1)
OR
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AHLoS Atomic Multilateration Example 2
EXAMPLE
Conditions Three beacons N1(0,1),N2(0,-1),N3(2,0)
One unknown node N0 The time of the ultrasound
propagation From N1 to N0, it is sqrt(2) ms From
N2 to N0, it is sqrt(2) ms From N3 to N0, it is 1
ms Test Using the standard MMSE method to see if
we can get the coordinates of N0 or some other
interesting results.
N1(0,1)
N3(2,0)
1
N0(1,0)
N2(0,-1)
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AHLoS Atomic Multilateration Example 2
EXAMPLE
N1(0,1)
N3(2,0)
1
N0(1,0)
N2(0,-1)
Taking the algorithm on MMSE 3 beacons are not
enough to get a unique solution with unknown
speed s.
select
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AHLoS Conclusion in Atomic Multilateration

• With the unknown speed of ultrasound pulse or
  other efficient constraints, generally, it is
  impossible to get a unique location of one
  unknown node only depending 3 un-lined beacons
• Other constraints, such as a roughly scope of
  ultrasound speed, angle, etc, must be added to
  make the solution determined. Or 4 un-lines
  beacons determine one unknown nodes location
• The computation process on the paper is not
  robust.
• In the algorithms later, we assume the speed of
  ultrasound is known

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Outline

• Introduction
• AHLoS
• Ad-Hoc Localization Systeme and overview
• Atomic Multilateration
• Iterative Multilateration
• Collaborative Multilateration
• Performance evaluation
• Conclusion

33
Outline

• Introduction
• AHLoS
• Ad-Hoc Localization Systeme and overview
• Atomic Multilateration
• Iterative Multilateration
• Collaborative Multilateration
• Performance evaluation
• Conclusion

34
AHLoS Collaborative Multilateration

• One node estimates its position by considering
  use of location information over multiple hops
• How it works
• For one node, to decide which nodes should be in
  its participating node set S
• For node , i is connected to u,
  and node u is an unknown node, the goal function
  is the same as that of the atomic
  multi-lateration, to minimize the

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Outline

• Introduction
• AHLoS
• Ad-Hoc Localization Systeme and overview
• Atomic Multilateration
• Iterative Multilateration
• Collaborative Multilateration
• Performance evaluation
• Conclusion

36
Performance evaluation

• What kind of performance evaluation do we need
  for the localization? What do we care most about
  the localization?

Accuracy Scalability Cost
37
Performance evaluation Accuracy
Only Iterative Multilateration is included as we
talked earlier. What is the behind 1.How many
steps are there for accumulated error? 2.How
beacons are deployed? 3.Small scale
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Performance evaluation cost

• 117 nodes/10,000m2 Uniformly distributed, Range
  10

39
Performance evaluation cost
40
Outline

• Introduction
• AHLoS
• Ad-Hoc Localization Systeme and overview
• Atomic Multilateration
• Iterative Multilateration
• Collaborative Multilateration
• Performance evaluation
• Conclusion

41
Papers1.Dynamic Fine-Grained Localization in
Ad-Hoc Networks of Sensors2.Distributed
Fine-Grained Localization in Ad-Hoc
networks3.Localization in Ad-Hoc Sensor
Networks Slides1.Dynamic Fine-Grained
Localization in Ad-Hoc Networks of
Sensors presented by Kisuk Kweon
2.LOCALIZATION presented by Lewis
Girod3.Survey of Estimation of Location in
Sensor Networks Presented by Wei-Peng
Chen4.Dynamic Location Discovery in Ad-Hoc
Networks presented byAndreas Savvides, Boulis
and Mani B. Srivastava5.Distributed
localization in wireless ad-hoc sensor
network presented by Vaidyanathan Ramadurai
References
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Goals of this chapter

• Means for a node to determine its physical
  position (with respect to some coordinate system)
  or symbolic location
• Using the help of
• Anchor nodes that know their position
• Directly adjacent
• Over multiple hops
• Using different means to determine
  distances/angles locally

43
Overview

• Basic approaches
• Trilateration
• Multihop schemes

44
Localization positioning

• Determine physical position or logical location
• Coordinate system or symbolic reference
• Absolute or relative coordinates
• Options
• Centralized or distributed computation
• Scale (indoors, outdoors, global, )
• Sources of information
• 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,

45
Main approaches (information sources)

• Proximity
• Exploit finite range of wireless communication
• E.g. easy to determine location in a room with
  infrared room number announcements
• (Tri-/Multi-)lateration and angulation
• Use distance or angle estimates, simple geometry
  to compute position estimates
• Scene analysis
• Radio environment has characteristic signatures
  
• Can be measured beforehand, stored, compared with
  current situation

46
Estimating distances RSSI

• Received Signal Strength Indicator
• Send out signal of known strength, use received
  signal strength and path loss coefficient to
  estimate distance
• Problem Highly error-prone process Shown PDF
  for a fixed RSSI

PDF
PDF
Distance
Signal strength
Distance
47
Estimating distances other means

• Time of arrival (ToA)
• Use time of transmission, propagation speed, time
  of arrival to compute distance
• Problem Exact time synchronization
• Time Difference of Arrival (TDoA)
• Use two different signals with different
  propagation speeds
• Example ultrasound and radio signal
• Propagation time of radio negligible compared to
  ultrasound
• Compute difference between arrival times to
  compute distance
• Problem Calibration, expensive/energy-intensive
  hardware

48
Determining angles

• Directional antennas
• On the node
• Mechanically rotating or electrically steerable
• On several access points
• Rotating at different offsets
• Time between beacons allows to compute angles

49
Some range-free, single-hop localization
techniques

• Overlapping connectivity Position is estimated
  in the center of area where circles from which
  signal is heard/not heard overlap
• Approximate point in triangle
• Determine triangles of anchor nodes where node is
  inside, overlap them
• Check whether inside a given triangle move node
  or simulate movement by asking neighbors
• Only approximately correct

50
Overview

• Basic approaches
• Trilateration
• Multihop schemes

51
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
• Subtracting eq. 3 from 1 2
• Rearranging terms gives a linear equation in (xu,
  yu)!

52
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
• ! (xu,yu) (5,2)

53
Trilateration with distance errors

• What if only distance estimation ri0 ri ?i
  available?
• Use multiple anchors, overdetermined system of
  equations
• Use (xu, yu) that minimize mean square error,
  i.e,

54
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
• Normal equation
• Has unique solution (if A has full rank), which
  gives desired minimal mean square error
• Essentially similar for angulation as well

55
Overview

• Basic approaches
• Trilateration
• Multihop schemes

56
Multihop range estimation

• How to estimate range to a node to which no
  direct radio communication exists?
• No RSSI, TDoA,
• But Multihop communication is possible
• Idea 1 Count number of hops, assume length of
  one hop is known (DV-Hop)
• Start by counting hops between anchors, divide
  known distance
• Idea 2 If range estimates between neighbors
  exist, use them to improve total length of route
  estimation in previous method (DV-Distance)

57
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

58
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

59
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)

60
Acknowledgements

• Notes are partly from slides of
• Andreas Savvides, Athanassios Boulis and Mani
  B. Srivastava
• Networked and Embedded Systems Lab
• University of California, Los Angeles
• Yong Chen
• Department of Computer Science
• University of Virginia