线性离散系统状态和未知干扰的递归滤波算法研究  

Recursive Filtering Algorithm for State and Unknown Disturbance of Linear Discrete Systems

作　　者：徐迎菊 王娜[1,2] 花玉 XU Yingju;WANG Na;HUA Yu(College of Automation,Qingdao University,Qingdao 266071,China;Shandong Key Laboratory of Industrial Control Technology,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学自动化学院,山东青岛266071 [2]青岛大学山东省工业控制技术重点实验室,山东青岛266071

出　　处：《机械制造与自动化》2022年第5期8-11,共4页Machine Building & Automation

基　　金：国家自然科学基金资助项目(61703221);山东省自然科学基金资助项目(ZR2016FP10)。

摘　　要：研究了具有未知干扰、量测缺失和相关噪声的线性离散系统状态和未知干扰同时估计问题。用服从Bernoulli分布的随机序列模拟量测信息丢失的过程;系统过程噪声与量测噪声相互关联的情形用Kronecker delta函数表示。依据线性无偏最小方差的估计准则,设计一种能同时估计未知干扰和线性系统状态的递归滤波器;运用拉格朗日乘子法和矩阵对角理论知识推导计算滤波器中待定增益矩阵进而最小化估计误差协方差;通过数值仿真验证了该滤波算法的有效性。The problem of simultaneous estimation of unknown disturbances and states for linear discrete-time systems with unknown disturbances, missing measurements and correlated noises is studied. The process of missing measurement is simulated by a random sequence subordinated to Bernoulli distribution. Kronecker delta function is used to describe the correlation between process noise and measurement noise. According to the estimation criterion of linear unbiased minimum variance, a recursive filter is designed, which can estimate the unknown disturbances and the state of the linear system simultaneously. The estimation error covariance is minimized by Lagrange multiplier method and with matrix diagonal theory to deduce the unknown gain matrix in the filter. Numerical simulation is conducted to verify the effectiveness of the filtering oalgorithm.

关 键 词：未知干扰 量测缺失 相关噪声 矩阵不满秩 最小方差无偏估计 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]