Robust weighted fusion steady-state white noise deconvolution smoothers for multisensor systems with uncertain noise variances

• The minimax robust white noise smoothers with uncertain noise variances.
• The six robust weighted fusion steady-state white noise smoothers were presented.
• The robustness of the robust fusers was proved by the Lyapunov equation approach.
• We prove the accuracy relations among robust local smoothers and weighted fusers.

For the linear discrete time-invariant multisensor systems with uncertain noise variances, according to the minimax robust estimation principle, based on the worst-case systems with the conservative upper bounds of noise variances, using Kalman filtering approach, the six robust weighted fusion steady-state white noise deconvolution smoothers (WNDS) are presented, include three robust weighted state fuser weighted by matrices, diagonal matrices and scalars, a modified robust covariance intersection (CI) fuser, and two robust weighted measurement fusers. They have the robustness in the sense that their actual smoothing error variances are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. We prove their robustness based on the Lyapunov equation approach. The concept of the robust accuracy is presented, and the robust accuracy relations among the robust local smoothers and six weighted fusion smoothers are rigorously proved. The equivalence among two robust weighted measurement fusers and robust centralized fuser is proved based on the information filter. Three simulation examples are given to verify the robustness and show the effectiveness of the proposed results.