具有相关噪声和不确定观测系统的全局最优Kalman滤波  

Globally Optimal Kalman Filtering for Systems with Correlated Noises and Uncertain Measurements

作　　者：陈东彦[1] 余永龙[1] 胡军[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2015年第4期1-10,共10页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11271103;11301118)

摘　　要：研究了具有不同源噪声和不确定观测的离散线性随机系统的全局最优Kalman滤波问题.乘性噪声是用来描述系统的随机扰动,相关噪声包括了有限步自相关过程噪声和纵向相关噪声,不确定观测包括了一步随机时滞和多丢包.由Kronecker delta函数来描述有限步自相关过程噪声和纵向相关噪声,通过两个已知统计特性且相互独立的Bernoulli分布变量来描述一步随机时滞和多丢包现象.基于最优估计的定义,在最小均方误差意义下设计出全局最优Kalman滤波.最后,算例仿真验证滤波方法的有效性.This paper investigates the globally optimal Kalman filtering problem for discrete systems with different sources of noises and uncertain measurements. The multiplicative noises are terize the random disturbances existing in systems, the finite-step auto-correlated process noises and noises are included in the correlated noises, the random one-step sensor delay and multiple packet stochastic linear used to charac- cross-correlated dropouts are in- cluded in the uncertain measurements. Finite-step auto-correlated process noises and cross-correlated noises are de- scribed by Kronecker delta functions, and two mutually independent Bernoulli distributed random variables with known conditional probabilities are employed to describe the phenomena of the random one-step sensor delay and multiple packet dropouts. Based on the definition of optimal estimation, the globally optimal Kalman filter is de- signed in the sense of minimum mean square error （MMSE）. Finally, a simulation example is given to demonstrate the effectiveness of the proposed filtering approach.

关 键 词：全局最优Kalman滤波 不确定系统 乘性噪声 相关噪声 不确定观测 

分 类 号：O231.1[理学—运筹学与控制论]