Post on 18-Dec-2015
Mobile Assisted Localization in Wireless Sensor Networks
N.B. Priyantha, H. Balakrishnan, E.D. Demaine, S. TellerMIT Computer Science
Presenters:
Puneet Gupta
Sol Lederer
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
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
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.
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
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
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
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
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
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
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
AFL: Anchor-free localization
Elect five nodes as shown
Get crude coordinates based on hop count to anchors
AFL
Use non-linear optimization algorithm to minimize sum-squared energy E
Coordinate assignments satisfy all 1-hop node distances when E = 0
Critique
Pros: Innovative stategy
Cons: In a cumbersome terrain (e.g. forest) it
may not be feasible to deploy a roving node.