中文说明: 本章介绍两种非线性Kalman滤波器[15-17],一种是扩展Kalman滤波器(Extended Kalman Filter,简称EKF),其基本思想是利用泰勒展开,将非线性方程直接线性化。线性化后的系统模型和系统实际的非线性模型会有差别,非线性越强,差别就会越大。不过,EKF的优势也不容忽视,由于没有附加计算,EKF的计算量和基本的Kalman滤波器差不多。另一种非线性Kalman滤波器在原理上和EKF完全不同,称之为不敏Kalman滤波器(Unscented Kalman Filter ,简称UKF),和EKF相比,该滤波器由于使用了所谓的不敏变换,线性化带来的状态均值和协方差的改变要小些。本章将详细讲解这两种非线性估计方法。
English Description:
This chapter introduces two kinds of nonlinear Kalman filters [15-17]. One is extended Kalman filter (EKF). Its basic idea is to linearize the nonlinear equation directly by using Taylor expansion. There will be differences between the linearized system model and the actual nonlinear model. The stronger the nonlinearity is, the greater the difference will be. However, the advantage of EKF can not be ignored, because there is no additional calculation, the calculation amount of EKF is almost the same as that of the basic Kalman filter. Another kind of nonlinear Kalman filter is completely different from EKF in principle. It is called unscented Kalman filter (UKF). Compared with EKF, the change of state mean and covariance caused by linearization is smaller because of the so-called unscientific transformation. This chapter will explain these two nonlinear estimation methods in detail.