Mobile Location and Particle
Filter
Chris Pendley, REU
08/05/2005
Overview
•
•
•
•
•
•
Benefits of mobile location
Large-scale and short-scale fading
Aulin’s short-term model
Particle filter application
Results
Conclusion
Location Based Service
• Provides information based on the
geographical location
• Promising Market: Commercial,
Technological, and Regulatory Market
Drivers.
• Also can be used for emergency
applications
Large-Scale Fading
Large scale propagation models:
T-R separation distances are large
Main propagation mechanism: reflections
Attenuation of signal strength due to power loss along
distance traveled: shadowing
Distribution of power loss in dBs: Normal
Log-Normal shadowing model
Fluctuations around a slowly
varying mean
dX (t) = β (γ − X (t))dt + δ dW
n
n n
n
n
t
6
5
Xn(t) [dB s]
4
3
Large−Scale Fading
2
1
0
0
50
100
150
200
250
300
dχ (t) = α (γ − χ (t))dt + σ sqrt(χ ) dW
n
n n
n
n
n
t
6
5
χn(t)
4
3
2
Small−Scale Fading
1
0
0
50
100
150
time [us]
200
250
300
Small-Scale Fading
Small scale propagation:
T-R separation distances are small
Heavily populated, urban areas
Main propagation mechanism: scattering
Multiple copies of transmitted signal arriving at the transmitted
via different paths and at different time-delays, add vectotrially
at the receiver: fading
dX (t) = β (γ − X (t))dt + δ dW
n
n n
n
n
t
6
5
Xn(t) [dB s]
4
3
Large−Scale Fading
2
1
0
0
50
100
150
200
250
300
dχn(t) = αn(γn − χn(t))dt + σnsqrt(χn) dWt
6
5
4
χn(t)
Distribution of signal attenuation
coefficient: Rayleigh, Ricean.
Short-term fading model
Rapid and severe signal
fluctuations around a slowly
varying mean
3
2
Small−Scale Fading
1
0
0
50
100
150
time [us]
200
250
300
Aulin’s Wireless Model
• Designed for small-scale fading
• More useful in urban / sub-urban
environments
• Aulin’s model the most general model for
small-scale fading
• Relies upon multipath propagation
Aulin’s Wireless Model
Aulin’s Wireless Model
N
y ( t ) = ∑ rn cos (ωc t + ωn t + θ n ) S (t −τ n ) + n ( t )
n =1
where: rn denote Rayleigh fading envelope
n(t) is Gaussian noise
Notice that y(t) is nonlinear function of (x0, y0, z0, vx, yx)
ωn =
θn =
−2π
λ
(x
0
2π v
λ
cos ( γ − α n ) cos ( β n )
cos (α n ) cos ( β n ) + y0 sin (α n ) cos ( β n ) + z0 sin ( β n ) ) + φn
Particle Filter Review
• To use particle filter, must know:
– xk = fk(xk-1, vk-1) is known, where xk-1 is a state
sequence and vk-1 is a process noise sequence
– zk = hk(xk, nk) is known, where zk is an measurement
of xk and nk is a measurement noise sequence
– X and Y are not constant for this model
Location Estimation Model
For our model the state equation is
xk
1

0

=
0

0
.1
1
0
0
0
 .1 0 



0
.1
0
 w
xk −1 + 
 0 .1 k
.1



1
 0 .1
T


x k =  x, x, y , y 

k
•
where
0
0
1
0
•
wk = (wx , wy )k
T
The measurement equation
N
y ( t ) = ∑ rn cos (ωc t + ωn t + θ n ) S (t −τ n ) + n ( t )
n =1
Particle Filter Review
• Three main steps:
– 1: State Prediction
• Changes applied to the state prediction model
– 2: Importance Weights
– 3: Update of Prediction
Results
Results
Conclusions
• Particle filter method of mobile location is
more accurate than Extended Kalman Filter.
Moreover it has more tolerance towards
initial condition.
• Error is within LOS (~10 meters or less),
making emergency applications such as 911
possible
Future Work
• Future work:
– Increasing runtime speed so that it approaches
real time results.
– Gathering real data and using the system for
experimental runs