Reasonable Resolution of Fingerprint Wi-Fi Radio Map for Dense Map Interpolation

1. Reasonable Resolution of Fingerprint Wi-FiRadio Map for Dense Map Interpolation Auckland, New ZealandJanuary 13-16, 2014 The 2014 FTRA International Symposium on Frontierand Innovation in Future Computing and Communications University of Seoul Wonsun Bong, Yong Cheol Kim

2. Overview • Introduction • Previous Works on Wi-Fi Based Localization • Fingerprint Localization and Radio Map • DPS (Discontinuity Preserving Smoothing) • Adaptive Smoothing • Derivation of Reasonable Resolution of Map • Experimental Results • Comparison with other interpolation methods • Comparison with full density radio map • Conclusions

3. Introduction : Indoor Localization Service • With GPS-like indoor navigation, • Find restroom in a department store • Find the gate in an airport • Receive deals from retailers upon entering into a shop Indoor Geo-Service GPS GPS signal cannot reach inside of building COEX MALL

4. Previous Works on Wi-Fi Based Localization RSS = Received Signal Strength Propagation Model Triangulation Signal Strength RSS is a indicator of distance from source. Empirical Radio Map Fingerprinting Pattern matching of measured RSS with the RSS patterns in the radio map

5. Google Indoor Maps • 2005. 02 Google Maps Released (for PC) • 2008.10 Google Maps Application (for Smart Phones) • 2011.11 Google Indoor Maps Application (for Smart Phones) Available in some locations in Europe, Canada, U.S.A. and Japan. (mostly airports, large stores and hotels)  locations of Wi-Fi APs are collected by the same vehicles which collect street view image data. GoogleIndoor Map San Francisco Airport (2nd floor)

6. Triangulation • Fingerprinting Localization Using Wi-Fi Signal

7. Triangulation Least Mean-Squared Triangulation:with Estimation Errors Ideal Triangulation AP 2 AP 2 AP 3 AP 3 AP 1 AP 1 AP 4 AP 4 Actual Position of MD Estimated Position of MD (Mobile Device)

8. Path Loss Model Pt P(r0) P(r) r0 r AP Ideal Model Real RSS MD Measured RSSI : -40 dBm  Distance is 10 meters.

9. Fluctuations of RSS by Perturbation of Wi-Fi Signal Accurate Model is Hard to Obtain. Attenuation Perturbing Objects Reflection of Wave AP P(r) MD r Wall

10. Fingerprint Localization Measure RSS at each grid AP 2 Offline Step Create Radio Map AP 3 AP 1 Actual Position of MD AP 4 Measure RSS at MD Position Online Step Similarity Measure: Euclidean distance between RSS vectors Find the most similar RSS pattern OR Get the avg. of K similar patterns (K-NN) Estimated Position of MD (Mobile Device)

11. Why is DPS Required in Radio Map? • Adaptive Smoothing Using Wall Information • Experimental Results DPS: Discontinuity Preserving Smoothing

12. Interpolation of Radio Map • Interpolation of Low Density Radio Map • The cost of radio map is high • Interpolation of a coarse map into a dense one reduces cost. • Problems with Radio Map Interpolation • The measured RSS exhibits discontinuity at barriers, especially at the wall boundaries. • An interpolation simply fits the measured data into a parametric curve  discontinuity of RSS is not well preserved. • An interpolated map has low accuracy near a wall.

13. Preserving Discontinuity The path loss model and the actual data have a large difference, especially at the wall boundaries. • Measured RSS : • Considerable drop at wall boundary • 19 dBm (side A) • 16 dBm (side B). • But path loss model does not handle discontinuity

14. Previous Works on Radio Map Interpolation (1) • IDW(Inverse Distance Weight) • A linear interpolation with weights dependent on the distance • No means of accommodating the RSS discontinuity around walls. • Kriging • A linear sum of measured RSS of surrounding RPs. • The coefficients are determined by spatial correlation of signal strength. • Kriging does not provide means of handling the wall discontinuity.

15. Previous Works on Radio Map Interpolation (2) • Voronoi Tessellation • Based on path loss model • Grouping of RPs are guided by Voronoi tessellation of second order. • Estimated parameters reflect the local property of the cell which holds just two RPs. • There is no preventing of a cell having two RPs at opposite sides of a wall. M. Lee and D. Han, ”Voronoi Tessellation Based Interpolation Method for Wi-Fi Radio Map Construction,” IEEE Communications Letters, Vol. 16 , Issue: 3, pp.404-407. March, 2012

16. Motivations and Scope of this Work • Motivation of this Paper • To interpolate a low-density radio map into a high-density map which preserves RSS discontinuity at wall boundaries • To present a closed form solution of reasonable resolution of radio map • To reduce the cost in the off-line stage of fingerprint radio map, which involves data measurement and calibration • Scope of this Work • To apply adaptive smoothing for the DPS functionality in the interpolation of low density radio map • To examine the lower bound of sampling density which achieves comparable performance • To compare the above experimental lower bound of sampling density and the derived resolution of reasonable radio map

17. Proposed DPS : Adaptive Smoothing • Discontinuity Preserving Interpolation from Sparse Data • Regularization-based methods have been developed • Not applicable to Radio map interpolation • Adaptive Smoothing • Simple smoothing technique • Fluctuation is reduced and skeleton is preserved Original signal Adaptively smoothed signal P. Saint-Marc and J. Chen, ”Adaptive Smoothing: A General Tool for Early Vision,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. l3, No. 6, June, 1991

18. Adaptive Smoothing of RSS across Walls • Interpolation is almost separately performed on both sides of the wall • Interpolated value of RSS is affected mainly by those which lie on the same side of the. RSS (dBm) : Measured : DPS : Path loss model : Wall Adaptive smoothing accommodates barrier.

19. Real RSS Data: Wall Layout Information in Interpolation (Wall information fully used) Room with AP Adaptive Smoothing

20. Kernel In Adaptive Smoothing p = 10 two RPs are separated by a wall P = 1 two RPs are on the same side of a wall If a wall lies between two RPs’, then the weight is very small two RPS have little impact on the smoothing process. This way, the office layout information is effectively utilized in the reconstruction of full density radio map.

21. Reasonable Resolution of Radio Map (1) • RSS fluctuation affects positional accuracy. • (difference of RSS at ) corresponds to radial difference. • Measurement error of RSS • Error in Radio map can be decreased by taking the average of N measurements. • RSS on MD side is measured only once or twice. • Radio map with too fine resolution is not needed. • Error of 1.5 dBm corresponds to 1.9 meter error.

22. Reasonable Resolution of Radio Map (2) • Map resolution worth efforts of measurement • A reasonable value of radio map would be of the order of positional error resulting from RSS fluctuation. • : reasonable resolution of radio map : standard deviation of RSS over time • .

23. Reasonable Resolution of Radio Map (3) Reasonable resolution w.r.t. std. dev. of RSS

24. Experiments with Real RSS Data • Environment • Sixth floor of IT-Building in Univ. of SeoulRP : grid of 1.2m by 1.2m (# of RP = 145 ) • RSS Measurement • At all RPs, measure RSS 100 times during 200 secs. • The average is taken to reduce the effect of random fluctuation. • (noise power reduced to 10 %) Variation of RSS in 80 measurements. Standard deviation of Measured RSS

25. Fingerprint Localization with Real RSS Data (1) • RSS vectors of all 145 RPs are randomly selected with a sampling density varying from 10% to 95% in 5 % step. • We constructed a series of low density(10%∼95%) radio map to find the lower bound of sampling density. • DPS outperforms IDW-interpolation and Voronoi-based interpolation.

26. Fingerprint Localization with Real RSS Data (2) • Observations: • With sampling density ≥ 35%, accuracy approaches the original full density map. • With sampling density ≥ 60%, DPS-interpolated map is even better than the original full density map. • In continuous spatial smoothing, the random fluctuation gets further reduced.  higher accuracy in localization. • For the other two methods, the effect of spatial smoothing is weak.

27. 27 / 20 Fingerprint Localization with Real RSS Data (3) Improvement w.r.t. sampling density • The average error decreases as the sampling density increases.

28. Conclusions • Radio map for fingerprint localization has high cost. • Discontinuity preserving smoothing can be used to generate a high density map. • Advantage of interpolated radio map • RSS measurement can be reduced to 35%. • With sampling density >= 60%, better than the original full density map • Reasonable resolution of radio map • Rmap is of the order of positional error of RSS measurement. • Fits well with the experimental results.