Robust Positioning Algorithms for

peachpuceAI and Robotics

Nov 6, 2013 (3 years and 9 months ago)

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Robust Positioning Algorithms for
Distributed

Ad
-
Hoc Wireless Sensor Networks


ECE 7360

FISP(Optimal and Robust Control)

Anisha Arora

anishaarora@cc.usu.edu

Nov 24, 2003

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


Plume Detection using wireless
sensor networks.

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion
.


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


Positioning Problem: Ad
-
hoc Sensor
Networks


lack of infrastructure inherent to ad hoc
networks.


all nodes are considered equal, making it difficult
to rely on centralized computation to solve
network wide problems, such as positioning.


there must exist within this network a minimum
of four
anchor
nodes.


all nodes being considered in an instance of the
positioning algorithm must be included in the
same connected network.


Two most essential problems…


RANGE ERROR PROBLEM




SPARSE ANCHOR NODE PROBLEM

At least I think they are…

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


Geometric Interpretation


Goal of these algorithms


To determine a specific node’s location within a given global
coordinate system.



Done using Triangulation



Triangulation


Geometric technique


Uses edges between objects to determine position


Unique position of an object in a two
-
dimensional space: triangle


Ties between objects, in the form of measured distances and
angles


Geometric Interpretation

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


The Two
-
Phase Algorithm


Split in two parts


Start up phase


Addresses the sparse anchor node problem


Awareness of the anchor nodes’ positions throughout the
network


Allowing all nodes to arrive at initial position estimates


Refinement phase


Uses the results of the start
-
up phase


Improves upon initial position estimates


Range error problem is addressed


End goal


To deliver reliable position estimates to other parts of
the system


Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


The Two
-
Phase Algorithm


Start up phase algorithm #1


TERRAIN ALGORITHM


Triangulation via extended range and redundant associated
of intermediate node



Each node makes several independent maps one map for
each anchor node



Once a node is included in sufficient number of maps then it
aligns itself in the global co ordinate system



Suppose the node makes three maps with respect to three
anchor nodes then it can use the triangulation method to
find its position

TERRAIN ALGORITHM


Example

Pros and Cons of TERRAIN


Pros


Helps to position a node globally without complicated
arithmetic deductions


Easy to covert from a two dimensional positioning to a
three dimensional positional system


Cons


Unacceptably high tendency to exponentially intensify
error levels


Final position estimates are too noisy to be useful

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


The Two
-
Phase Algorithm


Start up phase algorithm #2


HOP TERRAIN ALGORITHM


Finds number of routing hops from a node to each
of anchor nodes in a network


Multiplies the number of routing hops by a shared
metric (average hop distance)


Estimates range between node and each anchor
node


Use these computed ranges to find positions using
the triangulation method


Each anchor node initializes this algorithm by
broadcasting it’s location and a hop count of zero

The Two
-
Phase Algorithm


The neighbors who hear this broadcast then
broadcast this further just changing the hop
count to 1



This procedure continues till it reaches the
normal node whose position we are trying to
determine

Pros and Cons


Pros


Reduces network traffic


Simplistic approach


Does not use the magnitude of range
measured


Checks to see if communication is established.


Does not iteratively compound errors



More robust


Yields more accurate and consistent positions

Possible Error In Hop Terrain Algorithm


strange or difficult topologies may cause strange
positioning errors in the Hop Terrain algorithm

Possible Error In Hop Terrain Algorithm


Nodes that are physically close to each other,
but separated by the obstacle, will receive hop
counts that are artificially large from having had
to travel around the obstacle


Distort the estimated ranges used to compute
positions, thus distorting the positions
themselves


The best solution to this warping effect would be
to add more anchor nodes in key locations to
mitigate the distortion created by the obstacle

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


The Refinement Algorithm


Objective


Obtain more accurate positions using the estimated
ranges between nodes


Algorithm


A node broadcasts its position estimate


Receives the positions and corresponding range
estimates from its neighbors


Computes a least squares triangulation solution to
determine its new position

Refinement Algorithm


Refinement revealed two important error causes


Errors propagate fast throughout the whole network. If the
network has a diameter
d
, then an error introduced by a node in
step
s
has (indirectly) affected every node in the network by step
s+d
because of the triangulate
-
hop
-
triangulate
-
hop… pattern



Some network topologies are inherently hard, or even impossible to
locate. For example, a cluster of
n
nodes (no anchors) connected
by a single link to the main network can be simply rotated around
the ‘entry’
-
point into the network while keeping the exact same
intra
-
node ranges.


Refinement Algorithm


To mitigate error propagation the Refinement algorithm was
modified to include a confidence metric associated with each
node’s position



Confidence metrics (between 0 and 1) are used to weigh the
equations when solving the system of linear equations



Anchors immediately start off with confidence value of 1



Unknown nodes start off at a low value (0.1) and may raise their
confidence after subsequent Refinement iterations



A node performs a successful triangulation it sets its confidence
level to the average of its neighbors’ confidence levels



Triangulations sometimes fail or the new position is rejected on
other grounds. In these cases the confidence is set to 0, so
neighbors will not use erroneous information of the inconsistent
node in the next iteration

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


Average Position Error After Hop
-

TERRAIN
(5% Range Errors)

Fraction Of Located Nodes

(2% Anchors, 5% Range Error)

Range Error Sensitivity Of Hop
-

TERRAIN
And TERRAIN

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


Obstacles to Accuracy


Poor topology


Exaggerated range errors


Excessive node mobility


Stationary obstacles, such as walls, could be a large
problem for Hop
-
TERRAIN due to the falsely inflated hop
counts that result


Obstacles artificially create poor topologies, leading to
inaccurately estimated extended ranges


obstacles create sections of the network that have low
connectivity levels, another example of poor topology


some objects may move through a network

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


Areas for Improvement and Future
Study


Improve the engine that drives both of these
algorithms:Use the least squares triangulation
method instead of the triangulation method



Attempt to alleviate the shortcomings of
Refinement in the presence of high range errors
is introduced

Presentation

Outline


Background


Why

I

chose

this

topic


The

Positioning

Problem

within

Ad
-
hoc

Sensor

Networks


Geometric

interpretation


Two

phase

algorithm


Terrain

algorithm


Hop

Terrain

algorithm


Refinement

algorithm


Simulation

Results


Obstacles

to

Accuracy


Areas

for

future

improvement


Conclusion


Papers

Reviewed


Robust

Positioning

Algorithms

for

Distributed


Ad
-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese


In Conclusion…


Would use Hop
-
TERRAIN Algorithm


More robust


Less sensitive to error


Second phase use the refinement
algorithm

References:


http://bwrc.eecs.berkeley.edu/Publications
/2002/thesis/robst_pstng_algrthms_dstrbt
d_adhoc/Savarese_MS_Thesis_FINAL.pdf



http://mas
-
net.ece.usu.edu/




Thanks for your patience…

Any Questions
???