1. Mobile-Assisted Localization in Sensor Network
Charles Zha
CSE 590 Fall 2005

2. Agenda Challenge of Current Localization Methods
Mobile-Assisted Localization (MAL) Strategy
Optimization Using Anchor-Free Localization (AFL)
MAL Performance Evaluation
Conclusion

3. Localization Challenges In Reality
Obstructions
Lack of line-of-sight connectivity prevents the nodes to obtain pairwise distance
Sparse Node Deployments
Not always possible to obtain rigid structure and unique solution
Geometric Dilution of Precision (GDOP)
May incur large errors in estimation and measurements if a node is far from the group

4. Mobile-Assisted Localization
Find four stationary nodes
Using Specific MAL Movement Strategy To Construct A Rigid Graph And Compute Inter-node Distance
Using Anchor-Free Localization to Compute Coordinates and Optimize Solution

5. Why 7 mobile positions are sufficient?
Calculating distances among 4 (or more) nodes
To compute the pairwise distances between j>=4 nodes n1,n2,….,nj
We require at least [(3j-5)/(j-3)] mobile positions (to reduce the degree of freedom to 0)
When j=4, the [(3j-5)/(j-3)]=7

6. MAL Movement Strategy Initialize:
Find Four Stationary Nodes that are visible (distance are measurable) to mobile location s s s s v

7. MAL Movement Strategy Initialize:
Move the mobile to at least seven nearby locations and measure distances v v v s s v s v s v v

8. MAL Movement Strategy Initialize:
Compute the pairwise distances between the four stationary nodes v v v s s v s v s v v

9. MAL Movement Strategy Initialize:
Localize the resulting tetrahedron using Rigidity Theorem v v v s s v s v s v v

10. MAL Movement Strategy Loop:
Pick a stationary node that has been localized but has not yet examined by this loop
Move the mobile around the stationary node and search for non-localized stationary node and 0,1 or 2 additional localized nodes
For each such mobile position: Compute the distance between those 2,3,or 4 stationary nodes and localize the node if it has 4 know distances.
Terminates the loop if every stationary node has been localized or no more progress can be made.

11. Why Anchor-Free Localization?
Most localization algorithms are designed for well-connected dense networks with relatively small obstacles.
AFL does specially well for network with large obstacles (indoors) and low connectivity, where MAL can be very helpful.

12. Anchor-Free Localization Algorithm
Initialization Phrase:
Computes an initial coordinate assignment for nodes
Runs multiple instances of Leader election algorithm to elect certain of nodes
Uses shortest path hop count to compute the initial coordinates of each node

13. Anchor-Free Localization Algorithm
For two nodes i,j, let hi,j denote the shortest path hp count, and let R denote the “range” of the nodes

14. Anchor-Free Localization Algorithm
AFL uses a non-linear optimization algorithm to minimize the sum-squared energy E of the graph defined by:
dm(i,j) is the distance between nodes i and j obtained by MAL. And because MAL produces rigid graph, E=0. dm(i,j) is an approximation to di,j , the coordinate assignment to the global minimum E results in graph that approximates the true embedded graph.

15. MAL Performance Evaluation
Coordinates obtained by MAL after running the AFL optimization.

16. MAL Performance Evaluation
Error decreases as number, coverage of reference nodes increase, and mobile positions increase.

17. Conclusion Easier to get around Obstructions by moving around
Easier to construct rigid graph to obtain unique solution
Smaller distance estimation errors, especially with larger mobile coverage area