modified random forest algorithm for wi fi indoor...

Modified Random Forest algorithm for Wi–FiIndoor Localization System

Rafal Gorak, Marcin Luckner

Faculty of Mathematics and Information SciencesWarsaw University of Technology

September 2016

Indoor Positioning System (IPS)

Problem

Provide a localization of the terminal inside the building based on:

Received Signal Strength (RSS) from different radio sources such asWi–Fi Access Points, or Base Transiver Stations of a cellularnetwork.

Sensor readings such as magnetometer, accelerometer or pressuresensor.

We present the solution that is based only on existing Wi-Fiinfrastructure inside the building of Faculty of Mathematics andInformation Science of Warsaw University of Technology.

Rafal Gorak, Marcin Luckner Modified Random Forest algorithm for Wi–Fi Indoor Localization System

Problem

The building

The concept of fingerprinting

Data sets

Building a localization model using Random Forest method

Lx : Rn 7→ R

Using a Random Forest method we grow regresion trees in order to

create Lx and Ly and for Lf the classification trees are grown.

LRF : Rn 7→ R2 × {0, 1, 2, ..., 5}

LRF (v) = (Lx(v), Ly(v), Lf(v))

LRF : Rn 7→ R2 × {0, 1, 2, ..., 5}

Modification of the Random Forest approach

The idea is to create for every Access Point

a the localization model

La = (Lax, La

y, Laf).

The idea is to create for every Access Point

a the localization model

La = (Lax, La

y, Laf).

How to built Lax?

Hence, we have a localization model

La = (Lax, La

y, Laf)

for every Access Point a from the academicnet inside the building.

Figure: Access Points a1,...,a4 and the position where the measurement v ∈ Rn

was taken

LmRF (v) = (x, y, f) where

x = (La1x (v) + La2

x (v) + La3x (v))/3

y = (La1y (v) + La2

y (v) + La3x (v))/3,

f = mode{La1f (v), La2

f (v), La3f (v)}.

x = (La1x (v) + La2

x (v) + La3x (v))/3

y = (La1y (v) + La2

y (v) + La3x (v))/3,

f (v), La3f (v)}.

x = (La1x (v) + La2

x (v) + La3x (v))/3

y = (La1y (v) + La2

y (v) + La3x (v))/3,

f (v), La3f (v)}.

Testing a localization model

L = LRF

orL = LmRF

L = LRF

orL = LmRF

L = LRF

orL = LmRF

L = LRF

orL = LmRF

Horizontal error =√

(x− x)2 + (y − y)2

(13− 14.52)2 + (15− 18.34)2

Floor is correctly predicted.

(x− x)2 + (y − y)2

(13− 14.52)2 + (15− 18.34)2

(x− x)2 + (y − y)2

(13− 14.52)2 + (15− 18.34)2

(x− x)2 + (y − y)2

(13− 14.52)2 + (15− 18.34)2

Results

HME − Horizontal Mean Error

FE − Floor Error - the rate of incorrectly predicted floors

Results

i FE HME1 0.0094 1.322 0.0284 3.663 0.0264 3.554 0.0849 4.365 0.0769 4.53

i FE HME1 0.0087 0.572 0.0291 3.343 0.0222 3.294 0.0822 4.115 0.0711 4.30

LRF LmRF

Results after 3 APs are turned off

i FE HME1 0.0094 1.322 0.0565 4.803 0.0581 4.364 0.1101 4.885 0.1089 5.09

i FE HME1 0.0087 0.572 0.0487 3.803 0.0436 3.744 0.1002 4.345 0.0933 4.58

LRF LmRF

Results after 3 APs are turned off

i FE HME1 0.0094 1.322 0.0565 4.803 0.0581 4.364 0.1101 4.885 0.1089 5.09

i FE HME1 0.0087 0.572 0.0487 3.803 0.0436 3.744 0.1002 4.345 0.0933 4.58

LRF LmRF

Comparison

Karwowski, J., Okulewicz, M., Legierski, J.:Application of particle swarm optimization algorithm toneural network training process in the localization ofthe mobile terminal.

Enginering Applications of Neural Networks14th International Conference,2013 Proceedings,Part I. Comunications in Computer and Information Science, vol 383, pp.122-131 Springer (2013)

Comparison

Karwowski, J., Okulewicz, M., Legierski, J.:Application of particle swarm optimization algorithm toneural network training process in the localization ofthe mobile terminal.

Enginering Applications of Neural Networks14th International Conference,2013 Proceedings,Part I. Comunications in Computer and Information Science, vol 383, pp.122-131 Springer (2013)

Acknowledgement

The research is supported by the National Centre for Research andDevelopment, grant No PBS2/B3/24/2014, application No 208921.

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