A COMBINED APPROACH FOR NLOS
MITIGATION IN CELLULAR
POSITIONING
WITH TOA MEASUREMENTS
Fernaz Alimoğlu
M. Bora Zeytinci
1/23
OUTLINE
• Location estimation
– Application areas
– Different methods
•Proposed solution
•Algorithms used
– Kalman Filter
– LOS/NLOS identification method
– Constrained Weighted Least Squares
• Simulation environment
• Simulation results
• Conclusions
2/23
LOCATION ESTIMATION: APPLICATION AREAS
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Emergency services
Mobile advertising
Location sensitive billing
Fraud protection
Asset tracking
Fleet management
Intelligent transportation systems
Mobile yellow pages
3/23
LOCATION ESTIMATION: DIFFERENT METHODS
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•
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Time of arrival (TOA)
Angle of arrival (AOA)
Time difference of arrival (TDOA)
Enhanced observed time difference (EOTD)
Cell global identification (CGI) and Timing
advance (TA)
• Signal strength (SS)
• Global Positioning System (GPS)
4/23
NLOS error
SCATTERING
5/23
Proposed Solution: Kalman & CWLS (I)
Range measurments
LOS
decision
Unbiased
Kalman
Variance
calculation
LOS/NLOS
Identification
CWLS
NLOS
decision
Biased
Kalman
Coordintes
of BS’s
Estimate
6/23
Proposed Solutions: Kalman & CWLS (II)
• Sliding window with length 20 is used for
variance calculation.
• Variance corresponding to each range
measurement is kept in data base until the end
of operation.
• Weighting matrix of CWLS is composed of
calculated variances and range measurements.
• Kalman Filter is used to smooth range
measurements.
• Biased or unbiased mode decision is done
according to these variances.
7/23
ALGORITHMS USED: KALMAN FILTER(I)
Previous data
Priori
estimate
Target motion
model
xn1  Axn  wn
xˆ

n 1
Prediction
 Axˆn
Model used in our simulation
 rn1   1 t   rn   0 


      wn
 vn1   0 1   vn   t 
8/23
ALGORITHMS USED: KALMAN FILTER(II)
Priori estimate
Measurement(s)
yn1  Hxn1  un1
Posteriori
estimate
Correction

xˆn1  xˆn1  K yn1  Hxˆn1

Model used in our simulation
 rn1 
yn1  1 0  
  un1
 vn1 
9/23
ALGORITHMS USED:KALMAN FILTER (III)
BIASING KALMAN FILTER
• Kalman filter works best at additive white Gaussian noise
with zero mean.
• Kalman Filter cannot follow an unexpectedly high
erroneous data such as an NLOS error.
• When an NLOS situation is detected the dependence of
the estimation on the measurements should be decreased.
• This is called BIASING.
• This can be done by
increasing the measurement
error covariance matrix
Recall

xˆn 1  xˆn1  K yn 1  Hxˆn1

n 1
K n 1  P H
T
 HP

n 1

H R
T
10/23

1
Biasing Kalman
11/23
LOS/NLOS IDENTIFICATION METHOD
• Can be implemented when a LOS error standard
deviation is available.
• Rough standard deviation:
1
ˆ m (k ) 
M
k

j  k  M 1
( ym ( j )  ym (k )) 2
is compared with the (known) standard deviation
of the measurement in LOS situation (  m )
– If ˆ m (k )   m the situation is NLOS
– γ is choosen to be 1.35 to prevent false alarm
– Moving window is used for LOS / NLOS identification.
12/23
Performance Analysis of LOS/NLOS identification
Measurements are taken from 5 base stations, with 2 of them
are NLOS at the same time.
13/23
Constrainted Weigthed Least Squares Method (I)
• Turns non linear equations into linear forms
 X 11
A  
X
 1M
X 21
X 2M
0.5 


0.5 
 x1 
 
   x2 
 R2 
 
 X 112  X 212  r12
1
b 
2
 X 2  X 2  r2
2M
M
 1M
A  b





• Based on Lagrange multipliers theory
m
f ( x* )   ihi ( x* )  0
i 1
• Finds
 that satisfies
  arg min( A  b)T W ( A  b)
14/23
Constrainted Weigthed Least Squares Method (II)
• Cost function
L(,  )  ( A  b)T W ( A  b)   (qT   T P)
• Advantage of weighting each measurment
inversely proportional to error.
ri 2  (di  ni )2  di 2  2di ni
 i  ri 2  di 2  2di ni
15/23
Simulation Environment (I)
• Movement of MS is
limited within a cell
• Seven cells are
hexagonally placed
• Flexible cell size
• Should be realistic
• Linear movement &
random movement is
considered.
16/23
Simulation Environment (II)
• Direction, velocity, number of BS s
(LOS & NLOS) are predetermined
• Number of samples in NLOS situation is
determined by the obstruction length and
velocity.
• BS s in NLOS situation are randomly selected.
• Measurment noise is white Gaussian noise.
  150m
• NLOS error has a uniform distribution between
0-1000m.
17/23
Simulation Results (I)
• Linear trajectory: MS follows a linear path
Trajectory
13000
only least squares
track
Kalman+CWLS
kalman+leastsquares
12000
11000
y coordinates
10000
9000
8000
7000
6000
5000
4000
3000
4000
6000
x coordinates
x 10
8000
1.6
1.6
1.4
1.4
1.2
1.2
1
0.8
0.6
0.6
0.4
0.4
0
500
1000
1500
samples
2000
2500
12000
ToA signals
x 10
1
0.8
0.2
10000
4
1.8
ToA(meters)
ToA(meters)
2000
ToA without noise
& Filtered ToA
4
1.8
0
0.2
18/23
0
500
1000
1500
samples
2000
2500
Simulation Results (II)
• Linear trajectory: MS follows a linear path
19/23
Simulation Results(III)
• Random movement: MS follows a path with several turns
Trajectory
9000
8000
y coordinates
7000
6000
5000
only least squares
track
Kalman+CWLS
kalman+leastsquares
4000
3000
1000
2000
3000
ToA without noise
& Filtered ToA
4000
5000
6000
x coordinates
7000
4
18000
1.8
16000
1.6
14000
8000
9000
ToA signals
x 10
1.4
ToA(meters)
ToA(meters)
12000
10000
8000
1.2
1
0.8
6000
0.6
4000
2000
0.4
0
0.2
20/23
0
500
1000
1500
samples
2000
2500
0
500
1000
1500
samples
2000
2500
Simulation Results (IV)
• Random movement: MS follows a path with several turns
21/23
Conclusion
• Results are close to FCC requirements.
• Kalman and CWLS enhance accuracy of
the estimate.
• NLOS period followed by a LOS period;
– Transient error;
– If BS changes direction in NLOS period, error
increases
– Increase Kalman gain to increase
dependence on measurements
• Tests with real data should be realized.
22/23
References
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23/23
ALGORITHMS USED:KALMAN FILTER(IV)
Target motion
model
Measurement(s)
xn1  Axn  wn
yn1  Hxn1  un1
Driving noise with
covariance matrix
Measurement noise
with covariance matrix
R
Q
• Aim
is to minimize posteriori estimate error covariance
Calculating the Kalman gain “K”
Pn1  APn AT  Q
Kalman
gain

n 1
K n 1  P H
T
 HP

n 1
Priori error cov.
H R
T
Pn1  1  Kn1H  Pn1

1
Posteriori error cov.
24/23