A hierarchical scheme for multi-objective state estimation with fading measurements

Engineering systems normally appear multiple dynamical structures due to external disturbances and noises, parameter variations, and varying operating conditions. In this paper, we present a novel hierarchical architecture for state estimation of discrete-time systems with multiple dynamical modes, and apply such scheme to the multi-objective design subject to fading observations. Firstly, a hierarchical estimation structure is established for choosing estimates of arbitrary branch to achieve autonomous switch among diverse estimators related to variant dynamical structures of the plant. Both Luenberger form estimators and general dynamical estimators, together with corresponding selecting operators, are explored. Secondly, based on the developed form, the problem of robust optimal state estimation over stochastic fading channels is studied, where a double-layer scheme with two estimators, dealing with the plant failure and the nominal operating condition, is adopted. For the former case, the desired estimator, characterized within the non-zero sum Nash game framework, is capable of ensuring robustness against faults and minimizing the estimation error under the worst fault. The resulting Nash equilibrium strategies, consisting of the optimal gain and the worst-case fault signal, are derived by a set of cross-coupled augmented modified algebraic Riccati equations (MAREs), and a rigorous analysis of mean square stability is also provided. For the nominal condition, a stationary Kalman filter with fading measurements is constructed via an MARE. Thirdly, the results are further extended to the time-varying case for addressing the estimation problem in the presence of data loss, where the two estimators are both synchronized with the acknowledgment, and the resulting design approaches are also provided. Finally, an example is included to show the effectiveness of the present methods.