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

Basestation Position Solving UsingTiming Advance Measurements

ICSIPChangsha 15.12.2010

Matti Raitoharju, Simo Ali-Löytty, Lauri Wirolahttp://math.tut.fi/posgroup

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Outline

·Background

·GSM range measurements 550 m

TA=1

TA=2

TA=3

TA=4

·Base station position solving

·Conclusions

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Motivation and objective

Basestation positions andcoverage areas are not in publicdomain

These are needed for positioningof phones without GPS

In this work we estimate bases-tation position using range mea-surements from GPS-equippedmobile phones

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Range measurements in GSM

Timing advance (TA) is used to compensatethe propagation delay of transmission due todistance between BS and GSM terminal

Transmission time of one GSM bit is 3.69µs

Radiowave propagates ≈ 1100m

TA granularity is 550m

LTE (4G) networks similar, granularity 78m

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Measured TA values

550 m

TA=0

TA=1

TA=2

TA=3

TA=4

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TA measurement modelling

Simple model:Range=TA ·550m+N(µ, σ2)

Alternative:separate error parametersRange=TAi · 550m+N(µi, σ

2

i)

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Measured TA distribution

0 550 1100 1650 2200 27500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance from BS [m]

Cum

ula

tive p

robabili

tyTA = 0

TA = 1

TA = 2

TA = 3

TA = 4

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Single normal distribution

0 550 1100 1650 2200 27500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance from BS [m]

Cum

ula

tive p

robabili

tyTA = 0

TA = 1

TA = 2

TA = 3

TA = 4

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Multiple normal distributions

0 550 1100 1650 2200 27500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance from BS [m]

Cum

ula

tive p

robabili

tyTA = 0

TA = 1

TA = 2

TA = 3

TA = 4

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Basestation position estimation

We compare two recursive Bayesian methods:

Point Mass Filter (PMF)

Gaussian Mixture Filter (GMF)

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Point Mass Filter

The probability density is approximated usinga grid of points

Optimal when number of grid points tends toinfinity

Easy to implement, but needs lots ofcomputational resources

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Gaussian Mixture Filter

The probability density is approximated usinga weighted sum of Gaussians

Measurements are linearized for each ofGaussian component in the estimation

Components are merged or deleted duringthe estimation

Much faster than PMF

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Real world examples

10 measurements 30 measurements

PMF:

GMF:550m

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Simulated BS position results

PMF uses exact measurement error model

PMF is used as a reference

Mean

Filter error [m]

GMF assuming ideal measurements 442

GMF using single error model 349

GMF using multiple error models 160

PMF 141

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Conclusions

TA measurements can be used to solve theBS position

Accuracy can be enhanced by TA modelingand TA measurement error separately fordifferent TA values

GMF performs fast and well in estimation

550 m

TA=0

TA=1

TA=2

TA=3

TA=4

0 550 1100 1650 2200 27500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance from BS [m]

Cum

ula

tive p

robabili

ty

TA = 0

TA = 1

TA = 2

TA = 3

TA = 4

http://math.tut.fi/posgroup– p. 15/??