Bayesian Indoor Positioning Systems Presented by: Eiman Elnahrawy Joint work with: David Madigan, Richard P. Martin, Wen-Hua Ju, P. Krishnan, A.S. Krishnakumar Rutgers University and Avaya Labs Infocom 2005

Wireless Explosion Technology trends creating cheap wireless communication in every computing device Device radios offer “indoors” localization opportunity in 2,3D New capability compared to traditional communication networks Can we localize every device having radio using only this available infrastructure?? 3 technology communities: WLAN (802.11x) Sensor networks (zigbee) Cell carriers(3G)

Radio-based Localization Signal decays linearly with log distance in laboratory setting S j = b 0j + b 1j log D j D j = sqrt((x-x j ) 2 + (y-y j ) 2 ) Use triangulation to compute (x,y) » Problem solved Not in real life!! noise, multi-path, reflections, systematic errors, etc. [-80,-67,-50] Fingerprint or RSS (x?,y?)

Supervised Learning-based Systems Training Offline phase Collect “labeled” training data [(x,y), S1,S2,S3,..] Online phase Match “unlabeled” RSS [(?,?), S1,S2,S3,..] to existing “labeled” training fingerprints [-80,-67,-50] Fingerprint or RSS (x?,y?)

Previous Work People have tried almost all existing supervised learning approaches Well known Radar (NN) Probabilistic, e.g., Bayes a posteriori likelihood Support Vector Machines Multi-layer Perceptrons … [Bahl00, Battiti02, Roos02,Youssef03, Krishnan04,…] All have a major drawback Labeled training fingerprints “profiling” Labor intensive (286 in 32 hrs!!) May need to be repeated over the time

Contribution Why don’t we try Bayesian Graphical Models (BGM)? any performance gains? Performance-wise: comparable Minimum labeled fingerprints Adaptive Simultaneously locate a set of objects In fact it can be a zero-profiling approach No more “labeled” training data needed Unlabeled data can be obtained using existing data traffic

Loocle TM General purpose localization analogous to general purpose communication! Can we make finding objects in the physical space as easy as Google ?

Can this dream come true? We believe we are so close Only existing infrastructure Localize with only the radios on existing devices Additional resources as performance enhancements Ad-hoc No more labeled data (our contribution)

Outline Motivations and Goals Experimental setup Bayesian background Models of increasing complexities [labeled-unlabeled] Comparison to previous work Conclusion and Future Work

Experimental Setup 3 Office buildings BR, CA Up, CA Down b radio Different sessions, days All give similar performance Focus on BR (no particular reason) BR: 5 access points, 225 ft x 175 ft, 254 measurements

Bayesian Graphical Models Encode dependencies/conditional independence between variables X Y D S Vertices = random variables Edges = relationships Example [(X,Y), S], AP at (x b, y b ) Log-based signal strength propagation S = b 0 + b 1 log D D= sqrt((X-x b ) 2 + (Y-y b ) 2 )

Model 1 (Simple): labeled data Xi Yi D1D1 S1S1 b 11 b 01 b 15 D2D2 D3D3 D4D4 D5D5 S2S2 S3S3 S4S4 S5S5 b 12 b 13 b 14 b 02 b 03 b 04 b 05 Position Variables Distances Observed Signal Strengths Base Station Parameters “Unknowns" Xi ~ uniform(0, Length) Yi ~ uniform(0, Width) Si ~ N(b 0i +b 1i log(Di), δ i ), i=1,2,3,4,5 b0i ~ N(0,1000), i=1,2,3,4,5 b1i ~ N(0,1000), i=1,2,3,4,5

Input Labeled: training [(x1,y1),(-40,-55,-90,..)][(x2,y2),(-60,-56,-80,..)][(x3,y3),(-80,-70,-30,..)][(x4,y4),(-64,-33,-70,..)] Unlabeled: mobile object(s) [(?,?),(-45,-65,-40,..)][(?,?),(-35,-45,-78,..)][(?,?),(-75,-55,-65,..)] Probability distributions for all the unknown variables Propagation constants b0i, b1i for each Base Station (x,y) for each (?,?) Output

Great! but now how do we find the location of the mobile? Closed form solution doesn’t usually exist » simulation/analytic approx We used MCMC simulation (Markov Chain Monte Carlo) to generate predictive samples from the joint distribution for every unknown (x,y) location

Example Output

Some Results.. M1 is better Comparable 25th Med 75th Min Max

Model 2 (Hierarchical): labeled data Motivation borrowing strength might provide some predictive benefits  Xi Yi D1D1 D2D2 D3D3 D4D4 D5D5 S1S1 S2S2 S3S3 S4S4 S5S5 b 11 b 12 b 13 b 14 b 15 b 01 b 02 b 03 b 04 b 05 Xi ~ uniform(0,Length) Yi ~ uniform(0,Width) Si ~ N(b 0i +b 1i log(Di), δi) b0i ~ N(b0, δ b0 ) b1i ~ N(b1, δ b1 ) b0 ~ N(0,1000) b1 ~ N(0,1000) δ 0 ~ Gamma(0.001,0.001) δ 1 ~ Gamma(0.001,0.001) i=1,2,3,4,5 Allowing any values for b’s too unconstrained! Assume all base-stations parameters normally distributed around a hidden variable with a mean and variance

M2 behaves similar to M1, but provides improvement for very small training sets Hmm, still comparable to SmoothNN More Results.. Leave-one-out error (feet) Size of labeled data Average Error (feet) Labeled M1 Labeled Hier M2 SmoothNN

Can we get reasonable estimates of position without any labeled data? Yes! Observe signal strengths from existing data packets (unlabeled by default) No more running around collecting data.. Over and over.. and over..

Input Labeled: training [(x1,y1),(-40,-55,-90,..)][(x2,y2),(-60,-56,-80,..)][(x3,y3),(-80,-70,-30,..)][(x4,y4),(-64,-33,-70,..)] Unlabeled: mobile object(s) [(?,?),(-45,-65,-40,..)][(?,?),(-35,-45,-78,..)][(?,?),(-75,-55,-65,..)] Probability distributions for all the unknowns Propagation constants b0i, b1i for each Base Station (x,y) for each (?,?) Output

Model 3 (Zero Profiling) Same graph as M2 (Hierarchical) but with (unlabeled data)  Xi Yi D1D1 D2D2 D3D3 D4D4 D5D5 S1S1 S2S2 S3S3 S4S4 S5S5 b 11 b 12 b 13 b 14 b 15 b 01 b 02 b 03 b 04 b 05 Hmm, why would this work? [1] Prior knowledge about distance-signal strength [2] Prior knowledge that access points behave similarly

Results Close to SmoothNN, BUT…!! Leave-one-out error (feet) Size of input data Average Error in Feet Zero Profiling M3 SmoothNN LABELED UNLABELED

Other ideas Corridor Effects What? RSS is stronger along corridors Variable c =1 if the point shares x or y with the AP No improvements Informative Prior distributions S1S1 S2S2 S3S3 S4S4 S5S5 11 22 33 44 55  D1D1 D2D2 D3D3 D4D4 D5D5 Yi Xi C1C1 C2C2 C3C3 C4C4 C5C5

Comparison to previous work Distance in feet Probability Error CDF Across Algorithms RADAR Probabilistic M1-labeled M3-unlabeled M2-labeled More ad-hoc Adaptive No labor investment

Conclusion and Future Work First time to actually use BGM Considerable promise for localization Performance comparable to existing approaches Zero profiling! (can we localize anything with a radio??) Where are we going? Other models Variational approximations Tracking applications Minimum extra infrastructure (more information - better accuracy)!

Thanks! ☺