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

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

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

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

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

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

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

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

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

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.

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.

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

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

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.

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

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

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