Location Fingerprint Analyses Toward
Efficient Indoor Positioning
Nattapong Swangmuang and Prashant Krishnamurthy
Graduate Program in Telecommunications and Networking
University of Pittsburgh
135 N. Bellefield Avenue, Pittsburgh, Pennsylvania 15260
5/18 study group by Jason
Outline
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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.
Indoor Localization Fingerprint Model
• 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).
Indoor Localization Fingerprint Model
• 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.
Indoor Localization Fingerprint Model
• PEP (pair-wise error prob.)and PCP(pair-wise
correct prob.)=1-PEP
Ri’
sdik’
Rk’
Indoor Localization Fingerprint Model
• 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.
Analytical Model for Probability
Distribution
• 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
Analytical Model for Probability
Distribution
– (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
Analytical Model for Probability
Distribution
• (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, sd <=max[sd , sd ].
uv
w
u
w
v
uw
vw
Analytical Model for Probability
Distribution
• 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
Performance Evaluation
Performance Evaluation
Performance Evaluation
Performance Evaluation
Performance Evaluation
Performance Evaluation
Performance Evaluation
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