Localization in Wireless Networks

1. Localization in Wireless Networks David Madigan Columbia University

2. The Problem • Estimate the physical location of a wireless terminal/user in an enterprise • Radio wireless communication network, specifically, 802.11-based

3. Example Applications • Use the closest resource, e.g., printing to the closest printer • Security: in/out of a building • Emergency 911 services • Privileges based on security regions (e.g., in a manufacturing plant) • Equipment location (e.g., in a hospital) • Mobile robotics • Museum information systems

5. Physical Features Available for Use • Received Signal Strength (RSS) from multiple access points • Angles of arrival • Time deltas of arrival • Which access point (AP) you are associated with • We use RSS and AP association • RSS is the only reasonable estimate with current commercial hardware

6. Known Properties of Signal Strength • Signal strength at a location is known to vary as a log-normal distribution with some environment-dependent  • Variation caused by people, appliances, climate, etc. Frequency (out of 1000) Signal Strength (dB) • The Physics: signal strength (SS; in dB) is known to decay with distance (d) as SS = k1 + k2 log d

8. Location Determination via Statistical Modeling • Data collection is slow, expensive (“profiling”) • “Productization” • Either the access points or the wireless devices can gather the data • Focus on predictive accuracy

9. Prior Work discrete, 3-D, etc. • Take signal strength measures at many points in the site and do a closest match to these points in signal strength vector space. [e.g. Microsoft’s RADAR system] • Take signal strength measures at many pointsinthe site and build a multivariate regression model to predict location (e.g., Tirri’s group in Finland) • Some work has utilized wall thickness and materials

11. Krishnan et al. Results Infocom 2004 • Smoothed signal map per access point + nearest neighbor

13. Tree Models

14. Age > 70? Age > 70? Age > 30? yes yes no no yes no 2/2 2/2 1/5 1/5 3/4 3/3 What do you predict for the 56-year-old?

15. Y1Hospital = “yes” NumClaims > 10? Age > 70? yes yes yes no no no 1/3 2/4 1/1 1/6 2/2 1/5

16. Y1Hospital = “yes” yes no MaxCharlson > 3 NumClaims > 10 yes no yes no 1/1 2/2 1/1 3/3

17. NumClaims Age

18. NumClaims < 4 yes no Age > 60 Age > 30 yes no yes no Age < 42 blue NumClaims < 5 yes no yes no red blue NumClaims < 2 red yes no blue Age < 38 NumClaims yes no 5 red blue 4 3 2 1 10 20 30 40 50 60 70 Age

19. Regression Trees idea: pick splits to minimize mean square error where

20. Nearest Neighbor Methods

21. Nearest Neighbor Methods • k-NN assigns an unknown object to the most common class of its k nearest neighbors • Choice of k? • Choice of distance metric?

22. numClaims age

26. Library(kknn) myModel <- kknn(yesno~dollar+bang+money,spam.train,spam.test,k=3) > names(myModel) [1] "fitted.values" "CL" "W" "D" "prob" "response" "distance" "call" "terms" > myModel$fitted.values [1] n y y n y n y y y y n n n n n y n n y n n n y n n n y n y n n y n y n n n n n n y y n n n n n n y n n n n y n n n n y y y n n n n y n y n y n n n n n y n

27. D1 D3 D4 D5 D2 Bayesian Graphical Model Approach Y X S1 S3 S4 S5 S2 average

28. D11 D21 Dn1 D23 Dn3 D13 Dn4 D14 D24 Dn5 D15 D25 D22 D12 Dn2 Y1 X1 Y2 X2 S11 S13 S14 S15 S12 Yn Xn S21 S23 S24 S25 S22 b50 b40 b20 b30 b10 b51 b41 b21 b31 b11 Sn1 Sn3 Sn4 Sn5 Sn2

29. Plate Notation Yi Xi Dij Sij i=1,…,n b1j b0j j=1,…,5

33. D1 D3 D4 D5 D2 Hierarchical Model Y X S1 S3 S4 S5 S2 b1 b3 b4 b5 b2 b

34. Hierarchical Model Yi Xi Dij Sij i=1,…,n b1j b0j j=1,…,5 m0 t0 t1 m1

35. Yi Xi full joint: [m0][t0][m1][t1][b0|m0,t0][b1|m1,t1][S|b0,b1,D][D|X,Y][X][Y] Dij metropolis moves one variable at a time from the full conditional, e.g b1: Sij “Gibbs sampling” [b1|b0,m1,t1,m0,t0,S,D,X,Y] b1j b0j [b1,b0,m1,t1,m0,t0,S,D,X,Y] m0 t0 [b1|m1,t1][S|b0,b1,D] t1 m1 sampling importance resampling, rejection sampling, slice sampling

37. Pros and Cons • Bayesian model produces a predictive distribution for location • MCMC can be slow • Difficult to automate MCMC (convergence issues) • Perl-WinBUGS (perl selects training and test data, writes the WinBUGS code, calls WinBUGS, parses the output file)

38. What if we had no locations in the training data?

41. Zero Profiling? • Simple sniffing devices can gather signal strength vectors from available WiFi devices • Can do this repeatedly • Locations of the Access Points

42. Why does this work? • Prior knowledge about distance-signal strength • Prior knowledge that access points behave similarly • Estimating several locations simultaneously

43. D1 D3 D4 D5 D2 Corridor Effects Y X C1 C3 C4 C5 C2 S1 S3 S4 S5 S2 b1 b3 b4 b5 b2 b

44. Results for N=20, no locations corridor main effect corridor -distance interaction average error 0 0 20.8 0 1 16.7 1 0 17.8 1 1 17.3 with mildly informative prior on the distance main effect… corridor main effect corridor -distance interaction average error 0 0 16.3 0 1 14.7 1 0 15.8 1 1 15.9

46. Discussion • Informative priors • Convenience and flexibility of the graphical modeling framework • Censoring (30% of the signal strength measurements) • Repeated measurements & normal error model • Tracking • Machine learning-style experimentation is clumsy with perl-WinBUGS

48. Prior Work • Use physical characteristics of signal strength propagation and build a model augmented with a wall attenuation factor • Needs detailed (wall) map of the building; model portability needs to be determined • [RADAR; INFOCOM 2000] based on [Rappaport 1992]