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independently extracted from filter probability distribution
and can ap-
proximate the posterior probability density by using weighted summation method. For
the target tracking task, it means to get the state of moving target as well. We can get
the posterior probability distribution
px z
(|
)
k
1:
k
px z
through the recursion shown below on
the condition of given priori probability density.
(|
)
k
1:
k
Measurements (A)
det ect ed by hard
deci sion from
differenced imageand
clust ering
Take ( A or B)
logic in whole
tracking
window
S >= 1
Ef f ect i ve
measurements
z(k)
Tr acki ng window
in input images
Deci sion and
fusi on by the
criteria included
the target gray
level
Error (S) of
the two
clust ering
center
Measurements (B )
detected by adaptive
t heroshol d deci si on
from current image, and
clust ering
Take ( A or B) l ogi c i n
ell ipse, and t ake (A & B)
logic outside ellipse in
tracking window
S <1
Fig. 2.
The scheme of effective measurements detection
State prediction:
px z
(|
)
=
px x
(|
)(|
px z
)
dx
(9)
k
1:
k
−
1
k
k
−
1
k
1:
k
−
1
k
−
1
Filtering update:
pz x px z
(|
)(|
)
px z
(|
)
=
k
k
k
1:
k
−
1
(10)
k
1:
k
pz z
(|
)
k
1:
k
−
1
px
(
|
z
)
Where
is the posterior probability distribution at time k-1
px x
−
(|
)
k
−
1
1:
k
−
1
i
k
1
is a first order Markov process , can be obtained by system equation(2);
pz x
is
likelihood functioncan be obtained by observation equation (5). From formula (10),
we can see that the state posterior probability distribution can be obtained through the
correction to priori probability by using observations
k
z
.
According to the assumption that the target's true measurements obey Gaussian
distribution [5], this paper uses the algorithm of Gaussian particle filter for target
tracking in which take the Gaussian density as approximation of the posterior proba-
bility density by using importance sampling method, then updating the state's mean
and covariance matrix. Compare to particle filtering, there is no need to resample, and
does not exist particle degradation problems [2, 6, 7], so that reduces the complexity
and computation load of particle filter. The Gaussian particle filter tracking algorithm
is described as below:
(|
)
k
k
