On conservative fusion of information with unknown non-Gaussian dependence

Abstract

Abstract — This paper examines the notions of consistency and conservativeness for data fusion involving dependent information, where the degree of dependency is unknown. We consider these notions in a general sense, for non-Gaussian probability distributions, in terms of structural consistency and information processing, notably the counting of common information. We consider the role of entropy in defining a conservative fusion rule. Finally, we investigate the normalised weighted geometric mean (NWGM) as a particular fusion rule, which generalises the covariance intersection rule to non-Gaussian pdfs. We derive key properties to demonstrate that the NWGM is both conservative and effective in combining information from dependent sources. Index Terms — Data fusion, conservative, consistent, non-Gaussian, covariance intersection, weighted geometric mean