Bayesian Indoor Bayesian Indoor Positioning SystemsPositioning Systems

Presented by: Eiman ElnahrawyPresented by: Eiman Elnahrawy

Joint work with: David Madigan, Richard P. Martin, Joint work with: David Madigan, Richard P. Martin, Wen-Hua Ju, P. Krishnan, A.S. KrishnakumarWen-Hua Ju, P. Krishnan, A.S. Krishnakumar

Rutgers University and Avaya LabsRutgers University and Avaya Labs

Infocom 2005Infocom 2005

Wireless ExplosionWireless Explosion

Technology trends creating cheap wireless Technology trends creating cheap wireless communication in every computing devicecommunication in every computing device

Device radios offer “indoors” localization opportunity in Device radios offer “indoors” localization opportunity in 2,3D 2,3D

New capability compared to traditional communication New capability compared to traditional communication networks networks

Can we localize every device having radio using only Can we localize every device having radio using only this available infrastructure??this available infrastructure??

3 technology communities: 3 technology communities: WLAN (802.11x)WLAN (802.11x)

Sensor networks (zigbee)Sensor networks (zigbee)

Cell carriers(3G)Cell carriers(3G)

Radio-based LocalizationRadio-based Localization

Signal decays linearly with Signal decays linearly with log distance in laboratory log distance in laboratory setting setting

SSjj = b = b0j0j + b + b1j1j log D log Djj

DDjj = sqrt((x-x = sqrt((x-xjj))22 + (y-y + (y-yjj))22))

Use triangulation to compute Use triangulation to compute (x,y)(x,y) » Problem solved » Problem solved

Not in real life!! Not in real life!! noise, multi-path, reflections, noise, multi-path, reflections, systematic errors, etc.systematic errors, etc.

[-80,-67,-50]

Fingerprint or RSS

(x?,y?)

Supervised Learning-based Supervised Learning-based SystemsSystems

TrainingTraining

Offline phaseOffline phaseCollect Collect “labeled”“labeled” training training data data [(x,y), S1,S2,S3,..] [(x,y), S1,S2,S3,..]

Online phaseOnline phase Match Match “unlabeled”“unlabeled” RSS RSS

[(?,?), S1,S2,S3,..][(?,?), S1,S2,S3,..] to to existing “labeled” training existing “labeled” training fingerprintsfingerprints

[-80,-67,-50]

Fingerprint or RSS

(x?,y?)

Previous WorkPrevious Work

People have tried almost all existing supervised People have tried almost all existing supervised learning approacheslearning approaches

Well known Radar (NN)Well known Radar (NN)Probabilistic, e.g., Bayes a posteriori likelihoodProbabilistic, e.g., Bayes a posteriori likelihoodSupport Vector MachinesSupport Vector MachinesMulti-layer PerceptronsMulti-layer Perceptrons… …

[Bahl00, Battiti02, Roos02,Youssef03, Krishnan04,…][Bahl00, Battiti02, Roos02,Youssef03, Krishnan04,…]

All have a major drawback All have a major drawback Labeled training fingerprints “profiling”Labeled training fingerprints “profiling”Labor intensive (286 in 32 hrs!!)Labor intensive (286 in 32 hrs!!)May need to be repeated over the timeMay need to be repeated over the time

ContributionContribution

Why don’t we try Why don’t we try Bayesian Graphical Models Bayesian Graphical Models (BGM)(BGM)? any performance gains? ? any performance gains?

Performance-wise: comparablePerformance-wise: comparable

Minimum labeled fingerprintsMinimum labeled fingerprints

AdaptiveAdaptive

Simultaneously locate a set of objectsSimultaneously locate a set of objects

In fact it can be a zero-profiling approachIn fact it can be a zero-profiling approachNo more “labeled” training data neededNo more “labeled” training data needed

Unlabeled data can be obtained using existing data Unlabeled data can be obtained using existing data traffictraffic

LLoooocclleeTMTM

General purpose localizationGeneral purpose localization analogous to general purpose analogous to general purpose communication!communication!

Can we make finding objects in the Can we make finding objects in the physical space as easy as physical space as easy as GGoooogglle e ? ?

Can this dream come Can this dream come true?true?

We believe we are so closeWe believe we are so close

Only existing infrastructureOnly existing infrastructureLocalize with only the radios on existing Localize with only the radios on existing devicesdevices

Additional resources as performance Additional resources as performance enhancementsenhancements

Ad-hoc Ad-hoc No more labeled data No more labeled data (our contribution)(our contribution)

OutlineOutline

Motivations and GoalsMotivations and Goals

Experimental setupExperimental setup

Bayesian backgroundBayesian background

Models of increasing complexities [labeled-Models of increasing complexities [labeled-unlabeled]unlabeled]

Comparison to previous workComparison to previous work

Conclusion and Future WorkConclusion and Future Work

Experimental SetupExperimental Setup3 Office buildings3 Office buildings

BR, CA Up, CA DownBR, CA Up, CA Down

802.11b radio802.11b radio

Different sessions, daysDifferent sessions, days

All give similar performanceAll give similar performance

Focus on BR Focus on BR (no particular (no particular reason)reason)

BR: 5 access points, 225 ft x 175 ft, 254 BR: 5 access points, 225 ft x 175 ft, 254 measurementsmeasurements

Bayesian Graphical Bayesian Graphical ModelsModels

Encode dependencies/conditional Encode dependencies/conditional independence between variablesindependence between variables

X Y

D

S

Vertices = random variablesVertices = random variablesEdges = relationshipsEdges = relationships

Example [(X,Y), S], AP at (Example [(X,Y), S], AP at (xxb, b, yybb))Log-based signal strength propagationLog-based signal strength propagation

S = bS = b00 + b + b11 log D log D

D= sqrt((X-xD= sqrt((X-xbb))22 + (Y-y + (Y-ybb))22))

Model 1 (Simple): labeled Model 1 (Simple): labeled datadata

Xi Yi

D1

S1

b11b01 b15

D2 D3 D4 D5

S2 S3 S4 S5

b12 b13 b14b02 b03 b04 b05

Position Variables

Distances

Observed Signal Strengths

Base Station Parameters“Unknowns"

Xi ~ uniform(0, Length) Yi ~ uniform(0, Width)Si ~ N(b0i+b1ilog(Di),δi), i=1,2,3,4,5b0i ~ N(0,1000), i=1,2,3,4,5 b1i ~ N(0,1000), i=1,2,3,4,5

InputInput

Labeled: trainingLabeled: training

[(x1,y1),(-40,-55,-90,..)][(x1,y1),(-40,-55,-90,..)]

[(x2,y2),(-60,-56,-80,..)][(x2,y2),(-60,-56,-80,..)]

[(x3,y3),(-80,-70,-30,..)][(x3,y3),(-80,-70,-30,..)]

[(x4,y4),(-64,-33,-70,..)][(x4,y4),(-64,-33,-70,..)]

Unlabeled: Unlabeled: mobile object(s)mobile object(s)

[(?,?),(-45,-65,-40,..)][(?,?),(-45,-65,-40,..)]

[(?,?),(-35,-45,-78,..)][(?,?),(-35,-45,-78,..)]

[(?,?),(-75,-55,-65,..)][(?,?),(-75,-55,-65,..)]

Probability Probability distributions for all the distributions for all the unknown variablesunknown variables

Propagation constantsPropagation constantsb0i, b1i for each Base b0i, b1i for each Base StationStation

(x,y) for each (?,?)(x,y) for each (?,?)

OutputOutput

Great! but now how do we Great! but now how do we find the location of the find the location of the

mobile?mobile?

Closed form solution doesn’t usually exist Closed form solution doesn’t usually exist » simulation/analytic approx » simulation/analytic approx

We used We used MCMC simulationMCMC simulation (Markov (Markov Chain Monte Carlo) to generate predictive Chain Monte Carlo) to generate predictive samples from the joint distribution for samples from the joint distribution for every unknown (x,y) locationevery unknown (x,y) location

Example OutputExample Output

Some Results..Some Results..

M1 is better

Comparable

25thMed

75th

Min

Max

Model 2 (Hierarchical): Model 2 (Hierarchical): labeled datalabeled data

MotivationMotivation borrowing strength might provide some predictive borrowing strength might provide some predictive benefitsbenefits

Xi Yi

D1 D2 D3 D4 D5

S1 S2 S3 S4 S5

b11 b12 b13 b14 b15b01 b02 b03 b04 b05

Xi ~ uniform(0,Length)

Yi ~ uniform(0,Width)Si ~ N(b0i+b1ilog(Di), δi) b0i ~ N(b0, δb0)b1i ~ N(b1, δb1) b0 ~ N(0,1000)b1 ~ N(0,1000) δ0 ~ Gamma(0.001,0.001)δ1 ~ Gamma(0.001,0.001) i=1,2,3,4,5

Allowing any values for b’s too unconstrained!Allowing any values for b’s too unconstrained!

Assume all base-stations parametersAssume all base-stations parametersnormally distributed around a hiddennormally distributed around a hiddenvariable with a mean and variancevariable with a mean and variance

M2 behaves similar to M1, but provides improvement for very small training setsM2 behaves similar to M1, but provides improvement for very small training setsHmm, still comparable to SmoothNNHmm, still comparable to SmoothNN

More Results..More Results..Leave-one-out error (feet)

Size of labeled data

Av

era

ge

Err

or

(fe

et)

Labeled M1

Labeled Hier M2

SmoothNN

1015

2025

3035

40

0 50 100 150 200 250

Can we get reasonable estimates Can we get reasonable estimates of position of position without any labeled without any labeled

datadata??Yes! Yes!

Observe signal strengths from existing Observe signal strengths from existing data packets (unlabeled by default) data packets (unlabeled by default)

No more running around collecting No more running around collecting data.. data..

Over and over.. and over..Over and over.. and over..

InputInput

Labeled: trainingLabeled: training

[(x1,y1),(-40,-55,-90,..)][(x1,y1),(-40,-55,-90,..)]

[(x2,y2),(-60,-56,-80,..)][(x2,y2),(-60,-56,-80,..)]

[(x3,y3),(-80,-70,-30,..)][(x3,y3),(-80,-70,-30,..)]

[(x4,y4),(-64,-33,-70,..)][(x4,y4),(-64,-33,-70,..)]

Unlabeled: Unlabeled: mobile object(s)mobile object(s)

[(?,?),(-45,-65,-40,..)][(?,?),(-45,-65,-40,..)]

[(?,?),(-35,-45,-78,..)][(?,?),(-35,-45,-78,..)]

[(?,?),(-75,-55,-65,..)][(?,?),(-75,-55,-65,..)]

Probability Probability distributions for all the distributions for all the unknownsunknowns

Propagation constantsPropagation constantsb0i, b1i for each Base b0i, b1i for each Base StationStation

(x,y) for each (?,?)(x,y) for each (?,?)

OutputOutput

Model 3 (Zero Profiling)Model 3 (Zero Profiling)

Same graph as M2 Same graph as M2 (Hierarchical) but with (Hierarchical) but with (unlabeled data)(unlabeled data)

Xi Yi

D1 D2 D3 D4 D5

S1 S2 S3 S4 S5

b11 b12 b13 b14 b15b01 b02 b03 b04 b05

Hmm, why would this work?Hmm, why would this work?[1] Prior knowledge about distance-signal strength

[2] Prior knowledge that access points behave similarly

Results Close to SmoothNN, Results Close to SmoothNN, BUT…!!BUT…!!

0 50 100 150 200 250

20

40

60

80

0 50 100 150 200 250

20

40

60

80

0 50 100 150 200 250

2040

6080

Leave-one-out error (feet)

Size of input data

Av

era

ge

Err

or

in F

eet

Zero Profiling M3

SmoothNN

LABELED

UNLABELED

Other ideasOther ideas

Corridor EffectsCorridor EffectsWhat? RSS is stronger What? RSS is stronger along corridorsalong corridors

Variable c =1 if the Variable c =1 if the point shares x or y with point shares x or y with the APthe AP

No improvementsNo improvements

Informative Prior Informative Prior distributionsdistributions

S1 S2 S3 S4 S5

1 2 3 4 5

D1 D2 D3 D4 D5

YiXi

C1 C2 C3 C4 C5

Comparison to previous Comparison to previous workwork

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance in feet

Pro

bab

ility

Error CDF Across Algorithms

RADARProbabilisticM1-labeled

M3-unlabeledM2-labeled

•More ad-hoc

•Adaptive

•No labor investment

Conclusion and Future Conclusion and Future WorkWork

First time to actually use BGM First time to actually use BGM Considerable promise for localizationConsiderable promise for localizationPerformance comparable to existing approachesPerformance comparable to existing approachesZero profiling! (can we localize anything with a Zero profiling! (can we localize anything with a radio??)radio??)

Where are we going?Where are we going?Other modelsOther modelsVariational approximationsVariational approximationsTracking applicationsTracking applicationsMinimum extra infrastructure (more information - Minimum extra infrastructure (more information - better accuracy)!better accuracy)!

Thanks! Thanks! ☺☺