Particle filter is the most widely used Bayesian sequential state estimation method for nonlinear dynamic systems. When importance sampling is adopted, it is still a challenge to select an appropriate importance function for sampling to avoid particle degeneracy. This paper suggests a novel particle filter, called second-order extended particle filter, which uses conditional normal distribution to approximate the theoretical optimal importance function in sequential state estimation. The approximation is fulfilled through taking logarithm to the optimal importance function and implementing second-order Taylor expansion. This method is suitable for exponential family observation models, which have numerous applications in state estimation research field.

中文翻译：

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具有指数族观测模型的二阶扩展粒子滤波器

粒子滤波器是非线性动态系统中应用最广泛的贝叶斯序列状态估计方法。当采用重要性采样时，选择合适的重要性函数进行采样以避免粒子退化仍然是一个挑战。本文提出了一种新的粒子滤波器，称为二阶扩展粒子滤波器，它使用条件正态分布来逼近序列状态估计中的理论最优重要性函数。通过对最优重要性函数取对数并实现二阶泰勒展开来实现近似。该方法适用于指数族观测模型，在状态估计研究领域有很多应用。