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Energy-Efficient localization for networks

of underwater drifters

Diba Mirza

Curt SchurgersDepartment of Electrical and Computer Engineering

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Underwater Sensing Applications

Larval transport

Marine Ecosystems

Ocean circulation patterns

Oil spills

Focus :Collect relevant data within the natural dynamics of the ocean.

Goals Understand various

physical, chemical & biological processes

How do they interact ? How are they correlated

in space and time?

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Underwater Sensing System

surface nodes

acoustic links

drifterOur drifter prototype

Network of freely drifting underwater explorers [1]

System features Localized sensing. Swarm deployments. Networked for

collaborative sensing.

[1] J. Jaffe, C. Schurgers. Sensor networks of freely drifting autonomous underwater explorers. In Proc. of WUWNET’06, Los Angeles, CA, pp. 93-96, Sept 2006.

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Network LocalizationNeed position information to Interpret data Obtain spatial map of processes

GPS not available underwater Obtain timely distance estimates (TOA ) Localization can be done using existing

methods.

Due to continuous motion induced by currents, localization is a recurring cost.

Embedding from distance estimates

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Trade Localization Accuracy vs. Energy

Position uncertainty

Position accuracy depends on the extent of TOA measurements

Can we select the minimum set of links to achieve a desired position accuracy ?

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Problem Setup Network application

setup

t2t3

t7

0 100 200 300 400

0

100

200

300

meters

meters

t1

t1

t1t2

t6 t5 t4 t3

t7

t5t4 t6

t2

t3

t7t5t4 t6

drifter 1

drifter 2

drifter 3

System setup

1. At {Tj}, select set of links {Lj}2. At {ti}, collect ranging info for links{Lj}

From ranging info, estimate positions of all devices at times {ti}

Track curve and annotate sensor data

Online (during the mission) Offline (post-mission)

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Determining the optimum link-set..

Need a measure of localization error. Use the Cramer Rao Lower Bound (achieved by ML

estimators)

Localization algorithmis run offline

Can be computationally intensive for

best performance

To obtain optimum set of links:

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Optimum link-set (contd.)

Optimization problem:

M

i

M

ij

jiIICost1

),()( MatrixConnectionBinaryI :

)(minarg ICostII

opt Constraint:

% nodes exceeding error threshold < α.N

Error in node position estimates as computed from the Cramer Rao Bound

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Optimum link-set (contd.)

Solution to Optimization Problem

Actual position uncertainty

Maximum allowable error

Find node with maximum error allowance

Remove the link that causes min increase in total error

(b)(a)

What are the gains?

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Spatial Gains

Performance versus node density.

Simulation Scenario 3-Hop Network Average no. of neighbors, λ

Protocol Overhead Transmit distance

estimates to a central location.

Communicate policies to nodes.

Up to 40 % reduction in measurements for λ =15when protocol overhead

is included.

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Error Tolerance & Topology Change

Θ

2

2 )(sin1

.

4][

N

G

,Θ

Region of ‘good’ geometry

Error depends on relative position of nodes Node positions continuously changing due to currents. What is the fidelity of the link-selection scheme over time?

Examine Geometric Dilution of Precision (GDOP) ,G:

Conclusion : Error is affected only by major changes in topology.

Total variance when all references are accurate

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Temporal Behavior

Performance of link-selection scheme in time

Position estimation error over time under dynamic current conditions

Simulations further validate error changes with major changes in topology.

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Adapting to changing requirements

Suppose target error of a group of nodes changes over time.Say, L groups, each can choose any of K different target errors.How can the link-selection scheme be adapted ?

Re-compute the link policy Involves collecting range estimates from all nodes. Over head can be large.

Pre-compute all possible policies Gives rise to KL different policies. Setting a particular policy requires global communication.

Is there a better way?

Possible Solutions:

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Adapting to changing requirements

A specific condition: Nodes with known positions restricted to a single plane (surface)Result: Error primarily depends on that of one-hop neighbors closer to the surface.

‘Levels’ capture proximity to surface nodes.

surface

z

y0 00

11

12

1

22

33

If target error at some ‘level’ changes, sufficient to:

1) Update link-policy with 1-hop neighbors at a lower level .

2) Communicate the required target error to 1-hop neighbors.

How is this better than methods suggested earlier?

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Adaptive Link-Selection

Figure 10. Adapting link selection policy

After eventBefore event

All links usedOptimal link selection

Advantages of adaptive link-selection scheme1) Smaller number of policies – only L.K.2) Localized communication (with only 1-hop neighbors).

Event occurs at hop 2. New target error for hop 2.

Nodes at hop 2 adapt locally by updating the links selected for ranging with nodes at hop 1.

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Conclusions

t2t3

t7

0 100 200 300 400

0

100

200

300

mts

mts

t1

t1

t1t2

t6 t5 t4 t3

t7

t5t4 t6

t2

t3

t7t5t4 t6

drifter 1

drifter 2

drifter 3

Figure drawn roughly to scale

Future : Investigate the scalability of the method .

Position uncertainty

Optimal link-selection results in fewer measurements for localization.

Unless major topology change do not have to reselect links Scenario on the right is achievable.