Image Processing Reference
In-Depth Information
ˆ
ˆ
Y
2
as
observations and using an iterative method for estimating the complete state. We can,
however, define an admittedly sub-optimal, but explicit, fusion method as follows:
⎧
⎨
A first idea consists of considering the partial estimation vectors
Y
1
and
σ
2
θ
1
+
σ
1
θ
2
,
1
σ
1
+
σ
2
θ
=
d
sin(
θ
)
α
1
−
v
=
,
[6.52]
⎩
α
2
d
sin(
θ
)
α
1
−
cpa
1
=
α
1
.
α
2
We can then show using Taylor series expansions [DON 00, DON 02] that this
estimator of
X
asymptotically follows the law:
⎛
⎝
⎞
⎠
−→ N
⎡
⎣
⎛
⎝
⎞
⎠
⎤
⎦
cpa
1
v
θ
t
cpa
1
cpa
1
v
θ
t
cpa
1
;
M
1
Γ
1
M
1
+
M
2
Γ
2
M
2
,
[6.53]
where:
v
1
α
1
d
cos(
θ
)
α
1
−
⎛
⎝
⎞
⎠
σ
2
σ
1
+
σ
2
α
1
α
1
−
−
0
α
2
α
2
σ
2
σ
1
+
σ
2
v
α
1
−
d
cos(
θ
)
α
1
−
−
0
α
2
α
2
M
1
=
,
[6.54]
σ
2
σ
1
+
σ
2
0
1
0
0
0
and:
v
α
1
α
1
−
α
1
d
cos(
θ
)
α
1
−
⎛
⎝
⎞
⎠
σ
1
σ
1
+
σ
2
0
α
2
α
2
σ
1
σ
1
+
σ
2
v
α
1
−
d
cos(
θ
)
α
1
−
0
α
2
α
2
M
2
=
.
[6.55]
σ
1
σ
1
+
σ
2
0
0
0
0
0
In the equation above, the matrix Γ
i
, (
i
=1
,
2) is unknown, which is why we have
to replace it with its estimate. We can then show that the performances of decentralized
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