A robust estimator for stochastic systems under unknown persistent excitation

A robust estimator for uncertain stochastic systems under unknown persistent disturbance is presented. The given discrete-time stochastic formulation neither requires a known bound on the magnitude of the unknown excitation nor assumes stability of the system. However, the proposed estimator assumes certain structural conditions on system uncertainties. Though the proposed estimator is developed based on stochastic Lyapunov analysis, its structure and performance are comparable to that of unbiased minimum-variance filters based on the disturbance decoupling technique. Unlike unbiased minimum-variance filters, implementation of the developed estimator only requires adding an auxiliary term to the nominal steady-state Kalman filter, and it does not involve any similarity transformation or propagation of matrix difference equations.