Image Processing Reference
In-Depth Information
of another sensor. However, this sensor can provide us with relevant information even
if it is delayed and there is no point in working without it. We will now present the
method in the general case.
We now have at our disposal a certain number of sensors providing elements of
information with the dates t a,i . These times are arranged chronologically so that
t a, 1 <t a, 2 <t a, 3 < , etc. For each of these instants, we have stored X ( t a,i ) obtained
directly from the measurement and X ( t a,i /t a,i ), which is the estimate of X that takes
into account all of the available measurements up until t a,i . Table 11.1 shows all of
the variables that are stored.
t a, 1
t a, 2
t a, 3
t a, 4
X ( t a, 1 ) X ( t a, 2 ) X ( t a, 3 ) X ( t a, 4 )
X ( t a, 1 /t a, 1 ) X ( t a, 2 /t a, 2 ) X ( t a, 3 /t a, 3 ) X ( t a, 4 /t a, 4 )
Table 11.1. Table of the variables stored at the different times
At the time t t , we have a new measurement that gives us X ( t a ), such that t a, 2 <
t a <t a, 3 . Table 11.1 then changes into Table 11.2.
t a
t t
t a, 1
t a, 2
t a, 3
t a, 4
X ( t a, 1 ) X ( t a, 2 ) X ( t a ) X ( t a, 3 ) X ( t a, 4 )
X ( t a, 1 ) X ( t a, 2 )
X ( t a, 3 ) X ( t a, 4 )
t t
Table 11.2. Table of the variables at the current time
This new estimate has to be taken into account as well as all of those that followed
it. The method consists of alternately using prediction and combination until obtaining
the prediction at the time t t . This method is illustrated by Table 11.3
Given that the sensors behave “monotonically”, when a measurement is provided
by the sensor C i , the previous measurement from the same sensor is forgotten. As a
result, the storing table has a number of columns equal to the number of sensors.

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