含未知输入非线性系统的扩展平方根容积卡尔曼滤波算法  

Extended Square-root Cubature Kalman Filtering Algorithm for Nonlinear Systems with Unknown Inputs

作　　者：鹿子豪 王娜[1,2] 林崇[1,3] 赵克友[1] 董世桂 LU Zi-hao;WANG Na;LIN Chong;ZHAO Ke-you;DONG Shi-gui(College of Automation,Qingdao University,Qingdao 266071,China;Shandong Key Laboratory of Industrial Control Technology,Qingdao University,Qingdao 266071,China;Institute of Complexity Science,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学自动化学院,青岛266071 [2]青岛大学山东省工业控制技术重点实验室,青岛266071 [3]青岛大学复杂性科学研究所,青岛266071

出　　处：《科学技术与工程》2024年第14期5892-5900,共9页Science Technology and Engineering

基　　金：崂山实验室科技创新项目(LSKJ202201904);国家自然科学基金(61703221);山东省自然科学基金(ZR2016FP10)。

摘　　要：针对工程实际应用中存在的未知输入会导致经典的非线性滤波器状态估计精度下降甚至滤波发散的问题,提出了一种基于最小方差无偏估计(minimum variance unbiased estimation,MVUE)准则的扩展平方根容积卡尔曼滤波(extended square-root cubature Kalman filter,ESRCKF)算法。首先,结合上一时刻未知输入估计值对状态一步预测值进行修正,得到含未知输入条件下的状态预测值。其次,设计新息并采用加权最小二乘(weighted least squares,WLS)法获取当前时刻未知输入的无偏估计。最后,通过最小化协方差矩阵的迹,同时采用拉格朗日乘子法和舒尔补引理得到系统状态的最小方差无偏估计。仿真结果表明,相比于现有的非线性滤波算法,ESRCKF算法提高了在处理含未知输入非线性系统时的状态估计精度,并能同时实现系统状态和未知输入的最优估计,验证了该算法的有效性。The unknown inputs in practical engineering applications will lead to the decline of the accuracy of the classical nonlinear filter state estimation and even the divergence of the filter.In order to address this problem,an extended square-root cubature Kalman filter(ESRCKF)algorithm according to the minimum variance unbiased estimation(MVUE)criterion was proposed.Firstly,the one-step predicted value of state was modified by combining with the unknown input estimated value at the previous time to obtain the predicted value of state under the condition of unknown input.Secondly,the unbiased estimation of the unknown input at the current time was obtained by using innovation and weighted least squares(WLS)method.Finally,the minimum variance unbiased estimation of the system state was obtained by minimizing the trace of the covariance matrix,while using the Lagrange multiplier method and the Schur complement lemma.Simulation results demonstrate that compared with the existing nonlinear filtering algorithms,ESRCKF algorithm improves the accuracy of state estimation when dealing with nonlinear systems with unknown inputs,and can simultaneously achieve the optimal estimation of system state and unknown inputs,which validates the effectiveness of the algorithm.

关 键 词：平方根容积卡尔曼滤波 最小方差无偏估计 加权最小二乘法 状态估计 未知输入估计 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]