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Finite mixture such as the Gaussian mixture is a flexible and powerfulprobabilistic modeling tool for representing the multimodal distribution widelyinvolved in many estimation and learning problems. The core of it isrepresenting the target distribution by the arithmetic average (AA) of a finitenumber of sub-distributions which constitute a mixture. While the mixture hasbeen widely used for single sensor filter design, it is only recent that the AAfusion demonstrates compelling performance for multi-sensor filter design. Inthis paper, some statistic and information-theoretic results are given on thecovariance consistency, mean square error, mode-preservation capacity, and theinformation divergence of the AA fusion approach. In particular, based on theconcept of conservative fusion, the relationship of the AA fusion with theexisting conservative fusion approaches such as covariance union and covarianceintersection is exposed. A suboptimal weighting approach has been proposed,which jointly with the best mixture-fit property of the AA fusion leads to amax-min optimization problem. Linear Gaussian models are considered foralgorithm illustration and simulation comparison, resulting in the first-everAA fusion-based multi-sensor Kalman filter.

Arithmetic Average Density Fusion -- Part I: Some Statistic and Information-theoretic Results