1. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20011 Locationing in Distributed Ad-hoc Wireless Sensor Networks Chris Savarese, Jan Beutel, Jan Rabaey ICASSP 2001 University of California at Berkeley

2. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20012 Introduction to PicoRadio and triangulation A brief look at other research in the field Using redundancy to improve accuracy in position estimates Establishing initial position estimates Presentation Outline

3. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20013 PicoRadio Overview Ad-hoc network of many sensors, monitors, and actuators (>100 total) No infrastructure Distributed computation Highly dynamic Limited radio range Every node capable of acting as repeater Obstacles Sensor data requires location tag to be useful

4. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20014 Positioning: The Problem Reference Positions, Map Database Other Networking Nodes, Distance and Geometric Constellation Finding the position of networking nodes Relative positioning vs. Absolute positioning

5. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20015 Positioning 101 Triangulation Core Computation Least Squares Minimum Mean Squared Error Measured Data Time of Arrival, Time Difference of Arrival require high clock Angle of Arrival too expensive – requires antenna arrays Preferred method: Received Signal Strength (RSSI) Ranges subject to as much as  50% error Geometric Interpretation 2-D requires 3 anchors 3-D requires 4 anchors

6. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20016 Dr. Yao, UCLA A Protocol for Distributed Node Location Does not consider error in range measurements Dr. Srivastava, UCLA Location Discovery in Ad-Hoc Wireless Networks Propagated awareness from closely packed anchors Kris Pister, Berkeley Smart Dust Centralized computation Other Research

7. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20017 Improve dilution of precision by incorporating redundancy into triangulation solution Exploit high connectivity Exploiting Redundancy Iteration on every node Receive neighbors’ positions Range estimation Position calculation Broadcast result to neighbors

8. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20018 Individual Triangulation 00.51 0 0.2 0.4 0.6 0.8 1 Delaunay Mesh of 25 Networked Nodes x 00.51 0 0.2 0.4 0.6 0.8 1 Solution on 25 Ranges and 50% Error x 00.5 1 0 0.2 0.4 0.6 0.8 1 50 Solutions and Mean x 0.40.450.50.550.6 0.4 0.45 0.5 0.55 0.6 Zoom on Error x dx 0.0054 dy 0.0058 1% error Position iterated on 25 ranges with 50% error

9. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 20019 0 10 30 20 50 40 0 20 60 40 6 5 4 3 Average Position Error (%) Initial Position Error (%) Range Error (%) Network-wide triangulation Average position error more sensitive to range error than to initial position estimate error Convergence problem related to quality of initial positions Parameters: 10 nodes, 3 anchors 25 iterations, 30 trials Given initial estimates, nodes reposition themselves with respect to their neighbors Iterate until desired accuracy achieved

10. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 200110 Assumption Based Coordinates (ABC) n 0 assumed to be at (0,0,0) n 1 assumed to be at (r 01,0,0) r 01 = RSSI range between n 0 and n 1 n 2 at ( Assumptions: n 3 at ( Assumption: r 01 2 + r 03 2 - r 13 2 2r 01,  r 03 2 -x 3 2 -y 3 2 ) r 03 2 – r 23 2 + x 2 2 + y 2 2 - 2x 2 x 3 2r 01, r 01 2 + r 02 2 - r 12 2 2r 01,  r 02 2 -x 2 2, 0) x y z n0n0 n1n1 n2n2 n3n3 positive square root z 2 = 0 positive square root Establishing Initial Position Estimates

11. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 200111 Triangulation via Extended Range and Redundant Association of Intermediate Nodes ABC algorithm creates maps Target node waits to be included in  3 maps Extended ranges calculated from respective maps Triangulation by target node based on extended ranges Iterate network-wide triangulation The TERRAIN Algorithm 1 2 3 radio range extended range intermediate node

12. C. Savarese, J. Beutel, J. Rabaey; UC BerkeleyICASSP 200112 Position estimates accurate to within 6% Working to understand convergence/divergence cases Characterizing convergence time and energy cost Exploring means of lowering energy consumption Minimize expensive start up cost Optimize core triangulation algorithm Adapting algorithms to include confidence metrics Scaling simulations to include much larger node populations Conclusions and Future Work