标题： 分裂协方差交叉融合的最优性 显示英文标题

标题： Optimality of Split Covariance Intersection Fusion

摘要： 线性融合是估计理论的基石。 在20世纪80年代，Bar-Shalom和Campo推导出了最优线性融合。 它需要了解估计器误差之间的交叉协方差。 在分布式或协作系统中，这些交叉协方差很难计算。 为了在这些交叉协方差未知时避免对误差的低估，必须进行保守融合。 保守融合提供了一个融合估计器，其协方差界保证大于误差的真实（但无法计算）协方差。 Reinhardt等人之前的研究所证明，如果不对估计器的误差做出额外假设，则融合两个估计器的最小边界由一种称为协方差交集（CI）的融合给出。 在实践中，由于动态或测量噪声被假定为独立的，估计器的误差通常具有不相关分量。 在这种情况下，CI不再是最佳方法，已经设计出一种称为分割协方差交集（SCI）的适应方法，以利用这些不相关分量。 本文的贡献是证明，在假设两个估计器具有不相关分量的情况下，SCI是融合两个估计器的最佳规则。 证明了SCI相对于任何递增成本函数提供了最优的协方差边界。 为了证明这一结果，推导出了应包含所有保守边界的最小体积，并证明SCI边界是唯一能够紧密包围该最小体积的边界。 显示英文摘要

摘要： Linear fusion is a cornerstone of estimation theory. Optimal linear fusion was derived by Bar-Shalom and Campo in the 1980s. It requires knowledge of the cross-covariances between the errors of the estimators. In distributed or cooperative systems, these cross-covariances are difficult to compute. To avoid an underestimation of the errors when these cross-covariances are unknown, conservative fusions must be performed. A conservative fusion provides a fused estimator with a covariance bound which is guaranteed to be larger than the true (but not computable) covariance of the error. Previous research by Reinhardt et al. proved that, if no additional assumption is made about the errors of the estimators, the minimal bound for fusing two estimators is given by a fusion called Covariance Intersection (CI). In practice, the errors of the estimators often have an uncorrelated component, because the dynamic or measurement noise is assumed to be independent. In this context, CI is no longer the optimal method and an adaptation called Split Covariance Intersection (SCI) has been designed to take advantage from these uncorrelated components. The contribution of this paper is to prove that SCI is the optimal fusion rule for two estimators under the assumption that they have an uncorrelated component. It is proved that SCI provides the optimal covariance bound with respect to any increasing cost function. To prove the result, a minimal volume that should contain all conservative bounds is derived, and the SCI bounds are proved to be the only bounds that tightly circumscribe this minimal volume.