Robust receding-horizon estimation for uncertain discrete-time linear systems

The problem of estimating the state of discrete-time linear systems when uncertainties affect the system matrices is addressed. A quadratic cost function is considered, involving a finite number of recent measurements and a prediction vector. This leads to state the estimation problem in the form of a regularized least-squares one with uncertain data. The optimal solution (involving on-line scalar minimization) together with a suitable closed-form approximation are given. For both the resulting receding-horizon estimators convergence results are derived and an operating procedure to select the design parameters is proposed.