Transcript Localization - Mohammad Reza Faghani

Localization
Introduction
We are here !
Applications
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Wildlife Tracking
Weather Monitoring
Location-based Authentication
Routing in ad-hoc networks
Surveillances
Properties of Localization
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Physical position versus symbolic location
Absolute versus relative coordinates
Localized versus centralized computation
Percision
Cost
Scale
Limitations
Possible Approaches
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Triangulation, Trilateration
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Scene Analysis
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Location determined using geometry.
Observed features used to infer location.
Proximity
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Detection of change near known location.
Scene Analysis
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Features of an observed scene
from a particular vantage point
used to infer location.

Not applicable in WSNs.
Proximity

Can be used for positioning when
several overlapping anchors are
avialalbe.
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Centronoid localization
It can be used to decide whether a
node is in the proximity of an anchor.
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E.g. Active Badge
Triangulation Vs. Lateration
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The proximity helps to determine
geometric relationship between nodes.
The distance between them or angle of
a singular triangle can be easily
estimated.
Lateration vs. Angulation
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When distances between entities are
used, the approach is called
lateration.
when angles between nodes are used,
one talks about angulation.
Trilateration

Using distances and anchor positions,
the node’s position has to be at the
intersection of three circles around the
anchors.
d
d
d
Distance measure Approaches
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RSSI
ToA
TDoA
Determining Angles
RSSI
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Known :
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Transmission power Ptx
The path loss model
Path lost coefficient α
Receiver can determine the distance d to the
transmitter :
Prcvd
Ptx
cPtx
c   d 
Prcvd
d
RSSI
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Challenges:
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Signal propagation issues, especially
indoors:
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Shadowing, Scattering, Multipath propagation.
It’s usually a random process.
Time of Arrival
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Conditions :
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The speed of propagation is known.
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Sound speed depends on environmental factors.
Receiver and sender are
synchronized.(drawback)
The distance can be estimated, using
the transmission time.
TDoA
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TDoA use two transmissions mediums
of different propagation speeds to
generate an implicit synchronization.

First signal is used to measure ToA of the
second one.
Triangulation
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Angulation: using angles to determine
distance with directional, or phasedarray antennas.
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2D position requires two angle + one distance
measurement.
3D position requires two angle + one length + one azimuth
measurement.
d
d is known
Mathematics of Lateration
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there are three anchors with known
positions. ( xi , yi ) i  1,2,3
For the unknown position of (xu,yu) and
those anchors we have :
xi  xu    yi  yu 
2
2
 ri , i  1,2,3
2
Mathematics of Lateration

After subtracting the third equ. and
reordering them we have :
2( x3  x1 ) xu  2( y3  y1 ) yu  (r12  r32 )  ( x12  x32 )  ( y12  y32 )
2( x3  x2 ) xu  2( y3  y2 ) yu  (r22  r32 )  ( x22  x32 )  ( y22  y32 )

That can be expressed using a linear
matrix.
Mathematics of Lateration
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Which the Matrix on the left side and
right side are known constant.
 x3  x1
2
 x3  x2
y3  y1   xu  (r12  r32 )  ( x12  x32 )  ( y12  y32 )
 2 2




y3  y2   yu  (r2  r3 )  ( x22  x32 )  ( y22  y32 )
Solving the Distance Errors.
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Distance measurements are not perfect
~
but only estimates r with an unknown
ri  ri   i
error ε are known. ~
How to Solve this ?
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More than three anchors are needed.
Use Multilateration Problem
Multilateration
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When order the so called Euclidian formula , we have :
 (r12  rn2 )  ( x12  xn2 )  ( y12  yn2 ) 
yn  y1 
 xn  x1
 xu  



2 .....

.....


  yu   ...
2
2
2
2
2
2
xn  xn1 yn  yn1   (rn1  rn )  ( xn1  xn )  ( yn1  yn )
 


 x



A

b
A solution can be computed that minimizes the mean
square error. which is :
2 AT Ax  2 AT b  0  AT Ax  AT b
Single Hop Localization

This is about systems where a node
with unknown position can directly
communicate with anchors.
Active Badge
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Every badge periodically, sends unique
identifier, via infrared, to the receivers.
receivers, receive this identifiers and
store it on a central server.
Central Server
Badge
IR sensor
(receiver)
Active office
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The devices which its position is to be
determinate act as ultrasound senders
Receivers are placed at well-known position,
mounted in array at the ceiling of a room.
controller sends a radio message which
contains the address of this specific device.
The device sends out an ultrasound pulse,
which is received by the array of receivers.
Active office
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This array computes the difference
between the arrival of the ultrasound
pulse and the time when the radio
signal was sent. (TDoA)
Cricket
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In both recent cases, infrastructure
determines device position.
Here the devices themselves can
compute their own positions or
locations.
Cricket
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Anchors spread in a building send
ultrasound pulses that combined with
radio pulses, which allow the receiver to
employ the TDoA to extract symbolic
location information of its position.
Overlapping Connectivity

Try to use only the observation of
connectivity to a set of anchors to
determine a node’s position.
x1  ...  xn y1  ...  y n
( xu , y u )  (
,
)
n
n
APIT
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Decide whether a node is within or
outside of a triangle formed by any
three anchors.
APIT
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Nodes cannot move always !
how to decide ?
APIT
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Approximate P.I.T Test: If no
neighbor of M is further from/closer to
all three anchors A, B and C
simultaneously, M assumes that it is
inside triangle ΔABC. Otherwise, M
assumes it resides outside this triangle.
Two possible Errors
Two possible Errors
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the percentage of APIT tests exhibiting
such an error is relatively small (14% in
the worst case).
APIT Aggregation
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APIT aggregates the results
(inside/outside decisions among which
some may be incorrect) through a grid
SCAN algorithm.
Using Angle of Arrival

use anchors nodes that use narrow, rotating beams where
the rotation speed is constant and known to all nodes.
    1
    1
    1
 cos( )  S sin( ) 
Sin(   )
,
Y

L

Sin
 S cos( )  Sin(  ) 
  arctan
S
L sin( )
, ( X p , Y p )  (Y cos( ), M  Y sin( ))
M sin( )
Positioning in MultiHop
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Recent approaches was based on
connectivity of nodes to anchors.
This assumption is not always true in a
WSN – not every node is in direct
contact with at least three anchors.
SDP
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Geometric constraints between nodes
are represented as linear matrix
inequalities (LMIs).
The LMIs can be combined to form a
single semidefinite program.
only constraints that form convex
regions are amenable to representation
as an LMI.
SDP
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Angle of arrival data can be represented
as a triangle and hop count data can be
represented as a circle, but precise
range data cannot be conveniently
represented.
SDP
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Given a set of convex constraints on a
node’s position, SDP simply finds the
intersection of the constraints.
MDS
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MDS-MAP is a centralized algorithm.

Suppose there are n points, suspended in a
volume. We don’t know the positions of the
points, but we do know the distance
between each pair of points. Find the
relative positions of the points based on
the pairwise distances.
MDS
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Estimates shortest path between any
pair of nodes , then applies a MDS , and
at the end Transform the estimates into
global coordinates using some number
of fixed anchor nodes using a CSR
routine.
MDS
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It is fairly stable with respect to anchor
placement, achieving good results even
if only few anchors are available or
placed.
Multihop Range Estimation
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Niculescu described three different
approach.
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DV-Hop
DV-Distance
Euclidean Distance
DV-Hop
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Count Shortest hop numbers between
all two nodes.
Each anchors estimate hop length and
propagates to the network.
Node calculates its position based on
average hop length and shortest path to
each anchor.
DV Hop
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L1 calculates average hope length :
100  40
 17.5
62
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So do L2 and L3 :
40  75
 16 .42
25
75  100
 15.90
65
ci


( xi  x j ) 2  ( yi  y j ) 2
h
i
DV-Hop
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Node A uses trilateration to estimate it’s
position by multiplying the average
hope length of every received anchor to
shortest path length it assumed.
DV-Distance
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Distance between neighboring nodes is
measured using radio signal strength
and is propagated in meters rather than
in hops.
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Range estimation is more precise.
The algorithm uses the same method to
estimate but shortest distance length
are assumed.
Euclidean Distance
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Assuming that the distances AB, AC,
BC, XB, XC are all known, it is possible
to compute the unknown distance XA.
Iterative Multilateration
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When a node is not located within a
range of three anchors, multilateration
can not be implemented.
use normal nodes, once they have
estimated their positions, just like
anchor nodes in a multilateration
algorithm.
Iterative Multilateration
Iterative Multilateration
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When more information becomes
available – more neighbors have
estimated their own position – it is
possible to use it to improve the
position estimate and propagate an
updated estimate to a node’s neighbors.
Collaborative Multilateration
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There can be nodes in the network that can not
estimate their position.
When this occurs a node can use location
information over multiple Hubs to attempt to
estimate its position.
Collaborative Multilateration
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Savvides : participating nodes can be
defined as nodes that have at least
three anchors or other participating
nodes as neighbours.

Nodes 2 and 4 are participating nodes and
its position can be solved.
Collaborative Multilateration
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Savarese : a sound node has
independent references to at least 3(4)
anchors. That is, the multi-hop routes
to the anchors have no link (edge) in
common. Node 2,4 are sounds.
Probabilistic Positioning
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As mentioned before an RSSI value, gives rise
to a probability density function, relating each
distance to a certain probability with which it
corresponds to the RSSI value.
Probabilistic Positioning

Once information from a second anchor
becomes available, the two density
functions can be convoluted and an
improved description of the node’s
position probabilities results.
Anchor Placement
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Properly placed anchor act an important role in
estimating the position.
Accuracy improves if more anchors are available.
Several Articles expressing a preference for
anchors to be placed in perimeter of a given area.
Some adaptive placement algorithms are available
for low density networks.
Global Positioning System
GPS

Consists of 24 MEO satellites that
transmit precise microwave signals.
GPS
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Four satellites are placed in each of six orbital
planes with 55° tilt to the equator.

Four to ten GPS satellites will be visible anywhere
in the world
GPS
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The satellite altitude is about 20,200km
above the Earth’s surface.
GPS
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The satellite constellation is managed
by the United States Air Force 50th
Space Wing in Colorado.
The cost of maintaining the system is
approximately US$750 million per year.
GPS Navigation Signals
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GPS satellites broadcast three different
types of data in the primary navigation
signal.
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Almanac
Ephemeris
Clock information
Almanac and Ephemeris
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Ephemeris :
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Contains orbital information that allows the
receiver to calculate the position of the
satellite, is transmitted every 30 sec.
Almanac:
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Information and status concerning all the
satellites; their locations and PRN
numbers.
framed in Navigation Message of 37500 bit
Clock informations
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The coordinates (the location) of the
satellites as a function of time.
The transmitted signals are controlled
by highly accurate atomic clocks.
Clock Information
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Coarse / Acquisition code
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Is freely available
Precise code, or P-code
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Restricted to public users by encrypting it.
CA code
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The C/A code is a 1,023 bit long PRN
broadcast at 1.023 MHz, repeating
every millisecond.
Each satellite sends a distinct C/A code,
which allows it to be uniquely identified.
P-code
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The P-code is a stream of about
2.35 × 1014 chips!.
It is also 10 times faster than the C/Acode (10.23 Mbps).
Segmented between satellites.
P-code is encrypted to Y-Code.
Positioning Requirements
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Current time.
The position of the satellite
Measured delay of the received signal.

The position accuracy is primarily
dependent on the satellite position and
signal delay.
Measuring Delay

The receiver compares the bit sequence
received from the satellite with an
internally generated version.
Measuring Delay

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Modern electronics can measure signal offset
to within about 1% of a bit time, or
approximately 10 nanoseconds for the C/A
code or about 3 meters.
Using the higher-speed P(Y) signal. Assuming
the same 1% bit time accuracy, the high
frequency P(Y) signal results in an accuracy
of about 30 centimeters.
Calculating Position
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Knowing Satellite position and
calculating distance using delay
One can use Lateration on at least 3
satellites to find out its position.
Calculating Positiong

Due to receiver clock error (bias) we
need forth satellite to solve this
problem using MMS.
xi  xu 2   yi  yu 2  zi  zu 2  bu  ri
User Segment
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A typical GPS device contains a 12channel receiver and an antenna to
capture satellite signals.
Most systems take around one to two
minutes to acquire a 3D fix during a
cold start, while some can take a few
minutes.
User Segment

BMW continues to offer onboard
navigation with voice recognition and
voice guidance on most of its new
vehicles, with prices starting at $1,800.
What Feature shoud I look for ?
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Display
Maps
Form factor
Navigation feature
Accessories
Acknowledge
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Thanks to audiences