Presenters: Puneet Gupta Sol Lederer

1. Mobile Assisted Localization in Wireless Sensor NetworksN.B. Priyantha, H. Balakrishnan, E.D. Demaine, S. TellerMIT Computer Science Presenters: Puneet Gupta Sol Lederer

2. Case for Mobile Assisted Localization • Obstructions, especially in indoor environments • Sparse node deployments • Geometric dilution of precision (GDOP) Hence, finding 4 reference points for each node for localization is difficult

3. Overview of scheme • Initially no nodes know their location • Mobile node finds cluster of nearby nodes • Explores “visibility region” and measures distance • # of measurements required is linear in the # of nodes • Virtual nodes are discarded

4. Theorem 1 • A graph is globally rigid if it is formed by starting from a clique of 4 non-coplanar nodes and repeatedly adding a node connected to at least 4 nodes.

5. MAL: Distance Measurement • First case: Two nodes, n0 and n1 , single unknown ||n0 - n1|| • Adding mobile node, m, introduces 3 unknowns (mx, my, mz), making problem more difficult • Necessary condition: # deg of freedom (unknowns – knowns) ≤ 0. • Solution: Use three mobile locations along the same line in a plane containing n0 and n1

6. Case of 2 nodes solved • 6 constraints from measurements of ||ni – mj|| for I = 0,1 and j = 0,1,2 • Extra constraint obtained from colinearity of mobile points • unknowns – knowns = 0 • Solve system of polynomial equations

7. Case of 3 nodes • Three nodes, n0 n1 n2, three unknowns, ||n0 - n1|| ||n1 - n2|| ||n0 - n2|| • Each mobile position gives #unknowns (mx, my, mz) = 3 #constraints (||m – ni||, i = 0,1,2) = 3 • Three additional constraints needed

8. Case of 3 nodes  Solution • Restriction: All mobile positions lie in a common plane • k mobile locations  k-3 additional co-planarity constraints • Solution: k = 6, geometry of n0, n1, n2 above the plane containing 6 coplanar points m0, m1, m2, m3, m4, m5 no three of which are collinear, determined by the distances ||mi - nj||, i = 0…5 & j = 0...2

9. Case of 4 or More • Number of nodes = j ≥ 4 • Initially: Number of unknowns = (3j – 5) • 3 coordinates per node • Minus 3 deg of translational motion • Minus 2 deg of rotational motion • Each mobile node adds (j – 3) deg of freedom (j distances – 3 coordinates of mobile position) • j – 3 >= 1

10. Case of 4 or more  Solution • Require at least (3j – 5)/(j – 3) mobile positions • E.g. for j = 4, required mobile positions to uniquely determine the geometry = 7 • But, no 4 of the 11 nodes (4 + 7) may be coplanar

11. MAL: Movement Strategy • Initialize: • Find 4 nodes that can all be seen from a common location • Move the mobile to 7 nearby locations & measure distances • Compute pair-wise distances • Loop: • Pick a localized stationary node (not yet considered by this loop) • Move mobile in perimeter of this node, searching for positions to hear a non-localized node • Localize this node

12. AFL: Anchor-free localization • Elect five nodes as shown • Get crude coordinates based on hop count to anchors

13. AFL • Use non-linear optimization algorithm to minimize sum-squared energy E • Coordinate assignments satisfy all 1-hop node distances when E = 0

14. Graph from running AFL—using RF connectivity information Graph obtained by MAL

15. Performance Layout of nodes in test scenario

16. Estimate error

17. Critique Pros: • Innovative stategy Cons: • In a cumbersome terrain (e.g. forest) it may not be feasible to deploy a roving node.

18. The End