A robust state estimator against constant measurement delay based on the sensitivity penalisation of model‐parameter errors for systems with no exogenous inputs

Abstract In this study, a class of linear system, which is with no exogenous input and suffered from constant measurement delay and uncertain model‐parameter errors, is under consideration. To combat both the parametric uncertainties and constant measurement delay, a novel robust state estimator is proposed. Accounting for the constant measurement delay, a clever approach is utilised to expand the state vector and the system model is converted into an augmented delay‐free model. Considering the deterioration of estimation performance caused by stochastic model‐parameter errors, the sensitivity penalisation function of model‐parameter errors is defined and introduced into the objective function of the regularised least‐squares (RLS) problem, whose solution is the standard Kalman filter. Furthermore, by restricting the range of introduced parameter, the objective function of the modified RLS problem is converted into a strict convex function. Then, the recursive procedure of the proposed estimator is derived. The asymptotic stability conditions of the proposed estimator and the conditions for boundness of the estimation error matrix are given. Numerical simulations show the effectiveness of the estimator proposed in this paper.