线性系统未知输入和状态扩展递归滤波方法

Extension Recursive Filtering of Unknown Input and State for Linear Systems

在环境监测、导航与控制、故障检测等领域中,由于环境影响、模型参数选取不当、设备故障等原因,系统状态方程和测量方程中往往含有未知输入。针对未知输入直接馈通到测量方程的情况,研究同时估计线性系统状态和未知输入的问题。在没有未知输入先验知识的前提下,针对测量方程中未知输入系数矩阵不满秩时无法应用经典递归三步滤波器的问题,依据线性最小方差无偏估计准则,提出了一种新的扩展递归三步滤波器,并提炼汇总出具体递归迭代步骤。仿真结果表明,与以往系数矩阵不满秩情况下的无偏最小方差状态估计方法相比,新的滤波器能够有效降低状态估计误差。

In the fields of environmental monitoring, navigation and control, and fault detection, the system state equations and measurement equations often contain unknown input due to the environmental impacts, improper selection of model parameters, equipment failures and other reasons. This paper studies the problem of estimating the state and the unknown input of the linear system simultaneously when the unknown input direct feedthrough the measurement equation. Without the prior knowledge of the unknown input, the classical recursive three-step filter cannot be applied in state estimation when the unknown input coefficient matrix in the measurement equation is not full rank. This paper proposes a novel extended recursive three-step filter(NERTSF) according to the linear minimum variance unbiased estimation criterion, and summarizes the specific recursive steps. The simulation results show that the new filter can effectively reduce the state estimation error compared with the unbiased minimum variance state estimation(UMVSE) method in the case where the coefficient matrix is not full rank.