基于影响力函数的自适应鲁棒卡尔曼滤波  

An adaptive robust Kalmanfilter based on influence function

作　　者：薛为 栾小丽 赵顺毅 刘飞 Wei XUE;Xiaoli LUAN;Shunyi ZHAO;Fei LIU(Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education),Jiangnan University,Wuxi 214122,China)

机构地区：[1]江南大学轻工过程先进控制教育部重点实验室,无锡214122

出　　处：《中国科学:信息科学》2025年第3期601-618,共18页Scientia Sinica(Informationis)

基　　金：江苏省研究生科研与实践创新计划(批准号:KYCX23_2437);国家自然科学基金(批准号:61991402,61973136)资助项目。

摘　　要：为解决卡尔曼(Kalman)滤波的工程应用难题,现有方法往往以过多的性能损失为代价来增强滤波算法鲁棒性,从而导致估计性能下降.为进一步提升滤波精度,本文借助于影响力函数,构建基于黎卡提(Riccati)方程的自适应鲁棒卡尔曼滤波(adaptive robust Kalman filter, ARKF)算法,削弱不确定性影响的同时,最小化性能损失.首先,利用影响力函数实时感知并量化不确定性影响;其次,根据量化结果反演不确定性导致的观测偏移量;然后,根据观测偏移量实时放缩黎卡提方程先验信息上界,实现卡尔曼滤波鲁棒性的自适应调整,减小性能损失;最后,通过数值仿真以及在四容水箱实验中的应用,证实所提算法的有效性及优越性.To solve the engineering application problems of the Kalmanfilter,the existing methods often enhance the robustness at the cost of excessive performance loss,which leads to performance degradation.To improve thefiltering accuracy,this paper constructs the adaptive robust Kalmanfilter(ARKF)algorithm based on the Riccati equation with the influence function to minimize the performance loss while reducing uncertainty.First,the influence function is used to perceive and quantify the uncertainty influence in real time;second,the observation deviation caused by uncertainty is inverted according to the quantification;then,the priori covariance matrix of the Riccati equation is adjusted according to the observation deviation,thus realizing the adaptive tuning of the robustness and minimizing the performance loss;lastly,the effectiveness and superiority of the proposed algorithm are demonstrated by numerical simulation and application in the quadruple-capacity water tank experiments.

关 键 词：卡尔曼滤波 自适应鲁棒滤波 影响力函数 黎卡提方程 不确定性 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]