SICI Fusion Kalman Filter for Multi-sensor Networked Systems with One-step Random Delays and Correlated Noises

The fusion estimation problem for multi-sensor networked systems with random delays is a popular research field, and accompanied with correlated noises, it becomes more complicated, because in ordinary fusion criterion, the cross-covariance matrices are required, which are always difficult to be obtained. In order to solve it, a SICI (Sequential Inverse Covariance Intersection) fusion Kalman filtering method is presented. Firstly, by the augmented state technology and the fictitious noise algorithm, the original systems with one-step random delays and correlated noises are transformed into a new one without delays. Secondly, using the Lyapunov equation method, the variance matrices of the fictitious noise is derived, and applying the classical Kalman filtering method, the local Kalman filters can be obtained. Inspired by the idea of sequential fusion structure, the ICI fusion algorithm is applied to avoid the calculation of the cross-covariance matrices, and then the SICI fusion structure is presented. Lastly, the accuracy relations among several fusion methods are proved, and compared with the SCI (Sequential Covariance Intersection) method, the SICI method has less conservativeness. A simulation example shows the effectiveness and the consistency of the presented SICI fusion Kalman filter.