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.

中文翻译：

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存在未知交叉协方差的最优数据融合算法

本文提出了一种在部分或全部交叉协方差未知时最小均方误差意义上的最佳数据融合公式和算法。该算法是通用的，因为它能够处理具有任何未知交叉协方差模式的任何维度的任意数量的测量向量。当所有交叉协方差未知且所有测量协方差矩阵都是对角线时，提供了封闭形式的解决方案。为最通用的情况提供了数值投影次梯度最优融合算法。众所周知的协方差相交方法显示出该公式的上界较弱。