带有状态时滞的非线性随机系统高斯滤波方法  

Gaussian filtering method of nonlinear stochastic systems with state delay

作　　者：王硕 何定洲 朱勇 沈敦亮 于霖 WANG Shuo;HE Dingzhou;ZHU Yong;SHEN Dunliang;YU Lin(Beijing Institute of Astronautical System Engineering,China Academy of Launch Vehicle Technology,Beijing 100076,China)

机构地区：[1]中国运载火箭技术研究院北京宇航系统工程研究所,北京100076

出　　处：《黑龙江大学自然科学学报》2021年第1期100-108,共9页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省自然科学基金资助项目(A2015016)。

摘　　要：针对带有状态时滞随机系统的估计问题,提出了一种改进的高斯滤波算法(Guassian filter,GF),给出了具体的实现形式—状态时滞容积卡尔曼滤波器(State-delayed cubature Kalman filters,SDCKF)。通过递归运算,获得当前和状态时滞的后验概率密度;根据高斯滤波框架分别对带有状态时滞的时间更新方程和量测更新方程进行了推导。根据三阶球径容积法则,给出了SDCKF滤波算法的详细设计过程。SDCKF作为一个通用的非线性滤波算法框架,根据不同的后验概率密度近似方法,可以有不同的实现形式,经典GF算法是本文所提出改进GF算法的一种特例。仿真结果表明,相比于EKF算法、UKF算法和CKF算法,SDCKF算法解决了含有状态时滞系统的状态估计问题,具有更高的精度和更好的数值稳定性。For the state estimation problem of state stochastic systems with time delays,an improved Guassian filter(GF)is proposed,and its specific implementation form,the state-delayed cubature Kalman filter(SDCKF)is given.The posterior probability density of current and time-delay states is obtained by recursive operation.According to the Gaussian filtering framework,the time update equation and the measurement update equation with time delay are derived respectively.The detailed design process of SDCKF filtering algorithm is given according to the third-order spherical diameter volume rule.Moreover,SDCKF as a general nonlinear filtering algorithm framework,can have different implementation forms according to different posterior probability density approximation methods.Traditional Gaussian filterring algorithm is a special case of the improved Gaussian filter algorithm proposed in this paper.Simulation results show that SDCKF algorithm can solve the state estimation problem of the system with state delay and has higher precision and better numerical stability compared with EKF algorithm,UKF algorithm and CKF algorithm.

关 键 词：非线性滤波 高斯滤波 状态时滞 容积卡尔曼滤波 

分 类 号：V448.2[航空宇航科学与技术—飞行器设计]