具有随机时滞和异步相关噪声的非线性系统的高斯滤波器设计  

Improved Gaussian filter algorithm for nonlinear system with random delay and asynchronously correlated noises

作　　者：于浛[1] 宋申民[1] 王硕[1] 李鹏[2] 

机构地区：[1]哈尔滨工业大学控制理论与制导技术研究中心,哈尔滨150001 [2]湘潭大学信息工程学院,湘潭411100

出　　处：《中国惯性技术学报》2015年第2期238-247,共10页Journal of Chinese Inertial Technology

基　　金：国家自然科学基金(61174037)

摘　　要：针对随机时滞和异步相关噪声情况下的状态估计问题,提出了一种改进的高斯滤波算法(GF),并给出了其适用于高维系统的实现形式—随机时滞和异步相关容积卡尔曼滤波器(CKF-RDCN)。首先,通过满足Bernoulli分布的互不相关随机序列,来描述系统观测数据中可能存在的随机时滞现象,将量测噪声作为状态变量用以实现对观测时滞后验概率密度的估计。其次,利用一阶斯特林插值公式来近似估计,由于过程噪声和量测噪声异步相关,而导致的含有随机变量的多维积分问题。最后,依据三阶球径容积法则,给出了CKF-RDCN滤波算法的详细设计。此外,经典GF算法是所提出的改进GF算法的特例,其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估计方法,可以有不同的实现形式。仿真结果表明,相比于扩展卡尔曼滤波算法(EKF)以及容积卡尔曼滤波算法(CKF),CKF-RDCN在解决含有观测时滞和相关噪声系统的状态估计问题时,具有更高的精度和更好的数值稳定性。To solve the problem of states estimation with randomly delayed measurements and correlated noises, an improved Gaussian filter（GF） is proposed, and its implementation in high-dimensional system is given, which is by cubature Kalman filters with randomly delay and correlated noises（CKF-RDCN）. Firstly, an independent random sequence of Bernoulli distribution is used to describe the phenomena of possible random delay in observation measurements, and the measurement noises are taken as state vectors to estimate the probability density function of the delayed observation. Secondly, the first-order of Stirling＇s interpolation is employed to calculate the multi-dimensional integrals with random variables caused by correlated noises. Finally, the proposed CKF-RDCN is deduced from the third-order spherical-radial rule. While the classical GF can be taken as a special form of the proposed novel GF, a general algorithm frame of nonlinear filter can have different implementations based on various approximate methods of probability density functions. Simulation results demonstrate that the CKF-RDCN is more accurate and stable than the extended Kalman filter and CKF in state estimation when with randomly delayed measurements and correlated noises.

关 键 词：非线性滤波 高斯滤波 随机时滞 相关噪声 容积卡尔曼滤波 

分 类 号：V448.133[航空宇航科学与技术—飞行器设计]