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, 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 points in the 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. What do you predict for the 56-year-old?
Age
MaxCharlson
Y1Hospital
NumClaims
Y2Hospital 75 4
Yes 12 1 No 35 38 15 3 5 23 2 11 56 22 ?
Age > 70?
1/5
2/2
yes no
Age > 70?
1/5
2/2
yes no
Age > 30?
3/3
3/4
yes no
What do you predict for the 56-year-old?

15. Age > 70? 1/5 2/2 NumClaims > 10? 1/6 1/1 Y1Hospital = “yes” 2/4
MaxCharlson
Y1Hospital
NumClaims
Y2Hospital 75 4
Yes 12 1 No 35 38 15 3 5 23 2 11 56 22 ?
Age > 70?
1/5
2/2
yes no
NumClaims > 10?
1/6
1/1
yes no
Y1Hospital = “yes”
2/4
1/3
yes no

16. Age
MaxCharlson
Y1Hospital
NumClaims
Y2Hospital 75 4
Yes 12 1 No 35 38 15 3 5 23 2 11
Y1Hospital = “yes” no
yes
MaxCharlson > 3
NumClaims > 10 no
yes no
yes
2/2
1/1
3/3
1/1

17. NumClaims
Age

18. 5 4 3 2 1 10 20 30 40 50 60 70 Age NumClaims NumClaims < 4no
yes
Age > 30
Age > 60
yes no
yes no
Age < 42
blue
NumClaims < 5 no
yes no
yes
red
blue
NumClaims < 2
red no
yes
blue
Age < 38
NumClaims 5 no
yes
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. Bayesian Graphical Model ApproachX Y D1 D2 D3 D4 D5 S1 S2 S3 S4 S5
average

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

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

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

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

35. Xi Yi
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]
b0j
b1j
[b1,b0,m1,t1,m0,t0,S,D,X,Y] m0 t0 m1 t1
[b1|m1,t1][S|b0,b1,D]
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. Corridor Effects X Y D1 D2 D3 D4 D5 C1 C2 C3 C4 C5 S1 S2 S3 S4 S5 b1

44. Results for N=20, no locations
corridor
main
effect
corridor
-distance
interaction
average
error
with mildly informative prior on the distance main effect…
corridor
main
effect
corridor
-distance
interaction
average
error

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]