Partially Localizable Networks by Goldenberg, Krishnamurthy, - - PowerPoint PPT Presentation

Partially Localizable Networks

by Goldenberg, Krishnamurthy, Maness, Yang, Young, Morse, Savvides and Anderson. Presented by Rik Sarkar

Overview

• Network Localization.
• Partially Localizable networks – PLNs
• A Formulation of Network Localizability
• Necessary and Sufficient Conditions
• Identifying Uniquely Localizable nodes
• Experimental Investigations (simulations) on

Partially Localizable Networks.

Localization

• Useful for Routing, Tracking, Location based

Query....

• Difficult
• Perfect localization may not be possible
• Erroneous config. may result in wrong conclusions.
• Test if localization is possible.
• Eren et al. Test localizability of entire graphs.

Partial Localizability

• Real networks are not likely to be entirely

localizable.

• Identify Uniquely Localizable nodes (A

sufficient condition is presented here)

• Simulate systems.
• What to do with UnLocalizable nodes?

Uses of Knowing Unlocalizable Nodes

• They can be ignored!
• Use them for routing..
• Make them localizable.
• Deploy beacons/nodes systematically.

Formulation of Global Network Localizability

• d (= 2 or 3) dimensions
• n nodes: m beacons, n-m non-beacons
• graph G given, with edges between nodes
• edge lengths are known
• Exact position of each beacon is known
• position of other nodes to be determined
• Graph Realization with edges between

beacons – Grounded Graph

Conditions for Localizability(1)

• Rigidity
• 3 node disjoint paths

to 3 beacons insufficient.

• A graph with 2n-3

edges is rigid if no subgraph has more than 2n'-3 edges.

Conditions for Localizability(2)

• Flip ambiguities
• A graph must be

d+1 vertex connected.

Conditions for Localizability(3)

• Remove edge – flip – add edge.
• Require redundant rigidity.
• Require triconnectedness.

Necessary & Sufficient Conditions for Network Localizability in 2D

• 3 Non-collinear beacons.
• Redundant Rigidity
• Triconnectedness – 3 node disjoint paths

between any two nodes.

• Extend to Node Localizability

RRT-3Beacon

• 3 Beacons
• Redundant Rigidity
• Triconnectedness
• RRT-3Beacon

RRT-3B

• Sufficient – NOT Necessary
• Ex : RRT-3B fails, though a is uniquely

localizable.

Identifying RRT Components

• Triconnectivity – remove vertices individually & check for

biconnectivity.

• Use pebble game to get RR subgraphs.
• Use recursive algo:

No Proof!

Simulation - % Localizable Nodes

Simulation – Increasing % of Beacons

Coverage of Sensed Area

• Coverage by All Nodes is Different from

Coverage by Localizable Nodes.

• Much higher density needed for Localizable

node coverage to match all-nodes coverage

Smart Beacon Deployment

• Put some beacons in, then add other beacons based on

RRT analysis.

• Results vary by distribution

Event Based Network Training

• Use known planned events for localizations.
• Time synchronization needed.
• Uniform vs systematic dispersal of events.
• Optimum Strategy depends on network

distribution/structure.

• Ex : events near beacons, events at

periphery, events a little inside the peripheri..

Other Studies

• Effect of PLNs on network routing.
• Joint source and network localizations.
• Source/target has known signal strength –

may be mobile.

Future

• Measurement errors
• Node deployment errors, eg. Beacon

deployment errors like in systematic beacon deployment.

• Looking at existing applications/algorithms

with the consideration of partial localizability.