中文摘要：

将具有不确定观测的ARMA信号滤波问题转化为具有不确定观测的状态空间模型的状态和白噪声滤波问题。利用射影理论,推导出了在线性最小方差意义下状态滤波器和白噪声滤波器。进而获得具有不确定观测的ARMA信号滤波器。对于存在不确定观测的ARMA信号,以往在完整观测数据下的AMRA信号滤波算法已经失去最优性。当不存在观测数据丢失时,算法等同于以往最优ARMA信号滤波器。仿真例子说明了其有效性。

英文摘要：

The filtering problem for ARMA signal with uncertain observation is translated into that for state and white noise of the state space model with uncertain observation.Based on projection theory,the optimal filters for state and white noise are derived in the linear minimum variance sense.Further,the filter for ARMA signal with uncertain observation is obtained.For the ARMA signal with uncertain observation,the previous filtering algorithm for ARMA signal with complete observation has lost the optimality.When there is no observation data loss,the proposed algorithm is equivalent to the previous optimal filter for ARMA signal.Simulation results show their effectiveness.