一种改进的高斯近似滤波方法

An Improved Gaussian Approximate Filtering Method

提出了一种改进的高斯近似(Gaussian approximate,GA)滤波方法,推导了它的一般解和特殊解,并证明了现有的高斯近似滤波方法是所提出的方法的一种特例.在提出的方法中,不需要基于高斯假设重复地产生求积点,而是直接地更新求积点.与现有的高斯近似滤波方法相比,提出的方法利用了量测求积点修正状态求积点,从而可以更好地捕获状态一步预测密度和状态后验密度的非高斯信息和高阶矩信息.此外,提出的方法不仅适用于确定的系统模型而且还适用于随机的系统模型.单变量非平稳增长模型、垂直落体模型、再入飞行器目标跟踪的仿真验证了提出的高斯近似滤波方法的有效性和与现有方法相比的优越性.

In this paper, an improved Gaussian approximate（GA） filtering method is proposed. Its general solution and special solution are derived, and the existing GA filtering method is proved to be its special case of the proposed method.In the proposed method, the quadrature points are no longer generated repeatedly based on Gaussian assumption, but updated directly. As compared with the existing GA filtering method, the proposed method can better capture the non-Gaussian information and high-order moment information of the one-step predicted density and posterior density of state, since the measurement quadrature points in the proposed method are used to correct the state quadrature points.Moreover, the proposed method is suitable for not only deterministic process model but also random process model. The efficiency and superiority of the proposed method are illustrated by simulations of univariate non-stationary growth model,vertically falling body model, and target tracking of re-entry vehicle.