Computer Engineering and Networks Laboratory

1. Computer Engineering and Networks Laboratory Positioning in Ad-Hoc Networks-Directions and ResultsJan BeutelComputer Engineering and Networks LabSwiss Federal Institute of Technology ZurichAugust 10, 2002

2. Ad-Hoc Network Scenarios • Low power • Small size • Very large population • No infrastructure necessary • Varying population density • Multihop environment • Partitioning

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

4. RSSI Samples Over Distance - Free Space Bluetooth 802.11b

5. 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. Delaunay Mesh of 25 Networked Nodes Solution on 25 Ranges and 50% Error 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 0.5 1 0 0.5 1 x x 50 Solutions and Mean Zoom on Error 1 0.6 0.8 0.55 0.6 dx 0.0054 0.5 dy 0.0058 0.4 0.45 0.2 0 0.4 0 0.5 0.4 0.45 0.5 0.55 0.6 1 x x Redundant Triangulation and Filtering Average over 25 individual triangulations with 50% range error 1% position error

7. Influence of Range Quantization

8. Very Large Errors and Topology 3 anchors ~ 94% 4 anchors ~ 6% 5 anchors >1%

9. Influence of Border Regions Center I Edge II Corner III

10. Influence of Border Regions

11. Ad-hoc Network Simulation Environment

12. extended range 2 radio range 1 3 intermediate node 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