TA M P E R E U N I V E R S I T Y O F T E C H N O L O G Y

M a t h e m a t i c s

Indoor positioning using WLANcoverage area estimates

IPIN 2010

Laura Koski , Tommi Perälä, Robert Piché

http://math.tut.fi/posgroup/

– p. 1/16

Outline

Coverage area estimation and positioning

Floor plan in filtering

Filters

RSSI measurements

Example

– p. 2/16

Coverage area -based positioning

Coverage area estimation

Collect fingerprint data

Arrange the fingerprintdata so that for every AP,there is a list of locationreports Y = (y1, . . . ,yn)

For every AP, calculatecoverage are estimates

Positioning

Measure IDs of heard APs

Use coverage areaestimates of heard APs todetermine the position

– p. 3/16

Coverage area estimation, Prior

Measurement model:

Y = 1nµT + ǫ, where ǫ(i)|µ,Σ ∼ N(02,Σ)

– p. 4/16

Coverage area estimation, Likelihood

– p. 5/16

Coverage area estimation, Posterior

x|c ∼ N(µ,Σ)

– p. 6/16

Position estimate

x ∼ N(x̂,C), in which

x̂ = (∑k

i=1 Σ−1i )−1(

∑k

i=1 Σ−1i µi) and

C = (∑k

i=1 Σ−1i )−1

– p. 7/16

Floor plan

Floor plan is divided into boxes

Graph describes the connection between boxes

1 2

3 4 5

G =

1 1 1 0 01 1 0 1 11 0 1 1 00 1 1 1 10 1 0 1 1

ΦT =

1/3 1/3 1/3 0 01/4 1/4 0 1/4 1/41/3 0 1/3 1/3 00 1/4 1/4 1/4 1/40 1/3 0 1/3 1/3

.

– p. 8/16

Filters, Box Filter (BF)

p = ((p)1, . . . , (p)nB)T is the state vector, (p)i is the

probability mass inside the ith box

use the transition matrix Φ for the state evolution

Predict: p−

k = Φpk−1

Update (pk)j = (p−

k )jπ(j),

π(j) is the probability mass inside the jth box

Position estimate xk =

nB∑

i=1

(pk)imi

– p. 9/16

Filters, Particle Filter (PF)

Standard bootstrap filter, but for every time step tk for everyparticle xk, we determine the box jk it is associated with

Weights are assigned as follows:

wik+1 ∝

L(c|xik+1) if Gji

kjik+1

= 1

0 if Gjikjik+1

= 0.

– p. 10/16

RSSI measurements

Discarding weak signals leads to

Smaller coverage area estimates

More accurate positioning performance

Difficulty: definition of RSSI may vary in different MT models.Idea: Each MT could construct its own histogram of RSSI valuesobserved over a long time interval.

−100 −90 −80 −70 −60 −50 −40 −30RSSI

probability

50 60 70 80 90RSSI

probability

– p. 11/16

Test deployment

96 calibration points

206 heard APs

∼29 heard APs per fingerprint

10 m

Calibration pointsTrack 1Track 2

– p. 12/16

ResultsTrack 1 Track 2

ME [m] Max [m] ME [m] Max [m]Coverage area 7.5 29.8 8.7 27.9NN 9.9 31.3 8.1 31.3KFCoverage area 7.4 26.4 7.1 12.6PKFNN 7.4 21.6 6.7 14.4BF 6.4 18.2 7.8 22.5PF 6.4 19.3 8.6 21.5

10 m

Track1KFBFPF

10 m

Track 2KFBFPF

– p. 13/16

Results, RSSI threshold

Threshold in coverage area estimation is median of RSSI valuesand in positioning mean of RSSI values

ME [m] Max [m]

KF 7.4 26.4

BF 6.4 18.2

PF 6.4 19.3

ME [m] Max [m]

KF 5.5 18.7

BF 4.5 14.2

PF 5.0 15.5It is not straightforward to find the optimal RSSI values thatworks in every environment.

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Conclusion

Coverage area -based positioning achieves same accuracyas NN

Floor plan improves the positioning accuracy

KF achieves almost the same accuracy as PF and BF withsignificantly lower computational load

Use of RSSI values improve positioning accuracy

– p. 15/16

Conclusion

Coverage area -based positioning achieves same accuracyas NN

Floor plan improves the positioning accuracy

KF achieves almost the same accuracy as PF and BF withsignificantly lower computational load

Use of RSSI values improve positioning accuracy

Thank You!Questions?

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