StarDust:

A

Flexible

Architecture

for

Passive

Localization

in

Wireless

Sensor

Networks

Radu

Stoleru,

Pascal

Vicaire,

Tian

He†,

John

A.

Stankovic

Department

of

Computer

Science,

University

of

Virginia

†Department

of

Computer

Science

and

Engineering,

University

of

Minnesota

{stoleru,

tianhe@cs.umn.edu,

stankovic@cs.virginia.edu

Abstract

The

problem

of

localization

in

wireless

sensor

networks

where

nodes

do

not

use

ranging

hardware,

remains

a

challenging

problem,

when

considering

the

required

location

accuracy,

energy

expenditure

and

the

duration

of

the

localization

phase.

In

this

paper

we

propose

a

framework,

called

StarDust,

for

wireless

sensor

network

localization

based

on

passive

optical

components.

In

the

StarDust

framework,

sensor

nodes

are

equipped

with

optical

retro-reflectors.

An

aerial

device

projects

light

towards

the

deployed

sensor

network,

and

records

an

image

of

the

reflected

light.

An

image

processing

algorithm

is

developed

for

obtaining

the

locations

of

sensor

nodes.

For

matching

a

node

ID

to

a

location

we

propose

a

constraint-based

label

relaxation

algorithm.

We

propose

and

develop

localization

techniques

based

on

four

types

of

constraints:

node

color,

neighbor

information,

deployment

time

for

a

node

and

deployment

location

for

a

node.

We

evaluate

the

performance

of

a

localization

system

based

on

our

framework

by

localizing

a

network

of

sensor

nodes

deployed

in

a

area.

The

localization

accuracy

ranges

from

ft

to

ft

while

the

localization

time

ranges

from

milliseconds

to

minutes.

Categories

and

Subject

Descriptors:

[Computer

Communications

Networks]:

Distributed

Systems;

[Special

Purpose

and

Application

Based

Systems]:

Real-time

and

embedded

systems

General

Terms:

Algorithms,

Measurement,

Performance,

Design,

Experimentation

Introduction

Wireless

Sensor

Networks

(WSN)

have

been

envisioned

to

revolutionize

the

way

humans

perceive

and

interact

with

the

surrounding

environment.

One

vision

is

to

embed

tiny

sensor

devices

in

outdoor

environments,

by

aerial

deployments

from

unmanned

air

vehicles.

The

sensor

nodes

form

a

network

and

collaborate

(to

compensate

for

the

extremely

scarce

resources

available

to

each

of

them:

computational

power,

memory

size,

communication

capabilities)

to

accomplish

the

mission.

Through

collaboration,

redundancy

and

fault

tolerance,

the

WSN

is

then

able

to

achieve

unprecedented

sensing

capabilities.

A

major

step

forward

has

been

accomplished

by

developing

systems

for

several

domains:

military

surveillance

habitat

monitoring

and

structural

monitoring

Even

after

these

successes,

several

research

problems

remain

open.

Among

these

open

problems

is

sensor

node

localization,

i.e.,

how

to

find

the

physical

position

of

each

sensor

node.

Despite

the

attention

the

localization

problem

in

WSN

has

received,

no

universally

acceptable

solution

has

been

developed.

There

are

several

reasons

for

this.

On

one

hand,

localization

schemes

that

use

ranging

are

typically

high

end

solutions.

GPS

ranging

hardware

consumes

energy,

it

is

relatively

expensive

(if

high

accuracy

is

required)

and

poses

form

factor

challenges

that

move

us

away

from

the

vision

of

dust

size

sensor

nodes.

Ultrasound

has

a

short

range

and

is

highly

directional.

Solutions

that

use

the

radio

transceiver

for

ranging

either

have

not

produced

encouraging

results

(if

the

received

signal

strength

indicator

is

used)

or

are

sensitive

to

environment

(e.g.,

multipath).

On

the

other

hand,

localization

schemes

that

only

use

the

connectivity

information

for

inferring

location

information

are

characterized

by

low

accuracies:

ft

in

controlled

environments,

ft

in

realistic

ones.

To

address

these

challenges,

we

propose

a

framework

for

WSN

localization,

called

StarDust,

in

which

the

complexity

associated

with

the

node

localization

is

completely

removed

from

the

sensor

node.

The

basic

principle

of

the

framework

is

localization

through

passivity:

each

sensor

node

is

equipped

with

a

corner-cube

retro-reflector

and

possibly

an

optical

filter

(a

coloring

device).

An

aerial

vehicle

projects

light

onto

the

deployment

area

and

records

images

containing

retro-reflected

light

beams

(they

appear

as

luminous

spots).

Through

image

processing

techniques,

the

locations

of

the

retro-reflectors

(i.e.,

sensor

nodes)

is

mined.

For

inferring

the

identity

of

the

sensor

node

present

at

a

particular

location,

the

StarDust

framework

develops

a

constraint-based

node

ID

relaxation

algorithm.

The

main

contributions

of

our

work

are

the

following.

We

propose

a

novel

framework

for

node

localization

in

WSNs

that

is

very

promising

and

allows

for

many

future

extensions

and

more

accurate

results.

We

propose

a

constraint-based

label

relaxation

algorithm

for

mapping

node

IDs

to

the

locations,

and

four

constraints

(node,

connectivity,

time

and

space),

which

are

building

blocks

for

very

accurate

and

very

fast

localization

systems.

We

develop

a

sensor

node

hardware

prototype,

called

a

SensorBall.

We

evaluate

the

performance

of

a

localization

system

for

which

we

obtain

location

accuracies

of

ft

with

a

localization

duration

ranging

from

milliseconds

to

minutes.

We

investigate

the

range

of

a

system

built

on

our

framework

by

considering

realities

of

physical

phenomena

that

occurs

during

light

propagation

through

the

atmosphere.

The

rest

of

the

paper

is

structured

as

follows.

Section

is

an

overview

of

the

state

of

art.

The

design

of

the

StarDust

framework

is

presented

in

Section

One

implementation

and

its

performance

evaluation

are

in

Sections

and

followed

by

a

suite

of

system

optimization

techniques,

in

Section

In

Section

we

present

our

conclusions.

Related

Work

We

present

the

prior

work

in

localization

in

two

major

categories:

the

range-based,

and

the

range-free

schemes.

The

range-based

localization

techniques

have

been

designed

to

use

either

more

expensive

hardware

(and

hence

higher

accuracy)

or

just

the

radio

transceiver.

Ranging

techniques

dependent

on

hardware

are

the

time-of-flight

(ToF)

and

the

time-difference-of-arrival(TDoA).

Solutions

that

use

the

radio

are

based

on

the

received

signal

strength

indicator

(RSSI)

and

more

recently

on

radio

interferometry.

The

ToF

localization

technique

that

is

most

widely

used

is

the

GPS.

GPS

is

a

costly

solution

for

a

high

accuracy

localization

of

a

large

scale

sensor

network.

AHLoS

employs

a

TDoA

ranging

technique

that

requires

extensive

hardware

and

solves

relatively

large

nonlinear

systems

of

equations.

The

Cricket

location-support

system

(TDoA)

can

achieve

a

location

granularity

of

tens

of

inches

with

highly

directional

and

short

range

ultrasound

transceivers.

In

the

location

of

a

sniper

is

determined

in

an

urban

terrain,

by

using

the

TDoA

between

an

acoustic

wave

and

a

radio

beacon.

The

PushPin

project

uses

the

TDoA

between

ultrasound

pulses

and

light

flashes

for

node

localization.

The

RADAR

system

uses

the

RSSI

to

build

a

map

of

signal

strengths

as

emitted

by

a

set

of

beacon

nodes.

A

mobile

node

is

located

by

the

best

match,

in

the

signal

strength

space,

with

a

previously

acquired

signature.

In

MAL

a

mobile

node

assists

in

measuring

the

distances

(acting

as

constraints)

between

nodes

until

a

rigid

graph

is

generated.

The

localization

problem

is

formulated

as

an

on-line

state

estimation

in

a

nonlinear

dynamic

system

A

cooperative

ranging

that

attempts

to

achieve

a

global

positioning

from

distributed

local

optimizations

is

proposed

in

A

very

recent,

remarkable,

localization

technique

is

based

on

radio

interferometry,

RIPS

which

utilizes

two

transmitters

to

create

an

interfering

signal.

The

frequencies

of

the

emitters

are

very

close

to

each

other,

thus

the

interfering

signal

will

have

a

low

frequency

envelope

that

can

be

easily

measured.

The

ranging

technique

performs

very

well.

The

long

time

required

for

localization

and

multi-path

environments

pose

significant

challenges.

Real

environments

create

additional

challenges

for

the

range

based

localization

schemes.

These

have

been

emphasized

by

several

studies

To

address

these

challenges,

and

others

(hardware

cost,

the

energy

expenditure,

the

form

factor,

the

small

range,

localization

time),

several

range-free

localization

schemes

have

been

proposed.

Sensor

nodes

use

primarily

connectivity

information

for

inferring

proximity

to

a

set

of

anchors.

In

the

Centroid

localization

scheme

a

sensor

node

localizes

to

the

centroid

of

its

proximate

beacon

nodes.

In

APIT

each

node

decides

its

position

based

on

the

possibility

of

being

inside

or

outside

of

a

triangle

formed

by

any

three

beacons

within

node"s

communication

range.

The

Gradient

algorithm

leverages

the

knowledge

about

the

network

density

to

infer

the

average

one

hop

length.

This,

in

turn,

can

be

transformed

into

distances

to

nodes

with

known

locations.

DV-Hop

uses

the

hop

by

hop

propagation

capability

of

the

network

to

forward

distances

to

landmarks.

More

recently,

several

localization

schemes

that

exploit

the

sensing

capabilities

of

sensor

nodes,

have

been

proposed.

Spotlight

creates

well

controlled

(in

time

and

space)

events

in

the

network

while

the

sensor

nodes

detect

and

timestamp

this

events.

From

the

spatiotemporal

knowledge

for

the

created

events

and

the

temporal

information

provided

by

sensor

nodes,

nodes"

spatial

information

can

be

obtained.

In

a

similar

manner,

the

Lighthouse

system

uses

a

parallel

light

beam,

that

is

emitted

by

an

anchor

which

rotates

with

a

certain

period.

A

sensor

node

detects

the

light

beam

for

a

period

of

time,

which

is

dependent

on

the

distance

between

it

and

the

light

emitting

device.

Many

of

the

above

localization

solutions

target

specific

sets

of

requirements

and

are

useful

for

specific

applications.

StarDust

differs

in

that

it

addresses

a

particular

demanding

set

of

requirements

that

are

not

yet

solved

well.

StarDust

is

meant

for

localizing

air

dropped

nodes

where

node

passiveness,

high

accuracy,

low

cost,

small

form

factor

and

rapid

localization

are

all

required.

Many

military

applications

have

such

requirements.

StarDust

System

Design

The

design

of

the

StarDust

system

(and

its

name)

was

inspired

by

the

similarity

between

a

deployed

sensor

network,

in

which

sensor

nodes

indicate

their

presence

by

emitting

light,

and

the

Universe

consisting

of

luminous

and

illuminated

objects:

stars,

galaxies,

planets,

etc.

The

main

difficulty

when

applying

the

above

ideas

to

the

real

world

is

the

complexity

of

the

hardware

that

needs

to

be

put

on

a

sensor

node

so

that

the

emitted

light

can

be

detected

from

thousands

of

feet.

The

energy

expenditure

for

producing

an

intense

enough

light

beam

is

also

prohibitive.

Instead,

what

we

propose

to

use

for

sensor

node

localization

is

a

passive

optical

element

called

a

retro-reflector.

The

most

common

retro-reflective

optical

component

is

a

Corner-Cube

Retroreflector

(CCR),

shown

in

Figure

It

consists

of

three

mutually

perpendicular

mirrors.

The

(a)

(b)

Figure

Corner-Cube

Retroreflector

(a)

and

an

array

of

CCRs

molded

in

plastic

(b)

esting

property

of

this

optical

component

is

that

an

incoming

beam

of

light

is

reflected

back,

towards

the

source

of

the

light,

irrespective

of

the

angle

of

incidence.

This

is

in

contrast

with

a

mirror,

which

needs

to

be

precisely

positioned

to

be

perpendicular

to

the

incident

light.

A

very

common

and

inexpensive

implementation

of

an

array

of

CCRs

is

the

retroreflective

plastic

material

used

on

cars

and

bicycles

for

night

time

detection,

shown

in

Figure

In

the

StarDust

system,

each

node

is

equipped

with

a

small

(e.g.

array

of

CCRs

and

the

enclosure

has

self-righting

capabilities

that

orient

the

array

of

CCRs

predominantly

upwards.

It

is

critical

to

understand

that

the

upward

orientation

does

not

need

to

be

exact.

Even

when

large

angular

variations

from

a

perfectly

upward

orientation

are

present,

a

CCR

will

return

the

light

in

the

exact

same

direction

from

which

it

came.

In

the

remaining

part

of

the

section,

we

present

the

architecture

of

the

StarDust

system

and

the

design

of

its

main

components.

System

Architecture

The

envisioned

sensor

network

localization

scenario

is

as

follows:

The

sensor

nodes

are

released,

possibly

in

a

controlled

manner,

from

an

aerial

vehicle

during

the

night.

The

aerial

vehicle

hovers

over

the

deployment

area

and

uses

a

strobe

light

to

illuminate

it.

The

sensor

nodes,

equipped

with

CCRs

and

optical

filters

(acting

as

coloring

devices)

have

self-righting

capabilities

and

retroreflect

the

incoming

strobe

light.

The

retro-reflected

light

is

either

white,

as

the

originating

source

light,

or

colored,

due

to

optical

filters.

The

aerial

vehicle

records

a

sequence

of

two

images

very

close

in

time

(msec

level).

One

image

is

taken

when

the

strobe

light

is

on,

the

other

when

the

strobe

light

is

off.

The

acquired

images

are

used

for

obtaining

the

locations

of

sensor

nodes

(which

appear

as

luminous

spots

in

the

image).

The

aerial

vehicle

executes

the

mapping

of

node

IDs

to

the

identified

locations

in

one

of

the

following

ways:

a)

by

using

the

color

of

a

retro-reflected

light,

if

a

sensor

node

has

a

unique

color;

b)

by

requiring

sensor

nodes

to

establish

neighborhood

information

and

report

it

to

a

base

station;

c)

by

controlling

the

time

sequence

of

sensor

nodes

deployment

and

recording

additional

imLight

Emitter

Sensor

Node

i

Transfer

Function

Φi(λ)

Ψ(λ)

Φ(Ψ(λ))

Image

Processing

Node

ID

Matching

Radio

Model

R

G(Λ,E)

Central

Device

V"

V"

Figure

The

StarDust

system

architecture

ages;

d)

by

controlling

the

location

where

a

sensor

node

is

deployed.

The

computed

locations

are

disseminated

to

the

sensor

network.

The

architecture

of

the

StarDust

system

is

shown

in

Figure

The

architecture

consists

of

two

main

components:

the

first

is

centralized

and

it

is

located

on

a

more

powerful

device.

The

second

is

distributed

and

it

resides

on

all

sensor

nodes.

The

Central

Device

consists

of

the

following:

the

Light

Emitter,

the

Image

Processing

module,

the

Node

ID

Mapping

module

and

the

Radio

Model.

The

distributed

component

of

the

architecture

is

the

Transfer

Function,

which

acts

as

a

filter

for

the

incoming

light.

The

aforementioned

modules

are

briefly

described

below:

Light

Emitter

It

is

a

strobe

light,

capable

of

producing

very

intense,

collimated

light

pulses.

The

emitted

light

is

non-monochromatic

(unlike

a

laser)

and

it

is

characterized

by

a

spectral

density

Ψ(λ),

a

function

of

the

wavelength.

The

emitted

light

is

incident

on

the

CCRs

present

on

sensor

nodes.

Transfer

Function

Φ(Ψ(λ))

This

is

a

bandpass

filter

for

the

incident

light

on

the

CCR.

The

filter

allows

a

portion

of

the

original

spectrum,

to

be

retro-reflected.

From

here

on,

we

will

refer

to

the

transfer

function

as

the

color

of

a

sensor

node.

Image

Processing

The

Image

Processing

module

acquires

high

resolution

images.

From

these

images

the

locations

and

the

colors

of

sensor

nodes

are

obtained.

If

only

one

set

of

pictures

can

be

taken

(i.e.,

one

location

of

the

light

emitter/image

analysis

device),

then

the

map

of

the

field

is

assumed

to

be

known

as

well

as

the

distance

between

the

imaging

device

and

the

field.

The

aforementioned

assumptions

(field

map

and

distance

to

it)

are

not

necessary

if

the

images

can

be

simultaneously

taken

from

different

locations.

It

is

important

to

remark

here

that

the

identity

of

a

node

can

not

be

directly

obtained

through

Image

Processing

alone,

unless

a

specific

characteristic

of

a

sensor

node

can

be

identified

in

the

image.

Node

ID

Matching

This

module

uses

the

detected

locations

and

through

additional

techniques

(e.g.,

sensor

node

coloring

and

connectivity

information

(G(Λ,E))

from

the

deployed

network)

to

uniquely

identify

the

sensor

nodes

observed

in

the

image.

The

connectivity

information

is

represented

by

neighbor

tables

sent

from

Algorithm

Image

Processing

Background

filtering

Retro-reflected

light

recognition

through

intensity

filtering

Edge

detection

to

obtain

the

location

of

sensor

nodes

Color

identification

for

each

detected

sensor

node

each

sensor

node

to

the

Central

Device.

Radio

Model

This

component

provides

an

estimate

of

the

radio

range

to

the

Node

ID

Matching

module.

It

is

only

used

by

node

ID

matching

techniques

that

are

based

on

the

radio

connectivity

in

the

network.

The

estimate

of

the

radio

range

R

is

based

on

the

sensor

node

density

(obtained

through

the

Image

Processing

module)

and

the

connectivity

information

(i.e.,

G(Λ,E)).

The

two

main

components

of

the

StarDust

architecture

are

the

Image

Processing

and

the

Node

ID

Mapping.

Their

design

and

analysis

is

presented

in

the

sections

that

follow.

Image

Processing

The

goal

of

the

Image

Processing

Algorithm

(IPA)

is

to

identify

the

location

of

the

nodes

and

their

color.

Note

that

IPA

does

not

identify

which

node

fell

where,

but

only

what

is

the

set

of

locations

where

the

nodes

fell.

IPA

is

executed

after

an

aerial

vehicle

records

two

pictures:

one

in

which

the

field

of

deployment

is

illuminated

and

one

when

no

illuminations

is

present.

Let

Pdark

be

the

picture

of

the

deployment

area,

taken

when

no

light

was

emitted

and

Plight

be

the

picture

of

the

same

deployment

area

when

a

strong

light

beam

was

directed

towards

the

sensor

nodes.

The

proposed

IPA

has

several

steps,

as

shown

in

Algorithm

The

first

step

is

to

obtain

a

third

picture

Pfilter

where

only

the

differences

between

Pdark

and

Plight

remain.

Let

us

assume

that

Pdark

has

a

resolution

of

n

m,

where

n

is

the

number

of

pixels

in

a

row

of

the

picture,

while

m

is

the

number

of

pixels

in

a

column

of

the

picture.

Then

Pdark

is

composed

of

n

m

pixels

noted

Pdark(i,

j),

i

i

j

m.

Similarly

Plight

is

composed

of

n

m

pixels

noted

Plight(i,

j),

i

j

m.

Each

pixel

P

is

described

by

an

RGB

value

where

the

R

value

is

denoted

by

PR,

the

G

value

is

denoted

by

PG,

and

the

B

value

is

denoted

by

PB.

IPA

then

generates

the

third

picture,

Pfilter,

through

the

following

transformations:

PR

filter(i,

j)

PR

light(i,

j)−PR

dark(i,

j)

PG

filter(i,

j)

PG

light(i,

j)−PG

dark(i,

j)

PB

filter(i,

j)

PB

light(i,

j)−PB

dark(i,

j)

After

this

transformation,

all

the

features

that

appeared

in

both

Pdark

and

Plight

are

removed

from

Pfilter.

This

simplifies

the

recognition

of

light

retro-reflected

by

sensor

nodes.

The

second

step

consists

of

identifying

the

elements

contained

in

Pfilter

that

retro-reflect

light.

For

this,

an

intensity

filter

is

applied

to

Pfilter.

First

IPA

converts

Pfilter

into

a

grayscale

picture.

Then

the

brightest

pixels

are

identified

and

used

to

create

Preflect.

This

step

is

eased

by

the

fact

that

the

reflecting

nodes

should

appear

much

brighter

than

any

other

illuminated

object

in

the

picture.

Support:

Q(λk)

ni

PN

λ1

λk

λN

Figure

Probabilistic

label

relaxation

The

third

step

runs

an

edge

detection

algorithm

on

Preflect

to

identify

the

boundary

of

the

nodes

present.

A

tool

such

as

Matlab

provides

a

number

of

edge

detection

techniques.

We

used

the

bwboundaries

function.

For

the

obtained

edges,

the

location

(x,y)

(in

the

image)

of

each

node

is

determined

by

computing

the

centroid

of

the

points

constituting

its

edges.

Standard

computer

graphics

techniques

are

then

used

to

transform

the

locations

of

sensor

nodes

detected

in

multiple

images

into

sensor

node

locations.

The

color

of

the

node

is

obtained

as

the

color

of

the

pixel

located

at

(x,y)

in

Plight.

Node

ID

Matching

The

goal

of

the

Node

ID

Matching

module

is

to

obtain

the

identity

(node

ID)

of

a

luminous

spot

in

the

image,

detected

to

be

a

sensor

node.

For

this,

we

define

V

to

be

the

set

of

locations

of

the

sensor

nodes,

as

detected

by

the

Image

Processing

module

and

Λ

to

be

the

set

of

unique

node

IDs

assigned

to

the

m

sensor

nodes,

before

deployment.

From

here

on,

we

refer

to

node

IDs

as

labels.

We

model

the

problem

of

finding

the

label

λj

of

a

node

ni

as

a

probabilistic

label

relaxation

problem,

frequently

used

in

image

processing/understanding.

In

the

image

processing

domain,

scene

labeling

(i.e.,

identifying

objects

in

an

image)

plays

a

major

role.

The

goal

of

scene

labeling

is

to

assign

a

label

to

each

object

detected

in

an

image,

such

that

an

appropriate

image

interpretation

is

achieved.

It

is

prohibitively

expensive

to

consider

the

interactions

among

all

the

objects

in

an

image.

Instead,

constraints

placed

among

nearby

objects

generate

local

consistencies

and

through

iteration,

global

consistencies

can

be

obtained.

The

main

idea

of

the

sensor

node

localization

through

probabilistic

label

relaxation

is

to

iteratively

compute

the

probability

of

each

label

being

the

correct

label

for

a

sensor

node,

by

taking

into

account,

at

each

iteration,

the

support

for

a

label.

The

support

for

a

label

can

be

understood

as

a

hint

or

proof,

that

a

particular

label

is

more

likely

to

be

the

correct

one,

when

compared

with

the

other

potential

labels

for

a

sensor

node.

We

pictorially

depict

this

main

idea

in

Figure

As

shown,

node

ni

has

a

set

of

candidate

labels

Each

of

the

labels

has

a

different

value

for

the

Support

function

Q(λk).

We

defer

the

explanation

of

how

the

Support

function

is

implemented

until

the

subsections

that

follow,

where

we

provide

four

concrete

techniques.

Formally,

the

algorithm

is

outlined

in

Algorithm

where

the

equations

necessary

for

computing

the

new

probability

Pni(λk)

for

a

label

λk

of

a

node

ni,

are

expressed

by

the

Algorithm

Label

Relaxation

for

each

sensor

node

ni

do

assign

equal

prob.

to

all

possible

labels

end

for

repeat

converged

true

for

each

sensor

node

ni

do

for

each

each

label

λj

of

ni

do

compute

the

Support

label

λj:

Equation

end

for

compute

K

for

the

node

ni:

Equation

for

each

each

label

λj

do

update

probability

of

label

λj:

Equation

if

|new

prob.−old

prob.|

ε

then

converged

false

end

if

end

for

end

for

until

converged

true

following

equations:

ni

(λk)

Kni

Ps

ni

(λk)Qs

ni

(λk)

where

Kni

is

a

normalizing

constant,

given

by:

Kni

N

Ps

ni

(λk)Qs

ni

(λk)

and

Qs

ni

(λk)

is:

Qs

ni

(λk)

support

for

label

λk

of

node

ni

The

label

relaxation

algorithm

is

iterative

and

it

is

polynomial

in

the

size

of

the

network(number

of

nodes).

The

pseudo-code

is

shown

in

Algorithm

It

initializes

the

probabilities

associated

with

each

possible

label,

for

a

node

ni,

through

a

uniform

distribution.

At

each

iteration

s,

the

algorithm

updates

the

probability

associated

with

each

label,

by

considering

the

Support

Qs

ni

(λk)

for

each

candidate

label

of

a

sensor

node.

In

the

sections

that

follow,

we

describe

four

different

techniques

for

implementing

the

Support

function:

based

on

node

coloring,

radio

connectivity,

the

time

of

deployment

(time)

and

the

location

of

deployment

(space).

While

some

of

these

techniques

are

simplistic,

they

are

primitives

which,

when

combined,

can

create

powerful

localization

systems.

These

design

techniques

have

different

trade-offs,

which

we

will

present

in

Section

Relaxation

with

Color

Constraints

The

unique

mapping

between

a

sensor

node"s

position

(identified

by

the

image

processing)

and

a

label

can

be

obtained

by

assigning

a

unique

color

to

each

sensor

node.

For

this

we

define

C

to

be

the

set

of

unique

colors

available

and

M

Λ

C

to

be

a

one-to-one

mapping

of

labels

to

colors.

This

mapping

is

known

prior

to

the

sensor

node

deployment

(from

node

manufacturing).

In

the

case

of

color

constrained

label

relaxation,

the

support

for

label

λk

is

expressed

as

follows:

Qs

ni

(λk)

As

a

result,

the

label

relaxation

algorithm

(Algorithm

consists

of

the

following

steps:

one

label

is

assigned

to

each

sensor

node

(lines

of

the

algorithm),

implicitly

having

a

probability

Pni(λk)

the

algorithm

executes

a

single

iteration,

when

the

support

function,

simply,

reiterates

the

confidence

in

the

unique

labeling.

However,

it

is

often

the

case

that

unique

colors

for

each

node

will

not

be

available.

It

is

interesting

to

discuss

here

the

influence

that

the

size

of

the

coloring

space

(i.e.,

|C|)

has

on

the

accuracy

of

the

localization

algorithm.

Several

cases

are

discussed

below:

If

|C|

no

colors

are

used

and

the

sensor

nodes

are

equipped

with

simple

CCRs

that

reflect

back

all

the

incoming

light

(i.e.,

no

filtering,

and

no

coloring

of

the

incoming

light).

From

the

image

processing

system,

the

position

of

sensor

nodes

can

still

be

obtained.

Since

all

nodes

appear

white,

no

single

sensor

node

can

be

uniquely

identified.

If

|C|

m

then

there

are

enough

unique

colors

for

all

nodes

(one

node

remains

white,

i.e.

no

coloring),

the

problem

is

trivially

solved.

Each

node

can

be

identified,

based

on

its

unique

color.

This

is

the

scenario

for

the

relaxation

with

color

constraints.

If

|C|

there

are

several

options

for

how

to

partition

the

coloring

space.

If

C

one

possibility

is

to

assign

the

color

to

a

single

node,

and

leave

the

remaining

sensor

nodes

white,

or

to

assign

the

color

to

more

than

one

sensor

node.

One

can

observe

that

once

a

color

is

assigned

uniquely

to

a

sensor

node,

in

effect,

that

sensor

node

is

given

the

status

of

anchor,

or

node

with

known

location.

It

is

interesting

to

observe

that

there

is

an

entire

spectrum

of

possibilities

for

how

to

partition

the

set

of

sensor

nodes

in

equivalence

classes

(where

an

equivalence

class

is

represented

by

one

color),

in

order

to

maximize

the

success

of

the

localization

algorithm.

One

of

the

goals

of

this

paper

is

to

understand

how

the

size

of

the

coloring

space

and

its

partitioning

affect

localization

accuracy.

Despite

the

simplicity

of

this

method

of

constraining

the

set

of

labels

that

can

be

assigned

to

a

node,

we

will

show

that

this

technique

is

very

powerful,

when

combined

with

other

relaxation

techniques.

Relaxation

with

Connectivity

Constraints

Connectivity

information,

obtained

from

the

sensor

network

through

beaconing,

can

provide

additional

information

for

locating

sensor

nodes.

In

order

to

gather

connectivity

information,

the

following

need

to

occur:

after

deployment,

through

beaconing

of

HELLO

messages,

sensor

nodes

build

their

neighborhood

tables;

each

node

sends

its

neighbor

table

information

to

the

Central

device

via

a

base

station.

First,

let

us

define

G

(Λ,E)

to

be

the

weighted

connectivity

graph

built

by

the

Central

device

from

the

received

neighbor

table

information.

In

G

the

edge

(λi,λj)

has

a

λ1

λ2

λN

ni

nj

λ1

λ2

λN

Pj,λN

Pi,λN

Figure

Label

relaxation

with

connectivity

constraints

weight

gij

represented

by

the

number

of

beacons

sent

by

λj

and

received

by

λi.

In

addition,

let

R

be

the

radio

range

of

the

sensor

nodes.

The

main

idea

of

the

connectivity

constrained

label

relaxation

is

depicted

in

Figure

in

which

two

nodes

ni

and

nj

have

been

assigned

all

possible

labels.

The

confidence

in

each

of

the

candidate

labels

for

a

sensor

node,

is

represented

by

a

probability,

shown

in

a

dotted

rectangle.

It

is

important

to

remark

that

through

beaconing

and

the

reporting

of

neighbor

tables

to

the

Central

Device,

a

global

view

of

all

constraints

in

the

network

can

be

obtained.

It

is

critical

to

observe

that

these

constraints

are

among

labels.

As

shown

in

Figure

two

constraints

exist

between

nodes

ni

and

nj.

The

constraints

are

depicted

by

and

the

number

of

beacons

sent

the

labels

and

λjM

and

received

by

the

label

The

support

for

the

label

λk

of

sensor

node

ni,

resulting

from

the

interaction

(i.e.,

within

radio

range)

with

sensor

node

nj

is

given

by:

Qs

ni

(λk)

M

gλkλm

Ps

nj

(λm)

As

a

result,

the

localization

algorithm

(Algorithm

consists

of

the

following

steps:

all

labels

are

assigned

to

each

sensor

node

(lines

of

the

algorithm),

and

implicitly

each

label

has

a

probability

initialized

to

Pni(λk)

in

each

iteration,

the

probabilities

for

the

labels

of

a

sensor

node

are

updated,

when

considering

the

interaction

with

the

labels

of

sensor

nodes

within

R.

It

is

important

to

remark

that

the

identity

of

the

nodes

within

R

is

not

known,

only

the

candidate

labels

and

their

probabilities.

The

relaxation

algorithm

converges

when,

during

an

iteration,

the

probability

of

no

label

is

updated

by

more

than

ε.

The

label

relaxation

algorithm

based

on

connectivity

constraints,

enforces

such

constraints

between

pairs

of

sensor

nodes.

For

a

large

scale

sensor

network

deployment,

it

is

not

feasible

to

consider

all

pairs

of

sensor

nodes

in

the

network.

Hence,

the

algorithm

should

only

consider

pairs

of

sensor

nodes

that

are

within

a

reasonable

communication

range

(R).

We

assume

a

circular

radio

range

and

a

symmetric

connectivity.

In

the

remaining

part

of

the

section

we

propose

a

simple

analytical

model

that

estimates

the

radio

range

R

for

medium-connected

networks

(less

than

neighbors

per

R).

We

consider

the

following

to

be

known:

the

size

of

the

deployment

field

(L),

the

number

of

sensor

nodes

deployed

(N)

Algorithm

Localization

Estimate

the

radio

range

R

Execute

the

Label

Relaxation

Algorithm

with

Support

Function

given

by

Equation

for

neighbors

less

than

R

apart

for

each

sensor

node

ni

do

node

identity

is

λk

with

max.

prob.

end

for

and

the

total

number

of

unidirectional

(i.e.,

not

symmetric)

one-hop

radio

connections

in

the

network

(k).

For

our

analysis,

we

uniformly

distribute

the

sensor

nodes

in

a

square

area

of

length

L,

by

using

a

grid

of

unit

length

L/

N.

We

use

the

substitution

u

L/

N

to

simplify

the

notation,

in

order

to

distinguish

the

following

cases:

if

u

R

each

node

has

four

neighbors

(the

expected

k

if

R

each

node

has

eight

neighbors

(the

expected

k

if

R

each

node

has

twelve

neighbors

the

expected

k

if

R

each

node

has

twenty

neighbors

(the

expected

k

For

a

given

t

we

take

R

to

be

the

middle

of

the

interval.

As

an

example,

if

t

then

R

A

quadratic

fitting

for

R

over

the

possible

values

of

t,

produces

the

following

closed-form

solution

for

the

communication

range

R,

as

a

function

of

network

connectivity

k,

assuming

L

and

N

constant:

R(k)

L

N

k

k

We

investigate

the

accuracy

of

our

model

in

Section

Relaxation

with

Time

Constraints

Time

constraints

can

be

treated

similarly

with

color

constraints.

The

unique

identification

of

a

sensor

node

can

be

obtained

by

deploying

sensor

nodes

individually,

one

by

one,

and

recording

a

sequence

of

images.

The

sensor

node

that

is

identified

as

new

in

the

last

picture

(it

was

not

identified

in

the

picture

before

last)

must

be

the

last

sensor

node

dropped.

In

a

similar

manner

with

color

constrained

label

relaxation,

the

time

constrained

approach

is

very

simple,

but

may

take

too

long,

especially

for

large

scale

systems.

While

it

can

be

used

in

practice,

it

is

unlikely

that

only

a

time

constrained

label

relaxation

is

used.

As

we

will

see,

by

combining

constrained-based

primitives,

realistic

localization

systems

can

be

implemented.

The

support

function

for

the

label

relaxation

with

time

constraints

is

defined

identically

with

the

color

constrained

relaxation:

Qs

ni

(λk)

The

localization

algorithm

(Algorithm

consists

of

the

following

steps:

one

label

is

assigned

to

each

sensor

node

(lines

of

the

algorithm),

and

implicitly

having

a

probability

Pni(λk)

the

algorithm

executes

a

single

iteration,

D

Figure

Relaxation

with

space

constraints

PDF

Distance

D

σ

σ

σ

Figure

Probability

distribution

of

distances

X

Y

Node

Density

Figure

Distribution

of

nodes

when

the

support

function,

simply,

reiterates

the

confidence

in

the

unique

labeling.

Relaxation

with

Space

Constraints

Spatial

information

related

to

sensor

deployment

can

also

be

employed

as

another

input

to

the

label

relaxation

algorithm.

To

do

that,

we

use

two

types

of

locations:

the

node

location

pn

and

the

label

location

pl.

The

former

pn

is

defined

as

the

position

of

nodes

(xn,yn,zn)

after

deployment,

which

can

be

obtained

through

Image

Processing

as

mentioned

in

Section

The

latter

pl

is

defined

as

the

location

(xl,yl,zl)

where

a

node

is

dropped.

We

use

Dni

λm

to

denote

the

horizontal

distance

between

the

location

of

the

label

λm

and

the

location

of

the

node

ni.

Clearly,

Dni

λm

(xn

+(yn

At

the

time

of

a

sensor

node

release,

the

one-to-one

mapping

between

the

node

and

its

label

is

known.

In

other

words,

the

label

location

is

the

same

as

the

node

location

at

the

release

time.

After

release,

the

label

location

information

is

partially

lost

due

to

the

random

factors

such

as

wind

and

surface

impact.

However,

statistically,

the

node

locations

are

correlated

with

label

locations.

Such

correlation

depends

on

the

airdrop

methods

employed

and

environments.

For

the

sake

of

simplicity,

let"s

assume

nodes

are

dropped

from

the

air

through

a

helicopter

hovering

in

the

air.

Wind

can

be

decomposed

into

three

components

X,Y

and

Z.

Only

X

and

Y

affect

the

horizontal

distance

a

node

can

travel.

According

to

we

can

assume

that

X

and

Y

follow

an

independent

normal

distribution.

Therefore,

the

absolute

value

of

the

wind

speed

follows

a

Rayleigh

distribution.

Obviously

the

higher

the

wind

speed

is,

the

further

a

node

would

land

away

horizontally

from

the

label

location.

If

we

assume

that

the

distance

D

is

a

function

of

the

wind

speed

V

we

can

obtain

the

probability

distribution

of

D

under

a

given

wind

speed

distribution.

Without

loss

of

generality,

we

assume

that

D

is

proportional

to

the

wind

speed.

Therefore,

D

follows

the

Rayleigh

distribution

as

well.

As

shown

in

Figure

the

spatial-based

relaxation

is

a

recursive

process

to

assign

the

probability

that

a

nodes

has

a

certain

label

by

using

the

distances

between

the

location

of

a

node

with

multiple

label

locations.

We

note

that

the

distribution

of

distance

D

affects

the

probability

with

which

a

label

is

assigned.

It

is

not

necessarily

true

that

the

nearest

label

is

always

chosen.

For

example,

if

D

follows

the

distribution,

we

can

obtain

the

Probability

Density

Function

(PDF)

of

distances

as

shown

in

Figure

This

figure

indicates

that

the

possibility

of

a

node

to

fall

vertically

is

very

small

under

windy

conditions

(σ

and

that

the

distance

D

is

affected

by

the

σ.

The

spatial

distribution

of

nodes

for

σ

is

shown

in

Figure

Strong

wind

with

a

high

σ

value

leads

to

a

larger

node

dispersion.

More

formally,

given

a

probability

density

function

PDF(D),

the

support

for

label

λk

of

sensor

node

ni

can

be

formulated

as:

Qs

ni

(λk)

PDF(Dni

λk

It

is

interesting

to

point

out

two

special

cases.

First,

if

all

nodes

are

released

at

once

(i.e.,

only

one

label

location

for

all

released

nodes),

the

distance

D

from

a

node

to

all

labels

is

the

same.

In

this

case,

ni

(λk)

Ps

ni

(λk),

which

indicates

that

we

can

not

use

the

spatial-based

relaxation

to

recursively

narrow

down

the

potential

labels

for

a

node.

Second,

if

nodes

are

released

at

different

locations

that

are

far

away

from

each

other,

we

have:

(i)

If

node

ni

has

label

λk,

Ps

ni

(λk)

when

s

(ii)

If

node

ni

does

not

have

label

λk,

Ps

ni

(λk)

when

s

In

this

second

scenario,

there

are

multiple

labels

(one

label

per

release),

hence

it

is

possible

to

correlate

release

times

(labels)

with

positions

on

the

ground.

These

results

indicate

that

spatial-based

relaxation

can

label

the

node

with

a

very

high

probability

if

the

physical

separation

among

nodes

is

large.

Relaxation

with

Color

and

Connectivity

Constraints

One

of

the

most

interesting

features

of

the

StarDust

architecture

is

that

it

allows

for

hybrid

localization

solutions

to

be

built,

depending

on

the

system

requirements.

One

example

is

a

localization

system

that

uses

the

color

and

connectivity

constraints.

In

this

scheme,

the

color

constraints

are

used

for

reducing

the

number

of

candidate

labels

for

sensor

nodes,

to

a

more

manageable

value.

As

a

reminder,

in

the

connectivity

constrained

relaxation,

all

labels

are

candidate

labels

for

each

sensor

node.

The

color

constraints

are

used

in

the

initialization

phase

of

Algorithm

(lines

After

the

initialization,

the

standard

connectivity

constrained

relaxation

algorithm

is

used.

For

a

better

understanding

of

how

the

label

relaxation

algorithm

works,

we

give

a

concrete

example,

exemplified

in

Figure

In

part

(a)

of

the

figure

we

depict

the

data

structures

ni

nj

(a)

ni

nj

(b)

Figure

A

step

through

the

algorithm.

After

initialization

(a)

and

after

the

iteration

for

node

ni

(b)

associated

with

nodes

ni

and

nj

after

the

initialization

steps

of

the

algorithm

(lines

as

well

as

the

number

of

beacons

between

different

labels

(as

reported

by

the

network,

through

G(Λ,E)).

As

seen,

the

potential

labels

(shown

inside

the

vertical

rectangles)

are

assigned

to

each

node.

Node

ni

can

be

any

of

the

following:

Also

depicted

in

the

figure

are

the

probabilities

associated

with

each

of

the

labels.

After

initialization,

all

probabilities

are

equal.

Part

(b)

of

Figure

shows

the

result

of

the

first

iteration

of

the

localization

algorithm

for

node

ni,

assuming

that

node

nj

is

the

first

wi

chosen

in

line

of

Algorithm

By

using

Equation

the

algorithm

computes

the

support

Q(λi)

for

each

of

the

possible

labels

for

node

ni.

Once

the

Q(λi)"s

are

computed,

the

normalizing

constant,

given

by

Equation

can

be

obtained.

The

last

step

of

the

iteration

is

to

update

the

probabilities

associated

with

all

potential

labels

of

node

ni,

as

given

by

Equation

One

interesting

problem,

which

we

explore

in

the

performance

evaluation

section,

is

to

assess

the

impact

the

partitioning

of

the

color

set

C

has

on

the

accuracy

of

localization.

When

the

size

of

the

coloring

set

is

smaller

than

the

number

of

sensor

nodes

(as

it

is

the

case

for

our

hybrid

connectivity/color

constrained

relaxation),

the

system

designer

has

the

option

of

allowing

one

node

to

uniquely

have

a

color

(acting

as

an

anchor),

or

multiple

nodes.

Intuitively,

by

assigning

one

color

to

more

than

one

node,

more

constraints

(distributed)

can

be

enforced.

Relaxation

Techniques

Analysis

The

proposed

label

relaxation

techniques

have

different

trade-offs.

For

our

analysis

of

the

trade-offs,

we

consider

the

following

metrics

of

interest:

the

localization

time

(duration),

the

energy

consumed

(overhead),

the

network

size

(scale)

that

can

be

handled

by

the

technique

and

the

localization

accuracy.

The

parameters

of

interest

are

the

following:

the

number

of

sensor

nodes

(N),

the

energy

spent

for

one

aerial

drop

(εd),

the

energy

spent

in

the

network

for

collecting

and

reporting

neighbor

information

εb

and

the

time

Td

taken

by

a

sensor

node

to

reach

the

ground

after

being

aerially

deployed.

The

cost

comparison

of

the

different

label

relaxation

techniques

is

shown

in

Table

As

shown,

the

relaxation

techniques

based

on

color

and

space

constraints

have

the

lowest

localization

duration,

zero,

for

all

practical

purposes.

The

scalability

of

the

color

based

relaxation

technique

is,

however,

limited

to

the

number

of

(a)

(b)

Figure

SensorBall

with

self-righting

capabilities

(a)

and

colored

CCRs

(b)

unique

color

filters

that

can

be

built.

The

narrower

the

Transfer

Function

Ψ(λ),

the

larger

the

number

of

unique

colors

that

can

be

created.

The

manufacturing

costs,

however,

are

increasing

as

well.

The

scalability

issue

is

addressed

by

all

other

label

relaxation

techniques.

Most

notably,

the

time

constrained

relaxation,

which

is

very

similar

to

the

colorconstrained

relaxation,

addresses

the

scale

issue,

at

a

higher

deployment

cost.

Criteria

Color

Connectivity

Time

Space

Duration

NTb

NTd

Overhead

εd

εd

+Nεb

Nεd

εd

Scale

|C|

|N|

|N|

|N|

Accuracy

High

Low

High

Medium

Table

Comparison

of

label

relaxation

techniques

System

Implementation

The

StarDust

localization

framework,

depicted

in

Figure

is

flexible

in

that

it

enables

the

development

of

new

localization

systems,

based

on

the

four

proposed

label

relaxation

schemes,

or

the

inclusion

of

other,

yet

to

be

invented,

schemes.

For

our

performance

evaluation

we

implemented

a

version

of

the

StarDust

framework,

namely

the

one

proposed

in

Section

where

the

constraints

are

based

on

color

and

connectivity.

The

Central

device

of

the

StarDust

system

consists

of

the

following:

the

Light

Emitter

we

used

a

common-off-theshelf

flash

light

(QBeam,

million

candlepower);

the

image

acquisition

was

done

with

a

megapixel

digital

camera

(Sony

which

provided

the

input

to

the

Image

Processing

algorithm,

implemented

in

Matlab.

For

sensor

nodes

we

built

a

custom

sensor

node,

called

SensorBall,

with

self-righting

capabilities,

shown

in

Figure

The

self-righting

capabilities

are

necessary

in

order

to

orient

the

CCR

predominantly

upwards.

The

CCRs

that

we

used

were

inexpensive,

plastic

molded,

night

time

warning

signs

commonly

available

on

bicycles,

as

shown

in

Figure

We

remark

here

the

low

quality

of

the

CCRs

we

used.

The

reflectivity

of

each

CCR

(there

are

tens

molded

in

the

plastic

container)

is

extremely

low,

and

each

CCR

is

not

built

with

mirrors.

A

reflective

effect

is

achieved

by

employing

finely

polished

plastic

surfaces.

We

had

colors

available,

in

addition

to

the

standard

CCR,

which

reflects

all

the

incoming

light

(white

CCR).

For

a

slightly

higher

price

(ours

were

better

quality

CCRs

can

be

employed.

Figure

The

field

in

the

dark

Figure

The

illuminated

field

Figure

The

difference:

Figure

Higher

quality

(better

mirrors)

would

translate

in

more

accurate

image

processing

(better

sensor

node

detection)

and

smaller

form

factor

for

the

optical

component

(an

array

of

CCRs

with

a

smaller

area

can

be

used).

The

sensor

node

platform

we

used

was

the

micaZ

mote.

The

code

that

runs

on

each

node

is

a

simple

application

which

broadcasts

beacons,

and

maintains

a

neighbor

table

containing

the

percentage

of

successfully

received

beacons,

for

each

neighbor.

On

demand,

the

neighbor

table

is

reported

to

a

base

station,

where

the

node

ID

mapping

is

performed.

System

Evaluation

In

this

section

we

present

the

performance

evaluation

of

a

system

implementation

of

the

StarDust

localization

framework.

The

three

major

research

questions

that

our

evaluation

tries

to

answer

are:

the

feasibility

of

the

proposed

framework

(can

sensor

nodes

be

optically

detected

at

large

distances),

the

localization

accuracy

of

one

actual

implementation

of

the

StarDust

framework,

and

whether

or

not

atmospheric

conditions

can

affect

the

recognition

of

sensor

nodes

in

an

image.

The

first

two

questions

are

investigated

by

evaluating

the

two

main

components

of

the

StarDust

framework:

the

Image

Processing

and

the

Node

ID

Matching.

These

components

have

been

evaluated

separately

mainly

because

of

lack

of

adequate

facilities.

We

wanted

to

evaluate

the

performance

of

the

Image

Processing

Algorithm

in

a

long

range,

realistic,

experimental

set-up,

while

the

Node

ID

Matching

required

a

relatively

large

area,

available

for

long

periods

of

time

(for

connectivity

data

gathering).

The

third

research

question

is

investigated

through

a

computer

modeling

of

atmospheric

phenomena.

For

the

evaluation

of

the

Image

Processing

module,

we

performed

experiments

in

a

football

stadium

where

we

deploy

sensor

nodes

in

a

grid.

The

distance

between

the

Central

device

and

the

sensor

nodes

is

approximately

ft.

The

metrics

of

interest

are

the

number

of

false

positives

and

false

negatives

in

the

Image

Processing

Algorithm.

For

the

evaluation

of

the

Node

ID

Mapping

component,

we

deploy

sensor

nodes

in

an

flat

area

of

a

stadium.

In

order

to

investigate

the

influence

the

radio

connectivity

has

on

localization

accuracy,

we

vary

the

height

above

ground

of

the

deployed

sensor

nodes.

Two

set-ups

are

used:

one

in

which

the

sensor

nodes

are

on

the

ground,

and

the

second

one,

in

which

the

sensor

nodes

are

raised

inches

above

ground.

From

here

on,

we

will

refer

to

these

two

experimental

set-ups

as

the

low

connectivity

and

the

high

connectivity

networks,

respectively

because

when

nodes

are

on

the

ground

the

communication

range

is

low

resulting

in

less

neighbors

than

when

the

nodes

are

elevated

and

have

a

greater

communication

range.

The

metrics

of

interest

are:

the

localization

error

(defined

as

the

distance

between

the

computed

location

and

the

true

location

known

from

the

manual

placement),

the

percentage

of

nodes

correctly

localized,

the

convergence

of

the

label

relaxation

algorithm,

the

time

to

localize

and

the

robustness

of

the

node

ID

mapping

to

errors

in

the

Image

Processing

module.

The

parameters

that

we

vary

experimentally

are:

the

angle

under

which

images

are

taken,

the

focus

of

the

camera,

and

the

degree

of

connectivity.

The

parameters

that

we

vary

in

simulations

(subsequent

to

image

acquisition

and

connectivity

collection)

the

number

of

colors,

the

number

of

anchors,

the

number

of

false

positives

or

negatives

as

input

to

the

Node

ID

Matching

component,

the

distance

between

the

imaging

device

and

sensor

network

(i.e.,

range),

atmospheric

conditions

(light

attenuation

coefficient)

and

CCR

reflectance

(indicative

of

its

quality).

Image

Processing

For

the

IPA

evaluation,

we

deploy

sensor

nodes

in

a

grid.

We

take

sets

of

pictures

using

different

orientations

of

the

camera

and

different

zooming

factors.

All

pictures

were

taken

from

the

same

location.

Each

set

is

composed

of

a

picture

taken

in

the

dark

and

of

a

picture

taken

with

a

light

beam

pointed

at

the

nodes.

We

process

the

pictures

offline

using

a

Matlab

implementation

of

IPA.

Since

we

are

interested

in

the

feasibility

of

identifying

colored

sensor

nodes

at

large

distance,

the

end

result

of

our

IPA

is

the

location

of

sensor

nodes

(position

in

the

image).

The

transformation

to

coordinates

can

be

done

through

standard

computer

graphics

techniques

One

set

of

pictures

obtained

as

part

of

our

experiment

is

shown

in

Figures

and

The

execution

of

our

IPA

algorithm

results

in

Figure

which

filters

out

the

background,

and

Figure

which

shows

the

output

of

the

edge

detection

step

of

IPA.

The

experimental

results

are

depicted

in

Figure

For

each

set

of

pictures

the

graph

shows

the

number

of

false

positives

(the

IPA

determines

that

there

is

a

node

Figure

Retroreflectors

detected

in

Figure

Experiment

Number

Count

False

Positives

False

Negatives

Figure

False

Positives

and

Negatives

for

the

nodes

while

there

is

none),

and

the

number

of

false

negatives

(the

IPA

determines

that

there

is

no

node

while

there

is

one).

In

about

of

the

cases,

we

obtained

perfect

results,

i.e.,

no

false

positives

and

no

false

negatives.

In

the

remaining

cases,

we

obtained

a

number

of

false

positives

of

at

most

one,

and

a

number

of

false

negatives

of

at

most

two.

We

exclude

two

pairs

of

pictures

from

Figure

In

the

first

excluded

pair,

we

obtain

false

positives

and

in

the

second

pair

false

positives

and

false

negatives.

By

carefully

examining

the

pictures,

we

realized

that

the

first

pair

was

taken

out

of

focus

and

that

a

car

temporarily

appeared

in

one

of

the

pictures

of

the

second

pair.

The

anomaly

in

the

second

set

was

due

to

the

fact

that

we

waited

too

long

to

take

the

second

picture.

If

the

pictures

had

been

taken

a

few

milliseconds

apart,

the

car

would

have

been

represented

on

either

both

or

of

the

pictures

and

the

IPA

would

have

filtered

it

out.

Node

ID

Matching

We

evaluate

the

Node

ID

Matching

component

of

our

system

by

collecting

empirical

data

(connectivity

information)

from

the

outdoor

deployment

of

nodes

in

the

area.

We

collect

sets

of

data

for

the

high

connectivity

and

low

connectivity

network

deployments.

Off-line

we

investigate

the

influence

of

coloring

on

the

metrics

of

interest,

by

randomly

assigning

colors

to

the

sensor

nodes.

For

one

experimental

data

set

we

generate

random

assignments

of

colors

to

sensor

nodes.

It

is

important

to

observe

that,

for

the

evaluation

of

the

Node

ID

Matching

algorithm

(color

and

connectivity

constrained),

we

simulate

the

color

assignment

to

sensor

nodes.

As

mentioned

in

Section

the

size

of

the

coloring

space

available

to

us

was

colors).

Through

simulations

of

color

assignment

(not

connectivity)

we

are

able

to

investigate

the

influence

that

the

size

of

the

coloring

space

has

on

the

accuracy

of

localization.

The

value

of

the

Distance

[feet]

Count

Connected

Not

Connected

Figure

The

number

of

existing

and

missing

radio

connections

in

the

sparse

connectivity

experiment

Distance

[feet]

Count

Connected

Not

Connected

Figure

The

number

of

existing

and

missing

radio

connections

in

the

high

connectivity

experiment

eter

ε

used

in

Algorithm

was

The

results

presented

here

represent

averages

over

the

randomly

generated

colorings

and

over

all

experimental

data

sets.

We

first

investigate

the

accuracy

of

our

proposed

Radio

Model,

and

subsequently

use

the

derived

values

for

the

radio

range

in

the

evaluation

of

the

Node

ID

matching

component.

Radio

Model

From

experiments,

we

obtain

the

average

number

of

observed

beacons

(k,

defined

in

Section

for

the

low

connectivity

network

of

beacons

and

for

the

high

connectivity

network

of

beacons.

From

our

Radio

Model

(Equation

we

obtain

a

radio

range

R

ft

for

the

low

connectivity

network

and

R

ft

for

the

high

connectivity

network.

To

estimate

the

accuracy

of

our

simple

model,

we

plot

the

number

of

radio

links

that

exist

in

the

networks,

and

the

number

of

links

that

are

missing,

as

functions

of

the

distance

between

nodes.

The

results

are

shown

in

Figures

and

We

define

the

average

radio

range

R

to

be

the

distance

over

which

less

than

of

potential

radio

links,

are

missing.

As

shown

in

Figure

the

radio

range

is

between

ft

and

ft.

For

the

higher

connectivity

network,

the

radio

range

was

between

ft

and

ft.

We

choose

two

conservative

estimates

of

the

radio

range:

ft

for

the

low

connectivity

case

and

ft

for

the

high

connectivity

case,

which

are

in

good

agreement

with

the

values

predicted

by

our

Radio

Model.

Localization

Error

vs.

Coloring

Space

Size

In

this

experiment

we

investigate

the

effect

of

the

number

of

colors

on

the

localization

accuracy.

For

this,

we

randomly

assign

colors

from

a

pool

of

a

given

size,

to

the

sensor

nodes.

Number

of

Colors

LocalizationError[feet]

Figure

Localization

error

Number

of

Colors

Figure

Percentage

of

nodes

correctly

localized

We

then

execute

the

localization

algorithm,

which

uses

the

empirical

data.

The

algorithm

is

run

for

three

different

radio

ranges:

and

ft,

to

investigate

its

influence

on

the

localization

error.

The

results

are

depicted

in

Figure

(localization

error)

and

Figure

(percentage

of

nodes

correctly

localized).

As

shown,

for

an

estimate

of

ft

for

the

radio

range

(as

predicted

by

our

Radio

Model)

we

obtain

the

smallest

localization

errors,

as

small

as

ft,

when

enough

colors

are

used.

Both

Figures

and

confirm

our

intuition

that

a

larger

number

of

colors

available

significantly

decrease

the

error

in

localization.

The

well

known

fact

that

relaxation

algorithms

do

not

always

converge,

was

observed

during

our

experiments.

The

percentage

of

successful

runs

(when

the

algorithm

converged)

is

depicted

in

Figure

As

shown,

in

several

situations,

the

algorithm

failed

to

converge

(the

algorithm

execution

was

stopped

after

iterations

per

node).

If

the

algorithm

does

not

converge

in

a

predetermined

number

of

steps,

it

will

terminate

and

the

label

with

the

highest

probability

will

provide

the

identity

of

the

node.

It

is

very

probable

that

the

chosen

label

is

incorrect,

since

the

probabilities

of

some

of

labels

are

constantly

changing

(with

each

iteration).The

convergence

of

relaxation

based

algorithms

is

a

well

known

issue.

Localization

Error

vs.

Color

Uniqueness

As

mentioned

in

the

Section

a

unique

color

gives

a

sensor

node

the

statute

of

an

anchor.

A

sensor

node

that

is

an

anchor

can

unequivocally

be

identified

through

the

Image

Processing

module.

In

this

section

we

investigate

the

effect

unique

colors

have

on

the

localization

accuracy.

Specifically,

we

want

to

experimentally

verify

our

intuition

that

assigning

more

nodes

to

a

color

can

benefit

the

localization

accuracy,

by

enforcing

more

constraints,

as

opposed

to

uniquely

assigning

a

color

to

a

single

node.

Number

of

Colors

Figure

Convergence

error

Number

of

Colors

LocalizationError[feet]

anchors

anchors

anchors

anchors

anchors

Figure

Localization

error

vs.

number

of

colors

For

this,

we

fix

the

number

of

available

colors

to

either

or

and

vary

the

number

of

nodes

that

are

given

unique

colors,

from

up

to

the

maximum

number

of

colors

or

Naturally,

if

we

have

a

maximum

number

of

colors

of

we

can

assign

at

most

anchors.

The

experimental

results

are

depicted

in

Figure

(localization

error)

and

Figure

(percentage

of

sensor

node

correctly

localized).

As

expected,

the

localization

accuracy

increases

with

the

increase

in

the

number

of

colors

available

(larger

coloring

space).

Also,

for

a

given

size

of

the

coloring

space

(e.g.,

colors

available),

if

more

colors

are

uniquely

assigned

to

sensor

nodes

then

the

localization

accuracy

decreases.

It

is

interesting

to

observe

that

by

assigning

colors

uniquely

to

nodes,

the

benefit

of

having

additional

colors

is

diminished.

Specifically,

if

colors

are

available

and

all

are

assigned

uniquely,

the

system

would

be

less

accurately

localized

(error

ft),

when

compared

to

the

case

of

colors

and

no

unique

assignments

of

colors

ft

localization

error).

The

same

trend,

of

a

less

accurate

localization

can

be

observed

in

Figure

which

shows

the

percentage

of

nodes

correctly

localized

(i.e.,

ft

localization

error).

As

shown,

if

we

increase

the

number

of

colors

that

are

uniquely

assigned,

the

percentage

of

nodes

correctly

localized

decreases.

Localization

Error

vs.

Connectivity

We

collected

empirical

data

for

two

network

deployments

with

different

degrees

of

connectivity

(high

and

low)

in

order

to

assess

the

influence

of

connectivity

on

location

accuracy.

The

results

obtained

from

running

our

localization

algorithm

are

depicted

in

Figure

and

Figure

We

varied

the

number

of

colors

available

and

assigned

no

anchors

(i.e.,

no

unique

assignments

of

colors).

In

both

scenarios,

as

expected,

localization

error

decrease

with

an

increase

in

the

number

of

colors.

It

is

interesting

to

observe,

however,

that

the

low

connectivity

scenario

Number

of

Colors

anchors

anchors

anchors

anchors

anchors

Figure

Percentage

of

nodes

correctly

localized

vs.

number

of

colors

Number

of

Colors

LocalizationError[feet]

Low

Connectivity

High

Connectivity

Figure

Localization

error

vs.

number

of

colors

proves

the

localization

accuracy

quicker,

from

the

additional

number

of

colors

available.

When

the

number

of

colors

becomes

relatively

large

(twelve

for

our

sensor

node

network),

both

scenarios

(low

and

high

connectivity)

have

comparable

localization

errors,

of

less

that

ft.

The

same

trend

of

more

accurate

location

information

is

evidenced

by

Figure

which

shows

that

the

percentage

of

nodes

that

are

localized

correctly

grows

quicker

for

the

low

connectivity

deployment.

Localization

Error

vs.

Image

Processing

Errors

So

far

we

investigated

the

sources

for

error

in

localization

that

are

intrinsic

to

the

Node

ID

Matching

component.

As

previously

presented,

luminous

objects

can

be

mistakenly

detected

to

be

sensor

nodes

during

the

location

detection

phase

of

the

Image

Processing

module.

These

false

positives

can

be

eliminated

by

the

color

recognition

procedure

of

the

Image

Processing

module.

More

problematic

are

false

negatives

(when

a

sensor

node

does

not

reflect

back

enough

light

to

be

detected).

They

need

to

be

handled

by

the

localization

algorithm.

In

this

case,

the

localization

algorithm

is

presented

with

two

sets

of

nodes

of

different

sizes,

that

need

to

be

matched:

one

coming

from

the

Image

Processing

(which

misses

some

nodes)

and

one

coming

from

the

network,

with

the

connectivity

information

(here

we

assume

a

fully

connected

network,

so

that

all

sensor

nodes

report

their

connectivity

information).

In

this

experiment

we

investigate

how

Image

Processing

errors

(false

negatives)

influence

the

localization

accuracy.

For

this

evaluation,

we

ran

our

localization

algorithm

with

empirical

data,

but

dropped

a

percentage

of

nodes

from

the

list

of

nodes

detected

by

the

Image

Processing

algorithm

(we

artificially

introduced

false

negatives

in

the

Image

Number

of

Colors

Low

Connectivity

High

Connectivity

Figure

Percentage

of

nodes

correctly

localized

False

Negatives

LocalizationError[feet]

colors

colors

colors

Figure

Impact

of

false

negatives

on

the

localization

error

ing).

The

effect

of

false

negatives

on

localization

accuracy

is

depicted

in

Figure

As

seen

in

the

figure

if

the

number

of

false

negatives

is

the

error

in

position

estimation

doubles

when

colors

are

available.

It

is

interesting

to

observe

that

the

scenario

when

more

colors

are

available

(e.g.,

colors)

is

being

affected

more

drastically

than

the

scenario

with

less

colors

(e.g.,

colors).

The

benefit

of

having

more

colors

available

is

still

being

maintained,

at

least

for

the

range

of

colors

we

investigated

through

colors).

Localization

Time

In

this

section

we

look

more

closely

at

the

duration

for

each

of

the

four

proposed

relaxation

techniques

and

two

combinations

of

them:

color-connectivity

and

color-time.

We

assume

that

unique

color

filters

can

be

manufactured,

that

the

sensor

network

is

deployed

from

ft

(necessary

for

the

time-constrained

relaxation)

and

that

the

time

required

for

reporting

connectivity

grows

linearly,

with

an

initial

reporting

period

of

as

used

in

a

real

world

tracking

application

The

localization

duration

results,

as

presented

in

Table

are

depicted

in

Figure

As

shown,

for

all

practical

purposes

the

time

required

by

the

space

constrained

relaxation

techniques

is

The

same

applies

to

the

color

constrained

relaxation,

for

which

the

localization

time

is

(if

the

number

of

colors

is

sufficient).

Considering

our

assumptions,

only

for

a

network

of

size

the

color

constrained

relaxation

works.

The

localization

duration

for

all

other

network

sizes

and

is

infinite

(i.e.,

unique

color

assignments

to

sensor

nodes

can

not

be

made,

since

only

colors

are

unique),

when

only

color

constrained

relaxation

is

used.

Both

the

connectivity

constrained

and

time

constrained

techniques

increase

linearly

with

the

network

size

(for

the

time

constrained,

the

Central

device

deploys

sensor

nodes

one

by

one,

recording

an

image

after

the

time

a

sensor

node

is

expected

to

reach

the

Color

Connectivity

Time

Space

ColorConenctivity

Color-Time

Localization

technique

Localizationtime[sec]

nodes

nodes

nodes

nodes

Figure

Localization

time

for

different

label

relaxation

schemes

r

[feet]

C

r

Figure

Apparent

contrast

in

a

clear

atmosphere

r

[feet]

C

r

Figure

Apparent

contrast

in

a

hazing

atmosphere

ground).

It

is

interesting

to

notice

in

Figure

the

improvement

in

the

localization

time

obtained

by

simply

combining

the

color

and

the

connectivity

constrained

techniques.

The

localization

duration

in

this

case

is

identical

with

the

connectivity

constrained

technique.

The

combination

of

color

and

time

constrained

relaxations

is

even

more

interesting.

For

a

reasonable

localization

duration

of

a

perfect

(i.e.,

ft

localization

error)

localization

system

can

be

built.

In

this

scenario,

the

set

of

sensor

nodes

is

split

in

batches,

with

each

batch

having

a

set

of

unique

colors.

It

would

be

very

interesting

to

consider

other

scenarios,

where

the

strength

of

the

space

constrained

relaxation

for

any

sensor

network

size)

is

used

for

improving

the

other

proposed

relaxation

techniques.

We

leave

the

investigation

and

rigorous

classification

of

such

technique

combination

for

future

work.

System

Range

In

this

section

we

evaluate

the

feasibility

of

the

StarDust

localization

framework

when

considering

the

realities

of

light

propagation

through

the

atmosphere.

The

main

factor

that

determines

the

range

of

our

system

is

light

scattering,

which

redirects

the

luminance

of

the

source

into

the

medium

(in

essence

equally

affecting

the

luminosity

of

the

target

and

of

the

background).

Scattering

limits

the

visibility

range

by

reducing

the

apparent

contrast

between

the

target

and

its

background

(approaches

zero,

as

the

distance

increases).

The

apparent

contrast

Cr

is

quantitatively

expressed

by

the

formula:

Cr

(Nt

r

−Nb

r

)/Nb

r

where

Nt

r

and

Nb

r

are

the

apparent

target

radiance

and

apparent

background

radiance

at

distance

r

from

the

light

source,

respectively.

The

apparent

radiance

Nt

r

of

a

target

at

a

distance

r

from

the

light

source,

is

given

by:

Nt

r

where

I

is

the

intensity

of

the

light

source,

ρt

is

the

target

reflectance,

σ

is

the

spectral

attenuation

coefficient

and

for

a

clear

and

a

hazy

atmosphere,

respectively)

and

is

the

radiance

of

the

atmospheric

backscatter,

and

it

can

be

expressed

as

follows:

2π

e−x

dx

where

G

is

a

backscatter

gain.

The

apparent

background

radiance

Nb

r

is

given

by

formulas

similar

with

Equations

and

where

only

the

target

reflectance

ρt

is

substituted

with

the

background

reflectance

ρb.

It

is

important

to

remark

that

when

Cr

reaches

its

lower

limit,

no

increase

in

the

source

luminance

or

receiver

sensitivity

will

increase

the

range

of

the

system.

From

Equations

and

it

can

be

observed

that

the

parameter

which

can

be

controlled

and

can

influence

the

range

of

the

system

is

ρt,

the

target

reflectance.

Figures

and

depict

the

apparent

contrast

Cr

as

a

function

of

the

distance

r

for

a

clear

and

for

a

hazy

atmosphere,

respectively.

The

apparent

contrast

is

investigated

for

reflectance

coefficients

ρt

ranging

from

to

(perfect

reflector).

For

a

contrast

C

of

at

least

as

it

can

be

seen

in

Figure

a

range

of

approximately

ft

can

be

achieved

if

the

atmosphere

is

clear.

The

performance

dramatically

deteriorates,

when

the

atmospheric

conditions

are

problematic.

As

shown

in

Figure

a

range

of

up

to

ft

is

achievable,

when

using

highly

reflective

CCR

components.

While

our

light

source

million

candlepower)

was

sufficient

for

a

range

of

a

few

hundred

feet,

we

remark

that

there

exist

commercially

available

light

sources

million

candlepower)

or

military

million

candlepower

powerful

enough

for

ranges

of

a

few

thousand

feet.

StarDust

System

Optimizations

In

this

section

we

describe

extensions

of

the

proposed

architecture

that

can

constitute

future

research

directions.

Chained

Constraint

Primitives

In

this

paper

we

proposed

four

primitives

for

constraintbased

relaxation

algorithms:

color,

connectivity,

time

and

space.

To

demonstrate

the

power

that

can

be

obtained

by

combining

them,

we

proposed

and

evaluated

one

combination

of

such

primitives:

color

and

connectivity.

An

interesting

research

direction

to

pursue

could

be

to

chain

more

than

two

of

these

primitives.

An

example

of

such

chain

is:

color,

temporal,

spatial

and

connectivity.

Other

research

directions

could

be

to

use

voting

scheme

for

deciding

which

primitive

to

use

or

assign

different

weights

to

different

relaxation

algorithms.

Location

Learning

If

after

several

iterations

of

the

algorithm,

of

the

label

probabilities

for

a

node

ni

converges

to

a

higher

value,

the

confidence

in

our

labeling

of

that

node

is

relatively

low.

It

would

be

interesting

to

associate

with

a

node,

more

than

one

label

(implicitly

more

than

one

location)

and

defer

the

label

assignment

decision

until

events

are

detected

in

the

network

(if

the

network

was

deployed

for

target

tracking).

Localization

in

Rugged

Environments

The

initial

driving

force

for

the

StarDust

localization

framework

was

to

address

the

sensor

node

localization

in

extremely

rugged

environments.

Canopies,

dense

vegetation,

extremely

obstructing

environments

pose

significant

challenges

for

sensor

nodes

localization.

The

hope,

and

our

original

idea,

was

to

consider

the

time

period

between

the

aerial

deployment

and

the

time

when

the

sensor

node

disappears

under

the

canopy.

By

recording

the

last

visible

position

of

a

sensor

node

(as

seen

from

the

aircraft)

a

reasonable

estimate

of

the

sensor

node

location

can

be

obtained.

This

would

require

that

sensor

nodes

posses

self-righting

capabilities,

while

in

mid-air.

Nevertheless,

we

remark

on

the

suitability

of

our

localization

framework

for

rugged,

non-line-of-sight

environments.

Conclusions

StarDust

solves

the

localization

problem

for

aerial

deployments

where

passiveness,

low

cost,

small

form

factor

and

rapid

localization

are

required.

Results

show

that

accuracy

can

be

within

ft

and

localization

time

within

milliseconds.

StarDust

also

shows

robustness

with

respect

to

errors.

We

predict

the

influence

the

atmospheric

conditions

can

have

on

the

range

of

a

system

based

on

the

StarDust

framework,

and

show

that

hazy

environments

or

daylight

can

pose

significant

challenges.

Most

importantly,

the

properties

of

StarDust

support

the

potential

for

even

more

accurate

localization

solutions

as

well

as

solutions

for

rugged,

non-line-of-sight

environments.

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