The interpretation of covariance intersection is based on its assumption of Gaussian distribution. Or we have to draw the covariance ellipse to illustrate the variation of such fusion. However, what happen to the fusion of other distribution?

In this paper, they formulate the combination of probability distribution such that the resulting distribution is conservative. Or to be more precise,

the probability assignment which most honestly describes what we know should be the most conservative assignment in the sense that it does not permit one to draw any conclusions not warranted by the data. (Jaynes, 2003)

The weighted Kullback-Leibler average is defined, and the proof of the degenerative case of covariance intersection is also given. In other words, we can apply the concept of covariance intersection on different families of distribution, e.g. exponential distribution.

Reference

- G. Battistelli, and L. Chisci, ``Kullback–Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability,'' Automatica, no. 50, pp. 707-718. 2014.