Digital Signal Processing Reference
In-Depth Information
2
The Observation Model of Image Sequences
The model of IR image sequences is defined in paper [3, 4], that is
F x yk
(, , )
=
F x yk
(, , )
+
F x yk
(, , )
+
N xyk
(, , )
,
k
=
1, 2, 3...
(1)
T
B
xy
coordinates of the image pixels
k
is the frame numberF
T
is mod-
eling for target pixel's space-time informationF
B
is modeling for background pix-
el's space-time information,
Where,
(, )
Nxyk
is the background clutter which follow
(, , )
Gaussian distribution that
.
N
(0,
σ
2
)
B
3
The Algorithm for Detection of Effective Measurements
When the state transition model is more close to the actual target motion, target track-
ing algorithm will have strong robustness. And when the observation model preserves
the perfect target features, the target tracking algorithm will have high accuracy.
3.1
The State Model of Target Movement
We can get the information from thermal imaged target in infrared image sequences
such as position
(, )
vv
, As well as the target gray level value
I
then
dim moving target's state transition equation can be expressed as a formula (2) shown
below:
velocity
(, )
x
xy
y
Xk
(
+=
)
FXk
( )
+
Gvk
( )
k
=
1, 2, 3...
(2)
Xk
() (, , , , ,
=
xyv v
Δ
Δ
)
In which
Xk
()
∈
R
is the state of the system at
n
x
x
y
x
y
Δ
are the velocity innovation at time k,
v
、
v
are the velocity.
In a short period of timebecause of the movement of infrared long distance target is
closely related to the velocity and velocity innovation at last moment k-1so the
target velocity innovation of next frame can be defined as formula (3), shown below;
Δ
、
time k
x
y
Δ=
vvv
−
−
2
+
k
=
3, 4, 5...
(3)
k
k
1
k
−
2
In which,
v
is velocity of target at current frameif
∈
is
normalized procedural noise
G
is a coefficient matrix stands for the radius of the
particle beam
F
is a transfer matrix that its definition is shown in formula (4):
10
<
时
Δ=
k
2
0
vk
()
R
n
T
0
T
0
01 0 0
001000
000100
000010
000001
T
T
(4)
F
=
