1

Mohammed M. Olama Seddik M. DjouadiMohammed M. Olama Seddik M. Djouadi

ECE Department/University of TennesseeECE Department/University of Tennessee

Ioannis G. PapageorgiouIoannis G. Papageorgiou Charalambos D. CharalambousCharalambos D. Charalambous

ECE Department/University of CyprusECE Department/University of Cyprus

Estimation of Mobile Station Position and Velocity in Multipath Wireless

Networks Using the Unscented Particle Filter

Conference on Decision and Control 2007Conference on Decision and Control 2007

CDC 2007CDC 2007

December 14, 2007December 14, 2007

2

Outline

1.1. Motivation and objective.Motivation and objective.

2.2. Aulin’s wave scattering channel model.Aulin’s wave scattering channel model.

3.3. State and measurement models.State and measurement models.

4.4. The unscented particle filter.The unscented particle filter.

5.5. Numerical example.Numerical example.

6.6. Conclusion.Conclusion.

3

Applications Emergency 911. Promising Market

Commercial Vehicle fleet management Location sensitive billing Fraud protection Mobile yellow pages

Technological Power control enhancement System capacity enhancement

4

Motivation (1)

The current literature and standards in estimating the mobile location are based mostly on time signal information, such as TDOA, OTDOA, E-OTD, GPS, etc.

However, most of them require new hardware since localization is not inherent in the current wireless systems, for instance, GPS demands a new GPS receiver and TDOA, E-OTD, OTDOA require additional location measurement units in the network.

In this paper, we consider estimating the mobile location and velocity based on the received signal level.

5

Motivation (2)

The standard target tracking literature rely on linearized motion models, measurement relations, and Gaussian assumptions

Here particle filtering (sequential Monte Carlo methods) is used for the estimation process, which considers linear/non-linear state and measurement models, and Gaussian/non-Gaussian assumptions.

6

Objective

Developing a new method for tracking mobile location and velocity in cellular networks based on the instantaneous electric field measurements.

The proposed method supports existing network infrastructure and channel signaling.

It takes into account NLOS and multipath propagation environments, which are usually encountered in wireless fading channels.

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Aulin’s Scattering Channel Model

8

Aulin’s Scattering Model

1

cosP

n c n nn

z t r t t n t

where

2cos cosn n n

v

The received signal at any receiving point is given by (Aulin, 1979)

0 0 0( , , )x y z

:

:

:

:

:

n

n

n

n

r

v

Amplitude

Doppler shift

Phase shift

Phase

Velocity of mobile

, :

:

( ) :

:

:

n na

n t

P

Spatial angles of arrival

Wavelength

White Gaussian noise

Total number of paths

Direction of motion

0 0 0

2cos cos sin cos sinn n n n n n nx y z

9

State Model

21

,11

21 ,2

1

/ 2 01 0 0

00 1 0 0

0 0 1 0 / 2

0 0 0 1 0

k

k

k

k

k kk

kk k

k k kk

k k

x

x

y

y

x

wx

y w

y

The dynamics of the mobile can be written as:

,1 ,2

and :

and :

:

and :

k k

k k

k

k k

x y

x y

w w

the Cartesian coordinates of the mobile at time k

the velocities of the mobile in the X and Y directions at time k

The measurement interval between time k and k + 1

Independent, discrete zero-mean state noise processes at time k

We choose the case when the velocity of the mobile is not known and is subject to unknown accelerations.

10

Measurement Model

1

cosk k k

P

k n c k n k n kn

z r t t v

The measurement equation is found from the discretized version of Aulin’s scattering model as

where

2 22

cos( )cosk k kn k n n

k kx y

0

2cos cos sin cos sin

k k k k k k kn n n n n n nk k zx y

:kv discrete zero-mean measurement noise process at time k.

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Comments Clearly, the measurement equation is a non-

linear function of the state-space vector. If we assume knowledge of the channel

parameters, which is attainable either through channel estimation at the receiver (e.g., GSM receiver), or through various estimation techniques (e.g., least-squares, Maximum Likelihood), then this problem falls under the broad area of non-linear parameter estimation from noisy data.

This problem can be solved using particle filtering.

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The Particle Filter (PF) The PF is simply a sequential Monte Carlo simulation. It

produces a discrete weighted approximation to the true posterior as:

The weights are chosen using the principle of importance sampling as:

where is the importance proposal distribution function that generates the samples .

| )k k(x Zp

1

ˆ| )N

k k k k kj

j j

(x Z x xp

1

1

| |

| ,

k k k k

kk k k

j j jj

j j

z x x x

x x z

p p

q

1| ,k k kj jx x zq

1ˆ

N

k jj

x

13

The Particle Filter (PF) The choice of the proposal distribution function is one of the

most critical design issues and determines the type of the PF.

Optimal:

Analytical evaluation of the optimal proposal function is not possible for many models, and thus has to be approximated using local linearization or the unscented transformation (the UPF).

Simple: The generic PF.

1 1| , | , k k k k k koptj jx x z x x zq p

1 1| , | k k k k kj jx x z x xq p

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The SUT The SUT method approximates the proposal distribution by a

Gaussian distribution, but it is specified using a minimal set of deterministically chosen sample points.

These sample points completely capture the true mean and covariance of the Gaussian distribution, and when propagated through the true nonlinear system, captures the posterior mean and covariance accurately to the 3rd order for any nonlinearity.

1( )k kx f x

01 1

1 1 1

1 1 1

0

20

, 1, ,

, 1, , 2

/

/ 1

1/ 2 , 1, , 2

k k

ik k x k x

i

ik k x k x x

i

mx

cx

m ci i x x

n i n

n i n n

W n

W n

W W n i n

x

x P

x P

X

X

X

1( ), 0, , 2i ik k xi n f X X

2

0

2

0

x

x

nm i

k i ki

nTc i i

k i k k k ki

W

W

x

P x x

X

X X

•

• •

•

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The UPF The UPF uses the same framework as the regular

PF, except that it approximates the optimal proposal distribution by a Gaussian distribution

using the SUT method.

Evaluating the importance weights as:

Resampling as the generic PF.

1| , , , 1, , k k k k koptj j j j j Nx x z x Pq N

1

1

| |

| ,

k k k k

kk k k

z j j jj

j j z

x x x

x x

p p

q

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Numerical Results/System Setup

The wireless communication network has the following parameters: The envelope of the received signal for all paths,

rn’s, are generated as Rayleigh iid RVs with parameter 0.5.

and are generated as uniform iid RVs in [0, 2π], [0, 0.2π], and [0, 2π], respectively.

The total number of paths P is 6, which represents urban environments.

The cell radius is 5000 meters. The particle filter has the following parameters:

Number of particles is 500. 100 Monte Carlo simulations were performed. The mean estimate of all particles is used as the

final estimate.

,n na n

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Numerical Results/Location and Velocity Estimates

0 10 20 30 40 501400

1600

1800

2000

2200

2400

Filter Steps

Y (

me

ters

)

2400

2600

2800

3000

3200

3400

X (

me

ters

)

ActualPFEKFEKF/MLEUPF25 26 27 28 29

2120

2130

2140

35 36 373170

3175

3180

3185

0

50

100

150

200

Vx

(me

ters

/se

con

d)

0 10 20 30 40 500

50

100

150

Filter Steps

Vy

(me

ters

/se

con

d)

ActualPFEKFEKF/MLEUPF

42 4748

55

33 34 3547

51

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Numerical Results/Location and Velocity RMSE

5 10 15 20 25 30 35 40 45 500

100

200

300

Lo

catio

n R

MS

E (

m)

5 10 15 20 25 30 35 40 45 500

50

100

150

Filter Steps

Ve

loci

ty R

MS

E (

m/s

)

EKFPFMLEEKF/MLEUPF

40 430

15

40 450

10

20

Performance Comparison

100 Monte Carlo simulations were performed.

MLE EKF EKF/MLE PF UPF

Diverged runs

_ 39 6 2 2

Position RMSE (m)

73.46 142.38 11.23 4.31 3.81

Velocity RMSE (m/sec)

_ 51.36 16.52 1.01 0.96

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Robustness We want to see how robust the particle filtering

approach is. Thus, we assume that we only know the channel parameters within certain tolerances

where , and are the nominal (actual)

values of the channel parameters.

0 0 0

0 0 0

0 0 0

(1 ), 5%, 10%, 20% and 30%

(1 ), 5%, 10%, 20% and 30%

(1 ), 5%, 10%, 20% and 30%

n n n n

n n n n

n n n n

r r r r

0nr

0n

0n

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Numerical Results/ Robustness

5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

Lo

catio

n R

MS

E (

m)

5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

Filter Steps

Ve

loci

ty R

MS

E (

m/s

ec)

Exact5% Error10% Error20% Error30% Error

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Conclusions A new estimation algorithm based on received

signal measurements is proposed to track the position and velocity of a MS in a cellular network based on the unscented particle filter.

It takes into account multipath propagation environment and NLOS conditions, which are usually encountered in wireless fading channels.

The assumptions are partial knowledge of the channel and access to the instantaneous received field, which are obtained through channel sounding samples from the receiver circuitry.

Numerical results for typical simulations show that they are highly accurate, robust, and consistent.