Image Processing Reference
In-Depth Information
A t
t,
1
The estimate
X
1
(
t
a,
1
) obtained from the measurement
Y
1
(
t
a,
1
) becomes available.
We assume that this estimate is more recent than that at
t
0
and therefore that
t
a,
1
>t
0
.
Then, we register
X
(
t
0
) until
t
a,
1
by using the evolutionary model to obtain:
X
t
a,
1
/t
0
=
M
X
X
t
0
,
t
a,
1
−
t
0
We can then combine these two estimates that correspond to the same date:
X
t
a,
1
/t
a,
1
=Comb
X
t
a,
1
/t
0
,X
1
t
a,
1
Finally, we predict this value until the present time:
X
t
t,
1
/t
a,
1
=
M
X
X
t
a,
1
/t
a,
1
,
t
t,
1
−
t
a,
1
However, we bear
X
1
(
t
a,
1
) and
X
(
t
a,
1
/t
a,
1
) in mind.
A t
t,
2
The estimate
X
2
(
t
a,
2
) obtained from the second sensor becomes available. We
assume that this estimate is more recent than that at
t
a,
1
. This time we register
X
(
t
a,
1
)
until
t
a,
2
by using the evolutionary model to obtain:
X
t
a,
2
/t
a,
1
=
M
X
X
t
a,
1
/t
a,
1
,
t
a,
2
−
t
a,
1
We can then combine these two estimates:
X
t
a,
2
/t
a,
2
=Comb
X
t
a,
2
/t
a,
1
,X
2
t
a,
2
Finally, we predict this value up until the present time:
X
t
t,
2
/t
a,
2
=
M
X
X
t
a,
2
/t
a,
2
,
t
t,
2
−
t
a,
2
In this example with two sensors, we have assumed that the measurements on the
two sensors arrived in the same order they were in when they were acquired, i.e., if
t
t,
1
<t
t,
2
, then
t
a,
1
<t
a,
2
. This condition is not always satisfied, particularly in the
case where a sensor has a long processing time compared with the sampling period
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