Optimal and Self-correcting Covariance Intersection Fusion Kalman Filters

Abstract

For the multi-sensor discrete linear time-invariant random system, the optimal covariance intersection (CI) fusion steady-state Kalman filters are presented, which have uncharted cross-covariance among the partial filtering errors. Their accuracies are higher than those of the partial optimal steady-state Kalman filters, and are lower than those of the optimal fusion Kalman filters which are fused by the cross-covariances. In the case that both the cross-covariance and the noise variances are uncharted, substituting the online consistent estimators of the noise variances into the optimal CI fusion Kalman filter, a self-correcting CI fusion Kalman filter is presented. I have proven its optimality asymptotically by the method of DESA (dynamic error system analysis) and the continuous properties of functions, i.e. the self-correcting CI Kalman fuser convergences to the optimal CI fuser in a implementation. One Monte-Carlo emulation example verifies the precision grade among the partial and fusion Kalman estimators, and the convergence of the self-correcting Kalman fuser.