Using Clustering Information for

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Computer Science

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Using Clustering Information for
Sensor Network Localization


Haowen Chan, Mark Luk, and Adrian Perrig

Carnegie Mellon University

fhaowenchan,mluk,perrigg@cmu.edu


Presented by: Duifa Long

Nov 21, 2005

Computer Science

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Outline


Introduction


Related works


Sensor Network Clustering


Localization Procedure


The Basic Cluster Localization Algorithm


Improved Position Refinement: Mesh Relaxation


Improved Initial Calibration


Self
-
orienting Anchor


Conclusion and future work

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Introduction



Localization is required by many sensor network
applications


--

location
-
aided routing, data aggregation, battle fields, etc.


Localization should be inexpensive, scalable, accuracy
even with obstacles or irregularities


--

No need for special equipments for measurement such as:


signal strength, directionality, ranging, and time


--

In a distributed way, not manually or centralized methods


--

No assumptions of a flat, unobstructed deployment area


--

Using less anchors to achieve good accuracy


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Related Works


Physical Range Measurement


--
Signal Strength or Directionality[7
-
11]


RSSI (received signal strength indicator)


AoA (angle of arrival)


--
Ultrasound ranging


Long range beacons[12
-
16]


Range
-
free Scheme


--
DV
-
Hop by Niculescu and Nath[1]


and by Nagpal et al.[19]


Clustering Algorithm


--
ACE(Algorithm for Cluster
Establishment)[20]


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Sensor Network Clustering


Advantages of using
clustering


--

it creates a regular pattern for
extracting location information


--

it helps reduce the amount of
communication overhead


Cluster
-
adjacency graph


Cluster
-
heads Adjacent


Cluster
-
adjacency edges





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Sensor Network Clustering (Cont.)


Overview the ACE Algorithm


1.
Two logical parts:


--
The spawning of new clusters


--
The migration of existing clusters


2.
Fixed 3 iterations, In each iteration
:


--
Unclustered node gradually self
-
elect to be a cluster
-
head


--
Each cluster
-
head migrates its cluster


--
Clustered nodes do nothing







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c

Modifying the ACE Algorithm

To improve the regularity of the separation between cluster
-
heads


The number of iterations is increased from 3 to 5


Modifying the migratory mechanism by approximation a


spring effect

between adjacent clusters


--
Each cluster
-
head evaluates the potential


fitness score

= d + g(s) for each candidate c



d
----

the total number of nodes in the neighborhood for each candidate C

s
----

the estimated separation between C and the adjacent cluster
-
head


by counting the number of common nodes in both clusters

s

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The Basic Cluster Localization Algorithm


Assumption
--
Locally
-
Aware Anchors


--
Anchor nodes are the start point of the algorithm


--
Themselves are cluster
-
heads and know their geographical


positions


--
Able to determine the geographical positions of all the adjacent
cluster
-
heads

•Expanding the Calibrated Set


--
Initial set = anchor nodes + their adjacent cluster
-
heads


--
Each cluster
-
head calibrates itself if


1. two or more of its adjacent cluster
-
heads have calibrated


2. it knows the topological configuration of its cluster
-
head


neighborhood


3. Assume some pre
-
determined standard value L for edges


to the calibrated adjacent cluster
-
heads

C

D

A

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The Basic Cluster Localization Algorithm
(cont’d)


Refining the Position Estimate


--
Each calibrating cluster
-
head just repeats the initial position


estimation once for each adjacent pair of calibrated cluster
-


head neighborhood


--

Take the average position of these results


--

Rebroadcast its updated position if it is a
major

position


update (difference > threshold)


•Refining termination conditions:


--
The node has reached maximum number of major position updates


--
The node has not received any position updates during the
past time


period
, indicating
convergence

•Calibration of Follower Nodes
---
non
-
cluster
-
head nodes


--
Take the average of the estimated positions of all the calibrated


nodes within its communication range


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Improved Position Refinement:


Mesh Relaxation


Modeling:


--

Cluster
-
head


mass point


--

The distance between adjacent cluster
-
heads


spring length

• Let




the coordinate of cluster
-
head A at time t


S
--

the set of A’s adjacent cluster
-
heads


F


the force of the spring exerting on the cluster
-
head




the displacement of a spring from its equilibrium length (set at the average


edge length L)


K


is the spring constant, set to 1 here


we want to update its position at time




Then the resultant Force on A at time t will be:

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the displacing position of A, a quantity proportional to the


resultant force on A


represents the unit vector in the direction of B from A


L


is the known average link length, the spring equilibrium length

Where
represents the 2
-
dimensional vector of the separation
between the estimated positions of cluster
-
heads B from A at time t

Mesh Relaxation (Cont’d)

Hence the updated position of A is:

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Improved Initial Calibration


Step 1: Ordering the adjacent cluster
-
heads


Assume A in the figure is the calibrating node


1. A is aware of its neighborhood set {D, C, F, B, E}
but not in its order at the beginning


2. Each cluster
-
head sends its neighborhood
information to all the members of its cluster
-
head
neighborhood


3. A selects any neighbor as a starting point


4. Find the next neighbor has direct or indirect link,
then appending it to the list, until return to the
starting point or all have been traversed


5. Otherwise, goes to the opposite direction from
starting point, pre
-
pending the find ones


6. Special case

crossing edges, choosing the node
that has the most common neighbors with itself


Terminology:

Calibrating node

Cluster
-
head neighborhood

Directly linked

Indirectly linked

Unlinked (gaps)

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Improved Initial Calibration (Cont’d)


Step 2: Assigning angles to adjacent cluster
-
heads


1. if all directly linked for members in circular list, assign equal angular shares to
each sector


2. for one or more indirect links, estimate indirect link as the square root of 2
times the angles in the directly linked case


3. in the case of gap is in the circular list, assign


α

= 60 for direct links and ß = 90 for indirect links

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Improved Initial Calibration (Cont’d)


Step 3: Performing the position estimate


--
Definition : Calibrated nodes


has a position estimate and its circular list of
its cluster
-
head neighborhood ordered in the canonical direction


--
Determine the canonically correct ordering


--
Using basic trigonometry method to estimate the calibrating node


--
Calculate the average of all of the estimates






Repeated Initial Calibration

--

It can be used for position refinement instead of performing mesh
relaxation

P

Q

A

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Self
-
orienting Anchors


Remove the two assumptions: Locally aware and aware of average edge
length


Now, initially sets the average edge length to 1, and using the angular share
system, we estimate all its cluster
-
head neighbor’s position, then we can
estimate all others.


Each anchor sends to A their estimates under A’s coordinate system and their
physical locations


A finds a transform T which yields the lowest sum of square errors for each of
the other anchors:


At least 2 other anchors are neede
d to uniquely

Determine T, once T is known, is flooded to the

Entire network for others actual physical locations


--

uses the estimate associated with the
closest anchor

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Conclusion and Future Work


Conclusion


Clustering
-
based localization is fully distributed and
provides good accuracy


It requires only three randomly placed anchor nodes


It works with sensor nodes without any special hardware
for signal or ranging measurement


Also provides accurate position information in topologies
with irregularity or obstacles.


Future work


--

explore more reliable self
-
calibration algorithms


Secure the clustering information for localization


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Questions?




Thank you!