Location Fingerprint Analyses Toward Efficient Indoor Positioning

Location Fingerprint Analyses Toward Efficient Indoor Positioning

Nattapong Swangmuang and Prashant KrishnamurthyGraduate Program in Telecommunications and Networking

University of Pittsburgh135 N. Bellefield Avenue, Pittsburgh, Pennsylvania 15260

5/18 study group by Jason

Outline

• Introduction & Related Work• Indoor Localization Fingerprint Model• Analytical Model for Probability Distribution• Performance Evaluation• Application to Offline phase

Introduction & Related Work

• Traditional techniques: TOA: time of arrival, AOA: angle of arrival…

• Modern techniques for indoor environment: Fingerprint, Bayesian modeling, Statistical learning…

Introduction & Related Work

• Euclidean distance between some set < variation of RSS measured from those sets

• The accuracy of deterministic approach or probabilistic approach has been reported to be similar

• Employing proximity graphs for predicting performance of the system

Indoor Localization Fingerprint Model

• WLAN based system• A square area with L*L=L^2 grids, using the mean of

the RSS from N Aps in the area.


• The sample vector is denoted as: R = [r1, r2, r3, ..., rN]– The random variables ri (in dBm) for all i are mutually

independent.– The random variables ri(in dBm) are normally (or

Gaussian) distributed.– The (sample) standard deviation of all the random

variables ri is assumed to be identical and denoted by (in dB).

– The mean of the random variable ri or E{ri} is denoted as ρi (in dBm).


• The assumption that the RSS is normally distributed is acceptable.

• When the APs are far from measured location and no direct LOS with, the distribution can be approximated by Gaussian.

• R’ = [ρ1, ρ2, ρ3, ..., ρN] as fingerprint vector• Z=norm(R-R’), with central or non-central chi

distribution.


• PEP (pair-wise error prob.)and PCP(pair-wise correct prob.)=1-PEP

Ri’ Rk’

sdik’


• Ck = || Ri’ − Ri|| − || Rk’ − Ri|| is taken to calculate probability of correct decision:

•With assumption of independence to simplify

Analytical Model for Probability Distribution

• Voronoi Diagram is a set of fingerprints defined as a division of the space according to the nearest-neighbor rules.


• Finding neighbor set is relative close to the target location

• Three proximity graph:– DG(Delaunay Graph): In the graph, there exists a

Delaunay edge between two points u, v if they share the same Voronoi edge as boundary


– (GG)Gabriel Graph: a graph that contains a Gabriel edge between two points u, v – if a diametral circle from these two points contains no other point w.

Satisfied: (ab)^2<(ac)^2+(bc)^2


• (RNG)Relative Neighbor Graph: a graph that contains an edge between two points u, v – if there is no other point w that is imultaneously closer to both points than they are to one another. Mathematically, sduv <=max[sduw, sdvw].

u v

w w


• Given the Mobile Station is at grid i• Remove the effect from remote grids

Performance Evaluation

We simulated 10,000 RSS samples from a given MS location and applied the nearest neighbor computation to estimate its location








Application to Offline Phase

• Strong RSSs(-60~-40dBm) have low standard deviation(1~2dB) at LOS areas

• Week RSSs(-95~-85dBm) have high standard deviation(6~7dB) at NLOS areas

• Eliminating unnecessary grids to save effort– Sparse grids on open and large areas– Still need trail-and-error to make sure ‘good’

fingerprints of grids.

Thanks and Q&A

Documents

Location Fingerprint Analyses Toward Efficient Indoor Positioning