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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
– p. 1/??
Outline
·Background
·GSM range measurements 550 m
TA=1
TA=2
TA=3
TA=4
·Base station position solving
·Conclusions
– p. 2/??
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
– p. 3/??
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
– p. 4/??
Measured TA values
550 m
TA=0
TA=1
TA=2
TA=3
TA=4
– p. 5/??
TA measurement modelling
Simple model:Range=TA ·550m+N(µ, σ2)
Alternative:separate error parametersRange=TAi · 550m+N(µi, σ
2
i)
– p. 6/??
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
– p. 7/??
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
– p. 8/??
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
– p. 9/??
Basestation position estimation
We compare two recursive Bayesian methods:
Point Mass Filter (PMF)
Gaussian Mixture Filter (GMF)
– p. 10/??
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
– p. 11/??
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
– p. 12/??
Real world examples
10 measurements 30 measurements
PMF:
GMF:550m
– p. 13/??
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
– p. 14/??
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/??
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