误差方差约束下不确定离散时间系统的鲁棒卡尔曼滤波

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。

Robust Kalman Filtering for Uncertain Discrete-time Systems with Error Variance Constraints

This paper is concerned with the problem of designing robust kalman filters for discrete-time systems with parameter uncertainty in both the state and measure matrices. The motivation for this study is that in the area of state estimation,the Performance requirements are usually described in terms of the upper bounds on the error variance of state estimation. The purpose of the addressed problem is to design the kalman filter gain such that the estimation error variance achieves the steady-state value which is not greater than the prespecified one. The necessary and sufficient conditions for the existence of desired robust filter gain and the analytical expression are also given. A numerical example is presented to demonstrate the directress and efficientness of the proposed design approach.