Abstract:

For the linear discrete time-invariant stochastic system with uncertain noise variances, according to the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, applying Kalman filter and the optimal white noise estimation theory, a robust steady-state white noise deconvolution smoother is presented. Its actual smoothing error variances are guaranteed to have a minimal upper bound for all admissible uncertain noise variances. Its robustness and the robust accuracy relation are proved based on the Lyapunov equation approach. A simulation example is given to verify the correctness and effectiveness of the proposed results.