考虑随机量测时滞和同步相关噪声的改进高斯滤波算法

An improved Gaussian filter with randomly delayed measurements and synchronously correlated noises

中文关键词  高斯滤波  容积卡尔曼滤波  随机时滞  同步相关噪声

英文关键词  Gaussian filter  cubature Kalman filter  random delay  synchronously correlated noises

中文摘要

      经典高斯滤波算法存在量测信息实时获取, 以及过程噪声和量测噪声相互独立的假设条件. 然而, 在工程 实际应用中该假设条件有时难以满足. 本文针对一类具有随机量测时滞和同步相关噪声的高斯系统的状态估计问 题, 设计了一种高斯滤波框架形式的最优估计算法, 并给出了所设计算法的三阶球径容积法则的次优实现形式--考 虑随机量测时滞和同步相关噪声的容积卡尔曼滤波器(CKF–RDSCN). 其借助Bernoulli随机序列, 来描述系统中可 能存在的量测时滞现象, 并利用高斯条件分布性质来解决噪声相关问题, 在此基础上构建所提出的最优估计算法. 仿真结果表明, 相比于扩展卡尔曼滤波(EKF), 无迹卡尔曼滤波(UKF)以及容积卡尔曼滤波(CKF), 在含有随机量测 时滞和噪声同步相关的状态估计问题中, CKF–RDSCN具有更高的精度和更好的数值稳定性.

英文摘要

      The classical Gaussian filters are based on the assumption that measurements are acquired in time and noises of process and measurement are independent of each other. However, this assumption is sometimes hard to satisfy in practical applications. In this paper, an optimal estimation algorithm in the form of Gaussian filter framework is designed to solve the problem of states estimation of a Gaussian system with randomly delayed measurements and synchronously correlated noises, and the rule of third-degree spherical-radial cubature is employed to deduced the suboptimal estimation implementation of the proposed algorithms which is named cubature Kalman filter with randomly delayed measurements and synchronously correlated noises(CKF–RDSCN). It takes random sequence of Bernoulli to describe the possible situation with respect to random delay in observation measurement and the property of Gaussian conditional distribution is utilized to solve the problem of noises correlation. Simulation results demonstrate that CKF–RDSCN is more accurate and stability than the extended Kalman filter(EKF), unscented Kalman filter(UKF) and CKF in the states estimation problem involved with randomly delayed measurements and synchronously correlated noises.