A Quarter Century of Covariance Intersection: Correlations Still Unknown? [Lecture Notes]
Robin Forsling, Benjamin Noack, Gustaf Hendeby · IEEE Control Systems · 2024
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 ofconservativenesshas 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 ofcovariance consistencyis often used to characterizeconservativeness. In this work, we use the latter term.