Moving horizon estimation with multirate measurements and correlated noises

This article is concerned with the moving horizon estimation (MHE) problem for a class of linear discrete-time systems subject to multirate measurements and correlated noises. The sensors of the plant are grouped into two nodes with different sampling periods, which give rise to the multirate measurements. Under the effects of multirate measurements, the underlying system is then described by a periodic system with correlated noises. A MHE strategy is formulated and the corresponding analytical solution of the state estimation is derived by using the "completing the square" technique. Based on the lifting approach, the dynamics of the estimation error covariance is analyzed and the desired estimator parameters are obtained by solving a set of linear matrix inequalities. An illustrative example is given to show the effectiveness of our proposed MHE method.