研究了一类非均匀采样离散随机系统的最优滤波问题,其中系统状态以快速率均匀进行更新,观测以慢速率非均匀进行采样,且状态更新率为观测采样率的整数倍.建立了在观测采样点上的非增广的状态模型. 应用射影理论提出了在观测采样点上的线性最小方差最状态滤波器.进而,基于观测采样点上的状态估值,提出了在状态更新点上的状态滤波器.最后,分析了所提出的滤波器的渐近稳定性和稳态性能.仿真研究验证了算法的有效性.

Optimal filtering problem for a class of non-uniform sampling discrete stochas- tic systems is studied, where the system 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 measure- ment sampling points is established. Optimal state filters at the measurement sampling points are presented in the linear minimum variance sense using projection theory. Furthermore, the state filters at the state update points are presented based on the estimates at the measurement sampling points. Finally, the asymptotic stability and steady-state property of the proposed filters are analyzed. The simulation results verify the effectiveness of the proposed algorithm.