含未知输入的离散线性系统新型递归滤波方法

Novel Recursive Filtering for Discrete Linear Systems with Unknown Inputs

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,系统状态方程中往往含有未知输入。针对受未知影响的系统,在研究的同时估计未知输入和线性系统状态的问题。在没有未知输入先验知识的前提下,针对系统方程中未知输入系数矩阵不满秩时无法应用经典滤波方法的问题,依据线性最小方差无偏估计准则,提出一种三步递归滤波方法,并提炼汇总出具体递归迭代步骤。仿真结果表明,新滤波方法能够有效估计系统状态及未知输入。

In the fields of environmental monitoring,navigation control and fault detection,system and measurement equations both have unknown input due to the environmental impacts,improper selection of model parameters and measurement equipment failures.This paper studies the problem of estimating the state and the unknown input of the linear system simultaneously when the unknown input affects the system equation.Without the prior knowledge of the unknown input,when the unknown input coefficient matrix in the system equation is not of full rank,the classic recursive three-step filter cannot be applied in state estimation.This paper proposes a novel recursive three-step filter according to the linear minimum variance unbiased estimation criterion,and summarizes the specific recursive steps.Simulation results show that the novel filter can estimate the state and the unknown input effectively.