1. Positioning with Multilevel Coverage Area Models
Matti Raitoharju, Marzieh Dashti,
Simo Ali-Löytty & Robert Piché

2. Problem
WLAN maps (radiomaps) are databases generated using fingerprints containing the location and access point IDs
What kind WLAN map is best for positioning?
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

3. Requirements Map size does not depend on number of fingerprints
Map is tolerant to outliers
Positioning accuracy with these maps is as good as conventional fingerprinting
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

4. Coverage area models
Model the coverage area as Student-t or normal distribution
R. Piché, “Robust estimation of a reception region from location fingerprints”
Prior is used → model may be constructed even from a single FP
Student-t is more robust to outliers
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

5. Multivariate Student-t models
Parameters for construction of a Student-t model
r – a typical range of an access point
ν – degree of freedom, if ν →∞ the distribution is normal
τ – strength of prior (σ=τr2)
d – dimension (2)
T – number of iterations
A coverage area is defined using parameters
µ - mean of the model
Σ – shape matrix
P = ν/(ν-2) Σ – covariance matrix
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Student-t regression
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7. Positioning
With vague prior, position estimate is a weighted average of the coverage area centres
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

8. Multilevel coverage area models
CA approach only uses presence/absence of AP signal (i.e. single RSS threshold level)
To better use the RSS information: fit several CAs to each AP (multiple RSS threshold levels)
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

9. Model comparison 50m Outliers does not change the mean much
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

10. Storage In our outdoor data
For 2-level model, 10 numbers have to be stored
2 means
2 covariance matrices
In our outdoor data
conventional FP method
would need 114
numbers for each AP
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

11. Test setup Different prior and distribution parameters were tested
FP1
FP2
AP1
-50
-60
AP2
-55
-65
AP3
-70
AP4
-75
AP5
AP6
Different prior and distribution parameters were tested
Different criteria to set the level thresholds
RSS-level
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

12. Test setup Different prior and distribution parameters were tested
FP1
FP2
AP1
-50
-60
AP2
-55
-65
AP3
-70
AP4
-75
AP5
AP6
Different prior and distribution parameters were tested
Different criteria to set the level thresholds
RSS-level
n-strongest
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

13. Test setup Different prior and distribution parameters were tested
FP1
FP2
AP1
-50
-60
AP2
-55
-65
AP3
-70
AP4
-75
AP5
AP6
Different prior and distribution parameters were tested
Different criteria to set the level thresholds
RSS-level
n-strongest
x%-strongest
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

14. Indoor results
50m
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

15. Indoor results
Two CA models improved positioning accuracy compared to one
Two and three level models had similar positioning accuracy
For all threshold criteria there were good parameters
The Student-t models with weak and small prior produced the best results
Mean error was slightly smaller than conventional fingerprinting
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

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Indoor results
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17. Outdoor results
Multilevel coverage area models did not improve positioning performance much
Optimal prior was stronger and larger than in indoor test
Student-t was worse than normal models
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning

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Outdoor results
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21. Conclusions and outlook
Use of two level coverage areas slightly improved the positioning accuracy indoors
Order of RSS values can be used for dividing FPs to weak and strong
Positioning with Student-t?
Mixture of Gaussians or Students?
Matti Raitoharju Using Unlocated Fingerprints in Generation of WLAN Maps for Indoor Positioning