交互粒子滤波器用于同时状态和参数估计
Interacting particle filters for simultaneous state and parameter estimation
AI总结：
本文提出一种交互粒子滤波器，用于高维状态空间模型中同时估计状态和参数，结合卡尔曼-布西滤波和通用粒子滤波，应用于未知波速的波动方程。
摘要：
同时状态和参数估计出现在各种应用领域，但存在重大计算挑战。大多数可用的马尔可夫链或顺序蒙特卡洛技术仅适用于低维问题。替代方法，如集合卡尔曼滤波或其他集合变换滤波器，已成功应用于高维状态估计问题。本文提出将这些技术扩展到高维状态空间模型，该模型依赖于少量未知参数。更具体地说，我们结合了用于连续时间过滤问题的集合卡尔曼-布西滤波器和通用集合变换粒子滤波器，用于间歇性参数更新。我们演示了这种两阶段更新滤波器在具有未知波速参数的波动方程中的性能。
英文摘要：
Simultaneous state and parameter estimation arises from various applicational areas but presents a major computational challenge. Most available Markov chain or sequential Monte Carlo techniques are applicable to relatively low dimensional problems only. Alternative methods, such as the ensemble Kalman filter or other ensemble transform filters have, on the other hand, been successfully applied to high dimensional state estimation problems. In this paper, we propose an extension of these techniques to high dimensional state space models which depend on a few unknown parameters. More specifically, we combine the ensemble Kalman-Bucy filter for the continuous-time filtering problem with a generalized ensemble transform particle filter for intermittent parameter updates. We demonstrate the performance of this two stage update filter for a wave equation with unknown wave velocity parameter.
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