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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