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

Graph from running AFL—using RF connectivity information

Graph obtained by MAL

Performance

Layout of nodes in test scenario

Estimate error

Critique

Pros: Innovative stategy

Cons: In a cumbersome terrain (e.g. forest) it

may not be feasible to deploy a roving node.

The End