A Quarter Century of Covariance Intersection: Correlations Still Unknown? [Lecture Notes]
Robin Forsling, Benjamin Noack, Gustaf Hendeby
Abstract
Over the past two and a half decades, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">covariance intersection (CI)</i> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">conservativeness</i> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">covariance consistency</i> is often used to characterize <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">conservativeness</i> . In this work, we use the latter term.