非线性/非高斯序贯贝叶斯滤波

Nonlinear/Non-Gaussian Bayesian Sequential Filtering

序贯Bayesian滤波为Bayesian滤波的递归实现,为在线估计系统状态提供了一个合理的框架。序贯贝叶斯滤波是基于状态—空间模型的。在线性高斯状态—空间模型下,最佳序贯贝叶斯滤波为大家熟知的卡尔曼滤波。在非线性/非高斯状态—空间模型下,最佳序贯贝叶斯滤波不存在通用的解析解,基于卡尔曼滤波的方法和质点滤波方法为比较常用的两类次最佳序贯贝叶斯滤波。它们各有各的优势,是相互补充的。该文采用扩展卡尔曼滤波和序贯重要性重采样质点滤波对两个非线性/非高斯系统的状态进行跟踪,仿真表明系统非线性/非高斯不严重时采用扩展卡尔曼比较合适,非线性/非高斯较严重时采用序贯重要性重采样比较合适。

Bayesian sequential filtering, which is based on state-space model, is recursive, implementation of Bayesian filtedng, and iprovides a suitable framework for estimating the state of system on-line. For linear- Gaussian problems, optimal Bayesian sequential filtering is well-known Kalman filter. For nonlinear oi non- Gaussian problems ther6 is no general analytical expression for Optimal Bayesian sequential filtering, algo- rithms based on Kalman!andpartiele filters are the most popular suboptimal Bayesian Sequential filtering. They all have their place and： are complementary to each other. In this paper, two nonlinear or non-G, aussian proh- lems are resolved with extended Kalman and sequential importance resample. Simulation shows that when non- linear or non--Gaussian is mild, extended Kalman is an appropriate choice and when nonlinear or non-Gattssian is severe, sequential importance resamplelis a wise choice.