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Lost in Space or Positioning in Sensor Networks

Lost in Space or Positioning in Sensor Networks. Michael O’Dell Regina O’Dell Mirjam Wattenhofer Roger Wattenhofer. Positioning. What is positioning (a.k.a. localization)? Deduce coordinates GPS “software version” Why positioning? Sensible sensor networks

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Lost in Space or Positioning in Sensor Networks

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  1. Lost in SpaceorPositioning in Sensor Networks Michael O’Dell Regina O’Dell Mirjam Wattenhofer Roger Wattenhofer

  2. Positioning • What is positioning (a.k.a. localization)? • Deduce coordinates • GPS “software version” • Why positioning? • Sensible sensor networks • Heavy/costly localization hardware • Geometric routing benefits • Idea: • (Small) set of anchors • Others: location = f(network,communication,measurements) ? RealWSN 2005 Positioning in Sensor Networks

  3. Sensor Networks RealWSN 2005 Positioning in Sensor Networks

  4. Our Perspective Practice Theory → RealWSN 2005 Positioning in Sensor Networks

  5. Positioning – As We See It • Models of Sensor Networks • Positioning Algorithms • Hardware Description • Experiments • Lessons • Future Work Theory Practice RealWSN 2005 Positioning in Sensor Networks

  6. Part I: Theory RealWSN 2005 Positioning in Sensor Networks

  7. Models of Sensor Networks • Unit Disk Graph (UDG) • [Clark et al, 1990] • Widely used abstraction • Quasi-Unit Disk Graph (qUDG) • [Krumke et al, 2001] • [Barriere et al, 2003] • [Kuhn et al, 2003] • More realistic? • “well-behaved”) allow proofs 1 d ? 1 RealWSN 2005 Positioning in Sensor Networks

  8. Available Information • T[D]oA:time • GPS • Cricket [Priyantha et al, 2000] • RSS: signal strength • RADAR [Bahl, Padmanabhan, 2000] • Imply distance • AoA: angle • APS using AoA [Niculescu, Nath, 2003] • Relative distance to anchors • APiT [He et al, 2003] RealWSN 2005 Positioning in Sensor Networks

  9. Positioning Algorithms • Based on (q)UDG • (sometimes) provable statements • Abstraction ) rough idea • Virtual Coordinates Algorithm [Moscibroda et al, 2004] • Linear programming • Complex, time-consuming • 100-node network: several minutes on desktop • GHoST, HS [Bischoff, W., 2004] • Dense networks • Optimal in 1D • UDG crucial RealWSN 2005 Positioning in Sensor Networks

  10. Positioning Algorithms… cont’d • APS [Niculescu, Nath, 2001 & 2003] • Hop or distance based • Given distance estimate, use GPS triangulation • Least-squares optimization • Isotropic network helpful • General graphs • Given inter-node distances • Also: Internet graph (latencies) • Example: Spring Algorithms • Internet: Vivaldi [Dabek et al, 2004] • Ad hoc [Rao et al, 2003] RealWSN 2005 Positioning in Sensor Networks

  11. Spring Algorithm • Most practical? • Originally: graph drawing • Idea • Edge = spring • Rest length = distance • Embedding = minimal power configuration • Algorithm • Steepest descent, numerical methods • Simple: • New position = average of neighbors • Iterate Local vs. global RealWSN 2005 Positioning in Sensor Networks

  12. Our View = Assumptions • Minimal hardware • Low storage • Low computing power • Basic RSS measurements • Short range • Few meters • (RADAR: building – several dekameters) RealWSN 2005 Positioning in Sensor Networks

  13. Part II: Practice RealWSN 2005 Positioning in Sensor Networks

  14. Hardware Description • ESB • scatterweb.com • 32kHz CPU • 2kB RAM • Sensors and actuators • RSS: • Indirectly via packet loss • New version: • Actual RSS measurable at receiver • “Battery with Antenna” Desktop: • 3GHz • 512MB • Factor 105 RealWSN 2005 Positioning in Sensor Networks

  15. “software version” RSS • Older ESB (software) version • @sender: vary transmission power • Via potentiometer controlling current to tranceiver • Value s between 0 and 99 • Write s into packet • Repeat x times • @receiver: count number received packets • per s • Measurement: packet loss • Requirement • Distance increase → power increase • Correlation: to be determined • New version (software): • Direct read out Future work! RealWSN 2005 Positioning in Sensor Networks

  16. Experiment 1 – “Laboratory” • Power vs. Distance • A sends at power level s • x = 100 times • d = 1..120cm • Minimum • 90% s d Coffee machine? A B RealWSN 2005 Positioning in Sensor Networks

  17. Original Algorithm • Spring Embedding • Good for “easy” networks • Power-to-distance • Inverse of previous experiments • Results • Unusable! RealWSN 2005 Positioning in Sensor Networks

  18. A0 A2 N 11: 139 15: 278 16: 302 14: 365 A3 A1 Experiment 2 – “Room” • Localization in the plane • Rectangle: 4m x 3m • 4 anchors: corners • Test node: inside • Each anchor Ai • Send packet s = 0..99 • Next anchor • Test node N • Record packets received RealWSN 2005 Positioning in Sensor Networks

  19. Experiment 2 – “Room” … Results (without obstacles) RealWSN 2005 Positioning in Sensor Networks

  20. Experiment 3 – “Network” • 9 nodes in a room • Distances: 1..6m • 1 sender at a time • Send 1 packet at each level • Others: record minimum received • Report previous minima • Round robin • Minima: • Good approximation • Storage: save factor 100 per round RealWSN 2005 Positioning in Sensor Networks

  21. Experiment 3 – “Network” … Results • Error • Almost 30 units for same distance • Exp. 1: “nicer” curve • Longer range effects? • Symmetry! RealWSN 2005 Positioning in Sensor Networks

  22. Lessons • Average minimum • Stable • Good approximation • Saves storage • Symmetric links • Power versus Distance • Strongly environment dependant • Measurements between two nodes • Not generalizable • RSSI in sensor networks: good, but not for “reasonable” localization RealWSN 2005 Positioning in Sensor Networks

  23. Future Work • Here: more questions than answers • Hardware RSS measurements • Indication given by reviewer • Same experiments – different hardware • Same results/trend? • Long range vs. short range • More environments • New models Similar results mica2: in progress RealWSN 2005 Positioning in Sensor Networks

  24. Questions?Comments? DistributedComputing Group RealWSN 2005 Positioning in Sensor Networks

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