Fusion in Signal Processing - Information Fusion in Signal and Image Processing - page 31

5 for unlikely information; the number 6 denotes information for which the accuracy
cannot be estimated. Likewise, in a numerical context, this quality can be assessed by
taking into account the sensor's definition, the signal-to-noise ratio and it will be a
representation of the likelihood of the state we are trying to estimate.
2.3.3. Representativeness and accuracy of learning and a priori information
For each quantity we wish to fuse, we need a priori information characterizing
each type of object as well as one or several elements of perceptive information. This
pair of elements cannot be represented using the same formalism, probabilistic, pos-
sibilistic, belief function, etc. Assessing the compatibility of the observations and the
hypotheses of the frame of discernment has to be done with heterogenous elements of
information, which requires the implementation of hybrid fusion mechanisms. Even
the a priori information involving the attributes does not have to be homogenous. This
point has been discussed by many authors. Expressing how a possibilistic representa-
tion can still hold some meaning when suggesting to switch over to a representation
in probabilistic context is at the core of the theory explaining the meaning of each
representation, and was in fact its foundation [BLO 96]. A first idea is to switch to a
homogenous context, which reflects to a certain extent the accuracy with respect to
the real world and leads either to a loss of information, or to including information
without justification. In the case of non-homogenous combination between probabil-
ity and possibility distributions, it can be useful to rely on the strengths of these two
representations: the probabilistic representation holds a strong meaning for the part
of the medium where the value is high; the possibilistic representation holds a strong
meaning for the part where it is equal to zero. Hence, it is possible to suggest a dou-
ble representation system where each of the two brings its strength for the part of the
medium where it is strong [NIF 00].
Finally, we should point out the incompleteness of knowledge obtained through
learning.
2.4. Bibliography
[ABI 92] A BIDI M., G ONZALES C., Data fusion in robotics and machine intelligence , Aca-
demic Press, New York, 1992.
[ACK 70] A CKERSON G.A., F U K.S., “On state estimation in switching environment”, IEEE
Transactions on Automatic Control , vol. AC-15, no. 1, p. 10-17, 1970.
[APP 91] A PPRIOU A., “Probabilités et incertitude en fusion de données multi-senseurs”,
Revue scientifique et technique de la Défense , p. 27-40, 1st trimester 1991.
[APP 98] A PPRIOU A., “Uncertain data aggregation in classification and tracking processes”,
in B. B OUCHON -M EUNIER (ed.) Aggregation and fusion of imperfect information , p. 231-
260, Physica-Verlag, 1997.