# Robust Positioning Algorithms for

AI and Robotics

Nov 6, 2013 (4 years and 6 months ago)

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Robust Positioning Algorithms for
Distributed

-
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

-
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

-
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

-
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

-
Hoc

Wireless

Sensor

Networks

by

Chris

Savarese

-
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

-
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

-
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

-
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

-
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

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

-
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

-
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

-
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

-
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

-
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

-
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

-
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

-
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

-
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

-
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

-
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

-
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

-
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

-
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

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