1 Energy-Efficient localization for networks of underwater drifters Diba Mirza Curt Schurgers Department of Electrical and Computer Engineering

2 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?

3 Underwater Sensing System surface nodes acoustic links drifter Our 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 , Sept 2006.

4 Network Localization Need 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

5 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 ?

6 Problem Setup Network application setup t2t2 t3t3 t7t meters t1t1 t1t1 t1t1 t2t2 t6t6 t5t5 t4t4 t3t3 t7t7 t5t5 t4t4 t6t6 t2t2 t3t3 t7t7 t5t5 t4t4 t6t6 drifter 1 drifter 2 drifter 3 System setup 1. At {T j }, select set of links {L j } 2. At {t i }, collect ranging info for links{L j } From ranging info, estimate positions of all devices at times {t i } Track curve and annotate sensor data Online (during the mission) Offline (post-mission)

7 Determining the optimum link-set.. Need a measure of localization error. Use the Cramer Rao Lower Bound (achieved by ML estimators) Localization algorithm is run offline Can be computationally intensive for best performance To obtain optimum set of links:

8 Optimum link-set (contd.) Optimization problem: Constraint: % nodes exceeding error threshold < α.N Error in node position estimates as computed from the Cramer Rao Bound

9 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?

10 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 =15 when protocol overhead is included.

11 Error Tolerance & Topology Change Θ,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

12 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.

13 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 K L different policies.  Setting a particular policy requires global communication. Is there a better way? Possible Solutions:

14 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 y 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?

15 Adaptive Link-Selection Figure 10. Adapting link selection policy After event Before event All links used Optimal link selection Advantages of adaptive link-selection scheme 1)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.

16 Conclusions t2t2 t3t3 t7t mts t1t1 t1t1 t1t1 t2t2 t6t6 t5t5 t4t4 t3t3 t7t7 t5t5 t4t4 t6t6 t2t2 t3t3 t7t7 t5t5 t4t4 t6t6 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.