Robust white noise deconvolution estimators for systems with uncertain-variance linearly correlated white noises and missing measurements

Estimating input signal of a system is called deconvolution or input estimation. The white noise deconvolution has important applications in oil seismic exploration, communications, and signal processing. This paper addresses the problem of designing robust white noise deconvolution estimators for a class of uncertain systems with missing measurements, uncertain noise variances and linearly correlated white noises. By introducing fictitious noise, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, using Kalman filtering approach, the robust time-varying white noise deconvolution estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the three white noise deconvolution estimators are proved. A simulation example shows the effectiveness and correctness of the proposed results.