Minimax robust deconvolution filters under stochastic parametric and noise uncertainties

The author consider the design of robust deconvolution filters for linear discrete time systems with stochastic parameter and noise uncertainties. It is assumed that some large but bounded uncertainties exist in the driving and measurement noise covariances as well as the second-order statistics of stochastic parameters and initial conditions. Three kinds of minimax sensitivity criteria are used to develop the techniques to the synthesis of minimax deconvolution filters under uncertain linear stochastic systems. Their approach is based on saddle-point theory and the sensitivity analysis of Kalman filters. The design algorithms give the recursive realization of the minimax deconvolution filters for the time-varying uncertain systems under fairly general conditions. For the time-invariant uncertain case the existence and solutions of steady-state deconvolution filters are further developed. Finally, the utility of the minimax design approaches and the properties of the resulting minimax deconvolution filters are illustrated by a numerical example