1. Positioning in Ad-Hoc Networks - Directions and Results Jan Beutel Computer Engineering and Networks Lab Swiss Federal Institute of Technology Zurich August 10, 2002 Computer Engineering and Networks Laboratory

2. 2 ETH Zurich Jan Beutel, August 10, 2002 Ad-Hoc Network Scenarios Low power Small size Very large population No infrastructure necessary Varying population density Multihop environment Partitioning

3. 3 ETH Zurich Jan Beutel, August 10, 2002 Positioning: The Problem Finding the position of networking nodes Relative vs. Absolute Positioning Mode Reference Positions, Map Database Other Networking Nodes, Distance and Geometric Topology

4. 4 ETH Zurich Jan Beutel, August 10, 2002 RSSI Samples Over Distance - Free Space 802.11b Bluetooth

5. 5 ETH Zurich Jan Beutel, August 10, 2002 Redundant Triangulation Every node executes Identification of neighbors Establishing range estimates Maintaining a set of a minimum of 3 linear equations to the neighbors Solve for MMSE Dissemination of data over the network

6. 6 ETH Zurich Jan Beutel, August 10, 2002 Redundant Triangulation and Filtering Average over 25 individual triangulations with 50% range error 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% position error

7. 7 ETH Zurich Jan Beutel, August 10, 2002 Influence of Range Quantization

8. 8 ETH Zurich Jan Beutel, August 10, 2002 Very Large Errors and Topology 3 anchors ~ 94% 4 anchors ~ 6% 5 anchors >1%

9. 9 ETH Zurich Jan Beutel, August 10, 2002 Influence of Border Regions Center I Edge II Corner III

10. 10 ETH Zurich Jan Beutel, August 10, 2002 Influence of Border Regions

11. 11 ETH Zurich Jan Beutel, August 10, 2002 Ad-hoc Network Simulation Environment

12. 12 ETH Zurich Jan Beutel, August 10, 2002 The TERRAIN Algorithm. Triangulation via Extended Range and Redundant Association of Intermediate Nodes Algorithm creates local maps Every node waits to be included in  3 maps Extended ranges calculated from respective maps Triangulation node based on extended ranges Network-wide iterations 1 2 3 radio range extended range intermediate node