Covariance intersection fusion Kalman estimator for the two-sensor time-delayed system

For a two-sensor linear discrete time-invariant stochastic system with time-delayed measurements, an equivalent system without measurement delays is obtained by applying the measurement transformation method. Using the modern time series analysis method, based on the ARMA innovation model, the local steady-state optimal Kalman estimators are obtained. Then several fusion Kalman estimators are presented, including the Kalman fusers weighted by matrices, diagonal matrices, scalars and covariance intersection, respectively. Compared with other three fusers, the covariance intersection (CI) fusion Kalman estimator can avoid a large computational burden and handle the fusion problem for the system with unknown cross-covariances. The accuracy comparison of three weighting fusers with the CI fuser is presented. It is proved that the accuracy of the CI fuser is higher than that of each local estimator, and is lower than that of optimal Kalman fuser weighted by matrices. A Monte-Carlo simulation example shows the accuracy relation, and indicates that the actual accuracy of the CI fuser may be higher than those of the Kalman fusers weighted by diagonal matrices and scalars, and is close to that of the Kalman fuser weighted by matrices, so it has good performance.