Over the past two and a half decades, covariance intersection (CI) has provided a means for robust estimation in scenarios where the uncertainty information is incomplete. Estimation in distributed and decentralized data fusion (DDF) settings is typically characterized by having nonzero cross-correlations between the estimates to be merged. Mean-square-error (MSE) optimal estimators, such as the Kalman filter (KF), are limited to data fusion problems where these cross-correlations are fully known. Keeping track of cross-correlations is unfortunately not always possible. To quantify confidence in the estimate’s uncertainty, the concept of conservativeness has been introduced. A conservative estimator guarantees that the computed covariance matrix is not smaller than the actual covariance matrix. It turns out that CI guarantees conservativeness for any degree of unknown cross-correlations as long as the estimates to be fused are conservative. It should be noted that, in the CI literature, the notion of covariance consistency is often used to characterize conservativeness . In this work, we use the latter term.

中文翻译：

---

四分之一个世纪的协方差交集：相关性仍然未知？ [演讲笔记]

在过去的两年半里，协方差交集 (CI) 提供了一种在不确定性信息不完整的情况下进行稳健估计的方法。分布式和分散式数据融合 (DDF) 设置中的估计通常以要合并的估计之间具有非零互相关为特征。均方误差 (MSE) 最优估计器，例如卡尔曼滤波器 (KF)，仅限于完全已知这些互相关性的数据融合问题。不幸的是，跟踪互相关性并不总是可能的。为了量化估计不确定性的置信度，概念引入了保守性。保守估计器保证计算出的协方差矩阵不小于实际协方差矩阵。事实证明，只要要融合的估计是保守的，CI 就能保证任何程度的未知互相关的保守性。应该指出的是，在 CI 文献中，概念协方差一致性常常用来表征保守性。在这项工作中，我们使用后一个术语。