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/
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