Image Processing Reference

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or, if the model corresponds exactly to reality, remain constant. During the combi-

nation phase, since this is conjunctive, the confidence will increase according to the

quality of the measurement.

It is common for the sampling frequency to be too small for the application, i.e.

intermediate values of
X
between two sampling times would be needed. In this case,

we simply have to use the evolutionary model to register
X
with the times we are

interested in, without having to use new measurements for the combination.

11.7. Multi-sensor prediction-combination

We now wish to combine information gathered from different sources [ELE 96].

We saw in section 11.3.1 that a number of problems could arise from the synchroniza-

tion of sensors. We will deal with the most general case, where all of the sensors are

completely asynchronous, i.e. they have completely independent sampling frequencies

and processing times. The only hypothesis, which is usually true, is that the sensors

operate “monotonically”, i.e. for each sensor, the measurements are transmitted in the

same order they were acquired in. In the rest of this section, we will describe the

method for variables only, in order to have simpler equations. Obviously, in practice,

it is also necessary to deal with the confidence in the variables.

We begin by studying the case of two sensors
C
1
and
C
2
before generalizing to

any number of sensors. Let us assume that these two sensors deliver dated measure-

ments
Y
1
(
t
) and
Y
2
(
t
). We have at our disposal the inverse methods of these sensors

which make it possible to obtain estimates of
X
1
(
t
) and
X
2
(
t
) based solely on these

measurements. From now on, we will say that these sensors directly provide these two

estimates, thus implying that they are obtained from measurements. We will denote

by
t
a
the acquisition time and by
t
t
the transmission time such as they are represented

in Figure 11.6.

sensor 1

sensor 2

Figure 11.6.
Example of two asynchronous sensor fusion

Let us assume that we know an estimate of
X
at the time
t
0
denoted by
X
(
t
0
) and

that
t
a,
1
<t
a,
2
and
t
t,
1
<t
t,
2
.

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