中文摘要：

在量测数据丢失下滤波方程和Riccati方程出现一些新的性质变化．探测概率小于1的不完全量测条件下，利用正定矩阵性质和Lyapunov不等式，研究了离散系统修正Riccati差分方程（MRDE）与数据丢失位置之间的关系．结果表明在一定条件下MRDE解与丢失数据位置满足单调递减的函数关系．由于统计意义下的理论MRDE模型求解计算量随丢射探测数量增加而呈指数型递增，本文最后给出了一组便于工程应用的期望状态误差协方差上下界算法，算法复杂度为O（k^2）．

英文摘要：

There are some changes of property in the filter equation and Riccati equation when missing measurements occur. When the probability of detection is less than unity, by utilizing the properties of a positive-definite matrix and the Lyapunov inequality, we investigate the relation between the modified Riccati difference equation（MRDE） and the location of missing data in incomplete measurements for a discrete-time system. It is shown that under certain conditions the MRDE is a monotonically decreasing function of the location of missing data. Because the computation load for a theoretical MRDE statistically grows exponentially with respect to the number of possible miss/detection sequences, we give the upper and lower bounds of the covariance for the state-error for practical applications. The calculation complexity is O（k^2）.