在预测与滤波领域中，指标要求常常直接表现为状态分量的预测误差方差的上界形式。本文研究稳、暂态指标约束下的离散系统卡尔曼滤波问题，即设计滤波增益，使每个状态分量的预测误差方差不大于各自预先给定值，同时滤波矩阵满足给定的区域极点约束。本文给出了期望滤波增益的存在条件及其解析表达式。数值例子说明了本文设计方法的简单性与有效性。 In the field of prediction and filtering, the index requirements often appear directly as the upper bound of the variance of the prediction error of the state components. In this paper, we study the discrete-system Kalman filtering problem under the constraints of steady and transient indexes, that is, design the filter gain so that the prediction error variance of each state component is not greater than their respective pre-specified values, and the filter matrix satisfies the given regional pole constraints. In this paper, the existence conditions of the expected filter gain and its analytical expressions are given. Numerical examples illustrate the simplicity and effectiveness of this design method.