Reasonable Resolution of Fingerprint Wi-Fi Radio Map for Dense Map Interpolation University of Seoul Wonsun Bong, Yong Cheol Kim Auckland, New Zealand January 13-16, 2014 The 2014 FTRA International Symposium on Frontier and Innovation in Future Computing and Communications

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 2/28

Introduction : Indoor Localization Service 3/28 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 GPS GPS signal cannot reach inside of building

Previous Works on Wi-Fi Based Localization 4/28 Signal Strength Empirical Radio Map Propagation Model Triangulation Fingerprinting RSS is a indicator of distance from source. Pattern matching of measured RSS with the RSS patterns in the radio map RSS = Received Signal Strength

Google Indoor Maps  Google Maps Released (for PC)  Google Maps Application (for Smart Phones)  Google Indoor Maps Application (for Smart Phones) 5/28 locations of Wi-Fi APs are collected by the same vehicles which collect street view image data. Available in some locations in Europe, Canada, U.S.A. and Japan. (mostly airports, large stores and hotels) Google Indoor Map San Francisco Airport (2nd floor)

Localization Using Wi-Fi Signal  Triangulation  Fingerprinting 6/28

Triangulation Ideal Triangulation Estimated Position of MD (Mobile Device) AP 1 AP 2 AP 3 AP 4 AP 1 AP 2 AP 3 AP 4 Actual Position of MD Least Mean-Squared Triangulation: with Estimation Errors 7/28

Path Loss Model MD P(r)P(r) AP r r0r0 P(r0)P(r0)PtPt Measured RSSI : -40 dBm  Distance is 10 meters. Ideal Model Real RSS 8/28

Fluctuations of RSS by Perturbation of Wi-Fi Signal MD P(r)P(r) AP r Wall Perturbing ObjectsAttenuationReflection of Wave Accurate Model is Hard to Obtain. 9/28

Fingerprint Localization AP 1 AP 2 AP 3 AP 4 Estimated Position of MD (Mobile Device) Actual Position of MD Similarity Measure: Euclidean distance between RSS vectors Measure RSS at each grid Measure RSS at each grid Create Radio Map Measure RSS at MD Position Measure RSS at MD Position Find the most similar RSS pattern OR Get the avg. of K similar patterns (K-NN) Find the most similar RSS pattern OR Get the avg. of K similar patterns (K-NN) Offline Step Online Step 10/28

DPS: Discontinuity Preserving Smoothing  Why is DPS Required in Radio Map?  Adaptive Smoothing Using Wall Information  Experimental Results 11/28

 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. Interpolation of Radio Map 12/28

The path loss model and the actual data have a large difference, especially at the wall boundaries. Preserving Discontinuity Measured RSS : Considerable drop at wall boundary 19 dBm (side A) 16 dBm (side B). But path loss model does not handle discontinuity 13/28

 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. Previous Works on Radio Map Interpolation (1) 14/28

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. Previous Works on Radio Map Interpolation (2) M. Lee and D. Han, ”Voronoi Tessellation Based Interpolation Method for Wi-Fi Radio Map Construction,” IEEE Communications Letters, Vol. 16, Issue: 3, pp March, /28

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 16/28

 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 signalAdaptively smoothed signal Proposed DPS : Adaptive Smoothing 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, /28

 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. Adaptive smoothing accommodates barrier. Adaptive Smoothing of RSS across Walls 18/28 RSS (dBm) : Wall : Measured : DPS : Path loss model

Adaptive Smoothing Room with AP (Wall information fully used) Real RSS Data: Wall Layout Information in Interpolation 19/28

Kernel In Adaptive Smoothing 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. 20/28 p = 10 two RPs are separated by a wall P = 1 two RPs are on the same side of a wall

Reasonable Resolution of Radio Map (1) 21/28  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.

Reasonable Resolution of Radio Map (2) 22/28  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.

Reasonable Resolution of Radio Map (3) 23/28 Reasonable resolution w.r.t. std. dev. of RSS

 Environment Sixth floor of IT-Building in Univ. of Seoul RP : grid of 1.2m by 1.2m (# of RP = 145 ) IndexAP-1AP-2AP-3AP-4 σ [dBm] Variation of RSS in 80 measurements. Standard deviation of Measured RSS  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 %) Experiments with Real RSS Data 24/28

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. Fingerprint Localization with Real RSS Data (1) 25/28

 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. Fingerprint Localization with Real RSS Data (2) 26/28

27 / 20 The average error decreases as the sampling density increases. Improvement w.r.t. sampling density Fingerprint Localization with Real RSS Data (3) 27/28

 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 R map is of the order of positional error of RSS measurement. Fits well with the experimental results. Conclusions 28/28