1. Localization of Mobile Users Using Trajectory Matching ACM MELT’08 HyungJune Lee, Martin Wicke, Branislav Kusy, and Leonidas Guibas Stanford University

2. 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

3. 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 measurements 3 RSSI graph

4. Outline Trace Space Localization algorithm – Training Phase with RBF construction – Localization Phase Evaluation Conclusion and Future work 4

5. Trace Space Traces of RSSI readings form a trace space. Each trace T corresponds to a location Learn to match a trace to a position i.e., L(∙): → R 2 2 1 3 4 5 5 (x 1, y 1 ) (x 2, y 2 ) T = : → L = xyxy R2R2 (x 1, y 1 )

6. Training Phase with RBF Fitting Training input r in trace space Training output p in R 2 space Solve linear systems of training data by least-squares Obtain L(∙) function 6

7. 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 7 Illustration from “Scattered Data Interpolation with Multilevel B-Splines” [Lee97] Location X Location Y L X (T) L Y (T)

8. 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 3 2 1 7 6 8 9 45 10 1

9. Evaluation Training phase : (a), (b), (c), (d), (e) Testing phase : (f), (g), (h), (i) 5 runs for each path Error measures – Position error – Path error 9

10. Influence of Historical data 10 History size k 1.28 m 2.4 m

11. 11 Other Link Quality Measures 1.28 m 1.74 m 2.02 m

12. 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

13. Future work Prediction of future location Scalability Dynamic time warping for different speed 13

14. Questions? 14 HyungJune Lee abbado@stanford.edu

15. Radial Basis Function Fitting (Backup) Multi-quadratic function By least-squares 15

16. Influence of # of RBF centers N c (Backup) 16 # of RBF centers N c

17. Influence of Average Window Size b (Backup) 17 Burst window size b