Introduction to Sensor Networks

(1)

Introduction to Sensor Networks

Maria Potop-Butucaru, Franck Petit, Sébastien Tixeuil Université Pierre & Marie Curie - Paris 6, France

[email protected]

1

Outline

•

^Motivation

•

Architecture

•

^Overview

2

Motivation

3

Sensor Networks

•

Definition: Network of wireless nodes dedicated to a particular application

•

Purpose: Acquire sensed data and transmit to a processing station

•

Application domains: Military, Civilian, Environment, Wildlife, etc.

4

Applications

5 COMMON-Sense Net (CSN)

Tumkur, Karnataka http://commonsense.epfl.ch/

6-1

COMMON-Sense Net (CSN)

6-2

COMMON-Sense Net (CSN)

6-3

COMMON-Sense Net (CSN)

6-4

(2)

COMMON-Sense Net (CSN)

Tumkur, Karnataka

http://commonsense.epfl.ch/

6-5

COMMON-Sense Net (CSN)

http://commonsense.epfl.ch/

7 Habitat Monitoring (Berkeley)

8-1

Habitat Monitoring (Berkeley)

8-2

Habitat Monitoring

9-1

Habitat Monitoring

5 Feature Story: Motes in Controlled Environment Agriculture

 MEP410 with the battery box mounted on lexan plates Sandia used 27 of Crossbow’s environmental monitoring Motes, called the MEP410, to assist with monitoring air temperature, relative humidity, photosynthetic active radiation, and total solar radiation.

The MEP410 Motes and its battery box were mounted to lexan plates. The mounted sensors were suspended from the overhead frame of the greenhouse using nylon rope and slip bead stops for easy height adjustment. The sensors were hung vertically in groups of three with the low, middle, and upper Motes adjusted to be at 0.25 m, 1.15 m, and 2.1 m, from the ceiling, respectively. The 3-Mote arrays were hung at three different locations along the aisles.

The sensor network used a Stargate as an embedded server/network appliance for logging the data from the MEP410 Motes. The Stargate also had a mobile phone modem allowing researchers at Sandia’s California site to remotely download the data for post-processing.

Data from all of the Mote sensors was sampled, packaged, time-stamped and wirelessly sent to the Stargate unit, by each Mote in the network every 15 seconds. The Sandia group chose to use the 15 second sampling increment for these initial project investigations to provide sub-minute time resolution. For the configuration used in this project each node was able to send data directly to the Star- gate without the need for multi-hop routing through other nodes.

The data collected by the Stargate unit was remotely linked to Sandia via a secure file copy protocol in comma delimited format. The received data was then processed and configured into time series data files for the following environmental parameters at each node in the network: battery voltage, internal and external humidity,

internal and external temperature. All of the data processing was done in Matlab. Three main tasks were necessary for the initial analysis and visualization: 1) read in the data files, 2) clean the data, interpolate, and save in a Matlab standard format, and 3) post-process and visualize.

System Benefits

The initial conclusions are that significant water savings can be achieved with properly implemented and adjusted hydroponic forage production. Water use can potentially be reduced by a factor of 50 percent or more compared to open air farming.

Furthermore, the study demonstrated that wireless sensor networks have considerable potential for improving CEA systems by providing higher resolution monitoring.

Wireless sensor networks enable expandable and denser distributed sensing. This leads to more precise and real- time monitoring, adaptive control, and optimization of complex interactions among key environmental and crop systems.

The long term vision is to couple wireless SDACs with physics/chemistry based modeling and simulation, information fusion, embedded reasoning, systems control and automation, and decision support. These advances will make CEA systems economical and productive.

How to Apply

Customers interested in doing environment monitoring and want more information on the MEP Mote system should visit http://www.xbow.com/Products/products- details.aspx?sid=136.

 Temperature [°C] contours on planar cuts at heights above floor of Z=1.15 m, and Z=1.90 m at 50 minute increments.

9:21am 10:11am

11:01am 11:51am

external humidity sensor temperature filled contours external humidity sensor temperature filled contours

9-2

Environment Monitoring

Environmental Monitoring Application Note

Figure 1. Crossbow’s Wireless Environmental Monitoring System Overview The software components that come together to form this system are listed below and shown in Figure 2. All of these software components are available from Crossbow at no charge for use with our hardware.

MICA2 / MICA2DOT -based Enviromental Sensors:

! TinyOS operating system*

! XMesh (Surge Time Sync)* component which handles all networking and radio communications.

! XSensor sensor application* which is customized for sampling environmental sensors available from Crossbow (see Sensor section of Appnote)

Stargate Base Station and Sensor Data Server / Database :

! Basestation MICA2 mote running XMesh (Surge Time Sync) * for interfacing to Sensor Network

! XListen* software which parses mote data packets and stores into Postgres database.

! Postgres* database for local storage of data

! Linux* operating system for Stargate PC:

! MOTE-VIEW** Microsoft.net data visualization program for Windows based machines

Notes:

*Open source code in www.Sourceforge.net

** Free runtime executable from Crossbow

Page 2

10-1

Environment Monitoring

Environmental Monitoring Application Note

Figure 2. Software Components and Architecture of Mesh Network

Sensors

Crossbow’s MICA2/MICA2DOT platforms and wireless mesh network software are easily integrated with a wide variety of sensors. Presently, Crossbow offers the following low-power sensor combinations for environmental monitoring:

Page 3

10-2

Zebranet (Princeton)

S

Base station (car or plane) Sweetwaters Reserve, Kenya

11-1

(3)

Zebranet (Princeton)

S

Tracking node CPU, FLASH, radio, GPS

Base station (car or plane) Sweetwaters Reserve, Kenya

11-2

Zebranet

Attribute Zebranet Sensors Mobility High Low/static

Range Miles Meters

Frequency Constant Sporadic Power

Hundreds of mW Tens of mW

12

Zebranet

**!"#$%&"'()'%'*+(%,-(&".'()'"/+**

! )'%'*+

" 0%,*%$12(34456(7('"+'(89::%$+(-"/:91"-(9,(;"#$%+(<,(=",1%>((

?<$+'(-%'%($"8"<@"-6(ABACB3445

! &".'()'"/+

" D"E<,"(89::%$(-"+<F,G(+H<'8I('9(:9H"$J","$F1(KL)2(M"$F"(

NM/%:%(+9E'H%$"(*/-%'"(89-"(<,'9(E<,%:(89::%$+(

Sweetwaters Reserve, Kenya

13-1

Zebranet

**!"#$%&"'()'%'*+(%,-(&".'()'"/+**

! )'%'*+

" 0%,*%$12(34456(7('"+'(89::%$+(-"/:91"-(9,(;"#$%+(<,(=",1%>((

?<$+'(-%'%($"8"<@"-6(ABACB3445

! &".'()'"/+

" D"E<,"(89::%$(-"+<F,G(+H<'8I('9(:9H"$J","$F1(KL)2(M"$F"(

NM/%:%(+9E'H%$"(*/-%'"(89-"(<,'9(E<,%:(89::%$+(

**!"#$%&"'()'%'*+(%,-(&".'()'"/+**

! )'%'*+

" 0%,*%$12(34456(7('"+'(89::%$+(-"/:91"-(9,(;"#$%+(<,(=",1%>((

?<$+'(-%'%($"8"<@"-6(ABACB3445

! &".'()'"/+

" D"E<,"(89::%$(-"+<F,G(+H<'8I('9(:9H"$J","$F1(KL)2(M"$F"(

NM/%:%(+9E'H%$"(*/-%'"(89-"(<,'9(E<,%:(89::%$+(

Sweetwaters Reserve, Kenya

13-2

Motivation

•

Acquire data and feed a processing station

•

Application domains:

•

Military: risky area monitoring, intrusion detection, etc.

•

Civilian: fire detection, chemical facilities monitoring, etc.

14

Sensor vs. ad hoc

Sensors ad hoc Specific Generic Collaboration Selfishness

Many-to-one Any-to-any

No ID ID

Energy Throughput

15

Issues

•

ad hoc deployment

•

Unattended operation

•

^Untethered

•

Dynamic changes

16-1

Issues

•

ad hoc deployment

•

^Untethered

•

Dynamic changes

No infrastructure

16-2

Issues

•

ad hoc deployment

•

^Untethered

•

Dynamic changes

No human intervention

16-3

(4)

Issues

•

ad hoc deployment

•

^Untethered

•

Dynamic changes

permanent No power supply

16-4

Issues

•

ad hoc deployment

•

^Untethered

•

Dynamic changes

Changing environment

16-5

Architecture

17

Sensor Node Architecture

Battery

DC-DC

Sensor

ADC MCU

Memory

Radio

18

Available Devices

•

MicaZ (Crossbow)

•

2.94 GHz IEEE 802.15.4 Zigbee radio

•

128 KB program memory

•

512 KB data memory

•

^{8 mA draw}

19

Available Devices

•

Tmote Sky/invent (Moteiv)

•

2.94 GHz IEEE 802.15.4 Zigbee radio

•

8MHz processor

•

^{10 KB RAM}

•

48 KB Flash

20

Available Devices

•

Stargate (Crossbow)

•

Wired Ethernet

•

Wifi/Cellular via PCMCIA

•

INTEL PXA 255

•

Linux Kernel

Environmental Monitoring Application Note Data Interval

(minutes) Average MICA2 or MICA2DOT Current (µA)

1 677

3 315

6 196

The XMesh network has been extensively tested both at indoor and outdoor locations. In a typical indoor test, nodes were placed at every 300 sq ft. to cover a 10,000 sq ft facility. To simulate larger distance between nodes, the radio transmit power was turned down to -6dBm. In outdoor tests nodes were spread across several acres of rugged terrain with an average density of 1 mote per 10,000 sq ft and at full radio power. Statistical analysis across many deployments shows on average greater than 90% of all traffic generated at any node will be collected at the base station without the use of end-end acknowledgements.

Stargate Base Station

Figure 4. Stargate gateway as a base station The Crossbow Stargate gateway and microserver is an embedded Linux computer designed to be the primary access point for wireless sensor networks. The Stargate’s small form factor, reliability, and optional communication interfaces makes it ideal for remote, environmental monitoring. A base station mote (MICA2) is connected to the 51-pin connector on the Stargate.

A resident program, XListen, takes an input stream of wireless sensor data from the base station mote and stores it in a local Postgres database.

The Crossbow Stagate can be connected to a wide-area or back-haul network in one of the following ways:

! Wired Ethernet connection

! WiFi, using a Compact Flash card (Netgear MA701, AmbicomWL1100C-CF, etc.)

! Long Range WiFi using PCMCIA card (ZComax or SMC Wireless SMC2532W-B).

! Cell phone modem card (Sierra Wireless Aircard 555D) for remote cellular access.

Page 7

21

Available Devices

•

GreenNet (ST Micro)

•

802.15.4 radio

•

Solar energy harvesting

22

Sensors

•

Exterioceptors: information about the surroundings

•

Proprioceptors: information about the internal workings

23

(5)

Sensors

Measurand Transduction Physical Pressure

Piezoresistive, capacitive

Temperature

Thermistor, thermomechanical,

thermocouple

Humidity

Resistive, capacitive

Flow

Pressure change, thermistor

24

Sensors

Measurand Transduction Motion Position

E-mag, GPS, contact

Velocity

Doppler, Hall effect, optoelectronic

Angular velocity Optical encoder

Acceleration

Piezoresistive, piezoelectric, optical fiber

25

Sensors

Measurand Transduction Contact Strain

Piezoresistive

Force

Piezoelectric, piezoresistive

Torque

Piezoresistive, optoelectronic

Vibration

Piezoresistive, piezoelectric, optical fiber, sound,

ultrasound

26

Sensors

Measurand Transduction Presence Tactile

Contact switch, capacitive

Proximity

Hall effect, capacitive, magnetic, seismic, acoustic,

RF

Distance

E-mag (sonar, radar, lidar), magnetic, tunelling

Motion

E-mag, IR, acoustic, seismic

27

Sensors

Measurand Transduction Biochemical Agents

biochemical transduction

Identification Personal

features

^Vision

Personal ID

Fingerprints, retinal scan,

voice, heat plume, vision, motion analysis

28

Sensor Node Operating System

•

TinyOS concepts

•

Scheduler + Graph of components

•

^Component

•

Constrained storage model

•

Very Lean multithreading

•

Efficient Layering

29

TinyOS Application

Route Map Router Sensor Application

Active Messages

Radio Packet

Serial

Packet Temp Photo

Radio Byte

UART ADC Clock

RFM

Application

Packet Byte Bit

30

Programming TinyOS

•

TinyOS is written in NesC

•

Applications are written as system components

•

Syntax for concurrency and storage model

•

Compositional support

•

Separation of definition and linkage

31

Simulating TinyOS

•

Target platform: TOSSIM

•

Native instruction set

•

Event driven execution mapped to event drivent simulator

•

Storage model mapped to virtual nodes

•

Radio and environmental models

32

(6)

Other OSes for WSN

•

^MagnetOS

•

Virtual machines, byte code

•

^Mantis

•

Pure multithread

•

^Contiki

•

Dynamic linking of binaries

•

Event/Thread hybrid

33

Overview

34

Issues and Solutions

•

Localization

•

^Routing

•

Medium Access Control

•

Applications

35

Localization

36

Localization

•

Fine-grained

•

^Timing

•

Signal strength

•

Signal pattern matching

•

Directionality

•

Coarse-grained

37

Triangulation

38-1

Triangulation

A B

C

distance

a b

38-2

Triangulation

A B

C

distance

a b

distance

38-3

Trilateration

39-1

(7)

Trilateration

r1

39-2

Trilateration

r1

r2

39-3

Trilateration

r1

r2

r3

39-4

Trilateration

r1

r2

r3

d

39-5

Trilateration

r1

r2

r3

d j

39-6

Trilateration

r1

r2

r3

d j

i

39-7

Trilateration

r1

r2

r3

d j

i

r1²=x²+y²+z²

39-8

Trilateration

r1

r2

r3

d j

i

r²1=x²+y²+z² r²2= (x d)²+y²+z²

39-9

Trilateration

r1

r2

r3

d j

i

r1²=x²+y²+z²

r²₃= (x i)²+ (y j)²+z² r2²= (x d)²+y²+z²

39-10

(8)

Trilateration

r1

r2

r3

d j

i

39-11

Trilateration

r1

r2

r3

d j

i

x=r²1 r²2+d² 2d

39-12

Trilateration

r1

r2

r3

d j

i

x=r1² r²2+d² 2d y=r²1 r²3+ (x i)²

2j +j

2+x² 2j

39-13

Trilateration

r1

r2

r3

d j

i

x=r1² r²2+d² 2d y=r²1 r²3+ (x i)²

2j +j

2+x² 2j z= r₁² x² y²

39-14

Centroid

40-1

Centroid

40-2

Centroid

(Xest, Yest) = (X1+X2+X3

3 ,Y1+Y2+Y3

3 )

40-3

Routing

41

Routing

•

Classical flooding

•

^Implosion

•

Resource management

•

Negociation based protocols

•

^SPIN

•

Directed Diffusion

42

(9)

Negociation Based Protocols

•

SPIN: Sensor Protocols for Information via Negociation

•

Information descriptors for negociation prior to data transmission

•

Negociation relates to available energy

43

SPIN

•

ADV: advertize that new data is available and described

•

REQ: request to receive data

•

DATA: actual data

44

SPIN-PP

S R

45-1

SPIN-PP

S R

ADV

45-2

SPIN-PP

S R

ADV

REQ

45-3

SPIN-PP

S R

ADV

REQ

DATA

45-4

SPIN-EC

S R

46-1

SPIN-EC

S R

ADV

46-2

SPIN-EC

S R

ADV

REQ

46-3

(10)

SPIN-EC

S R

ADV

REQ

DATA

46-4

SPIN-EC

S R

47-1

SPIN-EC

S R

ADV

47-2

SPIN-EC

S R

ADV

R

47-3

SPIN-BC, SPIN-RL

S

R

R R

48-1

SPIN-BC, SPIN-RL

S

R

R R

ADV

48-2

SPIN-BC, SPIN-RL

S

R

R R

48-3

SPIN-BC, SPIN-RL

S

R

R R

REQ REQ

48-4

SPIN-BC, SPIN-RL

S

R

R R

48-5

(11)

SPIN-BC, SPIN-RL

S

R

R R

DATA

DATA DATA

48-6

SPIN-BC, SPIN-RL

S

R

R R

48-7

Directed Diffusion

•

Destination-initiated (sink) reactive routing technique

•

Data is named by an attribute-value pair

•

Sensing tasks are initiated in order to match events interests

•

All nodes maintain interest cache for each requested interest

49

Interests

item name value

type four-legged animal

interval 20 ms

duration 10 s

rect [-100, 100, 200, 400]

50

Returned Data

item name value

type four-legged animal coordinates [125, 220]

intensity 0.6

confidence 0.85

timestamp 01:20:40

51

Directed Diffusion

S N

N

N N

N

52-1

Directed Diffusion

S N

N

N N

N

52-2

Directed Diffusion

S N

N

N N

N

52-3

Directed Diffusion

S N

N

N N

N

52-4

(12)

Directed Diffusion

S N

N

N N

N

52-5

Directed Diffusion

S N

N

N N

N

52-6

Directed Diffusion

S N

N

N N

N

52-7

Directed Diffusion

S N

N

N N

N

52-8

Interest Cache

•

Periodically purged

•

No information about sink

•

Gradient table

•

rate per neighbor

•

^timestamp

•

^expiration

53

Interest Forwarding

•

When new interest/task is received, add to cache

•

Simplest policy: rebroadcast interest

•

No way of distinguishing new interests from repeated ones

•

Set up (very low rate) gradients between all neighbors

54

Message propagation

•

A node matching an interest generates replies at desired rate

•

When receiving a reply, lookup interest cache

•

Forward along given route(s) if found, drop otherwise

•

Loop prevention

55

Directed Diffusion

S E

N

N N

N

56-1

Directed Diffusion

S E

N

N N

N

56-2

(13)

Directed Diffusion

S E

N

N N

N

56-3

Directed Diffusion

S E

N

N N

N

56-4

Directed Diffusion

S E

N

N N

N

56-5

Directed Diffusion

S E

N

N N

N

Reinforcement request

56-6

Directed Diffusion

S E

N

N N

N

56-7

Directed Diffusion

S E

N

N N

N

56-8

Directed Diffusion

S E

N

N N

N

56-9

Directed Diffusion

S E

N

N N

N

56-10

Reinforcement

•

Sink can reissue the same request with a higher rate

•

“Draw down” higher quality data from a particular neighbor

•

Other nodes react when receiving

•

“Outflow” increased, must reinforce another node to increase “inflow”

57

(14)

Directed Diffusion

S E

N

N S

N

58-1

Directed Diffusion

S E

N

N S

N

58-2

Directed Diffusion

S E

N

N S

N

58-3

Directed Diffusion

S E

N

E

N N

N

59-1

Directed Diffusion

S E

N

E

N N

N

59-2

Directed Diffusion

S E

N

E

N N

N

59-3

Directed Diffusion

S E

N

N N

N

60-1

Directed Diffusion

S E

N

N N

N

60-2

Directed Diffusion

S E

N

N N

N

60-3

(15)

Directed Diffusion

S E

N

N N

N

60-4

Directed Diffusion

S E

N

N N

N

60-5

Directed Diffusion

S E

N

N N

N

60-6

Directed Diffusion

•

Local algorithm policies

•

Propagating interests

•

flood, cache information, GPS

•

Setting up gradients

•

first heard neighbor, highest energy neighbor

61

Directed Diffusion

•

Local algorithm policies

•

Data transmission

•

single path, striped multi-path, multiple sources, etc.

•

Reinforcement

•

observer losses, resources levels, etc.

62

Energy Aware Routing

•

Similar to Directed Diffusion

•

destination initiated

•

initial flooding to discover routes

•

several sub-optimal paths can be used (with a probabilistic distribution)

63

Energy Aware Routing

S E

N

N N

N

64-1

Energy Aware Routing

S E

N

N N

N

64-2

Energy Aware Routing

S E

N

N N

N 0.3 0.3 0.4

1 1

1

64-3

(16)

Medium Access Control

65

Classical Approaches

•

FDMA: Frequency division multiple access

•

TDMA: Time division multiple access

•

CDMA: Code division multiple access

•

CSMA: Carrier sense multiple access

•

CD: Collision detection

•

CA: Collision avoidance

66-1

Classical Approaches

•

One frequency available

66-2

Classical Approaches

•

One frequency available One code available

66-3

Classical Approaches

•

One frequency available One code available Can’t listen while transmitting

66-4

Hidden Terminal problem

S1 R S2

67-1

Hidden Terminal problem

S1 R S2

67-2

Hidden Terminal problem

S1 R S2

67-3

Hidden Terminal problem

S1 R S2

67-4

(17)

Hidden Terminal problem

S1 R S2

67-5

Exposed Terminal Problem

R1 S1 S2 R2

68-1

Exposed Terminal Problem

R1 S1 S2 R2

68-2

Exposed Terminal Problem

R1 S1 S2 R2

68-3

Exposed Terminal Problem

R1 S1 S2 R2

68-4

Exposed Terminal Problem

R1 S1 S2 R2

68-5

IEEE 802.11 RTS/CTS

S R

69-1

IEEE 802.11 RTS/CTS

S R

ADVRTS

69-2

IEEE 802.11 RTS/CTS

S R

ADV

REQ RTS

CTS

69-3

(18)

IEEE 802.11 RTS/CTS

S R

ADV

REQ

DATA RTS

CTS

69-4

IEEE 802.11 RTS/CTS

S1 R S2

70-1

IEEE 802.11 RTS/CTS

S1 R S2

70-2

IEEE 802.11 RTS/CTS

S1 R S2

70-3

IEEE 802.11 RTS/CTS

S1 R S2

70-4

IEEE 802.11 RTS/CTS

S1 R S2

70-5

IEEE 802.11 RTS/CTS

S1 R S2

70-6

IEEE 802.11 RTS/CTS

S1 R S2

70-7

IEEE 802.11 RTS/CTS

S1 R S2

70-8

(19)

IEEE 802.11 RTS/CTS

S1 R S2

70-9

IEEE 802.11 RTS/CTS

R1 S1 S2 R2

71-1

IEEE 802.11 RTS/CTS

R1 S1 S2 R2

71-2

IEEE 802.11 RTS/CTS

R1 S1 S2 R2

71-3

IEEE 802.11 RTS/CTS

R1 S1 S2 R2

71-4

IEEE 802.11 RTS/CTS

R1 S1 S2 R2

71-5

IEEE 802.11 RTS/CTS

R1 S1 S2 R2

71-6

IEEE 802.11 RTS/CTS

R1 S1 S2 R2

71-7

Duty Cycling

•

Reduces idle listening time

•

Sensors switch between sleep and active mode

•

Suits low traffic networks

•

If data rate is very low, it is not necessary to keep sensors listening all the time

•

Energy can be saved by turning off sensors

72

(20)

Duty Cycling

Sleeping Listening 1 second

73-1

Duty Cycling

Sleeping Listening 1 second

Data sampling

73-2

Duty Cycling

Sleeping Listening 1 second

Data sampling Extra Latency

73-3

Duty Cycling

Sleeping Listening

A

B

74-1

Duty Cycling

Sleeping Listening

A

B

Message Sending

74-2

Duty Cycling

Sleeping Listening

A

B

Message Sending Extra Latency

74-3

Duty Cycling

Sleeping Listening

A

B

Sleeping Listening

Listening Sleeping

75

Duty Cycling

Sleeping Listening

A Sleeping Listening

Sleeping Listening

B Sleeping Listening

76-1

Duty Cycling

Sleeping Listening

A Sleeping Listening

Sleeping Listening

B Sleeping Listening

long period (duty period * #of hops)

76-2

(21)

Time Synchronization

77

Time Synchronization

78-1

Time Synchronization

78-2

Time synchronization

•

Definition: providing a common time scale for local clocks of nodes in the network

•

Stamp event, duration between events, order events

•

No global clock of shared memory

79

Time Synchronization

C _p (t) = a _p t + d _p a _p : clock frequency d _p : offset

80

Remote Clock Reading

B

A T0 T1

TB

81-1

Remote Clock Reading

B

A T0 T1

TB

TB(T1) =TB+T1 T0

2

81-2

Time Transmission

B

A

T1

T2

Tn

R1 R2 Rn

82-1

Time Transmission

B

A

T1

T2

Tn

R1 R2 Rn

TB(Rn) =Rn 1 n

⇤n

i=1

Ri 1 n

⇤n

i=1

Ti

⇥ +d

82-2

(22)

Offset Delay Estimation

B

A T0

T0

T1 T2

T3

T0, T1, T2

83-1

Offset Delay Estimation

B

A T0

T0

T1 T2

T3

T0, T1, T2

=(T1 T0) (T3 T2) 2 Drift

83-2

Offset Delay Estimation

B

A T0

T0

T1 T2

T3

T0, T1, T2

=(T1 T0) (T3 T2)

2 d=(T1 T0) + (T3 T2) 2

Drift Offset

83-3

Set Valued Estimation

B

A T0

TB

Tr

84-1

Set Valued Estimation

B

A T0

TB

Tr

C

A

(t) = a

AB

C

B

(t) + d

AB

84-2

Set Valued Estimation

B

A T0

TB

Tr

C

A

(t) = a

AB

C

B

(t) + d

AB T₀< a_ABT_B+d_AB Tr> aABTB+dAB

84-3

Set Valued Estimation

CA(t)

CB(t)

85-1

Set Valued Estimation

T01

Tr1

CA(t)

CB(t)

85-2

Set Valued Estimation

T01

Tr1

dAB

CA(t)

CB(t)

85-3

(23)

Set Valued Estimation

T01

Tr1

dAB

CA(t)

CB(t)

85-4

Conclusion

86

Sensor Networks

•

Driven by applications

•

Connexion between Computer Science and Biology, Environment, Rescue, etc.

•

Hard problems yet to be solved