Information-Theoretic Justification for Covariance Intersection and Its Generalization

摘要

A technique for fusing Kalman filter information has been developed by Jeffrey Uhlmann, Simon Julier, et. al. that addresses the problems that arise from fusing correlated measurements. The researchers have named this technique 'covariance intersection' and have presented papers on it at several robotics and control theory conferences. The technique is applicable to these areas because robotic systems often have data flowing between multiple interconnected algorithms with no guarantee that the data flowing into any algorithm are independent. It can be shown that the covariance intersection technique is a log-linear combination of two Gaussian functions and is thus related to Chernoff information. Given this relationship, covariance intersection can be generalized to the fusion of any two probability density functions. One of the selection criteria suggested by the developers for the optimal combination of two Gaussian functions is the minimization of the determinant of the fused covariance, which is equivalent to the minimization of the Shannon information of the fused state. This equivalence justifies the selection of the determinant criterion for may applications of covariance intersection. Given the recognition of a more general rule for the covariance intersection technique, other probabilistic measures, such as the Chernoff information, may be appropriate for other fusion applications.