Suboptimal Gain Functions of Feedback Particle Filter Derived from Continuation Method
Suboptimal Gain Functions of Feedback Particle Filter Derived from Continuation Method
复制标题
连续法推导的反馈粒子滤波器的次优增益函数
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
R. Hirokawa
中科院分区：
文献类型：
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作者：
Yuki Matsuura;R. Ohata;K. Nakakuki;R. Hirokawa
提出了一种新的数值方法来获得反馈粒子滤波器的增益函数。最近的研究提供了几种基于控制的粒子滤波器（PF）配方的方法。这些新的PF基于贝叶斯规则控制先验粒子和后验粒子之间的过渡。FPF就是其中之一，FPF采用基于最优控制理论的反馈控制来调整后验概率密度。在每个时间步，需要通过求解基于粒子状态的欧拉-拉格朗日边值问题（E-L BVP）来获得最优增益函数。因此，几种近似方法，如伽辽金近似和常数增益近似，已被提出作为一个次优解。虽然这些方法为非线性估计问题提供了正确的估计，但这些方法难以确定称为基函数的内部参数。此外，还没有提供选择基函数的明确指导。在本文中，我们引入了一个数值次优解的E-L BVP没有基函数，以提高获得增益函数的容易性。我们的解决方案是一种连续的方法，增益函数是通过更新在每一个时间的最后一个增益函数。此外，为了减少计算成本，E-L BVP被近似为前向差分。我们将此方法应用于流行的基准问题的非线性估计。结果发现，我们的方法具有较低的估计误差比以前的方法，如恒定增益的方法。
This paper proposes a novel numerical approach to obtain gain functions of feedback particle filters (FPFs). Recent researches have provided several methods of control-based formulation for particle filters (PFs). These new PFs control transition between prior and posterior particles based on Bayes’ rule. FPF is one of them, and FPF uses feedback control based on optimal control theory to adjust probability density of the posteriors. The optimal gain function needs to be obtained at each time step by solving an Euler-Lagrange boundary value problem (E-L BVP) based on states of the particles. Therefore, several approximation approaches, such as Galerkin approximation and constant gain approximation, have been proposed as a suboptimal solution. Although these approaches provide a correct estimation for the nonlinear estimation problems, these have a difficulty of determining internal parameters called basis functions. Furthermore, clear guidelines for choosing basis functions are not provided yet. In this paper, we introduce a numerically suboptimal solution for the E-L BVPs without basis functions in order to enhance the ease of obtaining the gain functions. Our solution is a kind of continuation method, and the gain functions are obtained by updating the last gain functions at each time. Moreover, the E-L BVPs are approximated as forward differences in order to reduce the computational cost. We applied this method to popular benchmark problems of nonlinear estimation. It was found that our method exhibits lower estimation error than previous methods such as constant gain method.