Some Results on Generalized Ellipsoid Intersection Fusion

This paper generalizes the ellipsoid intersection method to fuse the probability density functions. The generalized ellipsoid intersection method is the log-linear combination of regularized probability density functions and it is equivalent to the weighted Kullback-Leibler average of regularized probability density functions. In the Gaussian case, the generalized ellipsoid intersection method is equivalent to the ellipsoid intersection method and the determinant of the covariance of the probability density function fused by the generalized ellipsoid intersection method is smaller than that of the generalized covariance intersection method. Two optimization criteria for the choice of fusion weights have been suggested. One is the minimization of the Shannon information of the fused density function. Another criterion is the regularized Chernoff information. These two criteria have lower computation complexity than minimizing the determinant of the fused covariance. Numerical examples demonstrate that the generalized ellipsoid intersection method has lower Shannon information and higher Chernoff information than the generalized covariance intersection method.