误差方差及圆形区域极点约束下状态估计问题的研究:连续时间情形

提出并讨论了线性连续随机系统在稳态估计误差方差及圆形区域极点约束下的状态估 计问题,即希望设计滤波增益,使得每个状态分量的估计误差方差稳态值不大于各自预先给 定值,同时滤波矩阵的极点位于给定圆形区域内,从而使滤波过程具有良好的稳、暂态特性. 文中利用一修正的代数Riccati方程,给出了期望滤波增益的存在条件及解析表达式.数值 例子说明了文中设计方法的直接性和有效性.

A Study of Error Variance and Circular Pole-Constrained State Estimation for Continuous Systems

The problem of state estimation with the steady-state estimation error variance constraints and the circular pole constraints is proposed and studied in this paper. The purpose of this problem is to design the filter gain such that the steady-state value of estimation error variance for each state is less than or equal to the prespecified value, and the poles of the filter matrix lie within the prespecified circular region, simultaneously. Therefore the filtering process will possess good behavior. It is shown that the solution of the addressed problem can be determined by a modified Riccati equation. The conditions for the existence and the explicit expression of the desired filter gains are given. Finally, a numerical example is provided to demonstrate the directness and simplicity of the present design method.