基于状态空间模型的许多传统滤波算法都基于 Rn空间中的高斯分布模型，但当状态向量中包含角变量或方向变量时，难以达到理想的效果。针对J. T. Horwood等提出的nS´R流形上的Gauss Von Mises (GVM)多变量概率密度分布，扩展了狄拉克混合逼近方法，给出了联合分布的GVM逼近方法，推导了后验分布的GVM参数计算公式，设计了量测更新状态估计算法。将J. T. Horwood等的时间更新算法与所提出的量测更新算法相结合，可实现基于 GVM 分布的递推贝叶斯滤波器(GVMF)。仿真结果表明，当状态向量符合GVM概率分布模型时，GVMF对角变量的估计明显优于传统的扩展卡尔曼滤波器。%Many traditional Kalman-based state estimation algorithms assume that the system state is uncertain and the measurements are Gaussian distributed. However, this assumption cannot catch the periodic nature of angular or orientation variables. Based on the Gauss von Mises (GVM) distribution defined on a cylindrical manifold, this paper extends the Dirac mixture approximation method to deal with sampling with GVM. The GVM approximation with joint distribution is proposed to perform recursive Bayesian filtering. The formula for computing the posterior distribution is deduced, and the measurement update algorithm is developed. The GVM filtering can be realized by combined with the time update algorithm proposed by J.T.Horwood. Simulation results demonstrates that, when state variables conform with GVM distributions, the GVM filter can achieve more accurate angular estimates than the traditional extended Kalman filter.
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