Sequential covariance intersection fusion Kalman filter

For multisensor system with unknown cross-covariances among local estimation errors, the batch covariance intersection (BCI) fusion estimation algorithm requires the optimization of a multi-dimensional nonlinear cost function, which yields a larger computational burden and computational complexity. A fast sequential covariance intersection (SCI) Kalman filtering algorithm is presented in this paper, which only requires to solve the optimization problem of several one-dimensional nonlinear cost functions. It is equivalent to several two-sensor covariance intersection (CI) Kalman fusers, and is a recursive two-sensor CI Kalman fuser. Its accuracy depends on the orders of sensors. It is proved that the SCI fuser is consistent, and its accuracy is higher than that of each local estimator and is lower than that of the optimal Kalman fuser with known cross-covariances. The geometric interpretation of accuracy relations based on the covariance ellipses is given, and the properties of the covariance ellipses are rigorously proved. Two Monte-Carlo simulation examples show the effectiveness of the proposed results, show that the accuracies of the SCI fusers are not very sensitive with respect to the orders of sensors, and show that its actual accuracy is close to that of the optimal Kalman fuser in general cases, and its robust accuracy is close to that of the BCI fuser, so it has good performances.