Localization of Mobile Users Using Trajectory Matching

ACM MELT’08HyungJune Lee, Martin Wicke,

Branislav Kusy, and Leonidas GuibasStanford University

Motivation

• Location is an important and useful resource– Push local information to nearby mobile users

• Restaurant, Café, Shopping center on sale, …

– Building automation, etc.

• GPS not available– Indoor, mobile environment

• ~1m-accuracy– Usable for location-based service

2

Motivation• RSSI-based localization• Indoor setting

– Due to reflection, refraction, and multi-path fading,specific model does not work

– More severe link variation caused by mobility

• Range-free methods– Connectivity & Triangulation:

DVhop[Niculescu03] , APIT[He05]– RSSI pattern matching:

RADAR[Bhal00], MoteTrack[Lorincz07]– Bayesian inference & Hidden Markov Model:

[Haeberlen04], [Ladd04], LOCADIO[Krumm04]

• Idea: Use historical RSSI measurements3

RSSI graph

Outline

• Trace Space• Localization algorithm

– Training Phase with RBF construction– Localization Phase

• Evaluation• Conclusion and Future work

4

Trace Space

• Traces of RSSI readings form a trace space .

• Each trace T corresponds to a location

• Learn to match a trace to a positioni.e., L( ): → ∙ R2

2 1

3

4

5

5

(x1, y1)

(x2, y2)

T =

: → L =

x y

R2

(x1, y1)

Nk ,

Nk ,

Nk ,

Training Phase with RBF Fitting• Training input r

in trace space

• Training output p

in R2 space

• Solve linear systems of training data by least-squares

• Obtain L( ) function∙

Tyx ppprL ] [)(

squares-leastby solved are

),,1( , , Cj Njbaw

6

center RBF a is where

)()(1

j

N

jjj

x

c

barcrwrLC

Tr vectorsRSSI Nk ,

• Localization phase– Calculate the L ( ) given current trace ∙ T in test sets

• Sparse interpolation in trace space– Handles noisy input data gracefully– Extrapolates to uncharted regions

Localization Phase

7Illustration from “Scattered Data Interpolation with Multilevel B-Splines” [Lee97]

Location X

Location Y

LX (T)

LY (T)

RSSI graph

Evaluation• MicaZ motes

– CC2420 radio chip

• 10 stationary nodes• 1 mobile node• 14 waypoints location

• Ground-truth: (r(t), p(t))– Training RSSI vector r(t)– Training position p(t)

• linear interpolation between waypoints

8

32 1

7

6

8

9

45

101

Evaluation• Training phase

: (a), (b), (c), (d), (e)• Testing phase

: (f), (g), (h), (i)• 5 runs for each path

• Error measures– Position error

– Path error9

Influence of Historical data

10

History size k

1.28 m

2.4 m

11

Other Link Quality Measures

1.28 m

1.74 m

2.02 m

Conclusion

• Historical RSSI values significantly increase the fidelity of localization (mean position error < 1.3 m)

• Our algorithm also works well with any link quality measurements, e.g., LQI or PRR, which allows flexibility of the algorithm

12

Future work

• Prediction of future location• Scalability• Dynamic time warping for different speed

13

Questions?

14

HyungJune Leeabbado@stanford.edu

Radial Basis Function Fitting(Backup)

• Multi-quadratic function

• By least-squares

15

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Influence of # of RBF centers Nc

(Backup)

16

# of RBF centers Nc

Influence of Average Window Size b (Backup)

17

Burst window size b