A Novel Observability Gramian-Based Fast Covariance Intersection Rule

Abstract

In this letter, a new type of fast covariance intersection (CI) rule to deal with unknown correlations is proposed. Different from the existing CI and its variants, our approach can obtain the optimized CI weights offline while preserving a guaranteed filtering accuracy and stability in the online implementation stage. To this end, the connection between the upper bound of the fused error covariances and the observability Gramian is first established. Next, the optimization of error covariances is converted into the optimization of observability Gramian, which is made of system matrices. Accordingly, the CI weights can be calculated prior to the real implementation. Moreover, the stability result of the fusion is also established with the help of the proposed jointly uniform observability condition. At last, simulations are given to demonstrate the effectiveness of the proposed fast CI method.