An Optimal Data Fusion Algorithm in the Presence of Unknown Cross Covariances

This paper presents an optimal data fusion formulation and algorithm in the sense of minimum mean-square error when some or all cross covariances are unknown. This algorithm is generic in that it is capable of processing any number of measurement vectors of any dimension with any pattern of unknown cross covariances. Closed-form solution is provided for the case when all cross covariances are unknown and all measurement covariance matrices are diagonal. Numerical projected subgradient optimal fusion algorithm is provided for the most generic case. The well known covariance intersection method is shown to have a weaker upper bound of this formulation.