标题： 基于Rao-Blackwellization和模块化的SDEs中联合参数-状态估计的有效滤波方法 显示英文标题

标题： Effective filtering approach for joint parameter-state estimation in SDEs via Rao-Blackwellization and modularization

摘要： 随机滤波是控制理论和统计学中一个充满活力的研究领域，在许多科学领域都有广泛的应用。 尽管其历史发展已经很悠久，但在随机微分方程中仍然缺乏一种有效的联合参数-状态估计方法。 最先进的粒子滤波方法要么面临样本退化问题，要么存在信息丢失问题，这些问题都源于用来表示系统参数的粒子的动力学特性。 本文通过Rao-Blackwellization和模块化方法，提供了一种新颖且有效的方法用于随机微分方程中的联合参数-状态估计。 我们的方法分为两个层次：第一层使用引导粒子滤波器估计系统状态，第二层显式地对系统参数进行边缘化处理。 这种策略避免了生成代表系统参数的粒子，从而减轻了与之相关的样本退化和信息丢失问题。 此外，我们的方法在积分参数时采用模块化方法，显著降低了计算复杂度。 所有这些设计确保了我们方法的优越性能。 最后，给出一个数值示例来说明我们的方法比现有方法有显著的优势。 显示英文摘要

摘要： Stochastic filtering is a vibrant area of research in both control theory and statistics, with broad applications in many scientific fields. Despite its extensive historical development, there still lacks an effective method for joint parameter-state estimation in SDEs. The state-of-the-art particle filtering methods suffer from either sample degeneracy or information loss, with both issues stemming from the dynamics of the particles generated to represent system parameters. This paper provides a novel and effective approach for joint parameter-state estimation in SDEs via Rao-Blackwellization and modularization. Our method operates in two layers: the first layer estimates the system states using a bootstrap particle filter, and the second layer marginalizes out system parameters explicitly. This strategy circumvents the need to generate particles representing system parameters, thereby mitigating their associated problems of sample degeneracy and information loss. Moreover, our method employs a modularization approach when integrating out the parameters, which significantly reduces the computational complexity. All these designs ensure the superior performance of our method. Finally, a numerical example is presented to illustrate that our method outperforms existing approaches by a large margin.