Part of the Joint Project by HKBU, HKIVE and Several Local Mobile Service Providers for Accurate Low-cost Mobile localization

SSupport upport VVector ector RRegression for egression for Location Estimation Using Location Estimation Using

GSM Propagation DataGSM Propagation Data

Dr. Chun-hung LiDepartment of Computer Science

Hong Kong Baptist UniversityJune, 2003

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Contents

• Introduction • Related Works• SVR via Missing Value Insensitive Kernel• Simulation & Field Test• Q & A

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Introduction

• Task • To estimate the location of a mobile device using the information based on the GSM Networks

• Approach -- Network-based Solutions• Provide the location service using the network information without modifying the mobile phone

• Baseline Accuracy• Federal Communications Commission rule - 100m (67% of the time)

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Introduction – GSM Network Information

• Returned from the mobile phone side 1. Serving Cell ID2. BSIC3. BCCH No4. Received signal strength (dBm)

• Other Station Information• Station Position (x & y) • Height• Bearing• Cell Type• Antenna Type• Station Power strength (dBm)• ……

1

3 2 4

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Related Works - Network-based solution

•Precise time and direction based methods - TOA: Time of Arrival- AOA: Angle of Arrival- TDOA: Time-Difference of Arrival- Require Synchronization Clock or Smart Antennas

•Signal Strength Attenuation Modeling Approach

- Mapping signal strength into distance-- e.g. Free Space Model, HATA model, …

- Recover coordinate from distance-- Cell-ID, Weighted CG-- Tri-lateration

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Related Works – Weighted CG & Cell-ID

• Based on Free Space Model– The distance and the received signal strength is an inversely

proportional function– Or Approximation:

• Weighted Central of Gravity (CG)– Smaller Distances -> nearer to stations

– If N is 1, obtain the Cell-ID Method

lg [ ]d s dBm

N

i i

i

N

i iN

i i

i

N

i i

s

xs

d

xd

x

1

1

1

1

1

1

1

1 where N is the number of neighboring base stations, Δs is the signal strength falloff in dBm

Related Works – Circular Trilateration

Transmitter

Estimated mobile location

r1

r2r3

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Related Works – Machine Learning Approach

•More robust calibration of Propagation Models• Statistical Modeling Approach

•Directly map signal strength to location output• Wireless LAN Positioning via

• Neural Network, • Support Vector Classification/Regression

• Fingerprinting Method

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Why using Machine Learning Approaches

• Hard to Obtain a Parametric Model • Terrain Factors, multi-path, occlusion, …• Noise Measurement, Weather Condition, …

• Comparably Easy to get a lot of data• Fit a nonparametric model to the data• No need for domain experts/domain models• Changes in models/parameters can be re-learned

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

• Adopting a mapping to transform all signal strength readings at a location into a series of descriptors:

•E.g.

•Linearly regress the series of descriptors into the position output

Introduction to Support Vector Regression

( )

1 2 1 2 1 2 1( , ,..., ) ( , , , ln ,..., ln ) (N Ns s s s s s s s s

From N Stations A usually long vector, possibly

s= s)

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

1 2 1 2 1

1 2 1 2 1

( , , , ln ,..., ln )

( , , , ln ,..., ln )

T

N x x

T

N y y

x s s s s s s w b

y s s s s s s w b

W is of the same length as the long descriptor vector

• w by solution is the linear combination of a set of descriptor vectors from l training data

•E.g.

• Location output (x or y) :

• The key is to seek a Kernel function

Introduction to Support Vector Regression – Cont.

1

[ ( ) ( ) ]l

T

i xi

x b

(i)r s

1

)l

ii

w

(i)(r

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

( , ( ) ( )Tk r s)= r s

Where r(i) denotes the i-th signal vector used for training

• e.g. RBF Kernel:

•S is a severely sparse vector• Only 3~9 signals are retrievable• e.g. two sample signal reading Vectors:

•Impute empty cells by values: •Too many! & What’s the physical meaning?

Incompetent Conventional Kernels

2 22 2( ,k e e

2 T||(r s)|| (r s)(r s)

r s)=

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Station 5 12 17 18 19 24

r -71 -60 N -76 -65 -74

s -57 -74 -70 N -72 N

• Sum of Exponential Kernel (SoE)

•Where

• It is a valid kernel by proof• Recently proved to be a variant of the 1st-order RBF-ANOVA Kernel

A New Missing Value Insensitive Kernel

22( , ( ) ( )k e

2

q q||(r s )||N

q qq=1

r s)= r s

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

0,

1,( ) { q if s is empty

q otherwises

A Kernel Matrix Evaluated from SoE

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Experimental Results – Simulation Study

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

• Model adapted from [Roos 2001]•Adding Occlusion and Noise effects

• Experiment Settings •30 km2 Data Collection Region•640 Training Markers, 200 Testing Markers•64 Base Stations, 8 receivable

RoosRBF without any

missing value handling

SoE

Mean Error (m) 403 6704 355

Data Collection

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Experimental Results – Field Data Test

Experimental Results – Field Data Test

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

•Experiment Settings

• A 350 x 550m data Collection Region• Total 15 Markers• 120 set of readings / marker• 50 Base Stations, 7~9 receivable

CG CT

mean Error(m)

85.29 95.18

Experimental Results – Field Data Test

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

• Experiment Results

• For SVR Training:• 9 Markers for Training• Multiple sets of readings from each training marker

• For SVR Testing:1. Predict one location for a single set of readings2. Predict one location for multiple sets of readings

acquired at the same site and in a short interval

1) 8 of 120 sets of training readings from each of the 9 of 15 markers2) 120 sets of testing readings from the remain 6 of 15 markers3) mean error = 47m

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

1) predict 120 sets of readings in each testing marker to one location2) interval: 2 min3) mean error = 21m

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

or shown in following diagram:

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression

Q & A

GSM Localization via Missing Value Insensitive Support Vector RegressionGSM Localization via Missing Value Insensitive Support Vector Regression