Fusion in Signal Processing - Information Fusion in Signal and Image Processing - page 21

efficiency for the system. Each sensor can work according to different modes compet-
ing with each other and, for each mode, a sensor can provide different attributes. For
each attribute, the system contains a set of a priori distributions conditionally to a set
of hypotheses in competition with each other.
Once the measurement involving an attribute has been validated, we calculate the
likelihood of each hypothesis for which an associated conditional distribution is avail-
able. For all of the measured attributes, we can define an encompassing set of com-
peting hypotheses, which we will refer to as the frame of discernment. For each of
the hypotheses in question, either we have its likelihood conditionally to the measure-
ment of an attribute, or we implant new mechanisms to extend the likelihoods to all
of the hypotheses in the frame of discernment. At this stage, the likelihoods are fused
to provide an overall likelihood of each hypothesis in the frame, conditionally to the
set of attribute measurements that have been conducted. It is then possible to implant
a decision mechanism.
We now consider problems involving reliability and/or data association. These are
questions related to concepts of uncertainty. The “right” method of combining ele-
ments of information necessarily takes into account the imprecisions and uncertain-
ties related to each source. It is worth noting that the choice of mechanisms strongly
depends on how knowledge is modeled, since either information is accurately mod-
eled, and the combinations are rather simple, or the modeling is not accurate, in which
case the focus should be placed on the mechanisms for taking into account reliability
problems.
Different techniques have been developed these past years, particularly in the field
of tracking [BAR 88, BLO 88a, BLO 88b, BLO 89, REI 79, SIN 74].
Let us assume that we are attempting to track a moving object (a target) using a
sensor. Let us also assume that the sensor is noisy, causing a certain number of false
alarms. The risk here is to take a false alarm into account in order to retime the target's
state vector. Once the track has been initialized, a prediction window (ellipsoidal with
three sigmas, for example) is available at the time t . The measurements appearing in
this window are validated. The other measurements are directly considered as false
alarms and are discarded.
There are two types of methods we can use:
- MHT (Multiple Hypothesis Tracking) [REI 79] in which each validated mea-
surement is associated with a track. By studying the likelihood over time of each of
these tracks, it is possible to weed out some of them. The hypotheses corresponding
to different tracks are managed using a tree diagram. Combinatorial aspects limit the
size of the solvable problems. This method is therefore adapted to cases with a limited
number of false alarms;