论文标题
当人工参数演变变得真实时：确定性动力学系统中时变参数估计的粒子过滤
When Artificial Parameter Evolution Gets Real: Particle Filtering for Time-Varying Parameter Estimation in Deterministic Dynamical Systems
论文作者
论文摘要
在各种现实世界应用中，来自有限数据的未知系统参数的估计和量化不确定性仍然是一个具有挑战性的反问题。尽管许多方法着重于估计恒定参数，但这些问题的一个子集包括具有未知进化模型的时变参数，通常无法直接观察到。这项工作开发了一种系统的粒子过滤方法，该方法将人工参数演化背后的想法折叠，以估计由确定性动力学系统引起的非组织反问题的时变参数。专注于以普通微分方程为模型的系统，我们提出了两种粒子滤波器算法，以进行时变参数估计：一个依赖于参数随机步行的噪声方差的固定值；另一个采用在线估计参数演化噪声方差以及感兴趣的随时间变化的参数。几个计算的示例证明了所提出的算法在估计具有不同基础功能形式的时变参数以及与系统状态（即添加剂与乘法）不同的关系的能力。
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of these problems includes time-varying parameters with unknown evolution models that often cannot be directly observed. This work develops a systematic particle filtering approach that reframes the idea behind artificial parameter evolution to estimate time-varying parameters in nonstationary inverse problems arising from deterministic dynamical systems. Focusing on systems modeled by ordinary differential equations, we present two particle filter algorithms for time-varying parameter estimation: one that relies on a fixed value for the noise variance of a parameter random walk; another that employs online estimation of the parameter evolution noise variance along with the time-varying parameter of interest. Several computed examples demonstrate the capability of the proposed algorithms in estimating time-varying parameters with different underlying functional forms and different relationships with the system states (i.e., additive vs. multiplicative).
