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A COMBINED APPROACH FOR NLOS MITIGATION IN CELLULAR

POSITIONINGWITH TOA MEASUREMENTS

Fernaz Alimoğlu M. Bora Zeytinci

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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

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LOCATION ESTIMATION: APPLICATION AREAS

• Emergency services

• Mobile advertising

• Location sensitive billing

• Fraud protection

• Asset tracking

• Fleet management

• Intelligent transportation systems

• Mobile yellow pages

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LOCATION ESTIMATION: DIFFERENT METHODS

• 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)

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NLOS error

REFLECTION SHA

DO

WIN

G

SCATTERING

LINE-O

F-SIG

HT

DIFFRACTION

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Proposed Solution: Kalman & CWLS (I)

Variance calculation

LOS/NLOSIdentification

LOSdecision

NLOSdecision

UnbiasedKalman

BiasedKalman

CWLS

Estimate

Range measurments

Coordintes of BS’s

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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.

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ALGORITHMS USED: KALMAN FILTER(I)

Previous data

Target motion model

Priori estimate

1n n nx Ax w 1ˆ ˆn nx Ax

1

1

1 0

0 1n n

nn n

r rtw

v v t

Model used in our simulation

Prediction

9/23

ALGORITHMS USED: KALMAN FILTER(II)

Measurement(s)

Priori estimatePosteriori estimate

1 1 1n n ny Hx u

Model used in our simulation

11 1

1

1 0 nn n

n

ry u

v

1 1 1 1ˆ ˆ ˆn n n nx x K y Hx

Correction

10/23

Recall

ALGORITHMS USED:KALMAN FILTER (III)

• 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.

1

1 1 1T T

n n nK P H HP H R

BIASING KALMAN FILTER

• This can be done by increasing the measurement error covariance matrix

1 1 1 1ˆ ˆ ˆn n n nx x K y Hx

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Biasing Kalman

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LOS/NLOS IDENTIFICATION METHOD

• Can be implemented when a LOS error standard deviation is available.

• Rough standard deviation:

is compared with the (known) standard deviation of the measurement in LOS situation ( )– If the situation is NLOS

– γ is choosen to be 1.35 to prevent false alarm

– Moving window is used for LOS / NLOS identification.

2

1

1ˆ ( ) ( ( ) ( ))

k

m m mj k M

k y j y kM

ˆ ( )m mk m

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Performance Analysis of LOS/NLOS identification

Measurements are taken from 5 base stations, with 2 of them are NLOS at the same time.

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Constrainted Weigthed Least Squares Method (I)

• Turns non linear equations into linear forms

• Based on Lagrange multipliers theory

• Finds that satisfies

* *

1

( ) ( ) 0m

i ii

f x h x

A b

11 21

1 2

0.5

0.5M M

X X

A

X X

1

2

2

x

x

R

2 2 211 21 1

2 2 21 2

1

2M M M

X X r

b

X X r

arg min( ) ( )TA b W A b

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Constrainted Weigthed Least Squares Method (II)

• Cost function

• Advantage of weighting each measurment inversely proportional to error.

( , ) ( ) ( ) ( )T T TL A b W A b q P

2 2 2i i i i ir d d n 2 2 2( ) 2i i i i i ir d n d d n

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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.

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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. • NLOS error has a uniform distribution between

0-1000m.

150m

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Simulation Results (I)

• Linear trajectory: MS follows a linear path

0 500 1000 1500 2000 25000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

4ToA without noise

& Filtered ToA

samples

ToA

(mete

rs)

0 500 1000 1500 2000 25000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

4 ToA signals

samples

ToA

(mete

rs)

0 2000 4000 6000 8000 10000 120003000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

x coordinates

y co

ordi

nate

s

Trajectory

only least squares

track

Kalman+CWLS

kalman+leastsquares

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Simulation Results (II)

• Linear trajectory: MS follows a linear pathLinear trajectory: MS follows a linear path

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Simulation Results(III)

• Random movement: MS follows a path with several turns

1000 2000 3000 4000 5000 6000 7000 8000 90003000

4000

5000

6000

7000

8000

9000

x coordinates

y co

ordi

nate

s

Trajectory

only least squares

trackKalman+CWLS

kalman+leastsquares

0 500 1000 1500 2000 25000

2000

4000

6000

8000

10000

12000

14000

16000

18000

ToA without noise& Filtered ToA

samples

ToA

(met

ers)

0 500 1000 1500 2000 25000.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

4 ToA signals

samples

ToA

(met

ers)

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Simulation Results (IV)

• Random movement: MS follows a path with several turnsRandom movement: MS follows a path with several turns

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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.

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References

• [1] A. H. Sayed, A. Tarighat, and N. Khajehnouri, “Network based wireless• location,” IEEE Signal Processing Magazine, pp. 24–40, July 2005.• [2] C. D. Wann, Y. M. Chen, and M. S. Lee, “Mobile location tracking with• nlos error mitigation,” vol. 2, Global Telecommunications Conference• (GLOBECOM’02). IEEE, 17-21 November 2002, pp. 1688–1692.• [3] G. Apaydin, “Comparison of location-estimation techniques of GSM• phones with the simulations,” Master’s thesis, Bogazici University, 2003.• [4] K. W. Cheung, H. C.So, W. K. Ma, and Y. T. Chan, “Least squares algorithms• for time-of-arrival-based mobile location,” IEEE Transactions• on Signal Processing, vol. 52, no. 4, April 2004.• [5] J. F. Liao and B. S. Chen, “Adaptive mobile location estimator with• NLOS mitigation using fuzzy interference scheme,” 2005, Ed. ISCOM• 2005, 20-22 November.• [6] E.Brookner, Tracking and Kalman Filtering Made Easy. Wiley-• Interscience, April 1998.• [7] B. L.Lee, K.Ahmet, and H.Tsuji, “Mobile location estimation with• NLOS mitigation using kalman filtering,” vol. 3. New Orleand, LA:• Proc. IEEE Wireless Communications and Networking (WCNC’03),• March 2003, pp. 1969–1973.• [8] G. Welch and G. Bishop, An Introduction to Kalman Filter. UNCChapel• Hill, 5 April 2004.• [9] D. P. Bertsekas, Nonlinear Programming. Athena Scientific, 1995, pp.• 253–269.• [10] [Online]. Available: http://mathworld.wolfram.com/polynomial.htm• [11] T. Rapaport, Wireless Communications: Principles and Practice, 2nd ed.,• ser. Communications engineering and emerging technlogies. Prentice• Hall, 2002.

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Measurement noise with covariance matrix

Driving noise with covariance matrix

ALGORITHMS USED:KALMAN FILTER(IV)

1n n nx Ax w 1 1 1n n ny Hx u

Q

Calculating the Kalman gain “K”

1T

n nP AP A Q

1

1 1 1T T

n n nK P H HP H R

1 1 11n n nP K H P

Target motion model

Measurement(s)

R

• Aim is to minimize posteriori estimate error covariance

Priori error cov.

Posteriori error cov.

Kalman gain