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本文研究状态矩阵及测量矩阵中均含有不确定性的离散时间系统的鲁棒卡尔曼滤波问题。在状态估计领域中，指标要求常直接以状态分量的估计误差方差上限的形式给出。为此，本文的目的在于设计卡尔曼滤波增益，使不确定系统的估计误差方差达到稳态且其值不大于预先指定值、文中给出了期望鲁棒滤波增益的存在条件及其解析表达式，并以数值算例说明设计方法的直接性与有效性。
In this paper, the robust Kalman filtering problem of discrete-time systems with uncertainties in both the state matrix and the measurement matrix is investigated. In the field of state estimation, the index requirements are often given directly as the upper bound of the variance of the estimated error of the state component. Therefore, the purpose of this paper is to design the gain of Kalman filter so that the variance of the estimation error of the uncertain system reaches the steady state and its value is not greater than the pre-specified value. The existence conditions of the expected robust filter gain and their analytical expressions The numerical examples are given to illustrate the directness and effectiveness of the design method.