Image Processing Reference
In-Depth Information
- resampling (the decision to resample is ensured by a test):
⎧
⎨
⎩
N
s
t
∼
q
t
δ
s
t
,
[6.37]
k
=1
q
t
=1
/N,
n
=1
,...,N.
Different forms of this filter and application examples in target motion analysis can
be found in [HUE 02]. Finally, still on the subject of filtering, models for maneuvering
targets hold great importance. Among them, we can mention a standard one, i.e. the
Singer model (with correlated noise):
⎧
⎨
x
(
t
)=
01
00
x
(
t
)+
0
1
a
(
t
)
,
[6.38]
⎩
cov
w
t
,w
t
−
τ
=
σ
2
e
−
ατ
.
a
(
t
)=
−
αa
(
t
)+
w
(
t
) where
r
(
τ
)
More generally, these models can be divided into the following categories:
- maneuvering models decoupled in co-ordinates:
- white noise models for which the command is a white noise,
- Markov models for which the input is a Markov process (includes the Singer
model),
- the Semi-Markov Jump Process.
- motion models: 2-D, for example, with a constant gyration rate, 3-D, ballistic;
- measurement models: cartesian, linearized, pseudo-measurements, modified po-
lar, curvilinear.
For the three categories above, we can give the following examples:
- Wiener acceleration model (discrete time):
⎡
⎤
⎡
⎤
1
TT
2
/
2
00
T
00
T
5
/
20
T
4
/
8
T
3
/
6
⎣
⎦
⎣
⎦
T
4
/
8
T
3
/
3
T
2
/
2
F
=
,
Q
=
;
[6.39]
T
3
/
6
T
2
/
2
1
T
- ARMA acceleration model:
⎡
⎤
⎡
⎤
01 0
0
0
0
0
1
⎣
⎦
⎣
⎦
00
β
1
β
2
x
(
t
)=
x
(
t
)+
;
[6.40]
00 0
1
00
−
α
2
−
α
1
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