预测误差方差约束下的稳态离散卡尔曼滤波

Steady-state Kalman Filtering for Discrete-TimeSystems with Estimation Error Variance Constraints

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 area of estimation and filtering, performance requirements are naturally described in terms of the upper bounds on the estimation error variances of system states.This paper studies the problem of discrete-time Kalman filtering with steady-state and transient requirement constraints. The problem we address is the design of a filter gain such that the estimation error variance for each state is not greater than the individual prespecified value, and the filter matrix satisfies the prespecified regional pole constraints, simultaneously. The conditions for the existence of desired filter gains and the analytical expression are given. A numerical example demonstrates the simplicity and effectiveness of the present design method.