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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