CS321: Introduction, Applications, State Estimationgraphics.stanford.edu/courses/cs321-05-fall/Lectures/05...Data acquisition of physical and chemical properties, at various spatial

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CS321: Introduction, CS321: Introduction, Applications, State EstimationApplications, State Estimation

Leonidas GuibasComputer Science Dept.Stanford University

Sensing Networking

Computation

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Class Mechanics

Replacement for Monday class: Friday 2:45-4:00 pm (hopefully still in Clark S361)Password-protected area of the class web pages: User: 05cs321

Password: 05cs321

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Sensor Network Researchpower awarenesssensor tasking and controlformation of sensor collaboration groupsin-network, distributed processingnode management, service establishment, software layerscoping with noise and uncertainty in the environment

Estimate fullworld-state

Sense Answer query,make decision

A key algorithmic problem is how to sense and aggregate only the portions of the world-state relevant to the task at hand, in a lightweight, energy-efficient manner.

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Some Questions to Consider, I

What size/capability nodes are best for a given application?Is a hierarchical structure appropriate for a sensor network (deploying a mix of nodes with different capabilities)?

Sensoria WINSNG 2.0CPU: 300 MIPS 1.1 GFLOP FPU32MB Flash32MB RAMSensors: external

More powerful

Crossbow Mica2dot mote4 MIPS CPU (integer only)8KB Flash512B RAMSensors: on board stack(accel, light , microphone)

Inexpensive & simple

Smart dust (in progress)CPU, Memory: TBD (LESS!)Sensors: integrated

Supercheap & tinyEasy to use

HP iPAQ w/802.11CPU: 240 MIPS32MB Flash64MB RAMBoth integrated and off-board sensors

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Some Questions to Consider, IIWhat sensors are needed?Where does sensor fusion happen?

wired links

wireless links

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Applications

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Habitat monitoring: www.greatduckisland.net

BBC News, October 10, 2002

“It will enable us to study ecosystems at a level that has not been conceived.”Steve Katona, College of the Atlantic biologist and president

Great Duck Island, 10 miles off the coast of Maine:

Remote wireless sensors are being used to find out more about birds in their natural habitat.

Petrel: Rarely seen by birdwatchers

Wireless biological sensors placed in nests

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Monitoring Plants at Huntington Botanical Garden

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Ecosystem MonitoringScience

Understand response of wild populations (plants and animals) to changing habitats over time.Develop in situ observation of species and ecosystem dynamics.

TechniquesData acquisition of physical and chemical properties, at variousspatial and temporal scales, appropriate to the ecosystem, species and habitat.

Automatic identification of organisms(current techniques involve close-range human observation).

Measurements over long period of time,taken in-situ.

Harsh environments with extremes in temperature, moisture, obstructions, ...

[From D. Estrin, UCLA]

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Seismic MonitoringInteraction between ground motions and structure/foundation response not well understood.

Current seismic networks not spatially dense enough to monitor structure deformation in response to ground motion, to sample wavefield without spatial aliasing.

ScienceUnderstand response of buildings and underlying soil to ground shaking Develop models to predict structure response for earthquake scenarios.

Technology/ApplicationsIdentification of seismic events that cause significant structure shaking.Local, at-node processing of waveforms.Dense structure monitoring systems.

[From D. Estrin, UCLA]

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1 km

• 38 strong-motion seismometers in 17-story steel-frame Factor Building.• 100 free-field seismometers in UCLA campus ground at 100-m spacing

[From D. Estrin, UCLA]

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Research ChallengesReal-time analysis for rapid response.

Massive amounts of data → Smart, efficient, innovative data management and analysis tools.

Poor signal-to-noise ratio due to traffic, construction, explosions, ….

Insufficient data for large earthquakes → Structure response must be extrapolated from small and moderate-size earthquakes, and force-vibration testing.

First steps

Monitor building motion

Develop algorithm for network to recognize significant seismic events using real-time monitoring.

Develop theoretical model of building motion and soil structure by numerical simulation and inversion.

Apply dense sensing of building and infrastructure (plumbing, ducts) with experimental nodes. [From D. Estrin, UCLA]

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Contaminant TransportScience

Understand intermedia contaminant transport and fate in real systems.

Identify risky situations before they become exposures.

Subterranean deployment.

Multiple modalities (e.g., pH, redox conditions, etc.)Micro sizes for some applications (e.g., pesticide transport in plant roots).Tracking contaminant “fronts”.At-node interpretation of potential for risk (in field deployment).

Soil Zone

Groundwater

Volatization

SpillPath

Air Emissions

Dissolution

Water Well

[From D. Estrin, UCLA]

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Contaminantplume

Research ImplicationsEnvironmental Micro-Sensors

Sensors capable of recognizing phases in air/water/soil mixtures.Sensors that withstand physically and chemically harsh conditions.Microsensors.

Signal ProcessingNodes capable of real-time analysis of signals.Collaborative signal processing to expend energy only where there is risk.

[From D. Estrin, UCLA]

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A Chemical Disaster Tracking ScenarioA large-scale chemical gas leak has been detected at a plant 20 minutes agoThe national guard has been activated to evacuate nearby towns, and to close roads/bridgesTo get a real-time situational assessment of the extent and movement of the gas release and inform the evacuation, a SWAT Teamis called inThree small UAVs are immediately launched from an open field 15 miles south of the attack site, each equipped with 1000 tiny chemical sensing nodesUpon flying over the vicinity of the attack site, the sensor nodes are releasedThe nodes self-organize into an ad hoc network, while airborne, and relay the tracking result back to the emergency response command center

Where is the plume, how big, how fast, which direction?

sensor dust

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Transportation and Urban Monitoring

Disaster Response

[From D. Estrin, UCLA]

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Traffic and Collision Control

V2V communication of Emergency Alert Messages. Early collision awareness and avoidance.

“Tell me your speed and position”

(x, v)(x, v)

(x, v)(x, v)

Traffic jam information collection and propagation.

[From J. Reich, PARC]

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Image Sensor Networks

CMOS technology enables the production of small, low-cost and low-power integrated image sensorsCameras (still or video) and other image sensors are becoming cheaper, smaller, and nearly ubiquitousHowever, truly distributed networked systems of image sensors are still not here

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Current Multi-Imager Networks

Data is transported over a wired network to a central locationHuman operators look at the data

This approach cannot scale:

vast amounts of data to movewiring is expensiveautomatic ways to filter the data are needed

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Distributed Imager ChallengesImagers are high data ratesensors; therefore data must be compressed and summarized

compression must take into account shared datagoal of compression need not be reconstruction

Vision algorithms can be expensive to run on weak capability, low power devicesVisibility is non-local and discontinuous (occlusions, etc)Issues of privacy, etc.

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Collaborative, Task-Driven Image Sensing

Large numbers of simple, inexpensive cameras collaborate over a wireless network to accomplish a taskData is compressed locally and aggregated within the network Cameras are only tasked as the situation demandsThe system can be expanded incrementally to large numbers of nodes

The goal is to estimate certainhigh-level, global attributes ofthe environment.

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Distributed AttentionSensor Networks in Complex, Urban Environments

[From J. Reich, PARC]

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What is Unique about Sensor Networks?Unique characteristics

Large area coverage: Distance/area covered, number of events, number of active queriesSpatial diversity: Dense spatial sampling, multi-aspect sensing, multiple sensing modalitiesSurvivability: Robust against node/link failuresUbiquity: Quick/flexible deployment, ubiquitous access, info timeliness

Particularly suited for detecting, classifying, trackingNon-local spatio-temporal events/objects

Simultaneous dense spatial sampling to identify and track large, spatially extended eventContinuous spatio-temporal sampling to track moving objects

Low-observable eventsDistributed information aggregationNon-local information validation

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Summary

Ubiquitous networked sensors provide a dense spatial and temporal sensing of the physical worldThey potentially provide low-latency access to information that is highly localized in time and space, and thus provide a way to sense and act on the physical world beyond what has been possible up to nowSensor networks raise many research issues at the physical node level, the system architecture level, and the algorithm deployment level

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Excursion intoProbabilistic Estimation

[From Thrun, Brugard, and Fox]

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Recursive State Estimation

State :external parameters describing the environment that are relevant to the sensing problem at hand (say vehicle locations in a tracking problem)internal sensor settings (say the direction a pan/tilt camera is aiming)

While internal state may be readily available to a node, external state is typically hidden – it cannot be directly observed but only indirectly estimated.

States may only be known probabilistically.

x

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Environmental Interaction

Control :a sensor node can change its internal parameters to improve its sensing abilities

Observation :a sensor node can take various measurements of the environment

Discrete Time : 0, 1, 2, 3, ...

u

z

t

, ,t t tx u z1 2 1 1 1 1 2: 1 2 3, , , , ,t t t t t t tz z z z z z� � �� �

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Basic Probability

Random variables (discr. or cont.) and probabilities

Independence of random variables

Conditional probability

( ) 1 or ( ) 1( ),x

x

p x px xX dxp � �� � �

( , ) ( , ) ( ) ( )P X x Y y p x y p x p y� � � �

( ) ( , )/ ( ) ( ( ) if and are independent)p x y p x y p y p x x y� �

( ) ( ) ( ) (discrete case)y

p x p x y p y��( ) ( ) ( ) (continuous case)

yp x p x y p y dy� �

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Bayes Rule

( ) ( ) ( ) ( )p x y p y x p x p y�'

( ) ( ) (discrete)

( ') ( ')x

p y x p x

p y x p x��

'

( ) ( ) (continuous)

( ') ( ') 'x

p y x p x

p y x p x dx��

( ) ( ) ( )p x z p z x p x��

probability of state x, givenmeasurement z probability of measurement z,

given state x (the sensor model)

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Expectation, Covariance, Entropy

Expectation

Covariance (or variance)

Entropy

( ) ( ) or ( )x x

E X x p x x p x dx�� � ( ) ( )E aX b aE X b� � �

2 2 2Cov( ) ( ( )) ( ) ( )X E X E X E X E X� � � �

( ) ( lg ( )) ( ) lg ( )x

H X E p X p x p x� � ���

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Probabilistic Generative Laws

State is generated stochastically by

Markovian assumption (state completeness)

tx

0: 1 1: 1 1:( , , )t t t tp x x z u� �

0: 1 1: 1 1: 1( , , ) ( , )t t t t t t tp x x z u p x x u� � ��

0: 1: 1 1:( , , ) ( )t t t t t tp z x z u p z x� �

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The Bayes Filter

Belief distributions

Algorithm Bayes_Filter

1: 1: 1: 1 1:( ) ( , ), ( ) ( , )t t t t t t t tb x p x z u b x p x z u�� �

the prior belief

1( ( ), , )t t tb x u z�

1 1

for all do

( ) ( , ) ( ) [prediction]

( ) ( ) ( ) [observation]

endforreturn ( )

t

t t t t t

t t t t

t

x

b x p x u x b x dx

b x p z x b x

b x

�

� ��

�

�

the posterior belief

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Gaussian Filters

Beliefs are represented by multivariate Gaussian distributions

Appropriate for unimodal distributions

112 1

( ) det(2 ) exp ( ) ( )2

Tp x x x� � �� �� �� � � � � � �

Here is the mean of the state, and its covariance� �

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The Kalman Filter

Next state probability must be a linear function, with added Gaussian noise [result still Gaussian]

Measurement probability must also be linear in it arguments, with added Gaussian noise

1t t t t t tx A x B u ��� � � Gaussian noise with zero meanand covariance

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1 1 1

1( , ) det(2 ) exp ( ) ( )

2T

t t t t t t t t t t t t t t tp x u x R x A x B u R x A x B u�� �

� � �

� �� �� �� � � � � �� �� �� �� �

t t t tz C x �� � Gaussian noise with zero meanand covariance

112 1

( ) det(2 ) exp ( ) ( )2

Tt t t t t t t t t tp z x Q z C x Q z C x�

� �� �� �� �� � � �� �� �� �� �

tR

tQ

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Kalman Filter Algorithm

Algorithm Kalman_Filter 1 1( , , , )t t t tu z� � ��

1

1

1( ) (the Kalman gain)

= ( )

( )

t t t tt

Tt t t t t

T Ttt t t tt

t t t t tt

tt t t

A B u

A A R

K C C C Q

K z C

I K C

� �

� � �

�

�

�

� �

� � � �

�� � �

� �

� � � �

belief predicted bysystem dynamics

belief updated using measurements

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Kalman Filter Illustration

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Kalman Filter Extensions

The Extended Kalman Filter (EKF)

Mixtures of Gaussians

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Non-Parametric Filters

Parametric filters parametrize a distribution by a fixed number of parameters (mean and covariance in the Gaussian case)Non-parametric filters are discrete approximations to continuous distributions, using variable size representations

essential for capturing more complex distributionsdo not require prior knowledge of the distribution shape

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Histogram Filters

Histogram from aGaussian, passedthrough a non-linear function

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The Particle Filter

Samples from aGaussian, passedthrough a non-linear function

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lllustration of Importance Sampling

We desire to sample f

We can only, however, sample g

Samples from g, reweightedby the ratio f(x)/g(x)

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The Particle Filter Algorithm

Algorithm Particle_Filter 1( , , )t t tX u z�

[ ] [ ]1

[ ] [ ] [ ] [ ]

[ ]

[ ]

for 1 to do

sample ( , )

( ); ,

endforfor 1 to do

draw with probability proportional to

add to

return

tt

m mt t t t

m m m mt tt t t t t

it

it t

t

X X

m M

x p x u x

w p z x X X x w

m M

i w

x X

X

�

� ��

�

� � �

�

�

stochastic propagation

importance weights

resampling, orimportance sampling

number of particles of unit weight

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The End