An optimal control approach to particle filtering
An optimal control approach to particle filtering
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DOI：
10.1016/j.automatica.2023.110894
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Qinsheng Zhang;A. Taghvaei;Yongxin Chen
中科院分区：
文献类型：
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作者：
Qinsheng Zhang;A. Taghvaei;Yongxin Chen
针对具有连续时间测量值的连续时间动力系统，提出了一种新的粒子滤波框架。我们的方法基于估计和最优控制之间的对偶性，这允许将固定时间窗口内的估计问题重新表述为最优控制问题。由此产生的最优控制问题具有依赖于测量的成本函数，最优控制下的闭环动力学与相应估计问题的轨迹上的后验分布一致。通过对这些最优控制问题进行近似递归求解，得到了一种基于粒子滤波的最优控制算法。我们的算法使用路径积分来计算粒子的权重，因此被称为路径积分粒子滤波器（PIPF）。该方法的一个显著特点是它在有限长的时间窗口内使用测量值，而不是在每个时间步使用单个测量值进行估计，类似于过滤的批处理方法，并提高了容错性。算例说明了算法的有效性。
We present a novel particle filtering framework for the continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows for reformulating the estimation problem over a fixed time window into an optimal control problem. The resulting optimal control problem has a cost function that depends on the measurements, and the closed-loop dynamics under optimal control coincides with the posterior distribution over the trajectories for the corresponding estimation problem. By recursively solving these optimal control problems approximately as new measurements become available, we obtain an optimal control based particle filtering algorithm. Our algorithm uses path integrals to compute the weights of the particles and is thus termed the path integrals particle filter (PIPF). A distinguishing feature of the proposed method is that it uses the measurements over a finite-length time window instead of a single measurement for the estimation at each time step, resembling the batch methods of filtering, and improving fault tolerance. The efficacy of our algorithm is illustrated with several numerical examples.