When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems
When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems
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DOI：
10.1088/1361-6420/aca55b
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发表时间：
2022-03
期刊：
影响因子：
2.1
通讯作者：
Andrea Arnold
中科院分区：
文献类型：
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作者：
Andrea Arnold
从有限的数据中估计和量化未知系统参数的不确定性在各种实际应用中仍然是一个具有挑战性的逆问题。虽然许多方法侧重于估计常数参数，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，这些参数通常不能直接观察到。这项工作发展了一种系统的粒子滤波方法，该方法重新构建了人工参数进化背后的思想，以估计由确定性动力系统引起的非平稳逆问题中的时变参数。针对由常微分方程建模的系统，我们提出了两种时变参数估计的粒子滤波算法：一种算法依赖于参数随机游走的噪声方差的固定值；另一种方法是对参数演化噪声方差随感兴趣的时变参数进行在线估计。几个计算实例证明了所提出的算法在估计具有不同底层函数形式和与系统状态（即加性与乘性）不同关系的时变参数方面的能力。
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).