Design of filters for a class of non-uniform sampling systems

The filtering problem for a class of non-uniform sampling discrete stochastic systems is studied, where the state is updated at a fast uniform sampling rate and the measurement is sampled at a slow non-uniform sampling rate. The state update rate is a multiple of the measurement sampling rate. The non-augmented state model at the measurement sampling points is established. Optimal state filters at the measurement sampling points are presented in the linear minimum variance sense by projection theory. Further, the state filters at the state update points are presented based on the estimates at the measurement sampling points. At last, the asymptotic stability of the proposed filters is analyzed. The simulation research verifies the effectiveness of the proposed algorithm.